%------------------------------------------------------------------------------
% File     : iProverMo---2.5-0.1
% Problem  : LCL755-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : iprover_modulo %s %d

% Computer : n018.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 11:39:02 EDT 2022

% Result   : Unsatisfiable 3.06s 3.33s
% Output   : CNFRefutation 3.06s
% 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(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__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__mono,axiom,
    class_Ring__and__Field_Omult__mono(tc_nat),
    input ).

fof(clsarity_nat__Ring__and__Field_Omult__mono_0,plain,
    ( class_Ring__and__Field_Omult__mono(tc_nat)
    | $false ),
    inference(orientation,[status(thm)],[clsarity_nat__Ring__and__Field_Omult__mono]) ).

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_Omult__mono1,axiom,
    class_Ring__and__Field_Omult__mono1(tc_nat),
    input ).

fof(clsarity_nat__Ring__and__Field_Omult__mono1_0,plain,
    ( class_Ring__and__Field_Omult__mono1(tc_nat)
    | $false ),
    inference(orientation,[status(thm)],[clsarity_nat__Ring__and__Field_Omult__mono1]) ).

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__Ring__and__Field_Oordered__semiring,axiom,
    class_Ring__and__Field_Oordered__semiring(tc_nat),
    input ).

fof(clsarity_nat__Ring__and__Field_Oordered__semiring_0,plain,
    ( class_Ring__and__Field_Oordered__semiring(tc_nat)
    | $false ),
    inference(orientation,[status(thm)],[clsarity_nat__Ring__and__Field_Oordered__semiring]) ).

cnf(clsarity_nat__Ring__and__Field_Opordered__semiring,axiom,
    class_Ring__and__Field_Opordered__semiring(tc_nat),
    input ).

fof(clsarity_nat__Ring__and__Field_Opordered__semiring_0,plain,
    ( class_Ring__and__Field_Opordered__semiring(tc_nat)
    | $false ),
    inference(orientation,[status(thm)],[clsarity_nat__Ring__and__Field_Opordered__semiring]) ).

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

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

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

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

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

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

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

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

cnf(clsarity_nat__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_Opordered__cancel__semiring,axiom,
    class_Ring__and__Field_Opordered__cancel__semiring(tc_nat),
    input ).

fof(clsarity_nat__Ring__and__Field_Opordered__cancel__semiring_0,plain,
    ( class_Ring__and__Field_Opordered__cancel__semiring(tc_nat)
    | $false ),
    inference(orientation,[status(thm)],[clsarity_nat__Ring__and__Field_Opordered__cancel__semiring]) ).

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,
    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] :
      ( 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_min__Suc__Suc_0,axiom,
    c_Orderings_Oord__class_Omin(c_Suc(V_m),c_Suc(V_n),tc_nat) = c_Suc(c_Orderings_Oord__class_Omin(V_m,V_n,tc_nat)),
    input ).

fof(cls_min__Suc__Suc_0_0,plain,
    ! [V_m,V_n] :
      ( c_Orderings_Oord__class_Omin(c_Suc(V_m),c_Suc(V_n),tc_nat) = c_Suc(c_Orderings_Oord__class_Omin(V_m,V_n,tc_nat))
      | $false ),
    inference(orientation,[status(thm)],[cls_min__Suc__Suc_0]) ).

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

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

cnf(cls_le__Suc__eq_2,axiom,
    c_lessequals(c_Suc(V_n),c_Suc(V_n),tc_nat),
    input ).

fof(cls_le__Suc__eq_2_0,plain,
    ! [V_n] :
      ( c_lessequals(c_Suc(V_n),c_Suc(V_n),tc_nat)
      | $false ),
    inference(orientation,[status(thm)],[cls_le__Suc__eq_2]) ).

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

fof(cls_Suc__diff__diff_0_0,plain,
    ! [V_k,V_m,V_n] :
      ( c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(c_Suc(V_m),V_n,tc_nat),c_Suc(V_k),tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat),V_k,tc_nat)
      | $false ),
    inference(orientation,[status(thm)],[cls_Suc__diff__diff_0]) ).

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

fof(cls_add__Suc__shift_0_0,plain,
    ! [V_m,V_n] :
      ( c_HOL_Oplus__class_Oplus(c_Suc(V_m),V_n,tc_nat) = c_HOL_Oplus__class_Oplus(V_m,c_Suc(V_n),tc_nat)
      | $false ),
    inference(orientation,[status(thm)],[cls_add__Suc__shift_0]) ).

cnf(cls_max__Suc__Suc_0,axiom,
    c_Orderings_Oord__class_Omax(c_Suc(V_m),c_Suc(V_n),tc_nat) = c_Suc(c_Orderings_Oord__class_Omax(V_m,V_n,tc_nat)),
    input ).

fof(cls_max__Suc__Suc_0_0,plain,
    ! [V_m,V_n] :
      ( c_Orderings_Oord__class_Omax(c_Suc(V_m),c_Suc(V_n),tc_nat) = c_Suc(c_Orderings_Oord__class_Omax(V_m,V_n,tc_nat))
      | $false ),
    inference(orientation,[status(thm)],[cls_max__Suc__Suc_0]) ).

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

fof(cls_add__Suc__right_0_0,plain,
    ! [V_m,V_n] :
      ( c_HOL_Oplus__class_Oplus(V_m,c_Suc(V_n),tc_nat) = c_Suc(c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat))
      | $false ),
    inference(orientation,[status(thm)],[cls_add__Suc__right_0]) ).

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

fof(cls_add__Suc_0_0,plain,
    ! [V_m,V_n] :
      ( c_HOL_Oplus__class_Oplus(c_Suc(V_m),V_n,tc_nat) = c_Suc(c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat))
      | $false ),
    inference(orientation,[status(thm)],[cls_add__Suc_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_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_diff__Suc__Suc_0,axiom,
    c_HOL_Ominus__class_Ominus(c_Suc(V_m),c_Suc(V_n),tc_nat) = c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat),
    input ).

fof(cls_diff__Suc__Suc_0_0,plain,
    ! [V_m,V_n] :
      ( c_HOL_Ominus__class_Ominus(c_Suc(V_m),c_Suc(V_n),tc_nat) = c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat)
      | $false ),
    inference(orientation,[status(thm)],[cls_diff__Suc__Suc_0]) ).

cnf(cls_dB_Osimps_I4_J_0,axiom,
    c_Lambda_OdB_OVar(V_nat) != 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) != 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_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_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_Suc__n__not__le__n_0,axiom,
    ~ c_lessequals(c_Suc(V_n),V_n,tc_nat),
    input ).

fof(cls_Suc__n__not__le__n_0_0,plain,
    ! [V_n] :
      ( ~ c_lessequals(c_Suc(V_n),V_n,tc_nat)
      | $false ),
    inference(orientation,[status(thm)],[cls_Suc__n__not__le__n_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_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_subst__eq_0,axiom,
    c_Lambda_Osubst(c_Lambda_OdB_OVar(V_k),V_u,V_k) = V_u,
    input ).

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

cnf(cls_dB_Osimps_I9_J_0,axiom,
    c_Lambda_OdB_OAbs(V_dB_H) != 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) != 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,
    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] :
      ( c_Lambda_OdB_OApp(V_dB1,V_dB2) != c_Lambda_OdB_OAbs(V_dB_H)
      | $false ),
    inference(orientation,[status(thm)],[cls_dB_Osimps_I8_J_0]) ).

cnf(cls_dB_Osimps_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__App_0,axiom,
    c_Lambda_Osubst(c_Lambda_OdB_OApp(V_t,V_u),V_s,V_k) = c_Lambda_OdB_OApp(c_Lambda_Osubst(V_t,V_s,V_k),c_Lambda_Osubst(V_u,V_s,V_k)),
    input ).

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

cnf(cls_add__mult__distrib2_0,axiom,
    c_HOL_Otimes__class_Otimes(V_k,c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(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_add__mult__distrib2_0_0,plain,
    ! [V_k,V_m,V_n] :
      ( c_HOL_Otimes__class_Otimes(V_k,c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(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_add__mult__distrib2_0]) ).

cnf(cls_add__mult__distrib_0,axiom,
    c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat),V_k,tc_nat) = c_HOL_Oplus__class_Oplus(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_add__mult__distrib_0_0,plain,
    ! [V_k,V_m,V_n] :
      ( c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat),V_k,tc_nat) = c_HOL_Oplus__class_Oplus(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_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_lift_Osimps_I3_J_0,axiom,
    c_Lambda_Olift(c_Lambda_OdB_OAbs(V_s),V_k) = c_Lambda_OdB_OAbs(c_Lambda_Olift(V_s,c_HOL_Oplus__class_Oplus(V_k,c_HOL_Oone__class_Oone(tc_nat),tc_nat))),
    input ).

fof(cls_lift_Osimps_I3_J_0_0,plain,
    ! [V_k,V_s] :
      ( c_Lambda_Olift(c_Lambda_OdB_OAbs(V_s),V_k) = c_Lambda_OdB_OAbs(c_Lambda_Olift(V_s,c_HOL_Oplus__class_Oplus(V_k,c_HOL_Oone__class_Oone(tc_nat),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_add__is__1_5,axiom,
    c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),
    input ).

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

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

fof(cls_min__diff_0_0,plain,
    ! [V_i,V_m,V_n] :
      ( c_Orderings_Oord__class_Omin(c_HOL_Ominus__class_Ominus(V_m,V_i,tc_nat),c_HOL_Ominus__class_Ominus(V_n,V_i,tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(c_Orderings_Oord__class_Omin(V_m,V_n,tc_nat),V_i,tc_nat)
      | $false ),
    inference(orientation,[status(thm)],[cls_min__diff_0]) ).

cnf(cls_eq__imp__le_0,axiom,
    c_lessequals(V_x,V_x,tc_nat),
    input ).

fof(cls_eq__imp__le_0_0,plain,
    ! [V_x] :
      ( c_lessequals(V_x,V_x,tc_nat)
      | $false ),
    inference(orientation,[status(thm)],[cls_eq__imp__le_0]) ).

cnf(cls_le__refl_0,axiom,
    c_lessequals(V_n,V_n,tc_nat),
    input ).

fof(cls_le__refl_0_0,plain,
    ! [V_n] :
      ( c_lessequals(V_n,V_n,tc_nat)
      | $false ),
    inference(orientation,[status(thm)],[cls_le__refl_0]) ).

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

fof(cls_diff__add__inverse_0_0,plain,
    ! [V_m,V_n] :
      ( c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(V_n,V_m,tc_nat),V_n,tc_nat) = V_m
      | $false ),
    inference(orientation,[status(thm)],[cls_diff__add__inverse_0]) ).

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

fof(cls_diff__add__inverse2_0_0,plain,
    ! [V_m,V_n] :
      ( c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat),V_n,tc_nat) = V_m
      | $false ),
    inference(orientation,[status(thm)],[cls_diff__add__inverse2_0]) ).

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

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

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

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

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

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

cnf(cls_mod__mult__self3_0,axiom,
    c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_k,V_n,tc_nat),V_m,tc_nat),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(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_k,V_n,tc_nat),V_m,tc_nat),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_le__cube_0,axiom,
    c_lessequals(V_m,c_HOL_Otimes__class_Otimes(V_m,c_HOL_Otimes__class_Otimes(V_m,V_m,tc_nat),tc_nat),tc_nat),
    input ).

fof(cls_le__cube_0_0,plain,
    ! [V_m] :
      ( c_lessequals(V_m,c_HOL_Otimes__class_Otimes(V_m,c_HOL_Otimes__class_Otimes(V_m,V_m,tc_nat),tc_nat),tc_nat)
      | $false ),
    inference(orientation,[status(thm)],[cls_le__cube_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_le__square_0,axiom,
    c_lessequals(V_m,c_HOL_Otimes__class_Otimes(V_m,V_m,tc_nat),tc_nat),
    input ).

fof(cls_le__square_0_0,plain,
    ! [V_m] :
      ( c_lessequals(V_m,c_HOL_Otimes__class_Otimes(V_m,V_m,tc_nat),tc_nat)
      | $false ),
    inference(orientation,[status(thm)],[cls_le__square_0]) ).

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

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

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

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

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

fof(cls_diff__Suc__eq__diff__pred_0_0,plain,
    ! [V_m,V_n] :
      ( c_HOL_Ominus__class_Ominus(V_m,c_Suc(V_n),tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(V_m,c_HOL_Oone__class_Oone(tc_nat),tc_nat),V_n,tc_nat)
      | $false ),
    inference(orientation,[status(thm)],[cls_diff__Suc__eq__diff__pred_0]) ).

cnf(cls_mod__less__eq__dividend_0,axiom,
    c_lessequals(c_Divides_Odiv__class_Omod(V_m,V_n,tc_nat),V_m,tc_nat),
    input ).

fof(cls_mod__less__eq__dividend_0_0,plain,
    ! [V_m,V_n] :
      ( c_lessequals(c_Divides_Odiv__class_Omod(V_m,V_n,tc_nat),V_m,tc_nat)
      | $false ),
    inference(orientation,[status(thm)],[cls_mod__less__eq__dividend_0]) ).

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

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

cnf(cls_le__0__eq_1,axiom,
    c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
    input ).

fof(cls_le__0__eq_1_0,plain,
    ( c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)
    | $false ),
    inference(orientation,[status(thm)],[cls_le__0__eq_1]) ).

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

fof(cls_not__add__less2_0_0,plain,
    ! [V_i,V_j] :
      ( ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(V_j,V_i,tc_nat),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(c_HOL_Oplus__class_Oplus(V_i,V_j,tc_nat),V_i,tc_nat),
    input ).

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

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_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_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_nat__minus__add__max_0,axiom,
    c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(V_n,V_m,tc_nat),V_m,tc_nat) = c_Orderings_Oord__class_Omax(V_n,V_m,tc_nat),
    input ).

fof(cls_nat__minus__add__max_0_0,plain,
    ! [V_m,V_n] :
      ( c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(V_n,V_m,tc_nat),V_m,tc_nat) = c_Orderings_Oord__class_Omax(V_n,V_m,tc_nat)
      | $false ),
    inference(orientation,[status(thm)],[cls_nat__minus__add__max_0]) ).

cnf(cls_le__iff__add_1,axiom,
    c_lessequals(V_m,c_HOL_Oplus__class_Oplus(V_m,V_x,tc_nat),tc_nat),
    input ).

fof(cls_le__iff__add_1_0,plain,
    ! [V_m,V_x] :
      ( c_lessequals(V_m,c_HOL_Oplus__class_Oplus(V_m,V_x,tc_nat),tc_nat)
      | $false ),
    inference(orientation,[status(thm)],[cls_le__iff__add_1]) ).

cnf(cls_le__add2_0,axiom,
    c_lessequals(V_n,c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat),tc_nat),
    input ).

fof(cls_le__add2_0_0,plain,
    ! [V_m,V_n] :
      ( c_lessequals(V_n,c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat),tc_nat)
      | $false ),
    inference(orientation,[status(thm)],[cls_le__add2_0]) ).

cnf(cls_le__add1_0,axiom,
    c_lessequals(V_n,c_HOL_Oplus__class_Oplus(V_n,V_m,tc_nat),tc_nat),
    input ).

fof(cls_le__add1_0_0,plain,
    ! [V_m,V_n] :
      ( c_lessequals(V_n,c_HOL_Oplus__class_Oplus(V_n,V_m,tc_nat),tc_nat)
      | $false ),
    inference(orientation,[status(thm)],[cls_le__add1_0]) ).

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

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

cnf(cls_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_le0_0,axiom,
    c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat),
    input ).

fof(cls_le0_0_0,plain,
    ! [V_n] :
      ( c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat)
      | $false ),
    inference(orientation,[status(thm)],[cls_le0_0]) ).

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

fof(cls_diff__commute_0_0,plain,
    ! [V_i,V_j,V_k] :
      ( c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(V_i,V_j,tc_nat),V_k,tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(V_i,V_k,tc_nat),V_j,tc_nat)
      | $false ),
    inference(orientation,[status(thm)],[cls_diff__commute_0]) ).

cnf(cls_diff__mult__distrib_0,axiom,
    c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat),V_k,tc_nat) = c_HOL_Ominus__class_Ominus(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_diff__mult__distrib_0_0,plain,
    ! [V_k,V_m,V_n] :
      ( c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat),V_k,tc_nat) = c_HOL_Ominus__class_Ominus(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_diff__mult__distrib_0]) ).

cnf(cls_diff__mult__distrib2_0,axiom,
    c_HOL_Otimes__class_Otimes(V_k,c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(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_diff__mult__distrib2_0_0,plain,
    ! [V_k,V_m,V_n] :
      ( c_HOL_Otimes__class_Otimes(V_k,c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(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_diff__mult__distrib2_0]) ).

cnf(cls_diff__le__self_0,axiom,
    c_lessequals(c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat),V_m,tc_nat),
    input ).

fof(cls_diff__le__self_0_0,plain,
    ! [V_m,V_n] :
      ( c_lessequals(c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat),V_m,tc_nat)
      | $false ),
    inference(orientation,[status(thm)],[cls_diff__le__self_0]) ).

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

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

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_diff__cancel_0,axiom,
    c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(V_k,V_m,tc_nat),c_HOL_Oplus__class_Oplus(V_k,V_n,tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat),
    input ).

fof(cls_diff__cancel_0_0,plain,
    ! [V_k,V_m,V_n] :
      ( c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(V_k,V_m,tc_nat),c_HOL_Oplus__class_Oplus(V_k,V_n,tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat)
      | $false ),
    inference(orientation,[status(thm)],[cls_diff__cancel_0]) ).

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

fof(cls_diff__cancel2_0_0,plain,
    ! [V_k,V_m,V_n] :
      ( c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(V_m,V_k,tc_nat),c_HOL_Oplus__class_Oplus(V_n,V_k,tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat)
      | $false ),
    inference(orientation,[status(thm)],[cls_diff__cancel2_0]) ).

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

fof(cls_diff__0__eq__0_0_0,plain,
    ! [V_n] :
      ( c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat)
      | $false ),
    inference(orientation,[status(thm)],[cls_diff__0__eq__0_0]) ).

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

fof(cls_diff__diff__left_0_0,plain,
    ! [V_i,V_j,V_k] :
      ( c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(V_i,V_j,tc_nat),V_k,tc_nat) = c_HOL_Ominus__class_Ominus(V_i,c_HOL_Oplus__class_Oplus(V_j,V_k,tc_nat),tc_nat)
      | $false ),
    inference(orientation,[status(thm)],[cls_diff__diff__left_0]) ).

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

fof(cls_diff__add__0_0_0,plain,
    ! [V_m,V_n] :
      ( c_HOL_Ominus__class_Ominus(V_n,c_HOL_Oplus__class_Oplus(V_n,V_m,tc_nat),tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat)
      | $false ),
    inference(orientation,[status(thm)],[cls_diff__add__0_0]) ).

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

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

cnf(cls_one__is__add_4,axiom,
    c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) = c_HOL_Oplus__class_Oplus(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
    input ).

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

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_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_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__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__mult__self4_0,axiom,
    c_Divides_Odiv__class_Omod(c_Suc(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_k,V_n,tc_nat),V_m,tc_nat)),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(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_k,V_n,tc_nat),V_m,tc_nat)),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_mult__Suc_0,axiom,
    c_HOL_Otimes__class_Otimes(c_Suc(V_m),V_n,tc_nat) = c_HOL_Oplus__class_Oplus(V_n,c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat),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) = c_HOL_Oplus__class_Oplus(V_n,c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat),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) = c_HOL_Oplus__class_Oplus(V_m,c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat),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) = c_HOL_Oplus__class_Oplus(V_m,c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat),tc_nat)
      | $false ),
    inference(orientation,[status(thm)],[cls_mult__Suc__right_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_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_min__0R_0,axiom,
    c_Orderings_Oord__class_Omin(V_n,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
    input ).

fof(cls_min__0R_0_0,plain,
    ! [V_n] :
      ( c_Orderings_Oord__class_Omin(V_n,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat)
      | $false ),
    inference(orientation,[status(thm)],[cls_min__0R_0]) ).

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

fof(cls_min__0L_0_0,plain,
    ! [V_n] :
      ( c_Orderings_Oord__class_Omin(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat)
      | $false ),
    inference(orientation,[status(thm)],[cls_min__0L_0]) ).

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

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

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

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

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

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

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

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

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

fof(cls_diff__less__Suc_0_0,plain,
    ! [V_m,V_n] :
      ( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat),c_Suc(V_m),tc_nat)
      | $false ),
    inference(orientation,[status(thm)],[cls_diff__less__Suc_0]) ).

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

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

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_natgb_Onoteq__reduce_1,axiom,
    c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_x,V_c,tc_nat),c_HOL_Otimes__class_Otimes(V_x,V_d,tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_x,V_d,tc_nat),c_HOL_Otimes__class_Otimes(V_x,V_c,tc_nat),tc_nat),
    input ).

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

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

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

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

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

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

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

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

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

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_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_less__add__Suc1_0,axiom,
    c_HOL_Oord__class_Oless(V_i,c_Suc(c_HOL_Oplus__class_Oplus(V_i,V_m,tc_nat)),tc_nat),
    input ).

fof(cls_less__add__Suc1_0_0,plain,
    ! [V_i,V_m] :
      ( c_HOL_Oord__class_Oless(V_i,c_Suc(c_HOL_Oplus__class_Oplus(V_i,V_m,tc_nat)),tc_nat)
      | $false ),
    inference(orientation,[status(thm)],[cls_less__add__Suc1_0]) ).

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

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

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

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

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

fof(cls_minus__nat_Odiff__0_0_0,plain,
    ! [V_m] :
      ( c_HOL_Ominus__class_Ominus(V_m,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = V_m
      | $false ),
    inference(orientation,[status(thm)],[cls_minus__nat_Odiff__0_0]) ).

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

fof(cls_diff__self__eq__0_0_0,plain,
    ! [V_m] :
      ( c_HOL_Ominus__class_Ominus(V_m,V_m,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat)
      | $false ),
    inference(orientation,[status(thm)],[cls_diff__self__eq__0_0]) ).

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

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

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

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

cnf(cls_nat__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_diff__Suc__1_0,axiom,
    c_HOL_Ominus__class_Ominus(c_Suc(V_n),c_HOL_Oone__class_Oone(tc_nat),tc_nat) = V_n,
    input ).

fof(cls_diff__Suc__1_0_0,plain,
    ! [V_n] :
      ( c_HOL_Ominus__class_Ominus(c_Suc(V_n),c_HOL_Oone__class_Oone(tc_nat),tc_nat) = V_n
      | $false ),
    inference(orientation,[status(thm)],[cls_diff__Suc__1_0]) ).

fof(def_lhs_atom1,axiom,
    ! [V_n] :
      ( lhs_atom1(V_n)
    <=> c_HOL_Ominus__class_Ominus(c_Suc(V_n),c_HOL_Oone__class_Oone(tc_nat),tc_nat) = V_n ),
    inference(definition,[],]) ).

fof(to_be_clausified_0,plain,
    ! [V_n] :
      ( lhs_atom1(V_n)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_diff__Suc__1_0_0,def_lhs_atom1]) ).

fof(def_lhs_atom2,axiom,
    ( lhs_atom2
  <=> 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_1,plain,
    ( lhs_atom2
    | $false ),
    inference(fold_definition,[status(thm)],[cls_nat__1__eq__mult__iff_2_0,def_lhs_atom2]) ).

fof(def_lhs_atom3,axiom,
    ! [V_t,V_s,V_k] :
      ( lhs_atom3(V_t,V_s,V_k)
    <=> c_Lambda_Olift(c_Lambda_OdB_OApp(V_s,V_t),V_k) = c_Lambda_OdB_OApp(c_Lambda_Olift(V_s,V_k),c_Lambda_Olift(V_t,V_k)) ),
    inference(definition,[],]) ).

fof(to_be_clausified_2,plain,
    ! [V_k,V_s,V_t] :
      ( lhs_atom3(V_t,V_s,V_k)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_lift_Osimps_I2_J_0_0,def_lhs_atom3]) ).

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

fof(to_be_clausified_3,plain,
    ! [V_m,V_n] :
      ( lhs_atom4(V_n,V_m)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_nat__add__commute_0_0,def_lhs_atom4]) ).

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

fof(to_be_clausified_4,plain,
    ! [V_m] :
      ( lhs_atom5(V_m)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_diff__self__eq__0_0_0,def_lhs_atom5]) ).

fof(def_lhs_atom6,axiom,
    ! [V_m] :
      ( lhs_atom6(V_m)
    <=> c_HOL_Ominus__class_Ominus(V_m,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = V_m ),
    inference(definition,[],]) ).

fof(to_be_clausified_5,plain,
    ! [V_m] :
      ( lhs_atom6(V_m)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_minus__nat_Odiff__0_0_0,def_lhs_atom6]) ).

fof(def_lhs_atom7,axiom,
    ! [V_x,V_m] :
      ( lhs_atom7(V_x,V_m)
    <=> c_HOL_Oord__class_Oless(V_m,c_Suc(c_HOL_Oplus__class_Oplus(V_m,V_x,tc_nat)),tc_nat) ),
    inference(definition,[],]) ).

fof(to_be_clausified_6,plain,
    ! [V_m,V_x] :
      ( lhs_atom7(V_x,V_m)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_less__iff__Suc__add_1_0,def_lhs_atom7]) ).

fof(def_lhs_atom8,axiom,
    ! [V_m,V_i] :
      ( lhs_atom8(V_m,V_i)
    <=> c_HOL_Oord__class_Oless(V_i,c_Suc(c_HOL_Oplus__class_Oplus(V_m,V_i,tc_nat)),tc_nat) ),
    inference(definition,[],]) ).

fof(to_be_clausified_7,plain,
    ! [V_i,V_m] :
      ( lhs_atom8(V_m,V_i)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_less__add__Suc2_0_0,def_lhs_atom8]) ).

fof(def_lhs_atom9,axiom,
    ! [V_m,V_i] :
      ( lhs_atom9(V_m,V_i)
    <=> c_HOL_Oord__class_Oless(V_i,c_Suc(c_HOL_Oplus__class_Oplus(V_i,V_m,tc_nat)),tc_nat) ),
    inference(definition,[],]) ).

fof(to_be_clausified_8,plain,
    ! [V_i,V_m] :
      ( lhs_atom9(V_m,V_i)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_less__add__Suc1_0_0,def_lhs_atom9]) ).

fof(def_lhs_atom10,axiom,
    ! [V_n] :
      ( lhs_atom10(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_9,plain,
    ! [V_n] :
      ( lhs_atom10(V_n)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_nat__mult__1__right_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,
    ( lhs_atom12
  <=> c_HOL_Oplus__class_Oplus(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
    inference(definition,[],]) ).

fof(to_be_clausified_11,plain,
    ( lhs_atom12
    | $false ),
    inference(fold_definition,[status(thm)],[cls_add__is__1_4_0,def_lhs_atom12]) ).

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

fof(to_be_clausified_12,plain,
    ! [V_n] :
      ( lhs_atom13(V_n)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_Suc__eq__plus1__left_0_0,def_lhs_atom13]) ).

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

fof(to_be_clausified_13,plain,
    ! [V_n] :
      ( lhs_atom14(V_n)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_Suc__eq__plus1_0_0,def_lhs_atom14]) ).

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

fof(to_be_clausified_14,plain,
    ! [V_x,V_y,V_z] :
      ( lhs_atom15(V_z,V_y,V_x)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_natgb_Oadd__mul__solve_1_0,def_lhs_atom15]) ).

fof(def_lhs_atom16,axiom,
    ! [V_x,V_d,V_c] :
      ( lhs_atom16(V_x,V_d,V_c)
    <=> c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_x,V_c,tc_nat),c_HOL_Otimes__class_Otimes(V_x,V_d,tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_x,V_d,tc_nat),c_HOL_Otimes__class_Otimes(V_x,V_c,tc_nat),tc_nat) ),
    inference(definition,[],]) ).

fof(to_be_clausified_15,plain,
    ! [V_c,V_d,V_x] :
      ( lhs_atom16(V_x,V_d,V_c)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_natgb_Onoteq__reduce_1_0,def_lhs_atom16]) ).

fof(def_lhs_atom17,axiom,
    ! [V_n,V_m] :
      ( lhs_atom17(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_16,plain,
    ! [V_m,V_n] :
      ( lhs_atom17(V_n,V_m)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_nat__mult__commute_0_0,def_lhs_atom17]) ).

fof(def_lhs_atom18,axiom,
    ( lhs_atom18
  <=> c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat) ),
    inference(definition,[],]) ).

fof(to_be_clausified_17,plain,
    ( lhs_atom18
    | $false ),
    inference(fold_definition,[status(thm)],[cls_add__is__0_2_0,def_lhs_atom18]) ).

fof(def_lhs_atom19,axiom,
    ! [V_n,V_m] :
      ( lhs_atom19(V_n,V_m)
    <=> c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat),c_Suc(V_m),tc_nat) ),
    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_diff__less__Suc_0_0,def_lhs_atom19]) ).

fof(def_lhs_atom20,axiom,
    ! [V_z,V_y,V_x] :
      ( lhs_atom20(V_z,V_y,V_x)
    <=> c_HOL_Oplus__class_Oplus(V_x,c_HOL_Oplus__class_Oplus(V_y,V_z,tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(V_y,c_HOL_Oplus__class_Oplus(V_x,V_z,tc_nat),tc_nat) ),
    inference(definition,[],]) ).

fof(to_be_clausified_19,plain,
    ! [V_x,V_y,V_z] :
      ( lhs_atom20(V_z,V_y,V_x)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_nat__add__left__commute_0_0,def_lhs_atom20]) ).

fof(def_lhs_atom21,axiom,
    ! [V_n,V_m,V_k] :
      ( lhs_atom21(V_n,V_m,V_k)
    <=> c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat),V_k,tc_nat) = c_HOL_Oplus__class_Oplus(V_m,c_HOL_Oplus__class_Oplus(V_n,V_k,tc_nat),tc_nat) ),
    inference(definition,[],]) ).

fof(to_be_clausified_20,plain,
    ! [V_k,V_m,V_n] :
      ( lhs_atom21(V_n,V_m,V_k)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_nat__add__assoc_0_0,def_lhs_atom21]) ).

fof(def_lhs_atom22,axiom,
    ! [V_m] :
      ( lhs_atom22(V_m)
    <=> ~ c_HOL_Oord__class_Oless(V_m,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ),
    inference(definition,[],]) ).

fof(to_be_clausified_21,plain,
    ! [V_m] :
      ( lhs_atom22(V_m)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_gr__implies__not0_0_0,def_lhs_atom22]) ).

fof(def_lhs_atom23,axiom,
    ! [V_n] :
      ( lhs_atom23(V_n)
    <=> ~ c_HOL_Oord__class_Oless(V_n,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ),
    inference(definition,[],]) ).

fof(to_be_clausified_22,plain,
    ! [V_n] :
      ( lhs_atom23(V_n)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_not__less0_0_0,def_lhs_atom23]) ).

fof(def_lhs_atom24,axiom,
    ! [V_n] :
      ( lhs_atom24(V_n)
    <=> c_Orderings_Oord__class_Omin(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat) ),
    inference(definition,[],]) ).

fof(to_be_clausified_23,plain,
    ! [V_n] :
      ( lhs_atom24(V_n)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_min__0L_0_0,def_lhs_atom24]) ).

fof(def_lhs_atom25,axiom,
    ! [V_n] :
      ( lhs_atom25(V_n)
    <=> c_Orderings_Oord__class_Omin(V_n,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat) ),
    inference(definition,[],]) ).

fof(to_be_clausified_24,plain,
    ! [V_n] :
      ( lhs_atom25(V_n)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_min__0R_0_0,def_lhs_atom25]) ).

fof(def_lhs_atom26,axiom,
    ( lhs_atom26
  <=> c_HOL_Oone__class_Oone(tc_nat) = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
    inference(definition,[],]) ).

fof(to_be_clausified_25,plain,
    ( lhs_atom26
    | $false ),
    inference(fold_definition,[status(thm)],[cls_One__nat__def_0_0,def_lhs_atom26]) ).

fof(def_lhs_atom27,axiom,
    ( lhs_atom27
  <=> 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_26,plain,
    ( lhs_atom27
    | $false ),
    inference(fold_definition,[status(thm)],[cls_less__Suc0_1_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) = c_HOL_Oplus__class_Oplus(V_m,c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat),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) = c_HOL_Oplus__class_Oplus(V_n,c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat),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_n,V_m,V_k] :
      ( lhs_atom30(V_n,V_m,V_k)
    <=> c_Divides_Odiv__class_Omod(c_Suc(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_k,V_n,tc_nat),V_m,tc_nat)),V_n,tc_nat) = c_Divides_Odiv__class_Omod(c_Suc(V_m),V_n,tc_nat) ),
    inference(definition,[],]) ).

fof(to_be_clausified_29,plain,
    ! [V_k,V_m,V_n] :
      ( lhs_atom30(V_n,V_m,V_k)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_mod__mult__self4_0_0,def_lhs_atom30]) ).

fof(def_lhs_atom31,axiom,
    ( lhs_atom31
  <=> 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_30,plain,
    ( lhs_atom31
    | $false ),
    inference(fold_definition,[status(thm)],[cls_mult__eq__1__iff_2_0,def_lhs_atom31]) ).

fof(def_lhs_atom32,axiom,
    ! [V_n] :
      ( lhs_atom32(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_31,plain,
    ! [V_n] :
      ( lhs_atom32(V_n)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_mult__is__0_1_0,def_lhs_atom32]) ).

fof(def_lhs_atom33,axiom,
    ! [V_m] :
      ( lhs_atom33(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_32,plain,
    ! [V_m] :
      ( lhs_atom33(V_m)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_mult__is__0_2_0,def_lhs_atom33]) ).

fof(def_lhs_atom34,axiom,
    ! [V_m] :
      ( lhs_atom34(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_33,plain,
    ! [V_m] :
      ( lhs_atom34(V_m)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_mod__1_0_0,def_lhs_atom34]) ).

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

fof(to_be_clausified_34,plain,
    ( lhs_atom35
    | $false ),
    inference(fold_definition,[status(thm)],[cls_one__is__add_4_0,def_lhs_atom35]) ).

fof(def_lhs_atom36,axiom,
    ( lhs_atom36
  <=> c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) = c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) ),
    inference(definition,[],]) ).

fof(to_be_clausified_35,plain,
    ( lhs_atom36
    | $false ),
    inference(fold_definition,[status(thm)],[cls_one__is__add_5_0,def_lhs_atom36]) ).

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

fof(to_be_clausified_36,plain,
    ! [V_m,V_n] :
      ( lhs_atom37(V_n,V_m)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_diff__add__0_0_0,def_lhs_atom37]) ).

fof(def_lhs_atom38,axiom,
    ! [V_k,V_j,V_i] :
      ( lhs_atom38(V_k,V_j,V_i)
    <=> c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(V_i,V_j,tc_nat),V_k,tc_nat) = c_HOL_Ominus__class_Ominus(V_i,c_HOL_Oplus__class_Oplus(V_j,V_k,tc_nat),tc_nat) ),
    inference(definition,[],]) ).

fof(to_be_clausified_37,plain,
    ! [V_i,V_j,V_k] :
      ( lhs_atom38(V_k,V_j,V_i)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_diff__diff__left_0_0,def_lhs_atom38]) ).

fof(def_lhs_atom39,axiom,
    ! [V_n] :
      ( lhs_atom39(V_n)
    <=> c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat) ),
    inference(definition,[],]) ).

fof(to_be_clausified_38,plain,
    ! [V_n] :
      ( lhs_atom39(V_n)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_diff__0__eq__0_0_0,def_lhs_atom39]) ).

fof(def_lhs_atom40,axiom,
    ! [V_n,V_m,V_k] :
      ( lhs_atom40(V_n,V_m,V_k)
    <=> c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(V_m,V_k,tc_nat),c_HOL_Oplus__class_Oplus(V_n,V_k,tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat) ),
    inference(definition,[],]) ).

fof(to_be_clausified_39,plain,
    ! [V_k,V_m,V_n] :
      ( lhs_atom40(V_n,V_m,V_k)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_diff__cancel2_0_0,def_lhs_atom40]) ).

fof(def_lhs_atom41,axiom,
    ! [V_n,V_m,V_k] :
      ( lhs_atom41(V_n,V_m,V_k)
    <=> c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(V_k,V_m,tc_nat),c_HOL_Oplus__class_Oplus(V_k,V_n,tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat) ),
    inference(definition,[],]) ).

fof(to_be_clausified_40,plain,
    ! [V_k,V_m,V_n] :
      ( lhs_atom41(V_n,V_m,V_k)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_diff__cancel_0_0,def_lhs_atom41]) ).

fof(def_lhs_atom42,axiom,
    ! [V_n] :
      ( lhs_atom42(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_41,plain,
    ! [V_n] :
      ( lhs_atom42(V_n)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_zero__less__Suc_0_0,def_lhs_atom42]) ).

fof(def_lhs_atom43,axiom,
    ! [V_x] :
      ( lhs_atom43(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_42,plain,
    ! [V_x] :
      ( lhs_atom43(V_x)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_gr0__conv__Suc_1_0,def_lhs_atom43]) ).

fof(def_lhs_atom44,axiom,
    ! [V_u,V_k,V_j,V_i] :
      ( lhs_atom44(V_u,V_k,V_j,V_i)
    <=> c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_i,V_u,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_j,V_u,tc_nat),V_k,tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(V_i,V_j,tc_nat),V_u,tc_nat),V_k,tc_nat) ),
    inference(definition,[],]) ).

fof(to_be_clausified_43,plain,
    ! [V_i,V_j,V_k,V_u] :
      ( lhs_atom44(V_u,V_k,V_j,V_i)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_left__add__mult__distrib_0_0,def_lhs_atom44]) ).

fof(def_lhs_atom45,axiom,
    ! [V_n,V_m] :
      ( lhs_atom45(V_n,V_m)
    <=> c_lessequals(c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat),V_m,tc_nat) ),
    inference(definition,[],]) ).

fof(to_be_clausified_44,plain,
    ! [V_m,V_n] :
      ( lhs_atom45(V_n,V_m)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_diff__le__self_0_0,def_lhs_atom45]) ).

fof(def_lhs_atom46,axiom,
    ! [V_n,V_m,V_k] :
      ( lhs_atom46(V_n,V_m,V_k)
    <=> c_HOL_Otimes__class_Otimes(V_k,c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(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_45,plain,
    ! [V_k,V_m,V_n] :
      ( lhs_atom46(V_n,V_m,V_k)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_diff__mult__distrib2_0_0,def_lhs_atom46]) ).

fof(def_lhs_atom47,axiom,
    ! [V_n,V_m,V_k] :
      ( lhs_atom47(V_n,V_m,V_k)
    <=> c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat),V_k,tc_nat) = c_HOL_Ominus__class_Ominus(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_46,plain,
    ! [V_k,V_m,V_n] :
      ( lhs_atom47(V_n,V_m,V_k)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_diff__mult__distrib_0_0,def_lhs_atom47]) ).

fof(def_lhs_atom48,axiom,
    ! [V_k,V_j,V_i] :
      ( lhs_atom48(V_k,V_j,V_i)
    <=> c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(V_i,V_j,tc_nat),V_k,tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(V_i,V_k,tc_nat),V_j,tc_nat) ),
    inference(definition,[],]) ).

fof(to_be_clausified_47,plain,
    ! [V_i,V_j,V_k] :
      ( lhs_atom48(V_k,V_j,V_i)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_diff__commute_0_0,def_lhs_atom48]) ).

fof(def_lhs_atom49,axiom,
    ! [V_n] :
      ( lhs_atom49(V_n)
    <=> c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat) ),
    inference(definition,[],]) ).

fof(to_be_clausified_48,plain,
    ! [V_n] :
      ( lhs_atom49(V_n)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_le0_0_0,def_lhs_atom49]) ).

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

fof(to_be_clausified_49,plain,
    ! [V_x] :
      ( lhs_atom50(V_x)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_nat__less__le_1_0,def_lhs_atom50]) ).

fof(def_lhs_atom51,axiom,
    ! [V_n] :
      ( lhs_atom51(V_n)
    <=> ~ c_HOL_Oord__class_Oless(V_n,V_n,tc_nat) ),
    inference(definition,[],]) ).

fof(to_be_clausified_50,plain,
    ! [V_n] :
      ( lhs_atom51(V_n)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_less__not__refl_0_0,def_lhs_atom51]) ).

fof(def_lhs_atom52,axiom,
    ! [V_t,V_s] :
      ( lhs_atom52(V_t,V_s)
    <=> c_Lambda_Obeta(c_Lambda_OdB_OApp(c_Lambda_OdB_OAbs(V_s),V_t),c_Lambda_Osubst(V_s,V_t,c_HOL_Ozero__class_Ozero(tc_nat))) ),
    inference(definition,[],]) ).

fof(to_be_clausified_51,plain,
    ! [V_s,V_t] :
      ( lhs_atom52(V_t,V_s)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_beta_0_0,def_lhs_atom52]) ).

fof(def_lhs_atom53,axiom,
    ! [V_n,V_m] :
      ( lhs_atom53(V_n,V_m)
    <=> c_lessequals(V_n,c_HOL_Oplus__class_Oplus(V_n,V_m,tc_nat),tc_nat) ),
    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_le__add1_0_0,def_lhs_atom53]) ).

fof(def_lhs_atom54,axiom,
    ! [V_n,V_m] :
      ( lhs_atom54(V_n,V_m)
    <=> c_lessequals(V_n,c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat),tc_nat) ),
    inference(definition,[],]) ).

fof(to_be_clausified_53,plain,
    ! [V_m,V_n] :
      ( lhs_atom54(V_n,V_m)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_le__add2_0_0,def_lhs_atom54]) ).

fof(def_lhs_atom55,axiom,
    ! [V_x,V_m] :
      ( lhs_atom55(V_x,V_m)
    <=> c_lessequals(V_m,c_HOL_Oplus__class_Oplus(V_m,V_x,tc_nat),tc_nat) ),
    inference(definition,[],]) ).

fof(to_be_clausified_54,plain,
    ! [V_m,V_x] :
      ( lhs_atom55(V_x,V_m)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_le__iff__add_1_0,def_lhs_atom55]) ).

fof(def_lhs_atom56,axiom,
    ! [V_n,V_m] :
      ( lhs_atom56(V_n,V_m)
    <=> c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(V_n,V_m,tc_nat),V_m,tc_nat) = c_Orderings_Oord__class_Omax(V_n,V_m,tc_nat) ),
    inference(definition,[],]) ).

fof(to_be_clausified_55,plain,
    ! [V_m,V_n] :
      ( lhs_atom56(V_n,V_m)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_nat__minus__add__max_0_0,def_lhs_atom56]) ).

fof(def_lhs_atom57,axiom,
    ( lhs_atom57
  <=> ~ 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_56,plain,
    ( lhs_atom57
    | $false ),
    inference(fold_definition,[status(thm)],[cls_neq0__conv_1_0,def_lhs_atom57]) ).

fof(def_lhs_atom58,axiom,
    ! [V_n,V_m] :
      ( lhs_atom58(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_57,plain,
    ! [V_m,V_n] :
      ( lhs_atom58(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_atom58]) ).

fof(def_lhs_atom59,axiom,
    ! [V_n,V_m] :
      ( lhs_atom59(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_58,plain,
    ! [V_m,V_n] :
      ( lhs_atom59(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_atom59]) ).

fof(def_lhs_atom60,axiom,
    ! [V_j,V_i] :
      ( lhs_atom60(V_j,V_i)
    <=> ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(V_i,V_j,tc_nat),V_i,tc_nat) ),
    inference(definition,[],]) ).

fof(to_be_clausified_59,plain,
    ! [V_i,V_j] :
      ( lhs_atom60(V_j,V_i)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_not__add__less1_0_0,def_lhs_atom60]) ).

fof(def_lhs_atom61,axiom,
    ! [V_j,V_i] :
      ( lhs_atom61(V_j,V_i)
    <=> ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(V_j,V_i,tc_nat),V_i,tc_nat) ),
    inference(definition,[],]) ).

fof(to_be_clausified_60,plain,
    ! [V_i,V_j] :
      ( lhs_atom61(V_j,V_i)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_not__add__less2_0_0,def_lhs_atom61]) ).

fof(def_lhs_atom62,axiom,
    ( lhs_atom62
  <=> c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ),
    inference(definition,[],]) ).

fof(to_be_clausified_61,plain,
    ( lhs_atom62
    | $false ),
    inference(fold_definition,[status(thm)],[cls_le__0__eq_1_0,def_lhs_atom62]) ).

fof(def_lhs_atom63,axiom,
    ! [V_t,V_s,V_k] :
      ( lhs_atom63(V_t,V_s,V_k)
    <=> c_Lambda_Osubst(c_Lambda_OdB_OAbs(V_t),V_s,V_k) = c_Lambda_OdB_OAbs(c_Lambda_Osubst(V_t,c_Lambda_Olift(V_s,c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oplus__class_Oplus(V_k,c_HOL_Oone__class_Oone(tc_nat),tc_nat))) ),
    inference(definition,[],]) ).

fof(to_be_clausified_62,plain,
    ! [V_k,V_s,V_t] :
      ( lhs_atom63(V_t,V_s,V_k)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_subst__Abs_0_0,def_lhs_atom63]) ).

fof(def_lhs_atom64,axiom,
    ! [V_n,V_m] :
      ( lhs_atom64(V_n,V_m)
    <=> c_lessequals(c_Divides_Odiv__class_Omod(V_m,V_n,tc_nat),V_m,tc_nat) ),
    inference(definition,[],]) ).

fof(to_be_clausified_63,plain,
    ! [V_m,V_n] :
      ( lhs_atom64(V_n,V_m)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_mod__less__eq__dividend_0_0,def_lhs_atom64]) ).

fof(def_lhs_atom65,axiom,
    ! [V_n,V_m] :
      ( lhs_atom65(V_n,V_m)
    <=> c_HOL_Ominus__class_Ominus(V_m,c_Suc(V_n),tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(V_m,c_HOL_Oone__class_Oone(tc_nat),tc_nat),V_n,tc_nat) ),
    inference(definition,[],]) ).

fof(to_be_clausified_64,plain,
    ! [V_m,V_n] :
      ( lhs_atom65(V_n,V_m)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_diff__Suc__eq__diff__pred_0_0,def_lhs_atom65]) ).

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

fof(to_be_clausified_65,plain,
    ! [V_n] :
      ( lhs_atom66(V_n)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_max__0R_0_0,def_lhs_atom66]) ).

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

fof(to_be_clausified_66,plain,
    ! [V_n] :
      ( lhs_atom67(V_n)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_max__0L_0_0,def_lhs_atom67]) ).

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

fof(to_be_clausified_67,plain,
    ! [V_m] :
      ( lhs_atom68(V_m)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_le__square_0_0,def_lhs_atom68]) ).

fof(def_lhs_atom69,axiom,
    ( lhs_atom69
  <=> 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_68,plain,
    ( lhs_atom69
    | $false ),
    inference(fold_definition,[status(thm)],[cls_nat__mult__eq__1__iff_2_0,def_lhs_atom69]) ).

fof(def_lhs_atom70,axiom,
    ! [V_n,V_m,V_k] :
      ( lhs_atom70(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_69,plain,
    ! [V_k,V_m,V_n] :
      ( lhs_atom70(V_n,V_m,V_k)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_mod__mult__distrib2_0_0,def_lhs_atom70]) ).

fof(def_lhs_atom71,axiom,
    ! [V_n,V_m,V_k] :
      ( lhs_atom71(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_70,plain,
    ! [V_k,V_m,V_n] :
      ( lhs_atom71(V_n,V_m,V_k)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_mod__mult__distrib_0_0,def_lhs_atom71]) ).

fof(def_lhs_atom72,axiom,
    ! [V_m] :
      ( lhs_atom72(V_m)
    <=> c_lessequals(V_m,c_HOL_Otimes__class_Otimes(V_m,c_HOL_Otimes__class_Otimes(V_m,V_m,tc_nat),tc_nat),tc_nat) ),
    inference(definition,[],]) ).

fof(to_be_clausified_71,plain,
    ! [V_m] :
      ( lhs_atom72(V_m)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_le__cube_0_0,def_lhs_atom72]) ).

fof(def_lhs_atom73,axiom,
    ! [V_n,V_m,V_k] :
      ( lhs_atom73(V_n,V_m,V_k)
    <=> c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_k,V_n,tc_nat),V_m,tc_nat),V_n,tc_nat) = c_Divides_Odiv__class_Omod(V_m,V_n,tc_nat) ),
    inference(definition,[],]) ).

fof(to_be_clausified_72,plain,
    ! [V_k,V_m,V_n] :
      ( lhs_atom73(V_n,V_m,V_k)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_mod__mult__self3_0_0,def_lhs_atom73]) ).

fof(def_lhs_atom74,axiom,
    ! [V_x] :
      ( lhs_atom74(V_x)
    <=> V_x = c_HOL_Oplus__class_Oplus(V_x,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ),
    inference(definition,[],]) ).

fof(to_be_clausified_73,plain,
    ! [V_x] :
      ( lhs_atom74(V_x)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_natgb_Oadd__r0__iff_1_0,def_lhs_atom74]) ).

fof(def_lhs_atom75,axiom,
    ! [V_n] :
      ( lhs_atom75(V_n)
    <=> c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat) = V_n ),
    inference(definition,[],]) ).

fof(to_be_clausified_74,plain,
    ! [V_n] :
      ( lhs_atom75(V_n)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_plus__nat_Oadd__0_0_0,def_lhs_atom75]) ).

fof(def_lhs_atom76,axiom,
    ! [V_m] :
      ( lhs_atom76(V_m)
    <=> c_HOL_Oplus__class_Oplus(V_m,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = V_m ),
    inference(definition,[],]) ).

fof(to_be_clausified_75,plain,
    ! [V_m] :
      ( lhs_atom76(V_m)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_Nat_Oadd__0__right_0_0,def_lhs_atom76]) ).

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

fof(to_be_clausified_76,plain,
    ! [V_m,V_n] :
      ( lhs_atom77(V_n,V_m)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_diff__add__inverse2_0_0,def_lhs_atom77]) ).

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

fof(to_be_clausified_77,plain,
    ! [V_m,V_n] :
      ( lhs_atom78(V_n,V_m)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_diff__add__inverse_0_0,def_lhs_atom78]) ).

fof(def_lhs_atom79,axiom,
    ! [V_n] :
      ( lhs_atom79(V_n)
    <=> c_lessequals(V_n,V_n,tc_nat) ),
    inference(definition,[],]) ).

fof(to_be_clausified_78,plain,
    ! [V_n] :
      ( lhs_atom79(V_n)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_le__refl_0_0,def_lhs_atom79]) ).

fof(def_lhs_atom80,axiom,
    ! [V_x] :
      ( lhs_atom80(V_x)
    <=> c_lessequals(V_x,V_x,tc_nat) ),
    inference(definition,[],]) ).

fof(to_be_clausified_79,plain,
    ! [V_x] :
      ( lhs_atom80(V_x)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_eq__imp__le_0_0,def_lhs_atom80]) ).

fof(def_lhs_atom81,axiom,
    ! [V_n,V_m,V_i] :
      ( lhs_atom81(V_n,V_m,V_i)
    <=> c_Orderings_Oord__class_Omin(c_HOL_Ominus__class_Ominus(V_m,V_i,tc_nat),c_HOL_Ominus__class_Ominus(V_n,V_i,tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(c_Orderings_Oord__class_Omin(V_m,V_n,tc_nat),V_i,tc_nat) ),
    inference(definition,[],]) ).

fof(to_be_clausified_80,plain,
    ! [V_i,V_m,V_n] :
      ( lhs_atom81(V_n,V_m,V_i)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_min__diff_0_0,def_lhs_atom81]) ).

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

fof(to_be_clausified_81,plain,
    ( lhs_atom82
    | $false ),
    inference(fold_definition,[status(thm)],[cls_add__is__1_5_0,def_lhs_atom82]) ).

fof(def_lhs_atom83,axiom,
    ! [V_x,V_d] :
      ( lhs_atom83(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_82,plain,
    ! [V_d,V_x] :
      ( lhs_atom83(V_x,V_d)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_mod__eq__0__iff_1_0,def_lhs_atom83]) ).

fof(def_lhs_atom84,axiom,
    ! [V_s,V_k] :
      ( lhs_atom84(V_s,V_k)
    <=> c_Lambda_Olift(c_Lambda_OdB_OAbs(V_s),V_k) = c_Lambda_OdB_OAbs(c_Lambda_Olift(V_s,c_HOL_Oplus__class_Oplus(V_k,c_HOL_Oone__class_Oone(tc_nat),tc_nat))) ),
    inference(definition,[],]) ).

fof(to_be_clausified_83,plain,
    ! [V_k,V_s] :
      ( lhs_atom84(V_s,V_k)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_lift_Osimps_I3_J_0_0,def_lhs_atom84]) ).

fof(def_lhs_atom85,axiom,
    ! [V_n,V_m,V_k] :
      ( lhs_atom85(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_84,plain,
    ! [V_k,V_m,V_n] :
      ( lhs_atom85(V_n,V_m,V_k)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_nat__mult__assoc_0_0,def_lhs_atom85]) ).

fof(def_lhs_atom86,axiom,
    ! [V_n,V_m,V_k] :
      ( lhs_atom86(V_n,V_m,V_k)
    <=> c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat),V_k,tc_nat) = c_HOL_Oplus__class_Oplus(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_85,plain,
    ! [V_k,V_m,V_n] :
      ( lhs_atom86(V_n,V_m,V_k)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_add__mult__distrib_0_0,def_lhs_atom86]) ).

fof(def_lhs_atom87,axiom,
    ! [V_n,V_m,V_k] :
      ( lhs_atom87(V_n,V_m,V_k)
    <=> c_HOL_Otimes__class_Otimes(V_k,c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(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_86,plain,
    ! [V_k,V_m,V_n] :
      ( lhs_atom87(V_n,V_m,V_k)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_add__mult__distrib2_0_0,def_lhs_atom87]) ).

fof(def_lhs_atom88,axiom,
    ! [V_u,V_t,V_s,V_k] :
      ( lhs_atom88(V_u,V_t,V_s,V_k)
    <=> c_Lambda_Osubst(c_Lambda_OdB_OApp(V_t,V_u),V_s,V_k) = c_Lambda_OdB_OApp(c_Lambda_Osubst(V_t,V_s,V_k),c_Lambda_Osubst(V_u,V_s,V_k)) ),
    inference(definition,[],]) ).

fof(to_be_clausified_87,plain,
    ! [V_k,V_s,V_t,V_u] :
      ( lhs_atom88(V_u,V_t,V_s,V_k)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_subst__App_0_0,def_lhs_atom88]) ).

fof(def_lhs_atom89,axiom,
    ! [V_nat,V_dB_H] :
      ( lhs_atom89(V_nat,V_dB_H)
    <=> c_Lambda_OdB_OAbs(V_dB_H) != c_Lambda_OdB_OVar(V_nat) ),
    inference(definition,[],]) ).

fof(to_be_clausified_88,plain,
    ! [V_dB_H,V_nat] :
      ( lhs_atom89(V_nat,V_dB_H)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_dB_Osimps_I7_J_0_0,def_lhs_atom89]) ).

fof(def_lhs_atom90,axiom,
    ! [V_dB_H,V_dB2,V_dB1] :
      ( lhs_atom90(V_dB_H,V_dB2,V_dB1)
    <=> c_Lambda_OdB_OApp(V_dB1,V_dB2) != c_Lambda_OdB_OAbs(V_dB_H) ),
    inference(definition,[],]) ).

fof(to_be_clausified_89,plain,
    ! [V_dB1,V_dB2,V_dB_H] :
      ( lhs_atom90(V_dB_H,V_dB2,V_dB1)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_dB_Osimps_I8_J_0_0,def_lhs_atom90]) ).

fof(def_lhs_atom91,axiom,
    ! [V_dB_H,V_dB2,V_dB1] :
      ( lhs_atom91(V_dB_H,V_dB2,V_dB1)
    <=> c_Lambda_OdB_OAbs(V_dB_H) != c_Lambda_OdB_OApp(V_dB1,V_dB2) ),
    inference(definition,[],]) ).

fof(to_be_clausified_90,plain,
    ! [V_dB1,V_dB2,V_dB_H] :
      ( lhs_atom91(V_dB_H,V_dB2,V_dB1)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_dB_Osimps_I9_J_0_0,def_lhs_atom91]) ).

fof(def_lhs_atom92,axiom,
    ! [V_u,V_k] :
      ( lhs_atom92(V_u,V_k)
    <=> c_Lambda_Osubst(c_Lambda_OdB_OVar(V_k),V_u,V_k) = V_u ),
    inference(definition,[],]) ).

fof(to_be_clausified_91,plain,
    ! [V_k,V_u] :
      ( lhs_atom92(V_u,V_k)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_subst__eq_0_0,def_lhs_atom92]) ).

fof(def_lhs_atom93,axiom,
    ! [V_n,V_m] :
      ( lhs_atom93(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_92,plain,
    ! [V_m,V_n] :
      ( lhs_atom93(V_n,V_m)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_mod__Suc__eq__Suc__mod_0_0,def_lhs_atom93]) ).

fof(def_lhs_atom94,axiom,
    ! [V_n] :
      ( lhs_atom94(V_n)
    <=> V_n != c_Suc(V_n) ),
    inference(definition,[],]) ).

fof(to_be_clausified_93,plain,
    ! [V_n] :
      ( lhs_atom94(V_n)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_n__not__Suc__n_0_0,def_lhs_atom94]) ).

fof(def_lhs_atom95,axiom,
    ! [V_n] :
      ( lhs_atom95(V_n)
    <=> c_Suc(V_n) != V_n ),
    inference(definition,[],]) ).

fof(to_be_clausified_94,plain,
    ! [V_n] :
      ( lhs_atom95(V_n)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_Suc__n__not__n_0_0,def_lhs_atom95]) ).

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

fof(to_be_clausified_95,plain,
    ! [V_n] :
      ( lhs_atom96(V_n)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_Suc__n__not__le__n_0_0,def_lhs_atom96]) ).

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

fof(to_be_clausified_96,plain,
    ! [V_x] :
      ( lhs_atom97(V_x)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_less__Suc__eq_2_0,def_lhs_atom97]) ).

fof(def_lhs_atom98,axiom,
    ! [V_n] :
      ( lhs_atom98(V_n)
    <=> c_HOL_Oord__class_Oless(V_n,c_Suc(V_n),tc_nat) ),
    inference(definition,[],]) ).

fof(to_be_clausified_97,plain,
    ! [V_n] :
      ( lhs_atom98(V_n)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_lessI_0_0,def_lhs_atom98]) ).

fof(def_lhs_atom99,axiom,
    ! [V_t,V_i] :
      ( lhs_atom99(V_t,V_i)
    <=> ~ c_Lambda_Obeta(c_Lambda_OdB_OVar(V_i),V_t) ),
    inference(definition,[],]) ).

fof(to_be_clausified_98,plain,
    ! [V_i,V_t] :
      ( lhs_atom99(V_t,V_i)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_beta__cases_I1_J_0_0,def_lhs_atom99]) ).

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

fof(to_be_clausified_99,plain,
    ! [V_m] :
      ( lhs_atom100(V_m)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_Suc__neq__Zero_0_0,def_lhs_atom100]) ).

fof(def_lhs_atom101,axiom,
    ! [V_nat_H] :
      ( lhs_atom101(V_nat_H)
    <=> c_Suc(V_nat_H) != c_HOL_Ozero__class_Ozero(tc_nat) ),
    inference(definition,[],]) ).

fof(to_be_clausified_100,plain,
    ! [V_nat_H] :
      ( lhs_atom101(V_nat_H)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_nat_Osimps_I3_J_0_0,def_lhs_atom101]) ).

fof(def_lhs_atom102,axiom,
    ! [V_nat,V_dB2_H,V_dB1_H] :
      ( lhs_atom102(V_nat,V_dB2_H,V_dB1_H)
    <=> c_Lambda_OdB_OVar(V_nat) != c_Lambda_OdB_OApp(V_dB1_H,V_dB2_H) ),
    inference(definition,[],]) ).

fof(to_be_clausified_101,plain,
    ! [V_dB1_H,V_dB2_H,V_nat] :
      ( lhs_atom102(V_nat,V_dB2_H,V_dB1_H)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_dB_Osimps_I4_J_0_0,def_lhs_atom102]) ).

fof(def_lhs_atom103,axiom,
    ! [V_n,V_m] :
      ( lhs_atom103(V_n,V_m)
    <=> c_HOL_Ominus__class_Ominus(c_Suc(V_m),c_Suc(V_n),tc_nat) = c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat) ),
    inference(definition,[],]) ).

fof(to_be_clausified_102,plain,
    ! [V_m,V_n] :
      ( lhs_atom103(V_n,V_m)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_diff__Suc__Suc_0_0,def_lhs_atom103]) ).

fof(def_lhs_atom104,axiom,
    ! [V_nat,V_dB_H] :
      ( lhs_atom104(V_nat,V_dB_H)
    <=> c_Lambda_OdB_OVar(V_nat) != c_Lambda_OdB_OAbs(V_dB_H) ),
    inference(definition,[],]) ).

fof(to_be_clausified_103,plain,
    ! [V_dB_H,V_nat] :
      ( lhs_atom104(V_nat,V_dB_H)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_dB_Osimps_I6_J_0_0,def_lhs_atom104]) ).

fof(def_lhs_atom105,axiom,
    ! [V_m] :
      ( lhs_atom105(V_m)
    <=> c_HOL_Ozero__class_Ozero(tc_nat) != c_Suc(V_m) ),
    inference(definition,[],]) ).

fof(to_be_clausified_104,plain,
    ! [V_m] :
      ( lhs_atom105(V_m)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_Zero__neq__Suc_0_0,def_lhs_atom105]) ).

fof(def_lhs_atom106,axiom,
    ! [V_nat_H] :
      ( lhs_atom106(V_nat_H)
    <=> c_HOL_Ozero__class_Ozero(tc_nat) != c_Suc(V_nat_H) ),
    inference(definition,[],]) ).

fof(to_be_clausified_105,plain,
    ! [V_nat_H] :
      ( lhs_atom106(V_nat_H)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_nat_Osimps_I2_J_0_0,def_lhs_atom106]) ).

fof(def_lhs_atom107,axiom,
    ! [V_n,V_m] :
      ( lhs_atom107(V_n,V_m)
    <=> c_HOL_Oplus__class_Oplus(c_Suc(V_m),V_n,tc_nat) = c_Suc(c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat)) ),
    inference(definition,[],]) ).

fof(to_be_clausified_106,plain,
    ! [V_m,V_n] :
      ( lhs_atom107(V_n,V_m)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_add__Suc_0_0,def_lhs_atom107]) ).

fof(def_lhs_atom108,axiom,
    ! [V_n,V_m] :
      ( lhs_atom108(V_n,V_m)
    <=> c_HOL_Oplus__class_Oplus(V_m,c_Suc(V_n),tc_nat) = c_Suc(c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat)) ),
    inference(definition,[],]) ).

fof(to_be_clausified_107,plain,
    ! [V_m,V_n] :
      ( lhs_atom108(V_n,V_m)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_add__Suc__right_0_0,def_lhs_atom108]) ).

fof(def_lhs_atom109,axiom,
    ! [V_n,V_m] :
      ( lhs_atom109(V_n,V_m)
    <=> c_Orderings_Oord__class_Omax(c_Suc(V_m),c_Suc(V_n),tc_nat) = c_Suc(c_Orderings_Oord__class_Omax(V_m,V_n,tc_nat)) ),
    inference(definition,[],]) ).

fof(to_be_clausified_108,plain,
    ! [V_m,V_n] :
      ( lhs_atom109(V_n,V_m)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_max__Suc__Suc_0_0,def_lhs_atom109]) ).

fof(def_lhs_atom110,axiom,
    ! [V_n,V_m] :
      ( lhs_atom110(V_n,V_m)
    <=> c_HOL_Oplus__class_Oplus(c_Suc(V_m),V_n,tc_nat) = c_HOL_Oplus__class_Oplus(V_m,c_Suc(V_n),tc_nat) ),
    inference(definition,[],]) ).

fof(to_be_clausified_109,plain,
    ! [V_m,V_n] :
      ( lhs_atom110(V_n,V_m)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_add__Suc__shift_0_0,def_lhs_atom110]) ).

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

fof(to_be_clausified_110,plain,
    ! [V_k,V_m,V_n] :
      ( lhs_atom111(V_n,V_m,V_k)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_Suc__diff__diff_0_0,def_lhs_atom111]) ).

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

fof(to_be_clausified_111,plain,
    ! [V_n] :
      ( lhs_atom112(V_n)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_le__Suc__eq_2_0,def_lhs_atom112]) ).

fof(def_lhs_atom113,axiom,
    ! [V_t,V_s,V_k] :
      ( lhs_atom113(V_t,V_s,V_k)
    <=> c_Lambda_Osubst(c_Lambda_Olift(V_t,V_k),V_s,V_k) = V_t ),
    inference(definition,[],]) ).

fof(to_be_clausified_112,plain,
    ! [V_k,V_s,V_t] :
      ( lhs_atom113(V_t,V_s,V_k)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_subst__lift_0_0,def_lhs_atom113]) ).

fof(def_lhs_atom114,axiom,
    ! [V_n,V_m] :
      ( lhs_atom114(V_n,V_m)
    <=> c_Orderings_Oord__class_Omin(c_Suc(V_m),c_Suc(V_n),tc_nat) = c_Suc(c_Orderings_Oord__class_Omin(V_m,V_n,tc_nat)) ),
    inference(definition,[],]) ).

fof(to_be_clausified_113,plain,
    ! [V_m,V_n] :
      ( lhs_atom114(V_n,V_m)
      | $false ),
    inference(fold_definition,[status(thm)],[cls_min__Suc__Suc_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_OApp(V_dB1_H,V_dB2_H) != c_Lambda_OdB_OVar(V_nat) ),
    inference(definition,[],]) ).

fof(to_be_clausified_114,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_I5_J_0_0,def_lhs_atom115]) ).

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

fof(to_be_clausified_115,plain,
    ( lhs_atom116
    | $false ),
    inference(fold_definition,[status(thm)],[clsarity_nat__OrderedGroup_Opordered__cancel__ab__semigroup__add_0,def_lhs_atom116]) ).

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

fof(to_be_clausified_116,plain,
    ( lhs_atom117
    | $false ),
    inference(fold_definition,[status(thm)],[clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add__imp__le_0,def_lhs_atom117]) ).

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

fof(to_be_clausified_117,plain,
    ( lhs_atom118
    | $false ),
    inference(fold_definition,[status(thm)],[clsarity_nat__Ring__and__Field_Oordered__comm__semiring__strict_0,def_lhs_atom118]) ).

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

fof(to_be_clausified_118,plain,
    ( lhs_atom119
    | $false ),
    inference(fold_definition,[status(thm)],[clsarity_nat__Ring__and__Field_Opordered__cancel__semiring_0,def_lhs_atom119]) ).

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

fof(to_be_clausified_119,plain,
    ( lhs_atom120
    | $false ),
    inference(fold_definition,[status(thm)],[clsarity_nat__Ring__and__Field_Oordered__semiring__strict_0,def_lhs_atom120]) ).

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

fof(to_be_clausified_120,plain,
    ( lhs_atom121
    | $false ),
    inference(fold_definition,[status(thm)],[clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add_0,def_lhs_atom121]) ).

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

fof(to_be_clausified_121,plain,
    ( lhs_atom122
    | $false ),
    inference(fold_definition,[status(thm)],[clsarity_nat__OrderedGroup_Opordered__comm__monoid__add_0,def_lhs_atom122]) ).

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

fof(to_be_clausified_122,plain,
    ( lhs_atom123
    | $false ),
    inference(fold_definition,[status(thm)],[clsarity_nat__OrderedGroup_Ocancel__ab__semigroup__add_0,def_lhs_atom123]) ).

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

fof(to_be_clausified_123,plain,
    ( lhs_atom124
    | $false ),
    inference(fold_definition,[status(thm)],[clsarity_nat__OrderedGroup_Ocancel__semigroup__add_0,def_lhs_atom124]) ).

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

fof(to_be_clausified_124,plain,
    ( lhs_atom125
    | $false ),
    inference(fold_definition,[status(thm)],[clsarity_nat__Ring__and__Field_Opordered__semiring_0,def_lhs_atom125]) ).

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

fof(to_be_clausified_125,plain,
    ( lhs_atom126
    | $false ),
    inference(fold_definition,[status(thm)],[clsarity_nat__Ring__and__Field_Oordered__semiring_0,def_lhs_atom126]) ).

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

fof(to_be_clausified_126,plain,
    ( lhs_atom127
    | $false ),
    inference(fold_definition,[status(thm)],[clsarity_nat__Ring__and__Field_Ono__zero__divisors_0,def_lhs_atom127]) ).

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

fof(to_be_clausified_127,plain,
    ( lhs_atom128
    | $false ),
    inference(fold_definition,[status(thm)],[clsarity_nat__Ring__and__Field_Oordered__semidom_0,def_lhs_atom128]) ).

fof(def_lhs_atom129,axiom,
    ( lhs_atom129
  <=> class_Ring__and__Field_Ocomm__semiring__1(tc_nat) ),
    inference(definition,[],]) ).

fof(to_be_clausified_128,plain,
    ( lhs_atom129
    | $false ),
    inference(fold_definition,[status(thm)],[clsarity_nat__Ring__and__Field_Ocomm__semiring__1_0,def_lhs_atom129]) ).

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

fof(to_be_clausified_129,plain,
    ( lhs_atom130
    | $false ),
    inference(fold_definition,[status(thm)],[clsarity_nat__OrderedGroup_Oab__semigroup__mult_0,def_lhs_atom130]) ).

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

fof(to_be_clausified_130,plain,
    ( lhs_atom131
    | $false ),
    inference(fold_definition,[status(thm)],[clsarity_nat__OrderedGroup_Ocomm__monoid__mult_0,def_lhs_atom131]) ).

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

fof(to_be_clausified_131,plain,
    ( lhs_atom132
    | $false ),
    inference(fold_definition,[status(thm)],[clsarity_nat__OrderedGroup_Oab__semigroup__add_0,def_lhs_atom132]) ).

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

fof(to_be_clausified_132,plain,
    ( lhs_atom133
    | $false ),
    inference(fold_definition,[status(thm)],[clsarity_nat__Ring__and__Field_Ocomm__semiring_0,def_lhs_atom133]) ).

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

fof(to_be_clausified_133,plain,
    ( lhs_atom134
    | $false ),
    inference(fold_definition,[status(thm)],[clsarity_nat__OrderedGroup_Ocomm__monoid__add_0,def_lhs_atom134]) ).

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

fof(to_be_clausified_134,plain,
    ( lhs_atom135
    | $false ),
    inference(fold_definition,[status(thm)],[clsarity_nat__Ring__and__Field_Ozero__neq__one_0,def_lhs_atom135]) ).

fof(def_lhs_atom136,axiom,
    ( lhs_atom136
  <=> class_Ring__and__Field_Omult__mono1(tc_nat) ),
    inference(definition,[],]) ).

fof(to_be_clausified_135,plain,
    ( lhs_atom136
    | $false ),
    inference(fold_definition,[status(thm)],[clsarity_nat__Ring__and__Field_Omult__mono1_0,def_lhs_atom136]) ).

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

fof(to_be_clausified_136,plain,
    ( lhs_atom137
    | $false ),
    inference(fold_definition,[status(thm)],[clsarity_nat__Ring__and__Field_Omult__zero_0,def_lhs_atom137]) ).

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

fof(to_be_clausified_137,plain,
    ( lhs_atom138
    | $false ),
    inference(fold_definition,[status(thm)],[clsarity_nat__Ring__and__Field_Omult__mono_0,def_lhs_atom138]) ).

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

fof(to_be_clausified_138,plain,
    ( lhs_atom139
    | $false ),
    inference(fold_definition,[status(thm)],[clsarity_nat__OrderedGroup_Omonoid__mult_0,def_lhs_atom139]) ).

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

fof(to_be_clausified_139,plain,
    ( lhs_atom140
    | $false ),
    inference(fold_definition,[status(thm)],[clsarity_nat__Ring__and__Field_Osemiring_0,def_lhs_atom140]) ).

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

fof(to_be_clausified_140,plain,
    ( lhs_atom141
    | $false ),
    inference(fold_definition,[status(thm)],[clsarity_nat__OrderedGroup_Omonoid__add_0,def_lhs_atom141]) ).

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

fof(to_be_clausified_141,plain,
    ( lhs_atom142
    | $false ),
    inference(fold_definition,[status(thm)],[clsarity_nat__Divides_Osemiring__div_0,def_lhs_atom142]) ).

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

fof(to_be_clausified_142,plain,
    ( lhs_atom143
    | $false ),
    inference(fold_definition,[status(thm)],[clsarity_nat__Orderings_Opreorder_0,def_lhs_atom143]) ).

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

fof(to_be_clausified_143,plain,
    ( lhs_atom144
    | $false ),
    inference(fold_definition,[status(thm)],[clsarity_nat__Orderings_Olinorder_0,def_lhs_atom144]) ).

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

fof(to_be_clausified_144,plain,
    ( lhs_atom145
    | $false ),
    inference(fold_definition,[status(thm)],[clsarity_nat__Orderings_Oorder_0,def_lhs_atom145]) ).

% Start CNF derivation
fof(c_0_0,axiom,
    ! [X13,X2,X3,X4] :
      ( lhs_atom88(X13,X2,X3,X4)
      | ~ $true ),
    file('<stdin>',to_be_clausified_87) ).

fof(c_0_1,axiom,
    ! [X13,X4,X12,X7] :
      ( lhs_atom44(X13,X4,X12,X7)
      | ~ $true ),
    file('<stdin>',to_be_clausified_43) ).

fof(c_0_2,axiom,
    ! [X1,X5] :
      ( lhs_atom59(X1,X5)
      | c_HOL_Otimes__class_Otimes(X5,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ),
    file('<stdin>',to_be_clausified_58) ).

fof(c_0_3,axiom,
    ! [X1,X5] :
      ( lhs_atom58(X1,X5)
      | c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),X5,tc_nat) = c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
    file('<stdin>',to_be_clausified_57) ).

fof(c_0_4,axiom,
    ! [X14,X19,X20] :
      ( lhs_atom115(X14,X19,X20)
      | ~ $true ),
    file('<stdin>',to_be_clausified_114) ).

fof(c_0_5,axiom,
    ! [X2,X3,X4] :
      ( lhs_atom113(X2,X3,X4)
      | ~ $true ),
    file('<stdin>',to_be_clausified_112) ).

fof(c_0_6,axiom,
    ! [X1,X5,X4] :
      ( lhs_atom111(X1,X5,X4)
      | ~ $true ),
    file('<stdin>',to_be_clausified_110) ).

fof(c_0_7,axiom,
    ! [X14,X19,X20] :
      ( lhs_atom102(X14,X19,X20)
      | ~ $true ),
    file('<stdin>',to_be_clausified_101) ).

fof(c_0_8,axiom,
    ! [X15,X16,X17] :
      ( lhs_atom91(X15,X16,X17)
      | ~ $true ),
    file('<stdin>',to_be_clausified_90) ).

fof(c_0_9,axiom,
    ! [X15,X16,X17] :
      ( lhs_atom90(X15,X16,X17)
      | ~ $true ),
    file('<stdin>',to_be_clausified_89) ).

fof(c_0_10,axiom,
    ! [X1,X5,X4] :
      ( lhs_atom87(X1,X5,X4)
      | ~ $true ),
    file('<stdin>',to_be_clausified_86) ).

fof(c_0_11,axiom,
    ! [X1,X5,X4] :
      ( lhs_atom86(X1,X5,X4)
      | ~ $true ),
    file('<stdin>',to_be_clausified_85) ).

fof(c_0_12,axiom,
    ! [X1,X5,X4] :
      ( lhs_atom85(X1,X5,X4)
      | ~ $true ),
    file('<stdin>',to_be_clausified_84) ).

fof(c_0_13,axiom,
    ! [X1,X5,X7] :
      ( lhs_atom81(X1,X5,X7)
      | ~ $true ),
    file('<stdin>',to_be_clausified_80) ).

fof(c_0_14,axiom,
    ! [X1,X5,X4] :
      ( lhs_atom73(X1,X5,X4)
      | ~ $true ),
    file('<stdin>',to_be_clausified_72) ).

fof(c_0_15,axiom,
    ! [X1,X5,X4] :
      ( lhs_atom71(X1,X5,X4)
      | ~ $true ),
    file('<stdin>',to_be_clausified_70) ).

fof(c_0_16,axiom,
    ! [X1,X5,X4] :
      ( lhs_atom70(X1,X5,X4)
      | ~ $true ),
    file('<stdin>',to_be_clausified_69) ).

fof(c_0_17,axiom,
    ! [X2,X3,X4] :
      ( lhs_atom63(X2,X3,X4)
      | ~ $true ),
    file('<stdin>',to_be_clausified_62) ).

fof(c_0_18,axiom,
    ! [X4,X12,X7] :
      ( lhs_atom48(X4,X12,X7)
      | ~ $true ),
    file('<stdin>',to_be_clausified_47) ).

fof(c_0_19,axiom,
    ! [X1,X5,X4] :
      ( lhs_atom47(X1,X5,X4)
      | ~ $true ),
    file('<stdin>',to_be_clausified_46) ).

fof(c_0_20,axiom,
    ! [X1,X5,X4] :
      ( lhs_atom46(X1,X5,X4)
      | ~ $true ),
    file('<stdin>',to_be_clausified_45) ).

fof(c_0_21,axiom,
    ! [X1,X5,X4] :
      ( lhs_atom41(X1,X5,X4)
      | ~ $true ),
    file('<stdin>',to_be_clausified_40) ).

fof(c_0_22,axiom,
    ! [X1,X5,X4] :
      ( lhs_atom40(X1,X5,X4)
      | ~ $true ),
    file('<stdin>',to_be_clausified_39) ).

fof(c_0_23,axiom,
    ! [X4,X12,X7] :
      ( lhs_atom38(X4,X12,X7)
      | ~ $true ),
    file('<stdin>',to_be_clausified_37) ).

fof(c_0_24,axiom,
    ! [X1,X5,X4] :
      ( lhs_atom30(X1,X5,X4)
      | ~ $true ),
    file('<stdin>',to_be_clausified_29) ).

fof(c_0_25,axiom,
    ! [X1,X5,X4] :
      ( lhs_atom21(X1,X5,X4)
      | ~ $true ),
    file('<stdin>',to_be_clausified_20) ).

fof(c_0_26,axiom,
    ! [X8,X9,X6] :
      ( lhs_atom20(X8,X9,X6)
      | ~ $true ),
    file('<stdin>',to_be_clausified_19) ).

fof(c_0_27,axiom,
    ! [X6,X10,X11] :
      ( lhs_atom16(X6,X10,X11)
      | ~ $true ),
    file('<stdin>',to_be_clausified_15) ).

fof(c_0_28,axiom,
    ! [X8,X9,X6] :
      ( lhs_atom15(X8,X9,X6)
      | ~ $true ),
    file('<stdin>',to_be_clausified_14) ).

fof(c_0_29,axiom,
    ! [X2,X3,X4] :
      ( lhs_atom3(X2,X3,X4)
      | ~ $true ),
    file('<stdin>',to_be_clausified_2) ).

fof(c_0_30,axiom,
    ! [X1,X5] :
      ( lhs_atom114(X1,X5)
      | ~ $true ),
    file('<stdin>',to_be_clausified_113) ).

fof(c_0_31,axiom,
    ! [X1,X5] :
      ( lhs_atom110(X1,X5)
      | ~ $true ),
    file('<stdin>',to_be_clausified_109) ).

fof(c_0_32,axiom,
    ! [X1,X5] :
      ( lhs_atom109(X1,X5)
      | ~ $true ),
    file('<stdin>',to_be_clausified_108) ).

fof(c_0_33,axiom,
    ! [X1,X5] :
      ( lhs_atom108(X1,X5)
      | ~ $true ),
    file('<stdin>',to_be_clausified_107) ).

fof(c_0_34,axiom,
    ! [X1,X5] :
      ( lhs_atom107(X1,X5)
      | ~ $true ),
    file('<stdin>',to_be_clausified_106) ).

fof(c_0_35,axiom,
    ! [X14,X15] :
      ( lhs_atom104(X14,X15)
      | ~ $true ),
    file('<stdin>',to_be_clausified_103) ).

fof(c_0_36,axiom,
    ! [X1,X5] :
      ( lhs_atom103(X1,X5)
      | ~ $true ),
    file('<stdin>',to_be_clausified_102) ).

fof(c_0_37,axiom,
    ! [X2,X7] :
      ( lhs_atom99(X2,X7)
      | ~ $true ),
    file('<stdin>',to_be_clausified_98) ).

fof(c_0_38,axiom,
    ! [X1,X5] :
      ( lhs_atom93(X1,X5)
      | ~ $true ),
    file('<stdin>',to_be_clausified_92) ).

fof(c_0_39,axiom,
    ! [X13,X4] :
      ( lhs_atom92(X13,X4)
      | ~ $true ),
    file('<stdin>',to_be_clausified_91) ).

fof(c_0_40,axiom,
    ! [X14,X15] :
      ( lhs_atom89(X14,X15)
      | ~ $true ),
    file('<stdin>',to_be_clausified_88) ).

fof(c_0_41,axiom,
    ! [X3,X4] :
      ( lhs_atom84(X3,X4)
      | ~ $true ),
    file('<stdin>',to_be_clausified_83) ).

fof(c_0_42,axiom,
    ! [X6,X10] :
      ( lhs_atom83(X6,X10)
      | ~ $true ),
    file('<stdin>',to_be_clausified_82) ).

fof(c_0_43,axiom,
    ! [X1,X5] :
      ( lhs_atom78(X1,X5)
      | ~ $true ),
    file('<stdin>',to_be_clausified_77) ).

fof(c_0_44,axiom,
    ! [X1,X5] :
      ( lhs_atom77(X1,X5)
      | ~ $true ),
    file('<stdin>',to_be_clausified_76) ).

fof(c_0_45,axiom,
    ! [X1,X5] :
      ( lhs_atom65(X1,X5)
      | ~ $true ),
    file('<stdin>',to_be_clausified_64) ).

fof(c_0_46,axiom,
    ! [X1,X5] :
      ( lhs_atom64(X1,X5)
      | ~ $true ),
    file('<stdin>',to_be_clausified_63) ).

fof(c_0_47,axiom,
    ! [X12,X7] :
      ( lhs_atom61(X12,X7)
      | ~ $true ),
    file('<stdin>',to_be_clausified_60) ).

fof(c_0_48,axiom,
    ! [X12,X7] :
      ( lhs_atom60(X12,X7)
      | ~ $true ),
    file('<stdin>',to_be_clausified_59) ).

fof(c_0_49,axiom,
    ! [X1,X5] :
      ( lhs_atom56(X1,X5)
      | ~ $true ),
    file('<stdin>',to_be_clausified_55) ).

fof(c_0_50,axiom,
    ! [X6,X5] :
      ( lhs_atom55(X6,X5)
      | ~ $true ),
    file('<stdin>',to_be_clausified_54) ).

fof(c_0_51,axiom,
    ! [X1,X5] :
      ( lhs_atom54(X1,X5)
      | ~ $true ),
    file('<stdin>',to_be_clausified_53) ).

fof(c_0_52,axiom,
    ! [X1,X5] :
      ( lhs_atom53(X1,X5)
      | ~ $true ),
    file('<stdin>',to_be_clausified_52) ).

fof(c_0_53,axiom,
    ! [X2,X3] :
      ( lhs_atom52(X2,X3)
      | ~ $true ),
    file('<stdin>',to_be_clausified_51) ).

fof(c_0_54,axiom,
    ! [X1,X5] :
      ( lhs_atom45(X1,X5)
      | ~ $true ),
    file('<stdin>',to_be_clausified_44) ).

fof(c_0_55,axiom,
    ! [X1,X5] :
      ( lhs_atom37(X1,X5)
      | ~ $true ),
    file('<stdin>',to_be_clausified_36) ).

fof(c_0_56,axiom,
    ! [X1,X5] :
      ( lhs_atom29(X1,X5)
      | ~ $true ),
    file('<stdin>',to_be_clausified_28) ).

fof(c_0_57,axiom,
    ! [X1,X5] :
      ( lhs_atom28(X1,X5)
      | ~ $true ),
    file('<stdin>',to_be_clausified_27) ).

fof(c_0_58,axiom,
    ! [X1,X5] :
      ( lhs_atom19(X1,X5)
      | ~ $true ),
    file('<stdin>',to_be_clausified_18) ).

fof(c_0_59,axiom,
    ! [X1,X5] :
      ( lhs_atom17(X1,X5)
      | ~ $true ),
    file('<stdin>',to_be_clausified_16) ).

fof(c_0_60,axiom,
    ! [X5,X7] :
      ( lhs_atom9(X5,X7)
      | ~ $true ),
    file('<stdin>',to_be_clausified_8) ).

fof(c_0_61,axiom,
    ! [X5,X7] :
      ( lhs_atom8(X5,X7)
      | ~ $true ),
    file('<stdin>',to_be_clausified_7) ).

fof(c_0_62,axiom,
    ! [X6,X5] :
      ( lhs_atom7(X6,X5)
      | ~ $true ),
    file('<stdin>',to_be_clausified_6) ).

fof(c_0_63,axiom,
    ! [X1,X5] :
      ( lhs_atom4(X1,X5)
      | ~ $true ),
    file('<stdin>',to_be_clausified_3) ).

fof(c_0_64,axiom,
    ! [X1] :
      ( lhs_atom112(X1)
      | ~ $true ),
    file('<stdin>',to_be_clausified_111) ).

fof(c_0_65,axiom,
    ! [X18] :
      ( lhs_atom106(X18)
      | ~ $true ),
    file('<stdin>',to_be_clausified_105) ).

fof(c_0_66,axiom,
    ! [X5] :
      ( lhs_atom105(X5)
      | ~ $true ),
    file('<stdin>',to_be_clausified_104) ).

fof(c_0_67,axiom,
    ! [X18] :
      ( lhs_atom101(X18)
      | ~ $true ),
    file('<stdin>',to_be_clausified_100) ).

fof(c_0_68,axiom,
    ! [X5] :
      ( lhs_atom100(X5)
      | ~ $true ),
    file('<stdin>',to_be_clausified_99) ).

fof(c_0_69,axiom,
    ! [X1] :
      ( lhs_atom98(X1)
      | ~ $true ),
    file('<stdin>',to_be_clausified_97) ).

fof(c_0_70,axiom,
    ! [X6] :
      ( lhs_atom97(X6)
      | ~ $true ),
    file('<stdin>',to_be_clausified_96) ).

fof(c_0_71,axiom,
    ! [X1] :
      ( lhs_atom96(X1)
      | ~ $true ),
    file('<stdin>',to_be_clausified_95) ).

fof(c_0_72,axiom,
    ! [X1] :
      ( lhs_atom95(X1)
      | ~ $true ),
    file('<stdin>',to_be_clausified_94) ).

fof(c_0_73,axiom,
    ! [X1] :
      ( lhs_atom94(X1)
      | ~ $true ),
    file('<stdin>',to_be_clausified_93) ).

fof(c_0_74,axiom,
    ! [X6] :
      ( lhs_atom80(X6)
      | ~ $true ),
    file('<stdin>',to_be_clausified_79) ).

fof(c_0_75,axiom,
    ! [X1] :
      ( lhs_atom79(X1)
      | ~ $true ),
    file('<stdin>',to_be_clausified_78) ).

fof(c_0_76,axiom,
    ! [X5] :
      ( lhs_atom76(X5)
      | ~ $true ),
    file('<stdin>',to_be_clausified_75) ).

fof(c_0_77,axiom,
    ! [X1] :
      ( lhs_atom75(X1)
      | ~ $true ),
    file('<stdin>',to_be_clausified_74) ).

fof(c_0_78,axiom,
    ! [X6] :
      ( lhs_atom74(X6)
      | ~ $true ),
    file('<stdin>',to_be_clausified_73) ).

fof(c_0_79,axiom,
    ! [X5] :
      ( lhs_atom72(X5)
      | ~ $true ),
    file('<stdin>',to_be_clausified_71) ).

fof(c_0_80,axiom,
    ! [X5] :
      ( lhs_atom68(X5)
      | ~ $true ),
    file('<stdin>',to_be_clausified_67) ).

fof(c_0_81,axiom,
    ! [X1] :
      ( lhs_atom67(X1)
      | ~ $true ),
    file('<stdin>',to_be_clausified_66) ).

fof(c_0_82,axiom,
    ! [X1] :
      ( lhs_atom66(X1)
      | ~ $true ),
    file('<stdin>',to_be_clausified_65) ).

fof(c_0_83,axiom,
    ! [X1] :
      ( lhs_atom51(X1)
      | ~ $true ),
    file('<stdin>',to_be_clausified_50) ).

fof(c_0_84,axiom,
    ! [X6] :
      ( lhs_atom50(X6)
      | ~ $true ),
    file('<stdin>',to_be_clausified_49) ).

fof(c_0_85,axiom,
    ! [X1] :
      ( lhs_atom49(X1)
      | ~ $true ),
    file('<stdin>',to_be_clausified_48) ).

fof(c_0_86,axiom,
    ! [X6] :
      ( lhs_atom43(X6)
      | ~ $true ),
    file('<stdin>',to_be_clausified_42) ).

fof(c_0_87,axiom,
    ! [X1] :
      ( lhs_atom42(X1)
      | ~ $true ),
    file('<stdin>',to_be_clausified_41) ).

fof(c_0_88,axiom,
    ! [X1] :
      ( lhs_atom39(X1)
      | ~ $true ),
    file('<stdin>',to_be_clausified_38) ).

fof(c_0_89,axiom,
    ! [X5] :
      ( lhs_atom34(X5)
      | ~ $true ),
    file('<stdin>',to_be_clausified_33) ).

fof(c_0_90,axiom,
    ! [X5] :
      ( lhs_atom33(X5)
      | ~ $true ),
    file('<stdin>',to_be_clausified_32) ).

fof(c_0_91,axiom,
    ! [X1] :
      ( lhs_atom32(X1)
      | ~ $true ),
    file('<stdin>',to_be_clausified_31) ).

fof(c_0_92,axiom,
    ! [X1] :
      ( lhs_atom25(X1)
      | ~ $true ),
    file('<stdin>',to_be_clausified_24) ).

fof(c_0_93,axiom,
    ! [X1] :
      ( lhs_atom24(X1)
      | ~ $true ),
    file('<stdin>',to_be_clausified_23) ).

fof(c_0_94,axiom,
    ! [X1] :
      ( lhs_atom23(X1)
      | ~ $true ),
    file('<stdin>',to_be_clausified_22) ).

fof(c_0_95,axiom,
    ! [X5] :
      ( lhs_atom22(X5)
      | ~ $true ),
    file('<stdin>',to_be_clausified_21) ).

fof(c_0_96,axiom,
    ! [X1] :
      ( lhs_atom14(X1)
      | ~ $true ),
    file('<stdin>',to_be_clausified_13) ).

fof(c_0_97,axiom,
    ! [X1] :
      ( lhs_atom13(X1)
      | ~ $true ),
    file('<stdin>',to_be_clausified_12) ).

fof(c_0_98,axiom,
    ! [X1] :
      ( lhs_atom11(X1)
      | ~ $true ),
    file('<stdin>',to_be_clausified_10) ).

fof(c_0_99,axiom,
    ! [X1] :
      ( lhs_atom10(X1)
      | ~ $true ),
    file('<stdin>',to_be_clausified_9) ).

fof(c_0_100,axiom,
    ! [X5] :
      ( lhs_atom6(X5)
      | ~ $true ),
    file('<stdin>',to_be_clausified_5) ).

fof(c_0_101,axiom,
    ! [X5] :
      ( lhs_atom5(X5)
      | ~ $true ),
    file('<stdin>',to_be_clausified_4) ).

fof(c_0_102,axiom,
    ! [X1] :
      ( lhs_atom1(X1)
      | ~ $true ),
    file('<stdin>',to_be_clausified_0) ).

fof(c_0_103,axiom,
    ( lhs_atom145
    | ~ $true ),
    file('<stdin>',to_be_clausified_144) ).

fof(c_0_104,axiom,
    ( lhs_atom144
    | ~ $true ),
    file('<stdin>',to_be_clausified_143) ).

fof(c_0_105,axiom,
    ( lhs_atom143
    | ~ $true ),
    file('<stdin>',to_be_clausified_142) ).

fof(c_0_106,axiom,
    ( lhs_atom142
    | ~ $true ),
    file('<stdin>',to_be_clausified_141) ).

fof(c_0_107,axiom,
    ( lhs_atom141
    | ~ $true ),
    file('<stdin>',to_be_clausified_140) ).

fof(c_0_108,axiom,
    ( lhs_atom140
    | ~ $true ),
    file('<stdin>',to_be_clausified_139) ).

fof(c_0_109,axiom,
    ( lhs_atom139
    | ~ $true ),
    file('<stdin>',to_be_clausified_138) ).

fof(c_0_110,axiom,
    ( lhs_atom138
    | ~ $true ),
    file('<stdin>',to_be_clausified_137) ).

fof(c_0_111,axiom,
    ( lhs_atom137
    | ~ $true ),
    file('<stdin>',to_be_clausified_136) ).

fof(c_0_112,axiom,
    ( lhs_atom136
    | ~ $true ),
    file('<stdin>',to_be_clausified_135) ).

fof(c_0_113,axiom,
    ( lhs_atom135
    | ~ $true ),
    file('<stdin>',to_be_clausified_134) ).

fof(c_0_114,axiom,
    ( lhs_atom134
    | ~ $true ),
    file('<stdin>',to_be_clausified_133) ).

fof(c_0_115,axiom,
    ( lhs_atom133
    | ~ $true ),
    file('<stdin>',to_be_clausified_132) ).

fof(c_0_116,axiom,
    ( lhs_atom132
    | ~ $true ),
    file('<stdin>',to_be_clausified_131) ).

fof(c_0_117,axiom,
    ( lhs_atom131
    | ~ $true ),
    file('<stdin>',to_be_clausified_130) ).

fof(c_0_118,axiom,
    ( lhs_atom130
    | ~ $true ),
    file('<stdin>',to_be_clausified_129) ).

fof(c_0_119,axiom,
    ( lhs_atom129
    | ~ $true ),
    file('<stdin>',to_be_clausified_128) ).

fof(c_0_120,axiom,
    ( lhs_atom128
    | ~ $true ),
    file('<stdin>',to_be_clausified_127) ).

fof(c_0_121,axiom,
    ( lhs_atom127
    | ~ $true ),
    file('<stdin>',to_be_clausified_126) ).

fof(c_0_122,axiom,
    ( lhs_atom126
    | ~ $true ),
    file('<stdin>',to_be_clausified_125) ).

fof(c_0_123,axiom,
    ( lhs_atom125
    | ~ $true ),
    file('<stdin>',to_be_clausified_124) ).

fof(c_0_124,axiom,
    ( lhs_atom124
    | ~ $true ),
    file('<stdin>',to_be_clausified_123) ).

fof(c_0_125,axiom,
    ( lhs_atom123
    | ~ $true ),
    file('<stdin>',to_be_clausified_122) ).

fof(c_0_126,axiom,
    ( lhs_atom122
    | ~ $true ),
    file('<stdin>',to_be_clausified_121) ).

fof(c_0_127,axiom,
    ( lhs_atom121
    | ~ $true ),
    file('<stdin>',to_be_clausified_120) ).

fof(c_0_128,axiom,
    ( lhs_atom120
    | ~ $true ),
    file('<stdin>',to_be_clausified_119) ).

fof(c_0_129,axiom,
    ( lhs_atom119
    | ~ $true ),
    file('<stdin>',to_be_clausified_118) ).

fof(c_0_130,axiom,
    ( lhs_atom118
    | ~ $true ),
    file('<stdin>',to_be_clausified_117) ).

fof(c_0_131,axiom,
    ( lhs_atom117
    | ~ $true ),
    file('<stdin>',to_be_clausified_116) ).

fof(c_0_132,axiom,
    ( lhs_atom116
    | ~ $true ),
    file('<stdin>',to_be_clausified_115) ).

fof(c_0_133,axiom,
    ( lhs_atom82
    | ~ $true ),
    file('<stdin>',to_be_clausified_81) ).

fof(c_0_134,axiom,
    ( lhs_atom69
    | ~ $true ),
    file('<stdin>',to_be_clausified_68) ).

fof(c_0_135,axiom,
    ( lhs_atom62
    | ~ $true ),
    file('<stdin>',to_be_clausified_61) ).

fof(c_0_136,axiom,
    ( lhs_atom57
    | ~ $true ),
    file('<stdin>',to_be_clausified_56) ).

fof(c_0_137,axiom,
    ( lhs_atom36
    | ~ $true ),
    file('<stdin>',to_be_clausified_35) ).

fof(c_0_138,axiom,
    ( lhs_atom35
    | ~ $true ),
    file('<stdin>',to_be_clausified_34) ).

fof(c_0_139,axiom,
    ( lhs_atom31
    | ~ $true ),
    file('<stdin>',to_be_clausified_30) ).

fof(c_0_140,axiom,
    ( lhs_atom27
    | ~ $true ),
    file('<stdin>',to_be_clausified_26) ).

fof(c_0_141,axiom,
    ( lhs_atom26
    | ~ $true ),
    file('<stdin>',to_be_clausified_25) ).

fof(c_0_142,axiom,
    ( lhs_atom18
    | ~ $true ),
    file('<stdin>',to_be_clausified_17) ).

fof(c_0_143,axiom,
    ( lhs_atom12
    | ~ $true ),
    file('<stdin>',to_be_clausified_11) ).

fof(c_0_144,axiom,
    ( lhs_atom2
    | ~ $true ),
    file('<stdin>',to_be_clausified_1) ).

fof(c_0_145,plain,
    ! [X13,X2,X3,X4] : lhs_atom88(X13,X2,X3,X4),
    inference(fof_simplification,[status(thm)],[c_0_0]) ).

fof(c_0_146,plain,
    ! [X13,X4,X12,X7] : lhs_atom44(X13,X4,X12,X7),
    inference(fof_simplification,[status(thm)],[c_0_1]) ).

fof(c_0_147,axiom,
    ! [X1,X5] :
      ( lhs_atom59(X1,X5)
      | c_HOL_Otimes__class_Otimes(X5,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_0_2 ).

fof(c_0_148,axiom,
    ! [X1,X5] :
      ( lhs_atom58(X1,X5)
      | c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),X5,tc_nat) = c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
    c_0_3 ).

fof(c_0_149,plain,
    ! [X14,X19,X20] : lhs_atom115(X14,X19,X20),
    inference(fof_simplification,[status(thm)],[c_0_4]) ).

fof(c_0_150,plain,
    ! [X2,X3,X4] : lhs_atom113(X2,X3,X4),
    inference(fof_simplification,[status(thm)],[c_0_5]) ).

fof(c_0_151,plain,
    ! [X1,X5,X4] : lhs_atom111(X1,X5,X4),
    inference(fof_simplification,[status(thm)],[c_0_6]) ).

fof(c_0_152,plain,
    ! [X14,X19,X20] : lhs_atom102(X14,X19,X20),
    inference(fof_simplification,[status(thm)],[c_0_7]) ).

fof(c_0_153,plain,
    ! [X15,X16,X17] : lhs_atom91(X15,X16,X17),
    inference(fof_simplification,[status(thm)],[c_0_8]) ).

fof(c_0_154,plain,
    ! [X15,X16,X17] : lhs_atom90(X15,X16,X17),
    inference(fof_simplification,[status(thm)],[c_0_9]) ).

fof(c_0_155,plain,
    ! [X1,X5,X4] : lhs_atom87(X1,X5,X4),
    inference(fof_simplification,[status(thm)],[c_0_10]) ).

fof(c_0_156,plain,
    ! [X1,X5,X4] : lhs_atom86(X1,X5,X4),
    inference(fof_simplification,[status(thm)],[c_0_11]) ).

fof(c_0_157,plain,
    ! [X1,X5,X4] : lhs_atom85(X1,X5,X4),
    inference(fof_simplification,[status(thm)],[c_0_12]) ).

fof(c_0_158,plain,
    ! [X1,X5,X7] : lhs_atom81(X1,X5,X7),
    inference(fof_simplification,[status(thm)],[c_0_13]) ).

fof(c_0_159,plain,
    ! [X1,X5,X4] : lhs_atom73(X1,X5,X4),
    inference(fof_simplification,[status(thm)],[c_0_14]) ).

fof(c_0_160,plain,
    ! [X1,X5,X4] : lhs_atom71(X1,X5,X4),
    inference(fof_simplification,[status(thm)],[c_0_15]) ).

fof(c_0_161,plain,
    ! [X1,X5,X4] : lhs_atom70(X1,X5,X4),
    inference(fof_simplification,[status(thm)],[c_0_16]) ).

fof(c_0_162,plain,
    ! [X2,X3,X4] : lhs_atom63(X2,X3,X4),
    inference(fof_simplification,[status(thm)],[c_0_17]) ).

fof(c_0_163,plain,
    ! [X4,X12,X7] : lhs_atom48(X4,X12,X7),
    inference(fof_simplification,[status(thm)],[c_0_18]) ).

fof(c_0_164,plain,
    ! [X1,X5,X4] : lhs_atom47(X1,X5,X4),
    inference(fof_simplification,[status(thm)],[c_0_19]) ).

fof(c_0_165,plain,
    ! [X1,X5,X4] : lhs_atom46(X1,X5,X4),
    inference(fof_simplification,[status(thm)],[c_0_20]) ).

fof(c_0_166,plain,
    ! [X1,X5,X4] : lhs_atom41(X1,X5,X4),
    inference(fof_simplification,[status(thm)],[c_0_21]) ).

fof(c_0_167,plain,
    ! [X1,X5,X4] : lhs_atom40(X1,X5,X4),
    inference(fof_simplification,[status(thm)],[c_0_22]) ).

fof(c_0_168,plain,
    ! [X4,X12,X7] : lhs_atom38(X4,X12,X7),
    inference(fof_simplification,[status(thm)],[c_0_23]) ).

fof(c_0_169,plain,
    ! [X1,X5,X4] : lhs_atom30(X1,X5,X4),
    inference(fof_simplification,[status(thm)],[c_0_24]) ).

fof(c_0_170,plain,
    ! [X1,X5,X4] : lhs_atom21(X1,X5,X4),
    inference(fof_simplification,[status(thm)],[c_0_25]) ).

fof(c_0_171,plain,
    ! [X8,X9,X6] : lhs_atom20(X8,X9,X6),
    inference(fof_simplification,[status(thm)],[c_0_26]) ).

fof(c_0_172,plain,
    ! [X6,X10,X11] : lhs_atom16(X6,X10,X11),
    inference(fof_simplification,[status(thm)],[c_0_27]) ).

fof(c_0_173,plain,
    ! [X8,X9,X6] : lhs_atom15(X8,X9,X6),
    inference(fof_simplification,[status(thm)],[c_0_28]) ).

fof(c_0_174,plain,
    ! [X2,X3,X4] : lhs_atom3(X2,X3,X4),
    inference(fof_simplification,[status(thm)],[c_0_29]) ).

fof(c_0_175,plain,
    ! [X1,X5] : lhs_atom114(X1,X5),
    inference(fof_simplification,[status(thm)],[c_0_30]) ).

fof(c_0_176,plain,
    ! [X1,X5] : lhs_atom110(X1,X5),
    inference(fof_simplification,[status(thm)],[c_0_31]) ).

fof(c_0_177,plain,
    ! [X1,X5] : lhs_atom109(X1,X5),
    inference(fof_simplification,[status(thm)],[c_0_32]) ).

fof(c_0_178,plain,
    ! [X1,X5] : lhs_atom108(X1,X5),
    inference(fof_simplification,[status(thm)],[c_0_33]) ).

fof(c_0_179,plain,
    ! [X1,X5] : lhs_atom107(X1,X5),
    inference(fof_simplification,[status(thm)],[c_0_34]) ).

fof(c_0_180,plain,
    ! [X14,X15] : lhs_atom104(X14,X15),
    inference(fof_simplification,[status(thm)],[c_0_35]) ).

fof(c_0_181,plain,
    ! [X1,X5] : lhs_atom103(X1,X5),
    inference(fof_simplification,[status(thm)],[c_0_36]) ).

fof(c_0_182,plain,
    ! [X2,X7] : lhs_atom99(X2,X7),
    inference(fof_simplification,[status(thm)],[c_0_37]) ).

fof(c_0_183,plain,
    ! [X1,X5] : lhs_atom93(X1,X5),
    inference(fof_simplification,[status(thm)],[c_0_38]) ).

fof(c_0_184,plain,
    ! [X13,X4] : lhs_atom92(X13,X4),
    inference(fof_simplification,[status(thm)],[c_0_39]) ).

fof(c_0_185,plain,
    ! [X14,X15] : lhs_atom89(X14,X15),
    inference(fof_simplification,[status(thm)],[c_0_40]) ).

fof(c_0_186,plain,
    ! [X3,X4] : lhs_atom84(X3,X4),
    inference(fof_simplification,[status(thm)],[c_0_41]) ).

fof(c_0_187,plain,
    ! [X6,X10] : lhs_atom83(X6,X10),
    inference(fof_simplification,[status(thm)],[c_0_42]) ).

fof(c_0_188,plain,
    ! [X1,X5] : lhs_atom78(X1,X5),
    inference(fof_simplification,[status(thm)],[c_0_43]) ).

fof(c_0_189,plain,
    ! [X1,X5] : lhs_atom77(X1,X5),
    inference(fof_simplification,[status(thm)],[c_0_44]) ).

fof(c_0_190,plain,
    ! [X1,X5] : lhs_atom65(X1,X5),
    inference(fof_simplification,[status(thm)],[c_0_45]) ).

fof(c_0_191,plain,
    ! [X1,X5] : lhs_atom64(X1,X5),
    inference(fof_simplification,[status(thm)],[c_0_46]) ).

fof(c_0_192,plain,
    ! [X12,X7] : lhs_atom61(X12,X7),
    inference(fof_simplification,[status(thm)],[c_0_47]) ).

fof(c_0_193,plain,
    ! [X12,X7] : lhs_atom60(X12,X7),
    inference(fof_simplification,[status(thm)],[c_0_48]) ).

fof(c_0_194,plain,
    ! [X1,X5] : lhs_atom56(X1,X5),
    inference(fof_simplification,[status(thm)],[c_0_49]) ).

fof(c_0_195,plain,
    ! [X6,X5] : lhs_atom55(X6,X5),
    inference(fof_simplification,[status(thm)],[c_0_50]) ).

fof(c_0_196,plain,
    ! [X1,X5] : lhs_atom54(X1,X5),
    inference(fof_simplification,[status(thm)],[c_0_51]) ).

fof(c_0_197,plain,
    ! [X1,X5] : lhs_atom53(X1,X5),
    inference(fof_simplification,[status(thm)],[c_0_52]) ).

fof(c_0_198,plain,
    ! [X2,X3] : lhs_atom52(X2,X3),
    inference(fof_simplification,[status(thm)],[c_0_53]) ).

fof(c_0_199,plain,
    ! [X1,X5] : lhs_atom45(X1,X5),
    inference(fof_simplification,[status(thm)],[c_0_54]) ).

fof(c_0_200,plain,
    ! [X1,X5] : lhs_atom37(X1,X5),
    inference(fof_simplification,[status(thm)],[c_0_55]) ).

fof(c_0_201,plain,
    ! [X1,X5] : lhs_atom29(X1,X5),
    inference(fof_simplification,[status(thm)],[c_0_56]) ).

fof(c_0_202,plain,
    ! [X1,X5] : lhs_atom28(X1,X5),
    inference(fof_simplification,[status(thm)],[c_0_57]) ).

fof(c_0_203,plain,
    ! [X1,X5] : lhs_atom19(X1,X5),
    inference(fof_simplification,[status(thm)],[c_0_58]) ).

fof(c_0_204,plain,
    ! [X1,X5] : lhs_atom17(X1,X5),
    inference(fof_simplification,[status(thm)],[c_0_59]) ).

fof(c_0_205,plain,
    ! [X5,X7] : lhs_atom9(X5,X7),
    inference(fof_simplification,[status(thm)],[c_0_60]) ).

fof(c_0_206,plain,
    ! [X5,X7] : lhs_atom8(X5,X7),
    inference(fof_simplification,[status(thm)],[c_0_61]) ).

fof(c_0_207,plain,
    ! [X6,X5] : lhs_atom7(X6,X5),
    inference(fof_simplification,[status(thm)],[c_0_62]) ).

fof(c_0_208,plain,
    ! [X1,X5] : lhs_atom4(X1,X5),
    inference(fof_simplification,[status(thm)],[c_0_63]) ).

fof(c_0_209,plain,
    ! [X1] : lhs_atom112(X1),
    inference(fof_simplification,[status(thm)],[c_0_64]) ).

fof(c_0_210,plain,
    ! [X18] : lhs_atom106(X18),
    inference(fof_simplification,[status(thm)],[c_0_65]) ).

fof(c_0_211,plain,
    ! [X5] : lhs_atom105(X5),
    inference(fof_simplification,[status(thm)],[c_0_66]) ).

fof(c_0_212,plain,
    ! [X18] : lhs_atom101(X18),
    inference(fof_simplification,[status(thm)],[c_0_67]) ).

fof(c_0_213,plain,
    ! [X5] : lhs_atom100(X5),
    inference(fof_simplification,[status(thm)],[c_0_68]) ).

fof(c_0_214,plain,
    ! [X1] : lhs_atom98(X1),
    inference(fof_simplification,[status(thm)],[c_0_69]) ).

fof(c_0_215,plain,
    ! [X6] : lhs_atom97(X6),
    inference(fof_simplification,[status(thm)],[c_0_70]) ).

fof(c_0_216,plain,
    ! [X1] : lhs_atom96(X1),
    inference(fof_simplification,[status(thm)],[c_0_71]) ).

fof(c_0_217,plain,
    ! [X1] : lhs_atom95(X1),
    inference(fof_simplification,[status(thm)],[c_0_72]) ).

fof(c_0_218,plain,
    ! [X1] : lhs_atom94(X1),
    inference(fof_simplification,[status(thm)],[c_0_73]) ).

fof(c_0_219,plain,
    ! [X6] : lhs_atom80(X6),
    inference(fof_simplification,[status(thm)],[c_0_74]) ).

fof(c_0_220,plain,
    ! [X1] : lhs_atom79(X1),
    inference(fof_simplification,[status(thm)],[c_0_75]) ).

fof(c_0_221,plain,
    ! [X5] : lhs_atom76(X5),
    inference(fof_simplification,[status(thm)],[c_0_76]) ).

fof(c_0_222,plain,
    ! [X1] : lhs_atom75(X1),
    inference(fof_simplification,[status(thm)],[c_0_77]) ).

fof(c_0_223,plain,
    ! [X6] : lhs_atom74(X6),
    inference(fof_simplification,[status(thm)],[c_0_78]) ).

fof(c_0_224,plain,
    ! [X5] : lhs_atom72(X5),
    inference(fof_simplification,[status(thm)],[c_0_79]) ).

fof(c_0_225,plain,
    ! [X5] : lhs_atom68(X5),
    inference(fof_simplification,[status(thm)],[c_0_80]) ).

fof(c_0_226,plain,
    ! [X1] : lhs_atom67(X1),
    inference(fof_simplification,[status(thm)],[c_0_81]) ).

fof(c_0_227,plain,
    ! [X1] : lhs_atom66(X1),
    inference(fof_simplification,[status(thm)],[c_0_82]) ).

fof(c_0_228,plain,
    ! [X1] : lhs_atom51(X1),
    inference(fof_simplification,[status(thm)],[c_0_83]) ).

fof(c_0_229,plain,
    ! [X6] : lhs_atom50(X6),
    inference(fof_simplification,[status(thm)],[c_0_84]) ).

fof(c_0_230,plain,
    ! [X1] : lhs_atom49(X1),
    inference(fof_simplification,[status(thm)],[c_0_85]) ).

fof(c_0_231,plain,
    ! [X6] : lhs_atom43(X6),
    inference(fof_simplification,[status(thm)],[c_0_86]) ).

fof(c_0_232,plain,
    ! [X1] : lhs_atom42(X1),
    inference(fof_simplification,[status(thm)],[c_0_87]) ).

fof(c_0_233,plain,
    ! [X1] : lhs_atom39(X1),
    inference(fof_simplification,[status(thm)],[c_0_88]) ).

fof(c_0_234,plain,
    ! [X5] : lhs_atom34(X5),
    inference(fof_simplification,[status(thm)],[c_0_89]) ).

fof(c_0_235,plain,
    ! [X5] : lhs_atom33(X5),
    inference(fof_simplification,[status(thm)],[c_0_90]) ).

fof(c_0_236,plain,
    ! [X1] : lhs_atom32(X1),
    inference(fof_simplification,[status(thm)],[c_0_91]) ).

fof(c_0_237,plain,
    ! [X1] : lhs_atom25(X1),
    inference(fof_simplification,[status(thm)],[c_0_92]) ).

fof(c_0_238,plain,
    ! [X1] : lhs_atom24(X1),
    inference(fof_simplification,[status(thm)],[c_0_93]) ).

fof(c_0_239,plain,
    ! [X1] : lhs_atom23(X1),
    inference(fof_simplification,[status(thm)],[c_0_94]) ).

fof(c_0_240,plain,
    ! [X5] : lhs_atom22(X5),
    inference(fof_simplification,[status(thm)],[c_0_95]) ).

fof(c_0_241,plain,
    ! [X1] : lhs_atom14(X1),
    inference(fof_simplification,[status(thm)],[c_0_96]) ).

fof(c_0_242,plain,
    ! [X1] : lhs_atom13(X1),
    inference(fof_simplification,[status(thm)],[c_0_97]) ).

fof(c_0_243,plain,
    ! [X1] : lhs_atom11(X1),
    inference(fof_simplification,[status(thm)],[c_0_98]) ).

fof(c_0_244,plain,
    ! [X1] : lhs_atom10(X1),
    inference(fof_simplification,[status(thm)],[c_0_99]) ).

fof(c_0_245,plain,
    ! [X5] : lhs_atom6(X5),
    inference(fof_simplification,[status(thm)],[c_0_100]) ).

fof(c_0_246,plain,
    ! [X5] : lhs_atom5(X5),
    inference(fof_simplification,[status(thm)],[c_0_101]) ).

fof(c_0_247,plain,
    ! [X1] : lhs_atom1(X1),
    inference(fof_simplification,[status(thm)],[c_0_102]) ).

fof(c_0_248,plain,
    lhs_atom145,
    inference(fof_simplification,[status(thm)],[c_0_103]) ).

fof(c_0_249,plain,
    lhs_atom144,
    inference(fof_simplification,[status(thm)],[c_0_104]) ).

fof(c_0_250,plain,
    lhs_atom143,
    inference(fof_simplification,[status(thm)],[c_0_105]) ).

fof(c_0_251,plain,
    lhs_atom142,
    inference(fof_simplification,[status(thm)],[c_0_106]) ).

fof(c_0_252,plain,
    lhs_atom141,
    inference(fof_simplification,[status(thm)],[c_0_107]) ).

fof(c_0_253,plain,
    lhs_atom140,
    inference(fof_simplification,[status(thm)],[c_0_108]) ).

fof(c_0_254,plain,
    lhs_atom139,
    inference(fof_simplification,[status(thm)],[c_0_109]) ).

fof(c_0_255,plain,
    lhs_atom138,
    inference(fof_simplification,[status(thm)],[c_0_110]) ).

fof(c_0_256,plain,
    lhs_atom137,
    inference(fof_simplification,[status(thm)],[c_0_111]) ).

fof(c_0_257,plain,
    lhs_atom136,
    inference(fof_simplification,[status(thm)],[c_0_112]) ).

fof(c_0_258,plain,
    lhs_atom135,
    inference(fof_simplification,[status(thm)],[c_0_113]) ).

fof(c_0_259,plain,
    lhs_atom134,
    inference(fof_simplification,[status(thm)],[c_0_114]) ).

fof(c_0_260,plain,
    lhs_atom133,
    inference(fof_simplification,[status(thm)],[c_0_115]) ).

fof(c_0_261,plain,
    lhs_atom132,
    inference(fof_simplification,[status(thm)],[c_0_116]) ).

fof(c_0_262,plain,
    lhs_atom131,
    inference(fof_simplification,[status(thm)],[c_0_117]) ).

fof(c_0_263,plain,
    lhs_atom130,
    inference(fof_simplification,[status(thm)],[c_0_118]) ).

fof(c_0_264,plain,
    lhs_atom129,
    inference(fof_simplification,[status(thm)],[c_0_119]) ).

fof(c_0_265,plain,
    lhs_atom128,
    inference(fof_simplification,[status(thm)],[c_0_120]) ).

fof(c_0_266,plain,
    lhs_atom127,
    inference(fof_simplification,[status(thm)],[c_0_121]) ).

fof(c_0_267,plain,
    lhs_atom126,
    inference(fof_simplification,[status(thm)],[c_0_122]) ).

fof(c_0_268,plain,
    lhs_atom125,
    inference(fof_simplification,[status(thm)],[c_0_123]) ).

fof(c_0_269,plain,
    lhs_atom124,
    inference(fof_simplification,[status(thm)],[c_0_124]) ).

fof(c_0_270,plain,
    lhs_atom123,
    inference(fof_simplification,[status(thm)],[c_0_125]) ).

fof(c_0_271,plain,
    lhs_atom122,
    inference(fof_simplification,[status(thm)],[c_0_126]) ).

fof(c_0_272,plain,
    lhs_atom121,
    inference(fof_simplification,[status(thm)],[c_0_127]) ).

fof(c_0_273,plain,
    lhs_atom120,
    inference(fof_simplification,[status(thm)],[c_0_128]) ).

fof(c_0_274,plain,
    lhs_atom119,
    inference(fof_simplification,[status(thm)],[c_0_129]) ).

fof(c_0_275,plain,
    lhs_atom118,
    inference(fof_simplification,[status(thm)],[c_0_130]) ).

fof(c_0_276,plain,
    lhs_atom117,
    inference(fof_simplification,[status(thm)],[c_0_131]) ).

fof(c_0_277,plain,
    lhs_atom116,
    inference(fof_simplification,[status(thm)],[c_0_132]) ).

fof(c_0_278,plain,
    lhs_atom82,
    inference(fof_simplification,[status(thm)],[c_0_133]) ).

fof(c_0_279,plain,
    lhs_atom69,
    inference(fof_simplification,[status(thm)],[c_0_134]) ).

fof(c_0_280,plain,
    lhs_atom62,
    inference(fof_simplification,[status(thm)],[c_0_135]) ).

fof(c_0_281,plain,
    lhs_atom57,
    inference(fof_simplification,[status(thm)],[c_0_136]) ).

fof(c_0_282,plain,
    lhs_atom36,
    inference(fof_simplification,[status(thm)],[c_0_137]) ).

fof(c_0_283,plain,
    lhs_atom35,
    inference(fof_simplification,[status(thm)],[c_0_138]) ).

fof(c_0_284,plain,
    lhs_atom31,
    inference(fof_simplification,[status(thm)],[c_0_139]) ).

fof(c_0_285,plain,
    lhs_atom27,
    inference(fof_simplification,[status(thm)],[c_0_140]) ).

fof(c_0_286,plain,
    lhs_atom26,
    inference(fof_simplification,[status(thm)],[c_0_141]) ).

fof(c_0_287,plain,
    lhs_atom18,
    inference(fof_simplification,[status(thm)],[c_0_142]) ).

fof(c_0_288,plain,
    lhs_atom12,
    inference(fof_simplification,[status(thm)],[c_0_143]) ).

fof(c_0_289,plain,
    lhs_atom2,
    inference(fof_simplification,[status(thm)],[c_0_144]) ).

fof(c_0_290,plain,
    ! [X14,X15,X16,X17] : lhs_atom88(X14,X15,X16,X17),
    inference(variable_rename,[status(thm)],[c_0_145]) ).

fof(c_0_291,plain,
    ! [X14,X15,X16,X17] : lhs_atom44(X14,X15,X16,X17),
    inference(variable_rename,[status(thm)],[c_0_146]) ).

fof(c_0_292,plain,
    ! [X6,X7] :
      ( lhs_atom59(X6,X7)
      | c_HOL_Otimes__class_Otimes(X7,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = c_HOL_Otimes__class_Otimes(X6,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_147]) ).

fof(c_0_293,plain,
    ! [X6,X7] :
      ( lhs_atom58(X6,X7)
      | c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),X7,tc_nat) = c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),X6,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_148]) ).

fof(c_0_294,plain,
    ! [X21,X22,X23] : lhs_atom115(X21,X22,X23),
    inference(variable_rename,[status(thm)],[c_0_149]) ).

fof(c_0_295,plain,
    ! [X5,X6,X7] : lhs_atom113(X5,X6,X7),
    inference(variable_rename,[status(thm)],[c_0_150]) ).

fof(c_0_296,plain,
    ! [X6,X7,X8] : lhs_atom111(X6,X7,X8),
    inference(variable_rename,[status(thm)],[c_0_151]) ).

fof(c_0_297,plain,
    ! [X21,X22,X23] : lhs_atom102(X21,X22,X23),
    inference(variable_rename,[status(thm)],[c_0_152]) ).

fof(c_0_298,plain,
    ! [X18,X19,X20] : lhs_atom91(X18,X19,X20),
    inference(variable_rename,[status(thm)],[c_0_153]) ).

fof(c_0_299,plain,
    ! [X18,X19,X20] : lhs_atom90(X18,X19,X20),
    inference(variable_rename,[status(thm)],[c_0_154]) ).

fof(c_0_300,plain,
    ! [X6,X7,X8] : lhs_atom87(X6,X7,X8),
    inference(variable_rename,[status(thm)],[c_0_155]) ).

fof(c_0_301,plain,
    ! [X6,X7,X8] : lhs_atom86(X6,X7,X8),
    inference(variable_rename,[status(thm)],[c_0_156]) ).

fof(c_0_302,plain,
    ! [X6,X7,X8] : lhs_atom85(X6,X7,X8),
    inference(variable_rename,[status(thm)],[c_0_157]) ).

fof(c_0_303,plain,
    ! [X8,X9,X10] : lhs_atom81(X8,X9,X10),
    inference(variable_rename,[status(thm)],[c_0_158]) ).

fof(c_0_304,plain,
    ! [X6,X7,X8] : lhs_atom73(X6,X7,X8),
    inference(variable_rename,[status(thm)],[c_0_159]) ).

fof(c_0_305,plain,
    ! [X6,X7,X8] : lhs_atom71(X6,X7,X8),
    inference(variable_rename,[status(thm)],[c_0_160]) ).

fof(c_0_306,plain,
    ! [X6,X7,X8] : lhs_atom70(X6,X7,X8),
    inference(variable_rename,[status(thm)],[c_0_161]) ).

fof(c_0_307,plain,
    ! [X5,X6,X7] : lhs_atom63(X5,X6,X7),
    inference(variable_rename,[status(thm)],[c_0_162]) ).

fof(c_0_308,plain,
    ! [X13,X14,X15] : lhs_atom48(X13,X14,X15),
    inference(variable_rename,[status(thm)],[c_0_163]) ).

fof(c_0_309,plain,
    ! [X6,X7,X8] : lhs_atom47(X6,X7,X8),
    inference(variable_rename,[status(thm)],[c_0_164]) ).

fof(c_0_310,plain,
    ! [X6,X7,X8] : lhs_atom46(X6,X7,X8),
    inference(variable_rename,[status(thm)],[c_0_165]) ).

fof(c_0_311,plain,
    ! [X6,X7,X8] : lhs_atom41(X6,X7,X8),
    inference(variable_rename,[status(thm)],[c_0_166]) ).

fof(c_0_312,plain,
    ! [X6,X7,X8] : lhs_atom40(X6,X7,X8),
    inference(variable_rename,[status(thm)],[c_0_167]) ).

fof(c_0_313,plain,
    ! [X13,X14,X15] : lhs_atom38(X13,X14,X15),
    inference(variable_rename,[status(thm)],[c_0_168]) ).

fof(c_0_314,plain,
    ! [X6,X7,X8] : lhs_atom30(X6,X7,X8),
    inference(variable_rename,[status(thm)],[c_0_169]) ).

fof(c_0_315,plain,
    ! [X6,X7,X8] : lhs_atom21(X6,X7,X8),
    inference(variable_rename,[status(thm)],[c_0_170]) ).

fof(c_0_316,plain,
    ! [X10,X11,X12] : lhs_atom20(X10,X11,X12),
    inference(variable_rename,[status(thm)],[c_0_171]) ).

fof(c_0_317,plain,
    ! [X12,X13,X14] : lhs_atom16(X12,X13,X14),
    inference(variable_rename,[status(thm)],[c_0_172]) ).

fof(c_0_318,plain,
    ! [X10,X11,X12] : lhs_atom15(X10,X11,X12),
    inference(variable_rename,[status(thm)],[c_0_173]) ).

fof(c_0_319,plain,
    ! [X5,X6,X7] : lhs_atom3(X5,X6,X7),
    inference(variable_rename,[status(thm)],[c_0_174]) ).

fof(c_0_320,plain,
    ! [X6,X7] : lhs_atom114(X6,X7),
    inference(variable_rename,[status(thm)],[c_0_175]) ).

fof(c_0_321,plain,
    ! [X6,X7] : lhs_atom110(X6,X7),
    inference(variable_rename,[status(thm)],[c_0_176]) ).

fof(c_0_322,plain,
    ! [X6,X7] : lhs_atom109(X6,X7),
    inference(variable_rename,[status(thm)],[c_0_177]) ).

fof(c_0_323,plain,
    ! [X6,X7] : lhs_atom108(X6,X7),
    inference(variable_rename,[status(thm)],[c_0_178]) ).

fof(c_0_324,plain,
    ! [X6,X7] : lhs_atom107(X6,X7),
    inference(variable_rename,[status(thm)],[c_0_179]) ).

fof(c_0_325,plain,
    ! [X16,X17] : lhs_atom104(X16,X17),
    inference(variable_rename,[status(thm)],[c_0_180]) ).

fof(c_0_326,plain,
    ! [X6,X7] : lhs_atom103(X6,X7),
    inference(variable_rename,[status(thm)],[c_0_181]) ).

fof(c_0_327,plain,
    ! [X8,X9] : lhs_atom99(X8,X9),
    inference(variable_rename,[status(thm)],[c_0_182]) ).

fof(c_0_328,plain,
    ! [X6,X7] : lhs_atom93(X6,X7),
    inference(variable_rename,[status(thm)],[c_0_183]) ).

fof(c_0_329,plain,
    ! [X14,X15] : lhs_atom92(X14,X15),
    inference(variable_rename,[status(thm)],[c_0_184]) ).

fof(c_0_330,plain,
    ! [X16,X17] : lhs_atom89(X16,X17),
    inference(variable_rename,[status(thm)],[c_0_185]) ).

fof(c_0_331,plain,
    ! [X5,X6] : lhs_atom84(X5,X6),
    inference(variable_rename,[status(thm)],[c_0_186]) ).

fof(c_0_332,plain,
    ! [X11,X12] : lhs_atom83(X11,X12),
    inference(variable_rename,[status(thm)],[c_0_187]) ).

fof(c_0_333,plain,
    ! [X6,X7] : lhs_atom78(X6,X7),
    inference(variable_rename,[status(thm)],[c_0_188]) ).

fof(c_0_334,plain,
    ! [X6,X7] : lhs_atom77(X6,X7),
    inference(variable_rename,[status(thm)],[c_0_189]) ).

fof(c_0_335,plain,
    ! [X6,X7] : lhs_atom65(X6,X7),
    inference(variable_rename,[status(thm)],[c_0_190]) ).

fof(c_0_336,plain,
    ! [X6,X7] : lhs_atom64(X6,X7),
    inference(variable_rename,[status(thm)],[c_0_191]) ).

fof(c_0_337,plain,
    ! [X13,X14] : lhs_atom61(X13,X14),
    inference(variable_rename,[status(thm)],[c_0_192]) ).

fof(c_0_338,plain,
    ! [X13,X14] : lhs_atom60(X13,X14),
    inference(variable_rename,[status(thm)],[c_0_193]) ).

fof(c_0_339,plain,
    ! [X6,X7] : lhs_atom56(X6,X7),
    inference(variable_rename,[status(thm)],[c_0_194]) ).

fof(c_0_340,plain,
    ! [X7,X8] : lhs_atom55(X7,X8),
    inference(variable_rename,[status(thm)],[c_0_195]) ).

fof(c_0_341,plain,
    ! [X6,X7] : lhs_atom54(X6,X7),
    inference(variable_rename,[status(thm)],[c_0_196]) ).

fof(c_0_342,plain,
    ! [X6,X7] : lhs_atom53(X6,X7),
    inference(variable_rename,[status(thm)],[c_0_197]) ).

fof(c_0_343,plain,
    ! [X4,X5] : lhs_atom52(X4,X5),
    inference(variable_rename,[status(thm)],[c_0_198]) ).

fof(c_0_344,plain,
    ! [X6,X7] : lhs_atom45(X6,X7),
    inference(variable_rename,[status(thm)],[c_0_199]) ).

fof(c_0_345,plain,
    ! [X6,X7] : lhs_atom37(X6,X7),
    inference(variable_rename,[status(thm)],[c_0_200]) ).

fof(c_0_346,plain,
    ! [X6,X7] : lhs_atom29(X6,X7),
    inference(variable_rename,[status(thm)],[c_0_201]) ).

fof(c_0_347,plain,
    ! [X6,X7] : lhs_atom28(X6,X7),
    inference(variable_rename,[status(thm)],[c_0_202]) ).

fof(c_0_348,plain,
    ! [X6,X7] : lhs_atom19(X6,X7),
    inference(variable_rename,[status(thm)],[c_0_203]) ).

fof(c_0_349,plain,
    ! [X6,X7] : lhs_atom17(X6,X7),
    inference(variable_rename,[status(thm)],[c_0_204]) ).

fof(c_0_350,plain,
    ! [X8,X9] : lhs_atom9(X8,X9),
    inference(variable_rename,[status(thm)],[c_0_205]) ).

fof(c_0_351,plain,
    ! [X8,X9] : lhs_atom8(X8,X9),
    inference(variable_rename,[status(thm)],[c_0_206]) ).

fof(c_0_352,plain,
    ! [X7,X8] : lhs_atom7(X7,X8),
    inference(variable_rename,[status(thm)],[c_0_207]) ).

fof(c_0_353,plain,
    ! [X6,X7] : lhs_atom4(X6,X7),
    inference(variable_rename,[status(thm)],[c_0_208]) ).

fof(c_0_354,plain,
    ! [X2] : lhs_atom112(X2),
    inference(variable_rename,[status(thm)],[c_0_209]) ).

fof(c_0_355,plain,
    ! [X19] : lhs_atom106(X19),
    inference(variable_rename,[status(thm)],[c_0_210]) ).

fof(c_0_356,plain,
    ! [X6] : lhs_atom105(X6),
    inference(variable_rename,[status(thm)],[c_0_211]) ).

fof(c_0_357,plain,
    ! [X19] : lhs_atom101(X19),
    inference(variable_rename,[status(thm)],[c_0_212]) ).

fof(c_0_358,plain,
    ! [X6] : lhs_atom100(X6),
    inference(variable_rename,[status(thm)],[c_0_213]) ).

fof(c_0_359,plain,
    ! [X2] : lhs_atom98(X2),
    inference(variable_rename,[status(thm)],[c_0_214]) ).

fof(c_0_360,plain,
    ! [X7] : lhs_atom97(X7),
    inference(variable_rename,[status(thm)],[c_0_215]) ).

fof(c_0_361,plain,
    ! [X2] : lhs_atom96(X2),
    inference(variable_rename,[status(thm)],[c_0_216]) ).

fof(c_0_362,plain,
    ! [X2] : lhs_atom95(X2),
    inference(variable_rename,[status(thm)],[c_0_217]) ).

fof(c_0_363,plain,
    ! [X2] : lhs_atom94(X2),
    inference(variable_rename,[status(thm)],[c_0_218]) ).

fof(c_0_364,plain,
    ! [X7] : lhs_atom80(X7),
    inference(variable_rename,[status(thm)],[c_0_219]) ).

fof(c_0_365,plain,
    ! [X2] : lhs_atom79(X2),
    inference(variable_rename,[status(thm)],[c_0_220]) ).

fof(c_0_366,plain,
    ! [X6] : lhs_atom76(X6),
    inference(variable_rename,[status(thm)],[c_0_221]) ).

fof(c_0_367,plain,
    ! [X2] : lhs_atom75(X2),
    inference(variable_rename,[status(thm)],[c_0_222]) ).

fof(c_0_368,plain,
    ! [X7] : lhs_atom74(X7),
    inference(variable_rename,[status(thm)],[c_0_223]) ).

fof(c_0_369,plain,
    ! [X6] : lhs_atom72(X6),
    inference(variable_rename,[status(thm)],[c_0_224]) ).

fof(c_0_370,plain,
    ! [X6] : lhs_atom68(X6),
    inference(variable_rename,[status(thm)],[c_0_225]) ).

fof(c_0_371,plain,
    ! [X2] : lhs_atom67(X2),
    inference(variable_rename,[status(thm)],[c_0_226]) ).

fof(c_0_372,plain,
    ! [X2] : lhs_atom66(X2),
    inference(variable_rename,[status(thm)],[c_0_227]) ).

fof(c_0_373,plain,
    ! [X2] : lhs_atom51(X2),
    inference(variable_rename,[status(thm)],[c_0_228]) ).

fof(c_0_374,plain,
    ! [X7] : lhs_atom50(X7),
    inference(variable_rename,[status(thm)],[c_0_229]) ).

fof(c_0_375,plain,
    ! [X2] : lhs_atom49(X2),
    inference(variable_rename,[status(thm)],[c_0_230]) ).

fof(c_0_376,plain,
    ! [X7] : lhs_atom43(X7),
    inference(variable_rename,[status(thm)],[c_0_231]) ).

fof(c_0_377,plain,
    ! [X2] : lhs_atom42(X2),
    inference(variable_rename,[status(thm)],[c_0_232]) ).

fof(c_0_378,plain,
    ! [X2] : lhs_atom39(X2),
    inference(variable_rename,[status(thm)],[c_0_233]) ).

fof(c_0_379,plain,
    ! [X6] : lhs_atom34(X6),
    inference(variable_rename,[status(thm)],[c_0_234]) ).

fof(c_0_380,plain,
    ! [X6] : lhs_atom33(X6),
    inference(variable_rename,[status(thm)],[c_0_235]) ).

fof(c_0_381,plain,
    ! [X2] : lhs_atom32(X2),
    inference(variable_rename,[status(thm)],[c_0_236]) ).

fof(c_0_382,plain,
    ! [X2] : lhs_atom25(X2),
    inference(variable_rename,[status(thm)],[c_0_237]) ).

fof(c_0_383,plain,
    ! [X2] : lhs_atom24(X2),
    inference(variable_rename,[status(thm)],[c_0_238]) ).

fof(c_0_384,plain,
    ! [X2] : lhs_atom23(X2),
    inference(variable_rename,[status(thm)],[c_0_239]) ).

fof(c_0_385,plain,
    ! [X6] : lhs_atom22(X6),
    inference(variable_rename,[status(thm)],[c_0_240]) ).

fof(c_0_386,plain,
    ! [X2] : lhs_atom14(X2),
    inference(variable_rename,[status(thm)],[c_0_241]) ).

fof(c_0_387,plain,
    ! [X2] : lhs_atom13(X2),
    inference(variable_rename,[status(thm)],[c_0_242]) ).

fof(c_0_388,plain,
    ! [X2] : lhs_atom11(X2),
    inference(variable_rename,[status(thm)],[c_0_243]) ).

fof(c_0_389,plain,
    ! [X2] : lhs_atom10(X2),
    inference(variable_rename,[status(thm)],[c_0_244]) ).

fof(c_0_390,plain,
    ! [X6] : lhs_atom6(X6),
    inference(variable_rename,[status(thm)],[c_0_245]) ).

fof(c_0_391,plain,
    ! [X6] : lhs_atom5(X6),
    inference(variable_rename,[status(thm)],[c_0_246]) ).

fof(c_0_392,plain,
    ! [X2] : lhs_atom1(X2),
    inference(variable_rename,[status(thm)],[c_0_247]) ).

fof(c_0_393,plain,
    lhs_atom145,
    c_0_248 ).

fof(c_0_394,plain,
    lhs_atom144,
    c_0_249 ).

fof(c_0_395,plain,
    lhs_atom143,
    c_0_250 ).

fof(c_0_396,plain,
    lhs_atom142,
    c_0_251 ).

fof(c_0_397,plain,
    lhs_atom141,
    c_0_252 ).

fof(c_0_398,plain,
    lhs_atom140,
    c_0_253 ).

fof(c_0_399,plain,
    lhs_atom139,
    c_0_254 ).

fof(c_0_400,plain,
    lhs_atom138,
    c_0_255 ).

fof(c_0_401,plain,
    lhs_atom137,
    c_0_256 ).

fof(c_0_402,plain,
    lhs_atom136,
    c_0_257 ).

fof(c_0_403,plain,
    lhs_atom135,
    c_0_258 ).

fof(c_0_404,plain,
    lhs_atom134,
    c_0_259 ).

fof(c_0_405,plain,
    lhs_atom133,
    c_0_260 ).

fof(c_0_406,plain,
    lhs_atom132,
    c_0_261 ).

fof(c_0_407,plain,
    lhs_atom131,
    c_0_262 ).

fof(c_0_408,plain,
    lhs_atom130,
    c_0_263 ).

fof(c_0_409,plain,
    lhs_atom129,
    c_0_264 ).

fof(c_0_410,plain,
    lhs_atom128,
    c_0_265 ).

fof(c_0_411,plain,
    lhs_atom127,
    c_0_266 ).

fof(c_0_412,plain,
    lhs_atom126,
    c_0_267 ).

fof(c_0_413,plain,
    lhs_atom125,
    c_0_268 ).

fof(c_0_414,plain,
    lhs_atom124,
    c_0_269 ).

fof(c_0_415,plain,
    lhs_atom123,
    c_0_270 ).

fof(c_0_416,plain,
    lhs_atom122,
    c_0_271 ).

fof(c_0_417,plain,
    lhs_atom121,
    c_0_272 ).

fof(c_0_418,plain,
    lhs_atom120,
    c_0_273 ).

fof(c_0_419,plain,
    lhs_atom119,
    c_0_274 ).

fof(c_0_420,plain,
    lhs_atom118,
    c_0_275 ).

fof(c_0_421,plain,
    lhs_atom117,
    c_0_276 ).

fof(c_0_422,plain,
    lhs_atom116,
    c_0_277 ).

fof(c_0_423,plain,
    lhs_atom82,
    c_0_278 ).

fof(c_0_424,plain,
    lhs_atom69,
    c_0_279 ).

fof(c_0_425,plain,
    lhs_atom62,
    c_0_280 ).

fof(c_0_426,plain,
    lhs_atom57,
    c_0_281 ).

fof(c_0_427,plain,
    lhs_atom36,
    c_0_282 ).

fof(c_0_428,plain,
    lhs_atom35,
    c_0_283 ).

fof(c_0_429,plain,
    lhs_atom31,
    c_0_284 ).

fof(c_0_430,plain,
    lhs_atom27,
    c_0_285 ).

fof(c_0_431,plain,
    lhs_atom26,
    c_0_286 ).

fof(c_0_432,plain,
    lhs_atom18,
    c_0_287 ).

fof(c_0_433,plain,
    lhs_atom12,
    c_0_288 ).

fof(c_0_434,plain,
    lhs_atom2,
    c_0_289 ).

cnf(c_0_435,plain,
    lhs_atom88(X1,X2,X3,X4),
    inference(split_conjunct,[status(thm)],[c_0_290]) ).

cnf(c_0_436,plain,
    lhs_atom44(X1,X2,X3,X4),
    inference(split_conjunct,[status(thm)],[c_0_291]) ).

cnf(c_0_437,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_atom59(X2,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_292]) ).

cnf(c_0_438,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_atom58(X2,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_293]) ).

cnf(c_0_439,plain,
    lhs_atom115(X1,X2,X3),
    inference(split_conjunct,[status(thm)],[c_0_294]) ).

cnf(c_0_440,plain,
    lhs_atom113(X1,X2,X3),
    inference(split_conjunct,[status(thm)],[c_0_295]) ).

cnf(c_0_441,plain,
    lhs_atom111(X1,X2,X3),
    inference(split_conjunct,[status(thm)],[c_0_296]) ).

cnf(c_0_442,plain,
    lhs_atom102(X1,X2,X3),
    inference(split_conjunct,[status(thm)],[c_0_297]) ).

cnf(c_0_443,plain,
    lhs_atom91(X1,X2,X3),
    inference(split_conjunct,[status(thm)],[c_0_298]) ).

cnf(c_0_444,plain,
    lhs_atom90(X1,X2,X3),
    inference(split_conjunct,[status(thm)],[c_0_299]) ).

cnf(c_0_445,plain,
    lhs_atom87(X1,X2,X3),
    inference(split_conjunct,[status(thm)],[c_0_300]) ).

cnf(c_0_446,plain,
    lhs_atom86(X1,X2,X3),
    inference(split_conjunct,[status(thm)],[c_0_301]) ).

cnf(c_0_447,plain,
    lhs_atom85(X1,X2,X3),
    inference(split_conjunct,[status(thm)],[c_0_302]) ).

cnf(c_0_448,plain,
    lhs_atom81(X1,X2,X3),
    inference(split_conjunct,[status(thm)],[c_0_303]) ).

cnf(c_0_449,plain,
    lhs_atom73(X1,X2,X3),
    inference(split_conjunct,[status(thm)],[c_0_304]) ).

cnf(c_0_450,plain,
    lhs_atom71(X1,X2,X3),
    inference(split_conjunct,[status(thm)],[c_0_305]) ).

cnf(c_0_451,plain,
    lhs_atom70(X1,X2,X3),
    inference(split_conjunct,[status(thm)],[c_0_306]) ).

cnf(c_0_452,plain,
    lhs_atom63(X1,X2,X3),
    inference(split_conjunct,[status(thm)],[c_0_307]) ).

cnf(c_0_453,plain,
    lhs_atom48(X1,X2,X3),
    inference(split_conjunct,[status(thm)],[c_0_308]) ).

cnf(c_0_454,plain,
    lhs_atom47(X1,X2,X3),
    inference(split_conjunct,[status(thm)],[c_0_309]) ).

cnf(c_0_455,plain,
    lhs_atom46(X1,X2,X3),
    inference(split_conjunct,[status(thm)],[c_0_310]) ).

cnf(c_0_456,plain,
    lhs_atom41(X1,X2,X3),
    inference(split_conjunct,[status(thm)],[c_0_311]) ).

cnf(c_0_457,plain,
    lhs_atom40(X1,X2,X3),
    inference(split_conjunct,[status(thm)],[c_0_312]) ).

cnf(c_0_458,plain,
    lhs_atom38(X1,X2,X3),
    inference(split_conjunct,[status(thm)],[c_0_313]) ).

cnf(c_0_459,plain,
    lhs_atom30(X1,X2,X3),
    inference(split_conjunct,[status(thm)],[c_0_314]) ).

cnf(c_0_460,plain,
    lhs_atom21(X1,X2,X3),
    inference(split_conjunct,[status(thm)],[c_0_315]) ).

cnf(c_0_461,plain,
    lhs_atom20(X1,X2,X3),
    inference(split_conjunct,[status(thm)],[c_0_316]) ).

cnf(c_0_462,plain,
    lhs_atom16(X1,X2,X3),
    inference(split_conjunct,[status(thm)],[c_0_317]) ).

cnf(c_0_463,plain,
    lhs_atom15(X1,X2,X3),
    inference(split_conjunct,[status(thm)],[c_0_318]) ).

cnf(c_0_464,plain,
    lhs_atom3(X1,X2,X3),
    inference(split_conjunct,[status(thm)],[c_0_319]) ).

cnf(c_0_465,plain,
    lhs_atom114(X1,X2),
    inference(split_conjunct,[status(thm)],[c_0_320]) ).

cnf(c_0_466,plain,
    lhs_atom110(X1,X2),
    inference(split_conjunct,[status(thm)],[c_0_321]) ).

cnf(c_0_467,plain,
    lhs_atom109(X1,X2),
    inference(split_conjunct,[status(thm)],[c_0_322]) ).

cnf(c_0_468,plain,
    lhs_atom108(X1,X2),
    inference(split_conjunct,[status(thm)],[c_0_323]) ).

cnf(c_0_469,plain,
    lhs_atom107(X1,X2),
    inference(split_conjunct,[status(thm)],[c_0_324]) ).

cnf(c_0_470,plain,
    lhs_atom104(X1,X2),
    inference(split_conjunct,[status(thm)],[c_0_325]) ).

cnf(c_0_471,plain,
    lhs_atom103(X1,X2),
    inference(split_conjunct,[status(thm)],[c_0_326]) ).

cnf(c_0_472,plain,
    lhs_atom99(X1,X2),
    inference(split_conjunct,[status(thm)],[c_0_327]) ).

cnf(c_0_473,plain,
    lhs_atom93(X1,X2),
    inference(split_conjunct,[status(thm)],[c_0_328]) ).

cnf(c_0_474,plain,
    lhs_atom92(X1,X2),
    inference(split_conjunct,[status(thm)],[c_0_329]) ).

cnf(c_0_475,plain,
    lhs_atom89(X1,X2),
    inference(split_conjunct,[status(thm)],[c_0_330]) ).

cnf(c_0_476,plain,
    lhs_atom84(X1,X2),
    inference(split_conjunct,[status(thm)],[c_0_331]) ).

cnf(c_0_477,plain,
    lhs_atom83(X1,X2),
    inference(split_conjunct,[status(thm)],[c_0_332]) ).

cnf(c_0_478,plain,
    lhs_atom78(X1,X2),
    inference(split_conjunct,[status(thm)],[c_0_333]) ).

cnf(c_0_479,plain,
    lhs_atom77(X1,X2),
    inference(split_conjunct,[status(thm)],[c_0_334]) ).

cnf(c_0_480,plain,
    lhs_atom65(X1,X2),
    inference(split_conjunct,[status(thm)],[c_0_335]) ).

cnf(c_0_481,plain,
    lhs_atom64(X1,X2),
    inference(split_conjunct,[status(thm)],[c_0_336]) ).

cnf(c_0_482,plain,
    lhs_atom61(X1,X2),
    inference(split_conjunct,[status(thm)],[c_0_337]) ).

cnf(c_0_483,plain,
    lhs_atom60(X1,X2),
    inference(split_conjunct,[status(thm)],[c_0_338]) ).

cnf(c_0_484,plain,
    lhs_atom56(X1,X2),
    inference(split_conjunct,[status(thm)],[c_0_339]) ).

cnf(c_0_485,plain,
    lhs_atom55(X1,X2),
    inference(split_conjunct,[status(thm)],[c_0_340]) ).

cnf(c_0_486,plain,
    lhs_atom54(X1,X2),
    inference(split_conjunct,[status(thm)],[c_0_341]) ).

cnf(c_0_487,plain,
    lhs_atom53(X1,X2),
    inference(split_conjunct,[status(thm)],[c_0_342]) ).

cnf(c_0_488,plain,
    lhs_atom52(X1,X2),
    inference(split_conjunct,[status(thm)],[c_0_343]) ).

cnf(c_0_489,plain,
    lhs_atom45(X1,X2),
    inference(split_conjunct,[status(thm)],[c_0_344]) ).

cnf(c_0_490,plain,
    lhs_atom37(X1,X2),
    inference(split_conjunct,[status(thm)],[c_0_345]) ).

cnf(c_0_491,plain,
    lhs_atom29(X1,X2),
    inference(split_conjunct,[status(thm)],[c_0_346]) ).

cnf(c_0_492,plain,
    lhs_atom28(X1,X2),
    inference(split_conjunct,[status(thm)],[c_0_347]) ).

cnf(c_0_493,plain,
    lhs_atom19(X1,X2),
    inference(split_conjunct,[status(thm)],[c_0_348]) ).

cnf(c_0_494,plain,
    lhs_atom17(X1,X2),
    inference(split_conjunct,[status(thm)],[c_0_349]) ).

cnf(c_0_495,plain,
    lhs_atom9(X1,X2),
    inference(split_conjunct,[status(thm)],[c_0_350]) ).

cnf(c_0_496,plain,
    lhs_atom8(X1,X2),
    inference(split_conjunct,[status(thm)],[c_0_351]) ).

cnf(c_0_497,plain,
    lhs_atom7(X1,X2),
    inference(split_conjunct,[status(thm)],[c_0_352]) ).

cnf(c_0_498,plain,
    lhs_atom4(X1,X2),
    inference(split_conjunct,[status(thm)],[c_0_353]) ).

cnf(c_0_499,plain,
    lhs_atom112(X1),
    inference(split_conjunct,[status(thm)],[c_0_354]) ).

cnf(c_0_500,plain,
    lhs_atom106(X1),
    inference(split_conjunct,[status(thm)],[c_0_355]) ).

cnf(c_0_501,plain,
    lhs_atom105(X1),
    inference(split_conjunct,[status(thm)],[c_0_356]) ).

cnf(c_0_502,plain,
    lhs_atom101(X1),
    inference(split_conjunct,[status(thm)],[c_0_357]) ).

cnf(c_0_503,plain,
    lhs_atom100(X1),
    inference(split_conjunct,[status(thm)],[c_0_358]) ).

cnf(c_0_504,plain,
    lhs_atom98(X1),
    inference(split_conjunct,[status(thm)],[c_0_359]) ).

cnf(c_0_505,plain,
    lhs_atom97(X1),
    inference(split_conjunct,[status(thm)],[c_0_360]) ).

cnf(c_0_506,plain,
    lhs_atom96(X1),
    inference(split_conjunct,[status(thm)],[c_0_361]) ).

cnf(c_0_507,plain,
    lhs_atom95(X1),
    inference(split_conjunct,[status(thm)],[c_0_362]) ).

cnf(c_0_508,plain,
    lhs_atom94(X1),
    inference(split_conjunct,[status(thm)],[c_0_363]) ).

cnf(c_0_509,plain,
    lhs_atom80(X1),
    inference(split_conjunct,[status(thm)],[c_0_364]) ).

cnf(c_0_510,plain,
    lhs_atom79(X1),
    inference(split_conjunct,[status(thm)],[c_0_365]) ).

cnf(c_0_511,plain,
    lhs_atom76(X1),
    inference(split_conjunct,[status(thm)],[c_0_366]) ).

cnf(c_0_512,plain,
    lhs_atom75(X1),
    inference(split_conjunct,[status(thm)],[c_0_367]) ).

cnf(c_0_513,plain,
    lhs_atom74(X1),
    inference(split_conjunct,[status(thm)],[c_0_368]) ).

cnf(c_0_514,plain,
    lhs_atom72(X1),
    inference(split_conjunct,[status(thm)],[c_0_369]) ).

cnf(c_0_515,plain,
    lhs_atom68(X1),
    inference(split_conjunct,[status(thm)],[c_0_370]) ).

cnf(c_0_516,plain,
    lhs_atom67(X1),
    inference(split_conjunct,[status(thm)],[c_0_371]) ).

cnf(c_0_517,plain,
    lhs_atom66(X1),
    inference(split_conjunct,[status(thm)],[c_0_372]) ).

cnf(c_0_518,plain,
    lhs_atom51(X1),
    inference(split_conjunct,[status(thm)],[c_0_373]) ).

cnf(c_0_519,plain,
    lhs_atom50(X1),
    inference(split_conjunct,[status(thm)],[c_0_374]) ).

cnf(c_0_520,plain,
    lhs_atom49(X1),
    inference(split_conjunct,[status(thm)],[c_0_375]) ).

cnf(c_0_521,plain,
    lhs_atom43(X1),
    inference(split_conjunct,[status(thm)],[c_0_376]) ).

cnf(c_0_522,plain,
    lhs_atom42(X1),
    inference(split_conjunct,[status(thm)],[c_0_377]) ).

cnf(c_0_523,plain,
    lhs_atom39(X1),
    inference(split_conjunct,[status(thm)],[c_0_378]) ).

cnf(c_0_524,plain,
    lhs_atom34(X1),
    inference(split_conjunct,[status(thm)],[c_0_379]) ).

cnf(c_0_525,plain,
    lhs_atom33(X1),
    inference(split_conjunct,[status(thm)],[c_0_380]) ).

cnf(c_0_526,plain,
    lhs_atom32(X1),
    inference(split_conjunct,[status(thm)],[c_0_381]) ).

cnf(c_0_527,plain,
    lhs_atom25(X1),
    inference(split_conjunct,[status(thm)],[c_0_382]) ).

cnf(c_0_528,plain,
    lhs_atom24(X1),
    inference(split_conjunct,[status(thm)],[c_0_383]) ).

cnf(c_0_529,plain,
    lhs_atom23(X1),
    inference(split_conjunct,[status(thm)],[c_0_384]) ).

cnf(c_0_530,plain,
    lhs_atom22(X1),
    inference(split_conjunct,[status(thm)],[c_0_385]) ).

cnf(c_0_531,plain,
    lhs_atom14(X1),
    inference(split_conjunct,[status(thm)],[c_0_386]) ).

cnf(c_0_532,plain,
    lhs_atom13(X1),
    inference(split_conjunct,[status(thm)],[c_0_387]) ).

cnf(c_0_533,plain,
    lhs_atom11(X1),
    inference(split_conjunct,[status(thm)],[c_0_388]) ).

cnf(c_0_534,plain,
    lhs_atom10(X1),
    inference(split_conjunct,[status(thm)],[c_0_389]) ).

cnf(c_0_535,plain,
    lhs_atom6(X1),
    inference(split_conjunct,[status(thm)],[c_0_390]) ).

cnf(c_0_536,plain,
    lhs_atom5(X1),
    inference(split_conjunct,[status(thm)],[c_0_391]) ).

cnf(c_0_537,plain,
    lhs_atom1(X1),
    inference(split_conjunct,[status(thm)],[c_0_392]) ).

cnf(c_0_538,plain,
    lhs_atom145,
    inference(split_conjunct,[status(thm)],[c_0_393]) ).

cnf(c_0_539,plain,
    lhs_atom144,
    inference(split_conjunct,[status(thm)],[c_0_394]) ).

cnf(c_0_540,plain,
    lhs_atom143,
    inference(split_conjunct,[status(thm)],[c_0_395]) ).

cnf(c_0_541,plain,
    lhs_atom142,
    inference(split_conjunct,[status(thm)],[c_0_396]) ).

cnf(c_0_542,plain,
    lhs_atom141,
    inference(split_conjunct,[status(thm)],[c_0_397]) ).

cnf(c_0_543,plain,
    lhs_atom140,
    inference(split_conjunct,[status(thm)],[c_0_398]) ).

cnf(c_0_544,plain,
    lhs_atom139,
    inference(split_conjunct,[status(thm)],[c_0_399]) ).

cnf(c_0_545,plain,
    lhs_atom138,
    inference(split_conjunct,[status(thm)],[c_0_400]) ).

cnf(c_0_546,plain,
    lhs_atom137,
    inference(split_conjunct,[status(thm)],[c_0_401]) ).

cnf(c_0_547,plain,
    lhs_atom136,
    inference(split_conjunct,[status(thm)],[c_0_402]) ).

cnf(c_0_548,plain,
    lhs_atom135,
    inference(split_conjunct,[status(thm)],[c_0_403]) ).

cnf(c_0_549,plain,
    lhs_atom134,
    inference(split_conjunct,[status(thm)],[c_0_404]) ).

cnf(c_0_550,plain,
    lhs_atom133,
    inference(split_conjunct,[status(thm)],[c_0_405]) ).

cnf(c_0_551,plain,
    lhs_atom132,
    inference(split_conjunct,[status(thm)],[c_0_406]) ).

cnf(c_0_552,plain,
    lhs_atom131,
    inference(split_conjunct,[status(thm)],[c_0_407]) ).

cnf(c_0_553,plain,
    lhs_atom130,
    inference(split_conjunct,[status(thm)],[c_0_408]) ).

cnf(c_0_554,plain,
    lhs_atom129,
    inference(split_conjunct,[status(thm)],[c_0_409]) ).

cnf(c_0_555,plain,
    lhs_atom128,
    inference(split_conjunct,[status(thm)],[c_0_410]) ).

cnf(c_0_556,plain,
    lhs_atom127,
    inference(split_conjunct,[status(thm)],[c_0_411]) ).

cnf(c_0_557,plain,
    lhs_atom126,
    inference(split_conjunct,[status(thm)],[c_0_412]) ).

cnf(c_0_558,plain,
    lhs_atom125,
    inference(split_conjunct,[status(thm)],[c_0_413]) ).

cnf(c_0_559,plain,
    lhs_atom124,
    inference(split_conjunct,[status(thm)],[c_0_414]) ).

cnf(c_0_560,plain,
    lhs_atom123,
    inference(split_conjunct,[status(thm)],[c_0_415]) ).

cnf(c_0_561,plain,
    lhs_atom122,
    inference(split_conjunct,[status(thm)],[c_0_416]) ).

cnf(c_0_562,plain,
    lhs_atom121,
    inference(split_conjunct,[status(thm)],[c_0_417]) ).

cnf(c_0_563,plain,
    lhs_atom120,
    inference(split_conjunct,[status(thm)],[c_0_418]) ).

cnf(c_0_564,plain,
    lhs_atom119,
    inference(split_conjunct,[status(thm)],[c_0_419]) ).

cnf(c_0_565,plain,
    lhs_atom118,
    inference(split_conjunct,[status(thm)],[c_0_420]) ).

cnf(c_0_566,plain,
    lhs_atom117,
    inference(split_conjunct,[status(thm)],[c_0_421]) ).

cnf(c_0_567,plain,
    lhs_atom116,
    inference(split_conjunct,[status(thm)],[c_0_422]) ).

cnf(c_0_568,plain,
    lhs_atom82,
    inference(split_conjunct,[status(thm)],[c_0_423]) ).

cnf(c_0_569,plain,
    lhs_atom69,
    inference(split_conjunct,[status(thm)],[c_0_424]) ).

cnf(c_0_570,plain,
    lhs_atom62,
    inference(split_conjunct,[status(thm)],[c_0_425]) ).

cnf(c_0_571,plain,
    lhs_atom57,
    inference(split_conjunct,[status(thm)],[c_0_426]) ).

cnf(c_0_572,plain,
    lhs_atom36,
    inference(split_conjunct,[status(thm)],[c_0_427]) ).

cnf(c_0_573,plain,
    lhs_atom35,
    inference(split_conjunct,[status(thm)],[c_0_428]) ).

cnf(c_0_574,plain,
    lhs_atom31,
    inference(split_conjunct,[status(thm)],[c_0_429]) ).

cnf(c_0_575,plain,
    lhs_atom27,
    inference(split_conjunct,[status(thm)],[c_0_430]) ).

cnf(c_0_576,plain,
    lhs_atom26,
    inference(split_conjunct,[status(thm)],[c_0_431]) ).

cnf(c_0_577,plain,
    lhs_atom18,
    inference(split_conjunct,[status(thm)],[c_0_432]) ).

cnf(c_0_578,plain,
    lhs_atom12,
    inference(split_conjunct,[status(thm)],[c_0_433]) ).

cnf(c_0_579,plain,
    lhs_atom2,
    inference(split_conjunct,[status(thm)],[c_0_434]) ).

cnf(c_0_580,plain,
    lhs_atom88(X1,X2,X3,X4),
    c_0_435,
    [final] ).

cnf(c_0_581,plain,
    lhs_atom44(X1,X2,X3,X4),
    c_0_436,
    [final] ).

cnf(c_0_582,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_atom59(X2,X1) ),
    c_0_437,
    [final] ).

cnf(c_0_583,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_atom58(X2,X1) ),
    c_0_438,
    [final] ).

cnf(c_0_584,plain,
    lhs_atom115(X1,X2,X3),
    c_0_439,
    [final] ).

cnf(c_0_585,plain,
    lhs_atom113(X1,X2,X3),
    c_0_440,
    [final] ).

cnf(c_0_586,plain,
    lhs_atom111(X1,X2,X3),
    c_0_441,
    [final] ).

cnf(c_0_587,plain,
    lhs_atom102(X1,X2,X3),
    c_0_442,
    [final] ).

cnf(c_0_588,plain,
    lhs_atom91(X1,X2,X3),
    c_0_443,
    [final] ).

cnf(c_0_589,plain,
    lhs_atom90(X1,X2,X3),
    c_0_444,
    [final] ).

cnf(c_0_590,plain,
    lhs_atom87(X1,X2,X3),
    c_0_445,
    [final] ).

cnf(c_0_591,plain,
    lhs_atom86(X1,X2,X3),
    c_0_446,
    [final] ).

cnf(c_0_592,plain,
    lhs_atom85(X1,X2,X3),
    c_0_447,
    [final] ).

cnf(c_0_593,plain,
    lhs_atom81(X1,X2,X3),
    c_0_448,
    [final] ).

cnf(c_0_594,plain,
    lhs_atom73(X1,X2,X3),
    c_0_449,
    [final] ).

cnf(c_0_595,plain,
    lhs_atom71(X1,X2,X3),
    c_0_450,
    [final] ).

cnf(c_0_596,plain,
    lhs_atom70(X1,X2,X3),
    c_0_451,
    [final] ).

cnf(c_0_597,plain,
    lhs_atom63(X1,X2,X3),
    c_0_452,
    [final] ).

cnf(c_0_598,plain,
    lhs_atom48(X1,X2,X3),
    c_0_453,
    [final] ).

cnf(c_0_599,plain,
    lhs_atom47(X1,X2,X3),
    c_0_454,
    [final] ).

cnf(c_0_600,plain,
    lhs_atom46(X1,X2,X3),
    c_0_455,
    [final] ).

cnf(c_0_601,plain,
    lhs_atom41(X1,X2,X3),
    c_0_456,
    [final] ).

cnf(c_0_602,plain,
    lhs_atom40(X1,X2,X3),
    c_0_457,
    [final] ).

cnf(c_0_603,plain,
    lhs_atom38(X1,X2,X3),
    c_0_458,
    [final] ).

cnf(c_0_604,plain,
    lhs_atom30(X1,X2,X3),
    c_0_459,
    [final] ).

cnf(c_0_605,plain,
    lhs_atom21(X1,X2,X3),
    c_0_460,
    [final] ).

cnf(c_0_606,plain,
    lhs_atom20(X1,X2,X3),
    c_0_461,
    [final] ).

cnf(c_0_607,plain,
    lhs_atom16(X1,X2,X3),
    c_0_462,
    [final] ).

cnf(c_0_608,plain,
    lhs_atom15(X1,X2,X3),
    c_0_463,
    [final] ).

cnf(c_0_609,plain,
    lhs_atom3(X1,X2,X3),
    c_0_464,
    [final] ).

cnf(c_0_610,plain,
    lhs_atom114(X1,X2),
    c_0_465,
    [final] ).

cnf(c_0_611,plain,
    lhs_atom110(X1,X2),
    c_0_466,
    [final] ).

cnf(c_0_612,plain,
    lhs_atom109(X1,X2),
    c_0_467,
    [final] ).

cnf(c_0_613,plain,
    lhs_atom108(X1,X2),
    c_0_468,
    [final] ).

cnf(c_0_614,plain,
    lhs_atom107(X1,X2),
    c_0_469,
    [final] ).

cnf(c_0_615,plain,
    lhs_atom104(X1,X2),
    c_0_470,
    [final] ).

cnf(c_0_616,plain,
    lhs_atom103(X1,X2),
    c_0_471,
    [final] ).

cnf(c_0_617,plain,
    lhs_atom99(X1,X2),
    c_0_472,
    [final] ).

cnf(c_0_618,plain,
    lhs_atom93(X1,X2),
    c_0_473,
    [final] ).

cnf(c_0_619,plain,
    lhs_atom92(X1,X2),
    c_0_474,
    [final] ).

cnf(c_0_620,plain,
    lhs_atom89(X1,X2),
    c_0_475,
    [final] ).

cnf(c_0_621,plain,
    lhs_atom84(X1,X2),
    c_0_476,
    [final] ).

cnf(c_0_622,plain,
    lhs_atom83(X1,X2),
    c_0_477,
    [final] ).

cnf(c_0_623,plain,
    lhs_atom78(X1,X2),
    c_0_478,
    [final] ).

cnf(c_0_624,plain,
    lhs_atom77(X1,X2),
    c_0_479,
    [final] ).

cnf(c_0_625,plain,
    lhs_atom65(X1,X2),
    c_0_480,
    [final] ).

cnf(c_0_626,plain,
    lhs_atom64(X1,X2),
    c_0_481,
    [final] ).

cnf(c_0_627,plain,
    lhs_atom61(X1,X2),
    c_0_482,
    [final] ).

cnf(c_0_628,plain,
    lhs_atom60(X1,X2),
    c_0_483,
    [final] ).

cnf(c_0_629,plain,
    lhs_atom56(X1,X2),
    c_0_484,
    [final] ).

cnf(c_0_630,plain,
    lhs_atom55(X1,X2),
    c_0_485,
    [final] ).

cnf(c_0_631,plain,
    lhs_atom54(X1,X2),
    c_0_486,
    [final] ).

cnf(c_0_632,plain,
    lhs_atom53(X1,X2),
    c_0_487,
    [final] ).

cnf(c_0_633,plain,
    lhs_atom52(X1,X2),
    c_0_488,
    [final] ).

cnf(c_0_634,plain,
    lhs_atom45(X1,X2),
    c_0_489,
    [final] ).

cnf(c_0_635,plain,
    lhs_atom37(X1,X2),
    c_0_490,
    [final] ).

cnf(c_0_636,plain,
    lhs_atom29(X1,X2),
    c_0_491,
    [final] ).

cnf(c_0_637,plain,
    lhs_atom28(X1,X2),
    c_0_492,
    [final] ).

cnf(c_0_638,plain,
    lhs_atom19(X1,X2),
    c_0_493,
    [final] ).

cnf(c_0_639,plain,
    lhs_atom17(X1,X2),
    c_0_494,
    [final] ).

cnf(c_0_640,plain,
    lhs_atom9(X1,X2),
    c_0_495,
    [final] ).

cnf(c_0_641,plain,
    lhs_atom8(X1,X2),
    c_0_496,
    [final] ).

cnf(c_0_642,plain,
    lhs_atom7(X1,X2),
    c_0_497,
    [final] ).

cnf(c_0_643,plain,
    lhs_atom4(X1,X2),
    c_0_498,
    [final] ).

cnf(c_0_644,plain,
    lhs_atom112(X1),
    c_0_499,
    [final] ).

cnf(c_0_645,plain,
    lhs_atom106(X1),
    c_0_500,
    [final] ).

cnf(c_0_646,plain,
    lhs_atom105(X1),
    c_0_501,
    [final] ).

cnf(c_0_647,plain,
    lhs_atom101(X1),
    c_0_502,
    [final] ).

cnf(c_0_648,plain,
    lhs_atom100(X1),
    c_0_503,
    [final] ).

cnf(c_0_649,plain,
    lhs_atom98(X1),
    c_0_504,
    [final] ).

cnf(c_0_650,plain,
    lhs_atom97(X1),
    c_0_505,
    [final] ).

cnf(c_0_651,plain,
    lhs_atom96(X1),
    c_0_506,
    [final] ).

cnf(c_0_652,plain,
    lhs_atom95(X1),
    c_0_507,
    [final] ).

cnf(c_0_653,plain,
    lhs_atom94(X1),
    c_0_508,
    [final] ).

cnf(c_0_654,plain,
    lhs_atom80(X1),
    c_0_509,
    [final] ).

cnf(c_0_655,plain,
    lhs_atom79(X1),
    c_0_510,
    [final] ).

cnf(c_0_656,plain,
    lhs_atom76(X1),
    c_0_511,
    [final] ).

cnf(c_0_657,plain,
    lhs_atom75(X1),
    c_0_512,
    [final] ).

cnf(c_0_658,plain,
    lhs_atom74(X1),
    c_0_513,
    [final] ).

cnf(c_0_659,plain,
    lhs_atom72(X1),
    c_0_514,
    [final] ).

cnf(c_0_660,plain,
    lhs_atom68(X1),
    c_0_515,
    [final] ).

cnf(c_0_661,plain,
    lhs_atom67(X1),
    c_0_516,
    [final] ).

cnf(c_0_662,plain,
    lhs_atom66(X1),
    c_0_517,
    [final] ).

cnf(c_0_663,plain,
    lhs_atom51(X1),
    c_0_518,
    [final] ).

cnf(c_0_664,plain,
    lhs_atom50(X1),
    c_0_519,
    [final] ).

cnf(c_0_665,plain,
    lhs_atom49(X1),
    c_0_520,
    [final] ).

cnf(c_0_666,plain,
    lhs_atom43(X1),
    c_0_521,
    [final] ).

cnf(c_0_667,plain,
    lhs_atom42(X1),
    c_0_522,
    [final] ).

cnf(c_0_668,plain,
    lhs_atom39(X1),
    c_0_523,
    [final] ).

cnf(c_0_669,plain,
    lhs_atom34(X1),
    c_0_524,
    [final] ).

cnf(c_0_670,plain,
    lhs_atom33(X1),
    c_0_525,
    [final] ).

cnf(c_0_671,plain,
    lhs_atom32(X1),
    c_0_526,
    [final] ).

cnf(c_0_672,plain,
    lhs_atom25(X1),
    c_0_527,
    [final] ).

cnf(c_0_673,plain,
    lhs_atom24(X1),
    c_0_528,
    [final] ).

cnf(c_0_674,plain,
    lhs_atom23(X1),
    c_0_529,
    [final] ).

cnf(c_0_675,plain,
    lhs_atom22(X1),
    c_0_530,
    [final] ).

cnf(c_0_676,plain,
    lhs_atom14(X1),
    c_0_531,
    [final] ).

cnf(c_0_677,plain,
    lhs_atom13(X1),
    c_0_532,
    [final] ).

cnf(c_0_678,plain,
    lhs_atom11(X1),
    c_0_533,
    [final] ).

cnf(c_0_679,plain,
    lhs_atom10(X1),
    c_0_534,
    [final] ).

cnf(c_0_680,plain,
    lhs_atom6(X1),
    c_0_535,
    [final] ).

cnf(c_0_681,plain,
    lhs_atom5(X1),
    c_0_536,
    [final] ).

cnf(c_0_682,plain,
    lhs_atom1(X1),
    c_0_537,
    [final] ).

cnf(c_0_683,plain,
    lhs_atom145,
    c_0_538,
    [final] ).

cnf(c_0_684,plain,
    lhs_atom144,
    c_0_539,
    [final] ).

cnf(c_0_685,plain,
    lhs_atom143,
    c_0_540,
    [final] ).

cnf(c_0_686,plain,
    lhs_atom142,
    c_0_541,
    [final] ).

cnf(c_0_687,plain,
    lhs_atom141,
    c_0_542,
    [final] ).

cnf(c_0_688,plain,
    lhs_atom140,
    c_0_543,
    [final] ).

cnf(c_0_689,plain,
    lhs_atom139,
    c_0_544,
    [final] ).

cnf(c_0_690,plain,
    lhs_atom138,
    c_0_545,
    [final] ).

cnf(c_0_691,plain,
    lhs_atom137,
    c_0_546,
    [final] ).

cnf(c_0_692,plain,
    lhs_atom136,
    c_0_547,
    [final] ).

cnf(c_0_693,plain,
    lhs_atom135,
    c_0_548,
    [final] ).

cnf(c_0_694,plain,
    lhs_atom134,
    c_0_549,
    [final] ).

cnf(c_0_695,plain,
    lhs_atom133,
    c_0_550,
    [final] ).

cnf(c_0_696,plain,
    lhs_atom132,
    c_0_551,
    [final] ).

cnf(c_0_697,plain,
    lhs_atom131,
    c_0_552,
    [final] ).

cnf(c_0_698,plain,
    lhs_atom130,
    c_0_553,
    [final] ).

cnf(c_0_699,plain,
    lhs_atom129,
    c_0_554,
    [final] ).

cnf(c_0_700,plain,
    lhs_atom128,
    c_0_555,
    [final] ).

cnf(c_0_701,plain,
    lhs_atom127,
    c_0_556,
    [final] ).

cnf(c_0_702,plain,
    lhs_atom126,
    c_0_557,
    [final] ).

cnf(c_0_703,plain,
    lhs_atom125,
    c_0_558,
    [final] ).

cnf(c_0_704,plain,
    lhs_atom124,
    c_0_559,
    [final] ).

cnf(c_0_705,plain,
    lhs_atom123,
    c_0_560,
    [final] ).

cnf(c_0_706,plain,
    lhs_atom122,
    c_0_561,
    [final] ).

cnf(c_0_707,plain,
    lhs_atom121,
    c_0_562,
    [final] ).

cnf(c_0_708,plain,
    lhs_atom120,
    c_0_563,
    [final] ).

cnf(c_0_709,plain,
    lhs_atom119,
    c_0_564,
    [final] ).

cnf(c_0_710,plain,
    lhs_atom118,
    c_0_565,
    [final] ).

cnf(c_0_711,plain,
    lhs_atom117,
    c_0_566,
    [final] ).

cnf(c_0_712,plain,
    lhs_atom116,
    c_0_567,
    [final] ).

cnf(c_0_713,plain,
    lhs_atom82,
    c_0_568,
    [final] ).

cnf(c_0_714,plain,
    lhs_atom69,
    c_0_569,
    [final] ).

cnf(c_0_715,plain,
    lhs_atom62,
    c_0_570,
    [final] ).

cnf(c_0_716,plain,
    lhs_atom57,
    c_0_571,
    [final] ).

cnf(c_0_717,plain,
    lhs_atom36,
    c_0_572,
    [final] ).

cnf(c_0_718,plain,
    lhs_atom35,
    c_0_573,
    [final] ).

cnf(c_0_719,plain,
    lhs_atom31,
    c_0_574,
    [final] ).

cnf(c_0_720,plain,
    lhs_atom27,
    c_0_575,
    [final] ).

cnf(c_0_721,plain,
    lhs_atom26,
    c_0_576,
    [final] ).

cnf(c_0_722,plain,
    lhs_atom18,
    c_0_577,
    [final] ).

cnf(c_0_723,plain,
    lhs_atom12,
    c_0_578,
    [final] ).

cnf(c_0_724,plain,
    lhs_atom2,
    c_0_579,
    [final] ).

% End CNF derivation
cnf(c_0_582_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_582,def_lhs_atom59]) ).

cnf(c_0_583_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_583,def_lhs_atom58]) ).

cnf(c_0_580_0,axiom,
    c_Lambda_Osubst(c_Lambda_OdB_OApp(X2,X1),X3,X4) = c_Lambda_OdB_OApp(c_Lambda_Osubst(X2,X3,X4),c_Lambda_Osubst(X1,X3,X4)),
    inference(unfold_definition,[status(thm)],[c_0_580,def_lhs_atom88]) ).

cnf(c_0_581_0,axiom,
    c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X4,X1,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X1,tc_nat),X2,tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X4,X3,tc_nat),X1,tc_nat),X2,tc_nat),
    inference(unfold_definition,[status(thm)],[c_0_581,def_lhs_atom44]) ).

cnf(c_0_584_0,axiom,
    c_Lambda_OdB_OApp(X3,X2) != c_Lambda_OdB_OVar(X1),
    inference(unfold_definition,[status(thm)],[c_0_584,def_lhs_atom115]) ).

cnf(c_0_585_0,axiom,
    c_Lambda_Osubst(c_Lambda_Olift(X1,X3),X2,X3) = X1,
    inference(unfold_definition,[status(thm)],[c_0_585,def_lhs_atom113]) ).

cnf(c_0_586_0,axiom,
    c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(c_Suc(X2),X1,tc_nat),c_Suc(X3),tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),X3,tc_nat),
    inference(unfold_definition,[status(thm)],[c_0_586,def_lhs_atom111]) ).

cnf(c_0_587_0,axiom,
    c_Lambda_OdB_OVar(X1) != c_Lambda_OdB_OApp(X3,X2),
    inference(unfold_definition,[status(thm)],[c_0_587,def_lhs_atom102]) ).

cnf(c_0_588_0,axiom,
    c_Lambda_OdB_OAbs(X1) != c_Lambda_OdB_OApp(X3,X2),
    inference(unfold_definition,[status(thm)],[c_0_588,def_lhs_atom91]) ).

cnf(c_0_589_0,axiom,
    c_Lambda_OdB_OApp(X3,X2) != c_Lambda_OdB_OAbs(X1),
    inference(unfold_definition,[status(thm)],[c_0_589,def_lhs_atom90]) ).

cnf(c_0_590_0,axiom,
    c_HOL_Otimes__class_Otimes(X3,c_HOL_Oplus__class_Oplus(X2,X1,tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(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_590,def_lhs_atom87]) ).

cnf(c_0_591_0,axiom,
    c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X2,X1,tc_nat),X3,tc_nat) = c_HOL_Oplus__class_Oplus(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_591,def_lhs_atom86]) ).

cnf(c_0_592_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_592,def_lhs_atom85]) ).

cnf(c_0_593_0,axiom,
    c_Orderings_Oord__class_Omin(c_HOL_Ominus__class_Ominus(X2,X3,tc_nat),c_HOL_Ominus__class_Ominus(X1,X3,tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(c_Orderings_Oord__class_Omin(X2,X1,tc_nat),X3,tc_nat),
    inference(unfold_definition,[status(thm)],[c_0_593,def_lhs_atom81]) ).

cnf(c_0_594_0,axiom,
    c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X1,tc_nat),X2,tc_nat),X1,tc_nat) = c_Divides_Odiv__class_Omod(X2,X1,tc_nat),
    inference(unfold_definition,[status(thm)],[c_0_594,def_lhs_atom73]) ).

cnf(c_0_595_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_595,def_lhs_atom71]) ).

cnf(c_0_596_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_596,def_lhs_atom70]) ).

cnf(c_0_597_0,axiom,
    c_Lambda_Osubst(c_Lambda_OdB_OAbs(X1),X2,X3) = c_Lambda_OdB_OAbs(c_Lambda_Osubst(X1,c_Lambda_Olift(X2,c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oplus__class_Oplus(X3,c_HOL_Oone__class_Oone(tc_nat),tc_nat))),
    inference(unfold_definition,[status(thm)],[c_0_597,def_lhs_atom63]) ).

cnf(c_0_598_0,axiom,
    c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X3,X2,tc_nat),X1,tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X3,X1,tc_nat),X2,tc_nat),
    inference(unfold_definition,[status(thm)],[c_0_598,def_lhs_atom48]) ).

cnf(c_0_599_0,axiom,
    c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),X3,tc_nat) = c_HOL_Ominus__class_Ominus(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_599,def_lhs_atom47]) ).

cnf(c_0_600_0,axiom,
    c_HOL_Otimes__class_Otimes(X3,c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(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_600,def_lhs_atom46]) ).

cnf(c_0_601_0,axiom,
    c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X3,X2,tc_nat),c_HOL_Oplus__class_Oplus(X3,X1,tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),
    inference(unfold_definition,[status(thm)],[c_0_601,def_lhs_atom41]) ).

cnf(c_0_602_0,axiom,
    c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X2,X3,tc_nat),c_HOL_Oplus__class_Oplus(X1,X3,tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),
    inference(unfold_definition,[status(thm)],[c_0_602,def_lhs_atom40]) ).

cnf(c_0_603_0,axiom,
    c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X3,X2,tc_nat),X1,tc_nat) = c_HOL_Ominus__class_Ominus(X3,c_HOL_Oplus__class_Oplus(X2,X1,tc_nat),tc_nat),
    inference(unfold_definition,[status(thm)],[c_0_603,def_lhs_atom38]) ).

cnf(c_0_604_0,axiom,
    c_Divides_Odiv__class_Omod(c_Suc(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X1,tc_nat),X2,tc_nat)),X1,tc_nat) = c_Divides_Odiv__class_Omod(c_Suc(X2),X1,tc_nat),
    inference(unfold_definition,[status(thm)],[c_0_604,def_lhs_atom30]) ).

cnf(c_0_605_0,axiom,
    c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X2,X1,tc_nat),X3,tc_nat) = c_HOL_Oplus__class_Oplus(X2,c_HOL_Oplus__class_Oplus(X1,X3,tc_nat),tc_nat),
    inference(unfold_definition,[status(thm)],[c_0_605,def_lhs_atom21]) ).

cnf(c_0_606_0,axiom,
    c_HOL_Oplus__class_Oplus(X3,c_HOL_Oplus__class_Oplus(X2,X1,tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(X2,c_HOL_Oplus__class_Oplus(X3,X1,tc_nat),tc_nat),
    inference(unfold_definition,[status(thm)],[c_0_606,def_lhs_atom20]) ).

cnf(c_0_607_0,axiom,
    c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat),
    inference(unfold_definition,[status(thm)],[c_0_607,def_lhs_atom16]) ).

cnf(c_0_608_0,axiom,
    c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X2,tc_nat),c_HOL_Otimes__class_Otimes(X3,X1,tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X1,tc_nat),c_HOL_Otimes__class_Otimes(X3,X2,tc_nat),tc_nat),
    inference(unfold_definition,[status(thm)],[c_0_608,def_lhs_atom15]) ).

cnf(c_0_609_0,axiom,
    c_Lambda_Olift(c_Lambda_OdB_OApp(X2,X1),X3) = c_Lambda_OdB_OApp(c_Lambda_Olift(X2,X3),c_Lambda_Olift(X1,X3)),
    inference(unfold_definition,[status(thm)],[c_0_609,def_lhs_atom3]) ).

cnf(c_0_610_0,axiom,
    c_Orderings_Oord__class_Omin(c_Suc(X2),c_Suc(X1),tc_nat) = c_Suc(c_Orderings_Oord__class_Omin(X2,X1,tc_nat)),
    inference(unfold_definition,[status(thm)],[c_0_610,def_lhs_atom114]) ).

cnf(c_0_611_0,axiom,
    c_HOL_Oplus__class_Oplus(c_Suc(X2),X1,tc_nat) = c_HOL_Oplus__class_Oplus(X2,c_Suc(X1),tc_nat),
    inference(unfold_definition,[status(thm)],[c_0_611,def_lhs_atom110]) ).

cnf(c_0_612_0,axiom,
    c_Orderings_Oord__class_Omax(c_Suc(X2),c_Suc(X1),tc_nat) = c_Suc(c_Orderings_Oord__class_Omax(X2,X1,tc_nat)),
    inference(unfold_definition,[status(thm)],[c_0_612,def_lhs_atom109]) ).

cnf(c_0_613_0,axiom,
    c_HOL_Oplus__class_Oplus(X2,c_Suc(X1),tc_nat) = c_Suc(c_HOL_Oplus__class_Oplus(X2,X1,tc_nat)),
    inference(unfold_definition,[status(thm)],[c_0_613,def_lhs_atom108]) ).

cnf(c_0_614_0,axiom,
    c_HOL_Oplus__class_Oplus(c_Suc(X2),X1,tc_nat) = c_Suc(c_HOL_Oplus__class_Oplus(X2,X1,tc_nat)),
    inference(unfold_definition,[status(thm)],[c_0_614,def_lhs_atom107]) ).

cnf(c_0_615_0,axiom,
    c_Lambda_OdB_OVar(X1) != c_Lambda_OdB_OAbs(X2),
    inference(unfold_definition,[status(thm)],[c_0_615,def_lhs_atom104]) ).

cnf(c_0_616_0,axiom,
    c_HOL_Ominus__class_Ominus(c_Suc(X2),c_Suc(X1),tc_nat) = c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),
    inference(unfold_definition,[status(thm)],[c_0_616,def_lhs_atom103]) ).

cnf(c_0_617_0,axiom,
    ~ c_Lambda_Obeta(c_Lambda_OdB_OVar(X2),X1),
    inference(unfold_definition,[status(thm)],[c_0_617,def_lhs_atom99]) ).

cnf(c_0_618_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_618,def_lhs_atom93]) ).

cnf(c_0_619_0,axiom,
    c_Lambda_Osubst(c_Lambda_OdB_OVar(X2),X1,X2) = X1,
    inference(unfold_definition,[status(thm)],[c_0_619,def_lhs_atom92]) ).

cnf(c_0_620_0,axiom,
    c_Lambda_OdB_OAbs(X2) != c_Lambda_OdB_OVar(X1),
    inference(unfold_definition,[status(thm)],[c_0_620,def_lhs_atom89]) ).

cnf(c_0_621_0,axiom,
    c_Lambda_Olift(c_Lambda_OdB_OAbs(X1),X2) = c_Lambda_OdB_OAbs(c_Lambda_Olift(X1,c_HOL_Oplus__class_Oplus(X2,c_HOL_Oone__class_Oone(tc_nat),tc_nat))),
    inference(unfold_definition,[status(thm)],[c_0_621,def_lhs_atom84]) ).

cnf(c_0_622_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_622,def_lhs_atom83]) ).

cnf(c_0_623_0,axiom,
    c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),X1,tc_nat) = X2,
    inference(unfold_definition,[status(thm)],[c_0_623,def_lhs_atom78]) ).

cnf(c_0_624_0,axiom,
    c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X2,X1,tc_nat),X1,tc_nat) = X2,
    inference(unfold_definition,[status(thm)],[c_0_624,def_lhs_atom77]) ).

cnf(c_0_625_0,axiom,
    c_HOL_Ominus__class_Ominus(X2,c_Suc(X1),tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X2,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X1,tc_nat),
    inference(unfold_definition,[status(thm)],[c_0_625,def_lhs_atom65]) ).

cnf(c_0_626_0,axiom,
    c_lessequals(c_Divides_Odiv__class_Omod(X2,X1,tc_nat),X2,tc_nat),
    inference(unfold_definition,[status(thm)],[c_0_626,def_lhs_atom64]) ).

cnf(c_0_627_0,axiom,
    ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),X2,tc_nat),
    inference(unfold_definition,[status(thm)],[c_0_627,def_lhs_atom61]) ).

cnf(c_0_628_0,axiom,
    ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X2,X1,tc_nat),X2,tc_nat),
    inference(unfold_definition,[status(thm)],[c_0_628,def_lhs_atom60]) ).

cnf(c_0_629_0,axiom,
    c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),X2,tc_nat) = c_Orderings_Oord__class_Omax(X1,X2,tc_nat),
    inference(unfold_definition,[status(thm)],[c_0_629,def_lhs_atom56]) ).

cnf(c_0_630_0,axiom,
    c_lessequals(X2,c_HOL_Oplus__class_Oplus(X2,X1,tc_nat),tc_nat),
    inference(unfold_definition,[status(thm)],[c_0_630,def_lhs_atom55]) ).

cnf(c_0_631_0,axiom,
    c_lessequals(X1,c_HOL_Oplus__class_Oplus(X2,X1,tc_nat),tc_nat),
    inference(unfold_definition,[status(thm)],[c_0_631,def_lhs_atom54]) ).

cnf(c_0_632_0,axiom,
    c_lessequals(X1,c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat),
    inference(unfold_definition,[status(thm)],[c_0_632,def_lhs_atom53]) ).

cnf(c_0_633_0,axiom,
    c_Lambda_Obeta(c_Lambda_OdB_OApp(c_Lambda_OdB_OAbs(X2),X1),c_Lambda_Osubst(X2,X1,c_HOL_Ozero__class_Ozero(tc_nat))),
    inference(unfold_definition,[status(thm)],[c_0_633,def_lhs_atom52]) ).

cnf(c_0_634_0,axiom,
    c_lessequals(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),X2,tc_nat),
    inference(unfold_definition,[status(thm)],[c_0_634,def_lhs_atom45]) ).

cnf(c_0_635_0,axiom,
    c_HOL_Ominus__class_Ominus(X1,c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
    inference(unfold_definition,[status(thm)],[c_0_635,def_lhs_atom37]) ).

cnf(c_0_636_0,axiom,
    c_HOL_Otimes__class_Otimes(c_Suc(X2),X1,tc_nat) = c_HOL_Oplus__class_Oplus(X1,c_HOL_Otimes__class_Otimes(X2,X1,tc_nat),tc_nat),
    inference(unfold_definition,[status(thm)],[c_0_636,def_lhs_atom29]) ).

cnf(c_0_637_0,axiom,
    c_HOL_Otimes__class_Otimes(X2,c_Suc(X1),tc_nat) = c_HOL_Oplus__class_Oplus(X2,c_HOL_Otimes__class_Otimes(X2,X1,tc_nat),tc_nat),
    inference(unfold_definition,[status(thm)],[c_0_637,def_lhs_atom28]) ).

cnf(c_0_638_0,axiom,
    c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),c_Suc(X2),tc_nat),
    inference(unfold_definition,[status(thm)],[c_0_638,def_lhs_atom19]) ).

cnf(c_0_639_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_639,def_lhs_atom17]) ).

cnf(c_0_640_0,axiom,
    c_HOL_Oord__class_Oless(X2,c_Suc(c_HOL_Oplus__class_Oplus(X2,X1,tc_nat)),tc_nat),
    inference(unfold_definition,[status(thm)],[c_0_640,def_lhs_atom9]) ).

cnf(c_0_641_0,axiom,
    c_HOL_Oord__class_Oless(X2,c_Suc(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat)),tc_nat),
    inference(unfold_definition,[status(thm)],[c_0_641,def_lhs_atom8]) ).

cnf(c_0_642_0,axiom,
    c_HOL_Oord__class_Oless(X2,c_Suc(c_HOL_Oplus__class_Oplus(X2,X1,tc_nat)),tc_nat),
    inference(unfold_definition,[status(thm)],[c_0_642,def_lhs_atom7]) ).

cnf(c_0_643_0,axiom,
    c_HOL_Oplus__class_Oplus(X2,X1,tc_nat) = c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),
    inference(unfold_definition,[status(thm)],[c_0_643,def_lhs_atom4]) ).

cnf(c_0_644_0,axiom,
    c_lessequals(c_Suc(X1),c_Suc(X1),tc_nat),
    inference(unfold_definition,[status(thm)],[c_0_644,def_lhs_atom112]) ).

cnf(c_0_645_0,axiom,
    c_HOL_Ozero__class_Ozero(tc_nat) != c_Suc(X1),
    inference(unfold_definition,[status(thm)],[c_0_645,def_lhs_atom106]) ).

cnf(c_0_646_0,axiom,
    c_HOL_Ozero__class_Ozero(tc_nat) != c_Suc(X1),
    inference(unfold_definition,[status(thm)],[c_0_646,def_lhs_atom105]) ).

cnf(c_0_647_0,axiom,
    c_Suc(X1) != c_HOL_Ozero__class_Ozero(tc_nat),
    inference(unfold_definition,[status(thm)],[c_0_647,def_lhs_atom101]) ).

cnf(c_0_648_0,axiom,
    c_Suc(X1) != c_HOL_Ozero__class_Ozero(tc_nat),
    inference(unfold_definition,[status(thm)],[c_0_648,def_lhs_atom100]) ).

cnf(c_0_649_0,axiom,
    c_HOL_Oord__class_Oless(X1,c_Suc(X1),tc_nat),
    inference(unfold_definition,[status(thm)],[c_0_649,def_lhs_atom98]) ).

cnf(c_0_650_0,axiom,
    c_HOL_Oord__class_Oless(X1,c_Suc(X1),tc_nat),
    inference(unfold_definition,[status(thm)],[c_0_650,def_lhs_atom97]) ).

cnf(c_0_651_0,axiom,
    ~ c_lessequals(c_Suc(X1),X1,tc_nat),
    inference(unfold_definition,[status(thm)],[c_0_651,def_lhs_atom96]) ).

cnf(c_0_652_0,axiom,
    c_Suc(X1) != X1,
    inference(unfold_definition,[status(thm)],[c_0_652,def_lhs_atom95]) ).

cnf(c_0_653_0,axiom,
    X1 != c_Suc(X1),
    inference(unfold_definition,[status(thm)],[c_0_653,def_lhs_atom94]) ).

cnf(c_0_654_0,axiom,
    c_lessequals(X1,X1,tc_nat),
    inference(unfold_definition,[status(thm)],[c_0_654,def_lhs_atom80]) ).

cnf(c_0_655_0,axiom,
    c_lessequals(X1,X1,tc_nat),
    inference(unfold_definition,[status(thm)],[c_0_655,def_lhs_atom79]) ).

cnf(c_0_656_0,axiom,
    c_HOL_Oplus__class_Oplus(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = X1,
    inference(unfold_definition,[status(thm)],[c_0_656,def_lhs_atom76]) ).

cnf(c_0_657_0,axiom,
    c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) = X1,
    inference(unfold_definition,[status(thm)],[c_0_657,def_lhs_atom75]) ).

cnf(c_0_658_0,axiom,
    X1 = c_HOL_Oplus__class_Oplus(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
    inference(unfold_definition,[status(thm)],[c_0_658,def_lhs_atom74]) ).

cnf(c_0_659_0,axiom,
    c_lessequals(X1,c_HOL_Otimes__class_Otimes(X1,c_HOL_Otimes__class_Otimes(X1,X1,tc_nat),tc_nat),tc_nat),
    inference(unfold_definition,[status(thm)],[c_0_659,def_lhs_atom72]) ).

cnf(c_0_660_0,axiom,
    c_lessequals(X1,c_HOL_Otimes__class_Otimes(X1,X1,tc_nat),tc_nat),
    inference(unfold_definition,[status(thm)],[c_0_660,def_lhs_atom68]) ).

cnf(c_0_661_0,axiom,
    c_Orderings_Oord__class_Omax(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) = X1,
    inference(unfold_definition,[status(thm)],[c_0_661,def_lhs_atom67]) ).

cnf(c_0_662_0,axiom,
    c_Orderings_Oord__class_Omax(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = X1,
    inference(unfold_definition,[status(thm)],[c_0_662,def_lhs_atom66]) ).

cnf(c_0_663_0,axiom,
    ~ c_HOL_Oord__class_Oless(X1,X1,tc_nat),
    inference(unfold_definition,[status(thm)],[c_0_663,def_lhs_atom51]) ).

cnf(c_0_664_0,axiom,
    ~ c_HOL_Oord__class_Oless(X1,X1,tc_nat),
    inference(unfold_definition,[status(thm)],[c_0_664,def_lhs_atom50]) ).

cnf(c_0_665_0,axiom,
    c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat),
    inference(unfold_definition,[status(thm)],[c_0_665,def_lhs_atom49]) ).

cnf(c_0_666_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_666,def_lhs_atom43]) ).

cnf(c_0_667_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_667,def_lhs_atom42]) ).

cnf(c_0_668_0,axiom,
    c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
    inference(unfold_definition,[status(thm)],[c_0_668,def_lhs_atom39]) ).

cnf(c_0_669_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_669,def_lhs_atom34]) ).

cnf(c_0_670_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_670,def_lhs_atom33]) ).

cnf(c_0_671_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_671,def_lhs_atom32]) ).

cnf(c_0_672_0,axiom,
    c_Orderings_Oord__class_Omin(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
    inference(unfold_definition,[status(thm)],[c_0_672,def_lhs_atom25]) ).

cnf(c_0_673_0,axiom,
    c_Orderings_Oord__class_Omin(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
    inference(unfold_definition,[status(thm)],[c_0_673,def_lhs_atom24]) ).

cnf(c_0_674_0,axiom,
    ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
    inference(unfold_definition,[status(thm)],[c_0_674,def_lhs_atom23]) ).

cnf(c_0_675_0,axiom,
    ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
    inference(unfold_definition,[status(thm)],[c_0_675,def_lhs_atom22]) ).

cnf(c_0_676_0,axiom,
    c_Suc(X1) = c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),
    inference(unfold_definition,[status(thm)],[c_0_676,def_lhs_atom14]) ).

cnf(c_0_677_0,axiom,
    c_Suc(X1) = c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),X1,tc_nat),
    inference(unfold_definition,[status(thm)],[c_0_677,def_lhs_atom13]) ).

cnf(c_0_678_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_678,def_lhs_atom11]) ).

cnf(c_0_679_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_679,def_lhs_atom10]) ).

cnf(c_0_680_0,axiom,
    c_HOL_Ominus__class_Ominus(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = X1,
    inference(unfold_definition,[status(thm)],[c_0_680,def_lhs_atom6]) ).

cnf(c_0_681_0,axiom,
    c_HOL_Ominus__class_Ominus(X1,X1,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
    inference(unfold_definition,[status(thm)],[c_0_681,def_lhs_atom5]) ).

cnf(c_0_682_0,axiom,
    c_HOL_Ominus__class_Ominus(c_Suc(X1),c_HOL_Oone__class_Oone(tc_nat),tc_nat) = X1,
    inference(unfold_definition,[status(thm)],[c_0_682,def_lhs_atom1]) ).

cnf(c_0_683_0,axiom,
    class_Orderings_Oorder(tc_nat),
    inference(unfold_definition,[status(thm)],[c_0_683,def_lhs_atom145]) ).

cnf(c_0_684_0,axiom,
    class_Orderings_Olinorder(tc_nat),
    inference(unfold_definition,[status(thm)],[c_0_684,def_lhs_atom144]) ).

cnf(c_0_685_0,axiom,
    class_Orderings_Opreorder(tc_nat),
    inference(unfold_definition,[status(thm)],[c_0_685,def_lhs_atom143]) ).

cnf(c_0_686_0,axiom,
    class_Divides_Osemiring__div(tc_nat),
    inference(unfold_definition,[status(thm)],[c_0_686,def_lhs_atom142]) ).

cnf(c_0_687_0,axiom,
    class_OrderedGroup_Omonoid__add(tc_nat),
    inference(unfold_definition,[status(thm)],[c_0_687,def_lhs_atom141]) ).

cnf(c_0_688_0,axiom,
    class_Ring__and__Field_Osemiring(tc_nat),
    inference(unfold_definition,[status(thm)],[c_0_688,def_lhs_atom140]) ).

cnf(c_0_689_0,axiom,
    class_OrderedGroup_Omonoid__mult(tc_nat),
    inference(unfold_definition,[status(thm)],[c_0_689,def_lhs_atom139]) ).

cnf(c_0_690_0,axiom,
    class_Ring__and__Field_Omult__mono(tc_nat),
    inference(unfold_definition,[status(thm)],[c_0_690,def_lhs_atom138]) ).

cnf(c_0_691_0,axiom,
    class_Ring__and__Field_Omult__zero(tc_nat),
    inference(unfold_definition,[status(thm)],[c_0_691,def_lhs_atom137]) ).

cnf(c_0_692_0,axiom,
    class_Ring__and__Field_Omult__mono1(tc_nat),
    inference(unfold_definition,[status(thm)],[c_0_692,def_lhs_atom136]) ).

cnf(c_0_693_0,axiom,
    class_Ring__and__Field_Ozero__neq__one(tc_nat),
    inference(unfold_definition,[status(thm)],[c_0_693,def_lhs_atom135]) ).

cnf(c_0_694_0,axiom,
    class_OrderedGroup_Ocomm__monoid__add(tc_nat),
    inference(unfold_definition,[status(thm)],[c_0_694,def_lhs_atom134]) ).

cnf(c_0_695_0,axiom,
    class_Ring__and__Field_Ocomm__semiring(tc_nat),
    inference(unfold_definition,[status(thm)],[c_0_695,def_lhs_atom133]) ).

cnf(c_0_696_0,axiom,
    class_OrderedGroup_Oab__semigroup__add(tc_nat),
    inference(unfold_definition,[status(thm)],[c_0_696,def_lhs_atom132]) ).

cnf(c_0_697_0,axiom,
    class_OrderedGroup_Ocomm__monoid__mult(tc_nat),
    inference(unfold_definition,[status(thm)],[c_0_697,def_lhs_atom131]) ).

cnf(c_0_698_0,axiom,
    class_OrderedGroup_Oab__semigroup__mult(tc_nat),
    inference(unfold_definition,[status(thm)],[c_0_698,def_lhs_atom130]) ).

cnf(c_0_699_0,axiom,
    class_Ring__and__Field_Ocomm__semiring__1(tc_nat),
    inference(unfold_definition,[status(thm)],[c_0_699,def_lhs_atom129]) ).

cnf(c_0_700_0,axiom,
    class_Ring__and__Field_Oordered__semidom(tc_nat),
    inference(unfold_definition,[status(thm)],[c_0_700,def_lhs_atom128]) ).

cnf(c_0_701_0,axiom,
    class_Ring__and__Field_Ono__zero__divisors(tc_nat),
    inference(unfold_definition,[status(thm)],[c_0_701,def_lhs_atom127]) ).

cnf(c_0_702_0,axiom,
    class_Ring__and__Field_Oordered__semiring(tc_nat),
    inference(unfold_definition,[status(thm)],[c_0_702,def_lhs_atom126]) ).

cnf(c_0_703_0,axiom,
    class_Ring__and__Field_Opordered__semiring(tc_nat),
    inference(unfold_definition,[status(thm)],[c_0_703,def_lhs_atom125]) ).

cnf(c_0_704_0,axiom,
    class_OrderedGroup_Ocancel__semigroup__add(tc_nat),
    inference(unfold_definition,[status(thm)],[c_0_704,def_lhs_atom124]) ).

cnf(c_0_705_0,axiom,
    class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat),
    inference(unfold_definition,[status(thm)],[c_0_705,def_lhs_atom123]) ).

cnf(c_0_706_0,axiom,
    class_OrderedGroup_Opordered__comm__monoid__add(tc_nat),
    inference(unfold_definition,[status(thm)],[c_0_706,def_lhs_atom122]) ).

cnf(c_0_707_0,axiom,
    class_OrderedGroup_Opordered__ab__semigroup__add(tc_nat),
    inference(unfold_definition,[status(thm)],[c_0_707,def_lhs_atom121]) ).

cnf(c_0_708_0,axiom,
    class_Ring__and__Field_Oordered__semiring__strict(tc_nat),
    inference(unfold_definition,[status(thm)],[c_0_708,def_lhs_atom120]) ).

cnf(c_0_709_0,axiom,
    class_Ring__and__Field_Opordered__cancel__semiring(tc_nat),
    inference(unfold_definition,[status(thm)],[c_0_709,def_lhs_atom119]) ).

cnf(c_0_710_0,axiom,
    class_Ring__and__Field_Oordered__comm__semiring__strict(tc_nat),
    inference(unfold_definition,[status(thm)],[c_0_710,def_lhs_atom118]) ).

cnf(c_0_711_0,axiom,
    class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat),
    inference(unfold_definition,[status(thm)],[c_0_711,def_lhs_atom117]) ).

cnf(c_0_712_0,axiom,
    class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat),
    inference(unfold_definition,[status(thm)],[c_0_712,def_lhs_atom116]) ).

cnf(c_0_713_0,axiom,
    c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),
    inference(unfold_definition,[status(thm)],[c_0_713,def_lhs_atom82]) ).

cnf(c_0_714_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_714,def_lhs_atom69]) ).

cnf(c_0_715_0,axiom,
    c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
    inference(unfold_definition,[status(thm)],[c_0_715,def_lhs_atom62]) ).

cnf(c_0_716_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_716,def_lhs_atom57]) ).

cnf(c_0_717_0,axiom,
    c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) = c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),
    inference(unfold_definition,[status(thm)],[c_0_717,def_lhs_atom36]) ).

cnf(c_0_718_0,axiom,
    c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) = c_HOL_Oplus__class_Oplus(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
    inference(unfold_definition,[status(thm)],[c_0_718,def_lhs_atom35]) ).

cnf(c_0_719_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_719,def_lhs_atom31]) ).

cnf(c_0_720_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_720,def_lhs_atom27]) ).

cnf(c_0_721_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_721,def_lhs_atom26]) ).

cnf(c_0_722_0,axiom,
    c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
    inference(unfold_definition,[status(thm)],[c_0_722,def_lhs_atom18]) ).

cnf(c_0_723_0,axiom,
    c_HOL_Oplus__class_Oplus(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),
    inference(unfold_definition,[status(thm)],[c_0_723,def_lhs_atom12]) ).

cnf(c_0_724_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_724,def_lhs_atom2]) ).

% Orienting (remaining) axiom formulas using strategy ClausalAll
% CNF of (remaining) axioms:
% Start CNF derivation
fof(c_0_0_001,axiom,
    ! [X15,X1,X2,X14,X8] :
      ( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X8,X15,tc_nat),X2,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X14,X15,tc_nat),X1,tc_nat),tc_nat)
      | ~ c_HOL_Oord__class_Oless(X2,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X14,X8,tc_nat),X15,tc_nat),X1,tc_nat),tc_nat)
      | ~ c_lessequals(X8,X14,tc_nat) ),
    file('<stdin>',cls_nat__less__add__iff2_1) ).

fof(c_0_1_002,axiom,
    ! [X15,X1,X2,X14,X8] :
      ( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X8,X15,tc_nat),X2,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X14,X15,tc_nat),X1,tc_nat),tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X8,X14,tc_nat),X15,tc_nat),X2,tc_nat),X1,tc_nat)
      | ~ c_lessequals(X14,X8,tc_nat) ),
    file('<stdin>',cls_nat__less__add__iff1_1) ).

fof(c_0_2_003,axiom,
    ! [X15,X1,X2,X14,X8] :
      ( c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X8,X15,tc_nat),X2,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X14,X15,tc_nat),X1,tc_nat),tc_nat)
      | ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X8,X14,tc_nat),X15,tc_nat),X2,tc_nat),X1,tc_nat)
      | ~ c_lessequals(X14,X8,tc_nat) ),
    file('<stdin>',cls_nat__le__add__iff1_1) ).

fof(c_0_3_004,axiom,
    ! [X15,X1,X2,X14,X8] :
      ( c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X8,X15,tc_nat),X2,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X14,X15,tc_nat),X1,tc_nat),tc_nat)
      | ~ c_lessequals(X2,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X14,X8,tc_nat),X15,tc_nat),X1,tc_nat),tc_nat)
      | ~ c_lessequals(X8,X14,tc_nat) ),
    file('<stdin>',cls_nat__le__add__iff2_1) ).

fof(c_0_4_005,axiom,
    ! [X39,X27,X20,X16,X17,X18] :
      ( ~ class_Ring__and__Field_Opordered__ring(X18)
      | c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X17,X39,X18),X20,X18),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X16,X39,X18),X27,X18),X18)
      | ~ c_lessequals(X20,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X16,X17,X18),X39,X18),X27,X18),X18) ),
    file('<stdin>',cls_le__add__iff2_1) ).

fof(c_0_5_006,axiom,
    ! [X39,X27,X20,X16,X17,X18] :
      ( ~ class_Ring__and__Field_Opordered__ring(X18)
      | c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X17,X39,X18),X20,X18),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X16,X39,X18),X27,X18),X18)
      | ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X17,X16,X18),X39,X18),X20,X18),X27,X18) ),
    file('<stdin>',cls_le__add__iff1_1) ).

fof(c_0_6_007,axiom,
    ! [X39,X27,X20,X16,X17,X18] :
      ( ~ class_Ring__and__Field_Opordered__ring(X18)
      | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X17,X39,X18),X20,X18),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X16,X39,X18),X27,X18),X18)
      | ~ c_HOL_Oord__class_Oless(X20,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X16,X17,X18),X39,X18),X27,X18),X18) ),
    file('<stdin>',cls_less__add__iff2_1) ).

fof(c_0_7_008,axiom,
    ! [X39,X27,X20,X16,X17,X18] :
      ( ~ class_Ring__and__Field_Opordered__ring(X18)
      | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X17,X39,X18),X20,X18),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X16,X39,X18),X27,X18),X18)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X17,X16,X18),X39,X18),X20,X18),X27,X18) ),
    file('<stdin>',cls_less__add__iff1_1) ).

fof(c_0_8_009,axiom,
    ! [X15,X1,X2,X14,X8] :
      ( c_HOL_Oord__class_Oless(X2,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X14,X8,tc_nat),X15,tc_nat),X1,tc_nat),tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X8,X15,tc_nat),X2,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X14,X15,tc_nat),X1,tc_nat),tc_nat)
      | ~ c_lessequals(X8,X14,tc_nat) ),
    file('<stdin>',cls_nat__less__add__iff2_0) ).

fof(c_0_9_010,axiom,
    ! [X15,X1,X2,X14,X8] :
      ( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X8,X14,tc_nat),X15,tc_nat),X2,tc_nat),X1,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X8,X15,tc_nat),X2,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X14,X15,tc_nat),X1,tc_nat),tc_nat)
      | ~ c_lessequals(X14,X8,tc_nat) ),
    file('<stdin>',cls_nat__less__add__iff1_0) ).

fof(c_0_10_011,axiom,
    ! [X15,X1,X2,X14,X8] :
      ( c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X8,X14,tc_nat),X15,tc_nat),X2,tc_nat),X1,tc_nat)
      | ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X8,X15,tc_nat),X2,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X14,X15,tc_nat),X1,tc_nat),tc_nat)
      | ~ c_lessequals(X14,X8,tc_nat) ),
    file('<stdin>',cls_nat__le__add__iff1_0) ).

fof(c_0_11_012,axiom,
    ! [X15,X1,X2,X14,X8] :
      ( c_lessequals(X2,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X14,X8,tc_nat),X15,tc_nat),X1,tc_nat),tc_nat)
      | ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X8,X15,tc_nat),X2,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X14,X15,tc_nat),X1,tc_nat),tc_nat)
      | ~ c_lessequals(X8,X14,tc_nat) ),
    file('<stdin>',cls_nat__le__add__iff2_0) ).

fof(c_0_12_013,axiom,
    ! [X39,X27,X20,X16,X17,X18] :
      ( ~ class_Ring__and__Field_Opordered__ring(X18)
      | c_lessequals(X20,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X16,X17,X18),X39,X18),X27,X18),X18)
      | ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X17,X39,X18),X20,X18),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X16,X39,X18),X27,X18),X18) ),
    file('<stdin>',cls_le__add__iff2_0) ).

fof(c_0_13_014,axiom,
    ! [X39,X27,X20,X16,X17,X18] :
      ( ~ class_Ring__and__Field_Opordered__ring(X18)
      | c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X17,X16,X18),X39,X18),X20,X18),X27,X18)
      | ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X17,X39,X18),X20,X18),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X16,X39,X18),X27,X18),X18) ),
    file('<stdin>',cls_le__add__iff1_0) ).

fof(c_0_14_015,axiom,
    ! [X39,X27,X20,X16,X17,X18] :
      ( ~ class_Ring__and__Field_Opordered__ring(X18)
      | c_HOL_Oord__class_Oless(X20,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X16,X17,X18),X39,X18),X27,X18),X18)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X17,X39,X18),X20,X18),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X16,X39,X18),X27,X18),X18) ),
    file('<stdin>',cls_less__add__iff2_0) ).

fof(c_0_15_016,axiom,
    ! [X39,X27,X20,X16,X17,X18] :
      ( ~ class_Ring__and__Field_Opordered__ring(X18)
      | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X17,X16,X18),X39,X18),X20,X18),X27,X18)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X17,X39,X18),X20,X18),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X16,X39,X18),X27,X18),X18) ),
    file('<stdin>',cls_less__add__iff1_0) ).

fof(c_0_16_017,axiom,
    ! [X15,X1,X2,X14,X8] :
      ( c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X8,X15,tc_nat),X2,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X14,X15,tc_nat),X1,tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(X2,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X14,X8,tc_nat),X15,tc_nat),X1,tc_nat),tc_nat)
      | ~ c_lessequals(X8,X14,tc_nat) ),
    file('<stdin>',cls_nat__diff__add__eq2_0) ).

fof(c_0_17_018,axiom,
    ! [X15,X1,X2,X14,X8] :
      ( c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X8,X15,tc_nat),X2,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X14,X15,tc_nat),X1,tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X8,X14,tc_nat),X15,tc_nat),X2,tc_nat),X1,tc_nat)
      | ~ c_lessequals(X14,X8,tc_nat) ),
    file('<stdin>',cls_nat__diff__add__eq1_0) ).

fof(c_0_18_019,axiom,
    ! [X15,X2,X14,X8] :
      ( ~ c_lessequals(X14,X8,tc_nat)
      | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X8,X15,tc_nat),X2,tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X14,X15,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X8,X14,tc_nat),X15,tc_nat),X2,tc_nat),tc_nat) ),
    file('<stdin>',cls_nat__eq__add__iff1_1) ).

fof(c_0_19_020,axiom,
    ! [X15,X1,X14,X8] :
      ( ~ c_lessequals(X8,X14,tc_nat)
      | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X8,X15,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X14,X8,tc_nat),X15,tc_nat),X1,tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X14,X15,tc_nat),X1,tc_nat) ),
    file('<stdin>',cls_nat__eq__add__iff2_1) ).

fof(c_0_20_021,axiom,
    ! [X18] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X18)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X18),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X18),c_HOL_Ozero__class_Ozero(X18),X18),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X18),c_HOL_Ozero__class_Ozero(X18),X18),X18),X18) ),
    file('<stdin>',cls_sum__squares__gt__zero__iff_0) ).

fof(c_0_21_022,axiom,
    ! [X39,X27,X16,X17,X18] :
      ( ~ class_Ring__and__Field_Oring(X18)
      | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X17,X39,X18),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X16,X17,X18),X39,X18),X27,X18),X18) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X16,X39,X18),X27,X18) ),
    file('<stdin>',cls_eq__add__iff2_1) ).

fof(c_0_22_023,axiom,
    ! [X39,X20,X16,X17,X18] :
      ( ~ class_Ring__and__Field_Oring(X18)
      | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X17,X39,X18),X20,X18) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X16,X39,X18),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X17,X16,X18),X39,X18),X20,X18),X18) ),
    file('<stdin>',cls_eq__add__iff1_1) ).

fof(c_0_23_024,axiom,
    ! [X6,X30,X20,X16] :
      ( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X16,c_Divides_Odiv__class_Omod(X30,X20,tc_nat),tc_nat),X6,tc_nat),c_HOL_Otimes__class_Otimes(X16,X20,tc_nat),tc_nat)
      | ~ c_HOL_Oord__class_Oless(X6,X16,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X20,tc_nat) ),
    file('<stdin>',cls_mod__lemma_0) ).

fof(c_0_24_025,axiom,
    ! [X9,X3,X18] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X18)
      | X3 = c_HOL_Ozero__class_Ozero(X18)
      | ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X3,X18),c_HOL_Otimes__class_Otimes(X9,X9,X18),X18),c_HOL_Ozero__class_Ozero(X18),X18) ),
    file('<stdin>',cls_sum__squares__le__zero__iff_0) ).

fof(c_0_25_026,axiom,
    ! [X9,X3,X18] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X18)
      | X9 = c_HOL_Ozero__class_Ozero(X18)
      | ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X3,X18),c_HOL_Otimes__class_Otimes(X9,X9,X18),X18),c_HOL_Ozero__class_Ozero(X18),X18) ),
    file('<stdin>',cls_sum__squares__le__zero__iff_1) ).

fof(c_0_26_027,axiom,
    ! [X9,X3,X18] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X18)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X3,X18),c_HOL_Otimes__class_Otimes(X9,X9,X18),X18),c_HOL_Ozero__class_Ozero(X18),X18) ),
    file('<stdin>',cls_not__sum__squares__lt__zero_0) ).

fof(c_0_27_028,axiom,
    ! [X15,X1,X2,X14,X8] :
      ( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X8,X15,tc_nat),X2,tc_nat) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X14,X15,tc_nat),X1,tc_nat)
      | ~ c_lessequals(X14,X8,tc_nat)
      | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X8,X14,tc_nat),X15,tc_nat),X2,tc_nat) = X1 ),
    file('<stdin>',cls_nat__eq__add__iff1_0) ).

fof(c_0_28_029,axiom,
    ! [X15,X1,X2,X14,X8] :
      ( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X8,X15,tc_nat),X2,tc_nat) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X14,X15,tc_nat),X1,tc_nat)
      | ~ c_lessequals(X8,X14,tc_nat)
      | X2 = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X14,X8,tc_nat),X15,tc_nat),X1,tc_nat) ),
    file('<stdin>',cls_nat__eq__add__iff2_0) ).

fof(c_0_29_030,axiom,
    ! [X19,X9,X3,X18] :
      ( ~ class_Orderings_Olinorder(X18)
      | c_lessequals(c_Orderings_Oord__class_Omax(c_Orderings_Oord__class_Omin(X3,X9,X18),c_Orderings_Oord__class_Omin(X3,X19,X18),X18),c_Orderings_Oord__class_Omin(X3,c_Orderings_Oord__class_Omax(X9,X19,X18),X18),X18) ),
    file('<stdin>',cls_min__max_Odistrib__inf__le_0) ).

fof(c_0_30_031,axiom,
    ! [X19,X9,X3,X18] :
      ( ~ class_Orderings_Olinorder(X18)
      | c_lessequals(c_Orderings_Oord__class_Omax(X3,c_Orderings_Oord__class_Omin(X9,X19,X18),X18),c_Orderings_Oord__class_Omin(c_Orderings_Oord__class_Omax(X3,X9,X18),c_Orderings_Oord__class_Omax(X3,X19,X18),X18),X18) ),
    file('<stdin>',cls_min__max_Odistrib__sup__le_0) ).

fof(c_0_31_032,axiom,
    ! [X39,X27,X20,X16,X17,X18] :
      ( ~ class_Ring__and__Field_Oring(X18)
      | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X17,X39,X18),X20,X18) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X16,X39,X18),X27,X18)
      | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X17,X16,X18),X39,X18),X20,X18) = X27 ),
    file('<stdin>',cls_eq__add__iff1_0) ).

fof(c_0_32_033,axiom,
    ! [X39,X27,X20,X16,X17,X18] :
      ( ~ class_Ring__and__Field_Oring(X18)
      | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X17,X39,X18),X20,X18) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X16,X39,X18),X27,X18)
      | X20 = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X16,X17,X18),X39,X18),X27,X18) ),
    file('<stdin>',cls_eq__add__iff2_0) ).

fof(c_0_33_034,axiom,
    ! [X39,X20,X16,X17,X18] :
      ( ~ class_Ring__and__Field_Osemiring(X18)
      | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X17,X39,X18),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X16,X39,X18),X20,X18),X18) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X17,X16,X18),X39,X18),X20,X18) ),
    file('<stdin>',cls_combine__common__factor_0) ).

fof(c_0_34_035,axiom,
    ! [X19,X9,X3,X40,X18] :
      ( ~ class_Ring__and__Field_Oidom(X18)
      | ~ class_Int_Onumber__ring(X18)
      | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X40,X9,X18),c_HOL_Otimes__class_Otimes(X3,X19,X18),X18) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X40,X19,X18),c_HOL_Otimes__class_Otimes(X3,X9,X18),X18)
      | X9 = X19
      | X40 = X3 ),
    file('<stdin>',cls_class__ringb_Oadd__mul__solve_0) ).

fof(c_0_35_036,axiom,
    ! [X27,X20,X16,X17,X18] :
      ( ~ class_Ring__and__Field_Oidom(X18)
      | ~ class_Int_Onumber__ring(X18)
      | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X17,X20,X18),c_HOL_Otimes__class_Otimes(X16,X27,X18),X18) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X17,X27,X18),c_HOL_Otimes__class_Otimes(X16,X20,X18),X18)
      | X20 = X27
      | X17 = X16 ),
    file('<stdin>',cls_class__ringb_Onoteq__reduce_0) ).

fof(c_0_36_037,axiom,
    ! [X27,X20,X16,X17] :
      ( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X17,X20,tc_nat),c_HOL_Otimes__class_Otimes(X16,X27,tc_nat),tc_nat) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X17,X27,tc_nat),c_HOL_Otimes__class_Otimes(X16,X20,tc_nat),tc_nat)
      | X20 = X27
      | X17 = X16 ),
    file('<stdin>',cls_natgb_Onoteq__reduce_0) ).

fof(c_0_37_038,axiom,
    ! [X19,X9,X3,X40] :
      ( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X40,X9,tc_nat),c_HOL_Otimes__class_Otimes(X3,X19,tc_nat),tc_nat) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X40,X19,tc_nat),c_HOL_Otimes__class_Otimes(X3,X9,tc_nat),tc_nat)
      | X9 = X19
      | X40 = X3 ),
    file('<stdin>',cls_natgb_Oadd__mul__solve_0) ).

fof(c_0_38_039,axiom,
    ! [X20,X16,X17,X18] :
      ( ~ class_Divides_Osemiring__div(X18)
      | c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X17,X16,X18),X20,X18) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(X17,X20,X18),c_Divides_Odiv__class_Omod(X16,X20,X18),X18),X20,X18) ),
    file('<stdin>',cls_mod__mult__eq_0) ).

fof(c_0_39_040,axiom,
    ! [X20,X16,X17,X18] :
      ( ~ class_Divides_Osemiring__div(X18)
      | c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X17,X16,X18),X20,X18) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(X17,X20,X18),c_Divides_Odiv__class_Omod(X16,X20,X18),X18),X20,X18) ),
    file('<stdin>',cls_mod__add__eq_0) ).

fof(c_0_40_041,axiom,
    ! [X20,X16,X17,X18] :
      ( ~ class_Divides_Oring__div(X18)
      | c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X17,X16,X18),X20,X18) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(c_Divides_Odiv__class_Omod(X17,X20,X18),c_Divides_Odiv__class_Omod(X16,X20,X18),X18),X20,X18) ),
    file('<stdin>',cls_mod__diff__eq_0) ).

fof(c_0_41_042,axiom,
    ! [X29,X15,X4,X14,X8] :
      ( c_Lambda_Osubst(c_Lambda_Osubst(X4,c_Lambda_Olift(X29,X8),c_Suc(X14)),c_Lambda_Osubst(X15,X29,X14),X8) = c_Lambda_Osubst(c_Lambda_Osubst(X4,X15,X8),X29,X14)
      | ~ c_HOL_Oord__class_Oless(X8,c_HOL_Oplus__class_Oplus(X14,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat) ),
    file('<stdin>',cls_subst__subst_0) ).

fof(c_0_42_043,axiom,
    ! [X4,X5,X14,X8] :
      ( c_Lambda_Olift(c_Lambda_Osubst(X4,X5,X14),X8) = c_Lambda_Osubst(c_Lambda_Olift(X4,c_HOL_Oplus__class_Oplus(X8,c_HOL_Oone__class_Oone(tc_nat),tc_nat)),c_Lambda_Olift(X5,X8),X14)
      | ~ c_HOL_Oord__class_Oless(X14,c_HOL_Oplus__class_Oplus(X8,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat) ),
    file('<stdin>',cls_lift__subst_0) ).

fof(c_0_43_044,axiom,
    ! [X18] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X18)
      | c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X18),c_HOL_Ozero__class_Ozero(X18),X18),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X18),c_HOL_Ozero__class_Ozero(X18),X18),X18),c_HOL_Ozero__class_Ozero(X18),X18) ),
    file('<stdin>',cls_sum__squares__le__zero__iff_2) ).

fof(c_0_44_045,axiom,
    ! [X20,X37,X16,X38,X17,X18] :
      ( ~ class_Divides_Osemiring__div(X18)
      | c_Divides_Odiv__class_Omod(X16,X20,X18) != c_Divides_Odiv__class_Omod(X37,X20,X18)
      | c_Divides_Odiv__class_Omod(X17,X20,X18) != c_Divides_Odiv__class_Omod(X38,X20,X18)
      | c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X17,X16,X18),X20,X18) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X38,X37,X18),X20,X18) ),
    file('<stdin>',cls_mod__add__cong_0) ).

fof(c_0_45_046,axiom,
    ! [X20,X37,X16,X38,X17,X18] :
      ( ~ class_Divides_Osemiring__div(X18)
      | c_Divides_Odiv__class_Omod(X16,X20,X18) != c_Divides_Odiv__class_Omod(X37,X20,X18)
      | c_Divides_Odiv__class_Omod(X17,X20,X18) != c_Divides_Odiv__class_Omod(X38,X20,X18)
      | c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X17,X16,X18),X20,X18) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X38,X37,X18),X20,X18) ),
    file('<stdin>',cls_mod__mult__cong_0) ).

fof(c_0_46_047,axiom,
    ! [X20,X37,X16,X38,X17,X18] :
      ( ~ class_Divides_Oring__div(X18)
      | c_Divides_Odiv__class_Omod(X16,X20,X18) != c_Divides_Odiv__class_Omod(X37,X20,X18)
      | c_Divides_Odiv__class_Omod(X17,X20,X18) != c_Divides_Odiv__class_Omod(X38,X20,X18)
      | c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X17,X16,X18),X20,X18) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X38,X37,X18),X20,X18) ),
    file('<stdin>',cls_mod__diff__cong_0) ).

fof(c_0_47_048,axiom,
    ! [X21,X22,X24,X23,X18] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X18)
      | c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X23,X24,X18),c_HOL_Otimes__class_Otimes(X22,X21,X18),X18) = c_HOL_Otimes__class_Otimes(X23,c_HOL_Otimes__class_Otimes(X24,c_HOL_Otimes__class_Otimes(X22,X21,X18),X18),X18) ),
    file('<stdin>',cls_class__semiring_Osemiring__rules_I14_J_0) ).

fof(c_0_48_049,axiom,
    ! [X21,X22,X24,X23,X18] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X18)
      | c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X23,X24,X18),c_HOL_Otimes__class_Otimes(X22,X21,X18),X18) = c_HOL_Otimes__class_Otimes(X22,c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X23,X24,X18),X21,X18),X18) ),
    file('<stdin>',cls_class__semiring_Osemiring__rules_I15_J_0) ).

fof(c_0_49_050,axiom,
    ! [X27,X20,X16,X17,X18] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X18)
      | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X17,X20,X18),c_HOL_Otimes__class_Otimes(X16,X27,X18),X18)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X18),X20,X18)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X18),X16,X18)
      | ~ c_HOL_Oord__class_Oless(X20,X27,X18)
      | ~ c_HOL_Oord__class_Oless(X17,X16,X18) ),
    file('<stdin>',cls_mult__strict__mono_0) ).

fof(c_0_50_051,axiom,
    ! [X27,X20,X16,X17,X18] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X18)
      | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X17,X20,X18),c_HOL_Otimes__class_Otimes(X16,X27,X18),X18)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X18),X20,X18)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X18),X17,X18)
      | ~ c_lessequals(X20,X27,X18)
      | ~ c_HOL_Oord__class_Oless(X17,X16,X18) ),
    file('<stdin>',cls_mult__less__le__imp__less_0) ).

fof(c_0_51_052,axiom,
    ! [X27,X20,X16,X17,X18] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X18)
      | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X17,X20,X18),c_HOL_Otimes__class_Otimes(X16,X27,X18),X18)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X18),X20,X18)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X18),X17,X18)
      | ~ c_HOL_Oord__class_Oless(X20,X27,X18)
      | ~ c_lessequals(X17,X16,X18) ),
    file('<stdin>',cls_mult__le__less__imp__less_0) ).

fof(c_0_52_053,axiom,
    ! [X27,X20,X16,X17,X18] :
      ( ~ class_Ring__and__Field_Opordered__semiring(X18)
      | c_lessequals(c_HOL_Otimes__class_Otimes(X17,X20,X18),c_HOL_Otimes__class_Otimes(X16,X27,X18),X18)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X18),X20,X18)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X18),X16,X18)
      | ~ c_lessequals(X20,X27,X18)
      | ~ c_lessequals(X17,X16,X18) ),
    file('<stdin>',cls_mult__mono_0) ).

fof(c_0_53_054,axiom,
    ! [X27,X20,X16,X17,X18] :
      ( ~ class_Ring__and__Field_Opordered__semiring(X18)
      | c_lessequals(c_HOL_Otimes__class_Otimes(X17,X20,X18),c_HOL_Otimes__class_Otimes(X16,X27,X18),X18)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X18),X20,X18)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X18),X17,X18)
      | ~ c_lessequals(X20,X27,X18)
      | ~ c_lessequals(X17,X16,X18) ),
    file('<stdin>',cls_mult__mono_H_0) ).

fof(c_0_54_055,axiom,
    ! [X27,X20,X16,X17,X18] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X18)
      | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X17,X20,X18),c_HOL_Otimes__class_Otimes(X16,X27,X18),X18)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X18),X20,X18)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X18),X17,X18)
      | ~ c_HOL_Oord__class_Oless(X20,X27,X18)
      | ~ c_HOL_Oord__class_Oless(X17,X16,X18) ),
    file('<stdin>',cls_mult__strict__mono_H_0) ).

fof(c_0_55_056,axiom,
    ! [X1,X2,X7] :
      ( c_lessequals(X2,X1,tc_nat)
      | ~ c_lessequals(c_HOL_Ominus__class_Ominus(X2,X7,tc_nat),c_HOL_Ominus__class_Ominus(X1,X7,tc_nat),tc_nat)
      | ~ c_lessequals(X7,X1,tc_nat)
      | ~ c_lessequals(X7,X2,tc_nat) ),
    file('<stdin>',cls_le__diff__iff_0) ).

fof(c_0_56_057,axiom,
    ! [X1,X2,X7] :
      ( c_HOL_Oord__class_Oless(X2,X1,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X2,X7,tc_nat),c_HOL_Ominus__class_Ominus(X1,X7,tc_nat),tc_nat)
      | ~ c_lessequals(X7,X1,tc_nat)
      | ~ c_lessequals(X7,X2,tc_nat) ),
    file('<stdin>',cls_less__diff__iff_0) ).

fof(c_0_57_058,axiom,
    ! [X9,X3,X18] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X18)
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X18),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X3,X18),c_HOL_Otimes__class_Otimes(X9,X9,X18),X18),X18)
      | X3 = c_HOL_Ozero__class_Ozero(X18) ),
    file('<stdin>',cls_sum__squares__gt__zero__iff_1) ).

fof(c_0_58_059,axiom,
    ! [X9,X3,X18] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X18)
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X18),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X3,X18),c_HOL_Otimes__class_Otimes(X9,X9,X18),X18),X18)
      | X9 = c_HOL_Ozero__class_Ozero(X18) ),
    file('<stdin>',cls_sum__squares__gt__zero__iff_2) ).

fof(c_0_59_060,axiom,
    ! [X9,X3,X18] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X18)
      | c_lessequals(c_HOL_Ozero__class_Ozero(X18),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X3,X18),c_HOL_Otimes__class_Otimes(X9,X9,X18),X18),X18) ),
    file('<stdin>',cls_sum__squares__ge__zero_0) ).

fof(c_0_60_061,axiom,
    ! [X9,X31,X32,X3,X1] :
      ( c_HOL_Oplus__class_Oplus(X3,c_HOL_Otimes__class_Otimes(X1,X32,tc_nat),tc_nat) != c_HOL_Oplus__class_Oplus(X9,c_HOL_Otimes__class_Otimes(X1,X31,tc_nat),tc_nat)
      | c_Divides_Odiv__class_Omod(X3,X1,tc_nat) = c_Divides_Odiv__class_Omod(X9,X1,tc_nat) ),
    file('<stdin>',cls_nat__mod__eq__iff_1) ).

fof(c_0_61_062,axiom,
    ! [X4,X5,X14,X8] :
      ( c_Lambda_Olift(c_Lambda_Osubst(X4,X5,X14),X8) = c_Lambda_Osubst(c_Lambda_Olift(X4,X8),c_Lambda_Olift(X5,X8),c_HOL_Oplus__class_Oplus(X14,c_HOL_Oone__class_Oone(tc_nat),tc_nat))
      | ~ c_HOL_Oord__class_Oless(X8,c_HOL_Oplus__class_Oplus(X14,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat) ),
    file('<stdin>',cls_lift__subst__lt_0) ).

fof(c_0_62_063,axiom,
    ! [X20,X16,X17,X18] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X18)
      | c_HOL_Oord__class_Oless(X17,X16,X18)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X18),X20,X18)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X17,X20,X18),c_HOL_Otimes__class_Otimes(X16,X20,X18),X18) ),
    file('<stdin>',cls_mult__less__imp__less__right_0) ).

fof(c_0_63_064,axiom,
    ! [X20,X16,X17,X18] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X18)
      | c_HOL_Oord__class_Oless(X17,X16,X18)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X18),X20,X18)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X20,X17,X18),c_HOL_Otimes__class_Otimes(X20,X16,X18),X18) ),
    file('<stdin>',cls_mult__less__imp__less__left_0) ).

fof(c_0_64_065,axiom,
    ! [X20,X16,X17,X18] :
      ( ~ class_Ring__and__Field_Oordered__semiring(X18)
      | c_HOL_Oord__class_Oless(X17,X16,X18)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X18),X20,X18)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X17,X20,X18),c_HOL_Otimes__class_Otimes(X16,X20,X18),X18) ),
    file('<stdin>',cls_mult__right__less__imp__less_0) ).

fof(c_0_65_066,axiom,
    ! [X20,X16,X17,X18] :
      ( ~ class_Ring__and__Field_Oordered__semiring(X18)
      | c_HOL_Oord__class_Oless(X17,X16,X18)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X18),X20,X18)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X20,X17,X18),c_HOL_Otimes__class_Otimes(X20,X16,X18),X18) ),
    file('<stdin>',cls_mult__left__less__imp__less_0) ).

fof(c_0_66_067,axiom,
    ! [X20,X16,X17,X18] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X18)
      | c_lessequals(X16,X17,X18)
      | ~ c_lessequals(c_HOL_Otimes__class_Otimes(X20,X17,X18),c_HOL_Otimes__class_Otimes(X20,X16,X18),X18)
      | ~ c_HOL_Oord__class_Oless(X20,c_HOL_Ozero__class_Ozero(X18),X18) ),
    file('<stdin>',cls_mult__le__cancel__left__neg_0) ).

fof(c_0_67_068,axiom,
    ! [X20,X16,X17,X18] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X18)
      | c_lessequals(X17,X16,X18)
      | ~ c_lessequals(c_HOL_Otimes__class_Otimes(X20,X17,X18),c_HOL_Otimes__class_Otimes(X20,X16,X18),X18)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X18),X20,X18) ),
    file('<stdin>',cls_mult__le__cancel__left__pos_0) ).

fof(c_0_68_069,axiom,
    ! [X20,X16,X17,X18] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X18)
      | c_lessequals(X17,X16,X18)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X18),X20,X18)
      | ~ c_lessequals(c_HOL_Otimes__class_Otimes(X20,X17,X18),c_HOL_Otimes__class_Otimes(X20,X16,X18),X18) ),
    file('<stdin>',cls_mult__left__le__imp__le_0) ).

fof(c_0_69_070,axiom,
    ! [X20,X16,X17,X18] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X18)
      | c_lessequals(X17,X16,X18)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X18),X20,X18)
      | ~ c_lessequals(c_HOL_Otimes__class_Otimes(X17,X20,X18),c_HOL_Otimes__class_Otimes(X16,X20,X18),X18) ),
    file('<stdin>',cls_mult__right__le__imp__le_0) ).

fof(c_0_70_071,axiom,
    ! [X20,X16,X17,X18] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X18)
      | c_HOL_Oord__class_Oless(X16,X17,X18)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X20,X17,X18),c_HOL_Otimes__class_Otimes(X20,X16,X18),X18)
      | ~ c_HOL_Oord__class_Oless(X20,c_HOL_Ozero__class_Ozero(X18),X18) ),
    file('<stdin>',cls_mult__less__cancel__left__neg_0) ).

fof(c_0_71_072,axiom,
    ! [X20,X16,X17,X18] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X18)
      | c_HOL_Oord__class_Oless(X17,X16,X18)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X20,X17,X18),c_HOL_Otimes__class_Otimes(X20,X16,X18),X18)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X18),X20,X18) ),
    file('<stdin>',cls_mult__less__cancel__left__pos_0) ).

fof(c_0_72_073,axiom,
    ! [X1,X2,X7] :
      ( c_lessequals(X2,X1,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X7,tc_nat)
      | ~ c_lessequals(c_HOL_Otimes__class_Otimes(X2,X7,tc_nat),c_HOL_Otimes__class_Otimes(X1,X7,tc_nat),tc_nat) ),
    file('<stdin>',cls_mult__le__cancel2_0) ).

fof(c_0_73_074,axiom,
    ! [X1,X2,X7] :
      ( c_lessequals(X2,X1,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X7,tc_nat)
      | ~ c_lessequals(c_HOL_Otimes__class_Otimes(X7,X2,tc_nat),c_HOL_Otimes__class_Otimes(X7,X1,tc_nat),tc_nat) ),
    file('<stdin>',cls_mult__le__cancel1_0) ).

fof(c_0_74_075,axiom,
    ! [X1,X2,X7] :
      ( c_lessequals(X2,X1,tc_nat)
      | ~ c_lessequals(c_HOL_Otimes__class_Otimes(X7,X2,tc_nat),c_HOL_Otimes__class_Otimes(X7,X1,tc_nat),tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X7,tc_nat) ),
    file('<stdin>',cls_nat__mult__le__cancel1_0) ).

fof(c_0_75_076,axiom,
    ! [X1,X2,X7] :
      ( c_HOL_Oord__class_Oless(X2,X1,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X7,X2,tc_nat),c_HOL_Otimes__class_Otimes(X7,X1,tc_nat),tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X7,tc_nat) ),
    file('<stdin>',cls_nat__mult__less__cancel1_0) ).

fof(c_0_76_077,axiom,
    ! [X20,X16,X17,X18] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X18)
      | c_HOL_Oord__class_Oless(X20,c_HOL_Ozero__class_Ozero(X18),X18)
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X18),X20,X18)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X20,X17,X18),c_HOL_Otimes__class_Otimes(X20,X16,X18),X18) ),
    file('<stdin>',cls_mult__less__cancel__left__disj_0) ).

fof(c_0_77_078,axiom,
    ! [X20,X16,X17,X18] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X18)
      | c_HOL_Oord__class_Oless(X20,c_HOL_Ozero__class_Ozero(X18),X18)
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X18),X20,X18)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X17,X20,X18),c_HOL_Otimes__class_Otimes(X16,X20,X18),X18) ),
    file('<stdin>',cls_mult__less__cancel__right__disj_0) ).

fof(c_0_78_079,axiom,
    ! [X3,X27,X20,X18] :
      ( ~ class_Ring__and__Field_Oidom(X18)
      | ~ class_Int_Onumber__ring(X18)
      | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X20,X18),c_HOL_Otimes__class_Otimes(X3,X27,X18),X18) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X27,X18),c_HOL_Otimes__class_Otimes(X3,X20,X18),X18) ),
    file('<stdin>',cls_class__ringb_Onoteq__reduce_1) ).

fof(c_0_79_080,axiom,
    ! [X19,X9,X3,X18] :
      ( ~ class_Ring__and__Field_Oidom(X18)
      | ~ class_Int_Onumber__ring(X18)
      | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X9,X18),c_HOL_Otimes__class_Otimes(X3,X19,X18),X18) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X19,X18),c_HOL_Otimes__class_Otimes(X3,X9,X18),X18) ),
    file('<stdin>',cls_class__ringb_Oadd__mul__solve_1) ).

fof(c_0_80_081,axiom,
    ! [X20,X16,X17,X18] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X18)
      | c_HOL_Oord__class_Oless(X20,c_HOL_Ozero__class_Ozero(X18),X18)
      | c_HOL_Oord__class_Oless(X17,X16,X18)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X17,X20,X18),c_HOL_Otimes__class_Otimes(X16,X20,X18),X18) ),
    file('<stdin>',cls_mult__less__cancel__right__disj_2) ).

fof(c_0_81_082,axiom,
    ! [X20,X16,X17,X18] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X18)
      | c_HOL_Oord__class_Oless(X16,X17,X18)
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X18),X20,X18)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X17,X20,X18),c_HOL_Otimes__class_Otimes(X16,X20,X18),X18) ),
    file('<stdin>',cls_mult__less__cancel__right__disj_1) ).

fof(c_0_82_083,axiom,
    ! [X20,X16,X17,X18] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X18)
      | c_HOL_Oord__class_Oless(X20,c_HOL_Ozero__class_Ozero(X18),X18)
      | c_HOL_Oord__class_Oless(X17,X16,X18)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X20,X17,X18),c_HOL_Otimes__class_Otimes(X20,X16,X18),X18) ),
    file('<stdin>',cls_mult__less__cancel__left__disj_2) ).

fof(c_0_83_084,axiom,
    ! [X20,X16,X17,X18] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X18)
      | c_HOL_Oord__class_Oless(X16,X17,X18)
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X18),X20,X18)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X20,X17,X18),c_HOL_Otimes__class_Otimes(X20,X16,X18),X18) ),
    file('<stdin>',cls_mult__less__cancel__left__disj_1) ).

fof(c_0_84_085,axiom,
    ! [X20,X16,X17,X18] :
      ( ~ class_Divides_Osemiring__div(X18)
      | c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(X17,X20,X18),X16,X18),X20,X18) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X17,X16,X18),X20,X18) ),
    file('<stdin>',cls_zmod__simps_I4_J_0) ).

fof(c_0_85_086,axiom,
    ! [X20,X16,X17,X18] :
      ( ~ class_Divides_Oring__div(X18)
      | c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X17,X16,X18),X20,X18) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(c_Divides_Odiv__class_Omod(X17,X20,X18),X16,X18),X20,X18) ),
    file('<stdin>',cls_mod__diff__left__eq_0) ).

fof(c_0_86_087,axiom,
    ! [X20,X16,X17,X18] :
      ( ~ class_Divides_Oring__div(X18)
      | c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X17,X16,X18),X20,X18) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X17,c_Divides_Odiv__class_Omod(X16,X20,X18),X18),X20,X18) ),
    file('<stdin>',cls_mod__diff__right__eq_0) ).

fof(c_0_87_088,axiom,
    ! [X21,X22,X24,X23,X18] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X18)
      | c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X23,X24,X18),c_HOL_Otimes__class_Otimes(X22,X21,X18),X18) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X23,X22,X18),c_HOL_Otimes__class_Otimes(X24,X21,X18),X18) ),
    file('<stdin>',cls_class__semiring_Osemiring__rules_I13_J_0) ).

fof(c_0_88_089,axiom,
    ! [X20,X16,X17,X18] :
      ( ~ class_Divides_Osemiring__div(X18)
      | c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X17,X16,X18),X20,X18) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(X17,X20,X18),X16,X18),X20,X18) ),
    file('<stdin>',cls_mod__add__left__eq_0) ).

fof(c_0_89_090,axiom,
    ! [X20,X16,X17,X18] :
      ( ~ class_Divides_Osemiring__div(X18)
      | c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X17,X16,X18),X20,X18) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X17,c_Divides_Odiv__class_Omod(X16,X20,X18),X18),X20,X18) ),
    file('<stdin>',cls_mod__add__right__eq_0) ).

fof(c_0_90_091,axiom,
    ! [X20,X16,X17,X18] :
      ( ~ class_Divides_Osemiring__div(X18)
      | c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X17,X16,X18),X20,X18) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(X17,X20,X18),X16,X18),X20,X18) ),
    file('<stdin>',cls_mod__mult__left__eq_0) ).

fof(c_0_91_092,axiom,
    ! [X20,X16,X17,X18] :
      ( ~ class_Divides_Osemiring__div(X18)
      | c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X17,X16,X18),X20,X18) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X17,c_Divides_Odiv__class_Omod(X16,X20,X18),X18),X20,X18) ),
    file('<stdin>',cls_mod__mult__right__eq_0) ).

fof(c_0_92_093,axiom,
    ! [X27,X20,X16,X17,X18] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X18)
      | c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X17,X16,X18),c_HOL_Oplus__class_Oplus(X20,X27,X18),X18) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X17,X20,X18),c_HOL_Oplus__class_Oplus(X16,X27,X18),X18) ),
    file('<stdin>',cls_class__semiring_Osemiring__rules_I20_J_0) ).

fof(c_0_93_094,axiom,
    ! [X20,X16,X17,X18] :
      ( ~ class_Divides_Osemiring__div(X18)
      | c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(X17,X20,X18),X16,X18),X20,X18) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X17,X16,X18),X20,X18) ),
    file('<stdin>',cls_zmod__simps_I1_J_0) ).

fof(c_0_94_095,axiom,
    ! [X20,X16,X17,X18] :
      ( ~ class_Divides_Osemiring__div(X18)
      | c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X17,c_Divides_Odiv__class_Omod(X16,X20,X18),X18),X20,X18) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X17,X16,X18),X20,X18) ),
    file('<stdin>',cls_zmod__simps_I2_J_0) ).

fof(c_0_95_096,axiom,
    ! [X20,X16,X17,X18] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X18)
      | c_HOL_Oord__class_Oless(X16,X17,X18)
      | c_HOL_Oord__class_Oless(X17,X16,X18)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X20,X17,X18),c_HOL_Otimes__class_Otimes(X20,X16,X18),X18) ),
    file('<stdin>',cls_mult__less__cancel__left__disj_3) ).

fof(c_0_96_097,axiom,
    ! [X20,X16,X17,X18] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X18)
      | c_HOL_Oord__class_Oless(X16,X17,X18)
      | c_HOL_Oord__class_Oless(X17,X16,X18)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X17,X20,X18),c_HOL_Otimes__class_Otimes(X16,X20,X18),X18) ),
    file('<stdin>',cls_mult__less__cancel__right__disj_3) ).

fof(c_0_97_098,axiom,
    ! [X3,X6,X27,X20,X18] :
      ( ~ class_Ring__and__Field_Oidom(X18)
      | ~ class_Int_Onumber__ring(X18)
      | c_HOL_Oplus__class_Oplus(X3,c_HOL_Otimes__class_Otimes(X6,X20,X18),X18) != c_HOL_Oplus__class_Oplus(X3,c_HOL_Otimes__class_Otimes(X6,X27,X18),X18)
      | X20 = X27
      | X6 = c_HOL_Ozero__class_Ozero(X18) ),
    file('<stdin>',cls_class__ringb_Oadd__scale__eq__noteq_0) ).

fof(c_0_98_099,axiom,
    ! [X2,X7,X14] :
      ( c_HOL_Ominus__class_Ominus(c_Suc(c_HOL_Ominus__class_Ominus(X14,X7,tc_nat)),X2,tc_nat) = c_HOL_Ominus__class_Ominus(c_Suc(X14),c_HOL_Oplus__class_Oplus(X7,X2,tc_nat),tc_nat)
      | ~ c_lessequals(X7,X14,tc_nat) ),
    file('<stdin>',cls_diff__Suc__diff__eq2_0) ).

fof(c_0_99_100,axiom,
    ! [X2,X7,X14] :
      ( c_HOL_Ominus__class_Ominus(X2,c_Suc(c_HOL_Ominus__class_Ominus(X14,X7,tc_nat)),tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X2,X7,tc_nat),c_Suc(X14),tc_nat)
      | ~ c_lessequals(X7,X14,tc_nat) ),
    file('<stdin>',cls_diff__Suc__diff__eq1_0) ).

fof(c_0_100_101,axiom,
    ! [X1,X2,X7] :
      ( c_lessequals(c_HOL_Ominus__class_Ominus(X2,X7,tc_nat),c_HOL_Ominus__class_Ominus(X1,X7,tc_nat),tc_nat)
      | ~ c_lessequals(X2,X1,tc_nat)
      | ~ c_lessequals(X7,X1,tc_nat)
      | ~ c_lessequals(X7,X2,tc_nat) ),
    file('<stdin>',cls_le__diff__iff_1) ).

fof(c_0_101_102,axiom,
    ! [X1,X2,X7] :
      ( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X2,X7,tc_nat),c_HOL_Ominus__class_Ominus(X1,X7,tc_nat),tc_nat)
      | ~ c_HOL_Oord__class_Oless(X2,X1,tc_nat)
      | ~ c_lessequals(X7,X1,tc_nat)
      | ~ c_lessequals(X7,X2,tc_nat) ),
    file('<stdin>',cls_less__diff__iff_1) ).

fof(c_0_102_103,axiom,
    ! [X27,X20,X16,X17,X18] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add(X18)
      | c_lessequals(X17,c_HOL_Oplus__class_Oplus(X16,X27,X18),X18)
      | ~ c_lessequals(X20,X27,X18)
      | ~ c_lessequals(X17,c_HOL_Oplus__class_Oplus(X16,X20,X18),X18) ),
    file('<stdin>',cls_le__add__right__mono_0) ).

fof(c_0_103_104,axiom,
    ! [X1,X2,X7] :
      ( c_HOL_Oord__class_Oless(X2,X1,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Suc(X7),X2,tc_nat),c_HOL_Otimes__class_Otimes(c_Suc(X7),X1,tc_nat),tc_nat) ),
    file('<stdin>',cls_Suc__mult__less__cancel1_0) ).

fof(c_0_104_105,axiom,
    ! [X1,X2,X7] :
      ( c_lessequals(X2,X1,tc_nat)
      | ~ c_lessequals(c_HOL_Otimes__class_Otimes(c_Suc(X7),X2,tc_nat),c_HOL_Otimes__class_Otimes(c_Suc(X7),X1,tc_nat),tc_nat) ),
    file('<stdin>',cls_Suc__mult__le__cancel1_0) ).

fof(c_0_105_106,axiom,
    ! [X3,X6,X27,X20] :
      ( c_HOL_Oplus__class_Oplus(X3,c_HOL_Otimes__class_Otimes(X6,X20,tc_nat),tc_nat) != c_HOL_Oplus__class_Oplus(X3,c_HOL_Otimes__class_Otimes(X6,X27,tc_nat),tc_nat)
      | X20 = X27
      | X6 = c_HOL_Ozero__class_Ozero(tc_nat) ),
    file('<stdin>',cls_natgb_Oadd__scale__eq__noteq_0) ).

fof(c_0_106_107,axiom,
    ! [X7,X14,X8] :
      ( c_lessequals(X8,c_HOL_Ominus__class_Ominus(X14,X7,tc_nat),tc_nat)
      | ~ c_lessequals(c_HOL_Oplus__class_Oplus(X8,X7,tc_nat),X14,tc_nat)
      | ~ c_lessequals(X7,X14,tc_nat) ),
    file('<stdin>',cls_le__diff__conv2_1) ).

fof(c_0_107_108,axiom,
    ! [X7,X14,X8] :
      ( c_lessequals(c_HOL_Oplus__class_Oplus(X8,X7,tc_nat),X14,tc_nat)
      | ~ c_lessequals(X8,c_HOL_Ominus__class_Ominus(X14,X7,tc_nat),tc_nat)
      | ~ c_lessequals(X7,X14,tc_nat) ),
    file('<stdin>',cls_le__diff__conv2_0) ).

fof(c_0_108_109,axiom,
    ! [X20,X16,X17,X18] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X18)
      | c_lessequals(X17,X16,X18)
      | ~ c_lessequals(c_HOL_Oplus__class_Oplus(X17,X20,X18),c_HOL_Oplus__class_Oplus(X16,X20,X18),X18) ),
    file('<stdin>',cls_add__le__cancel__right_0) ).

fof(c_0_109_110,axiom,
    ! [X20,X16,X17,X18] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X18)
      | c_lessequals(X17,X16,X18)
      | ~ c_lessequals(c_HOL_Oplus__class_Oplus(X20,X17,X18),c_HOL_Oplus__class_Oplus(X20,X16,X18),X18) ),
    file('<stdin>',cls_add__le__cancel__left_0) ).

fof(c_0_110_111,axiom,
    ! [X20,X16,X17,X18] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X18)
      | c_HOL_Oord__class_Oless(X17,X16,X18)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X17,X20,X18),c_HOL_Oplus__class_Oplus(X16,X20,X18),X18) ),
    file('<stdin>',cls_add__less__cancel__right_0) ).

fof(c_0_111_112,axiom,
    ! [X20,X16,X17,X18] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X18)
      | c_HOL_Oord__class_Oless(X17,X16,X18)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X20,X17,X18),c_HOL_Oplus__class_Oplus(X20,X16,X18),X18) ),
    file('<stdin>',cls_add__less__cancel__left_0) ).

fof(c_0_112_113,axiom,
    ! [X1,X2,X7] :
      ( c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X2,X7,tc_nat),c_HOL_Ominus__class_Ominus(X1,X7,tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(X2,X1,tc_nat)
      | ~ c_lessequals(X7,X1,tc_nat)
      | ~ c_lessequals(X7,X2,tc_nat) ),
    file('<stdin>',cls_Nat_Odiff__diff__eq_0) ).

fof(c_0_113_114,axiom,
    ! [X1,X2,X7] :
      ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X7,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X7,tc_nat),c_HOL_Otimes__class_Otimes(X1,X7,tc_nat),tc_nat) ),
    file('<stdin>',cls_mult__less__cancel2_0) ).

fof(c_0_114_115,axiom,
    ! [X1,X2,X7] :
      ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X7,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X7,X2,tc_nat),c_HOL_Otimes__class_Otimes(X7,X1,tc_nat),tc_nat) ),
    file('<stdin>',cls_mult__less__cancel1_0) ).

fof(c_0_115_116,axiom,
    ! [X1,X2,X7] :
      ( c_lessequals(X2,X1,tc_nat)
      | ~ c_lessequals(c_HOL_Oplus__class_Oplus(X7,X2,tc_nat),c_HOL_Oplus__class_Oplus(X7,X1,tc_nat),tc_nat) ),
    file('<stdin>',cls_nat__add__left__cancel__le_0) ).

fof(c_0_116_117,axiom,
    ! [X1,X2,X7] :
      ( c_HOL_Oord__class_Oless(X2,X1,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X7,X2,tc_nat),c_HOL_Otimes__class_Otimes(X7,X1,tc_nat),tc_nat) ),
    file('<stdin>',cls_mult__less__cancel1_1) ).

fof(c_0_117_118,axiom,
    ! [X1,X2,X7] :
      ( c_HOL_Oord__class_Oless(X2,X1,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X7,tc_nat),c_HOL_Otimes__class_Otimes(X1,X7,tc_nat),tc_nat) ),
    file('<stdin>',cls_mult__less__cancel2_1) ).

fof(c_0_118_119,axiom,
    ! [X1,X2,X7] :
      ( c_HOL_Oord__class_Oless(X2,X1,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X7,X2,tc_nat),c_HOL_Oplus__class_Oplus(X7,X1,tc_nat),tc_nat) ),
    file('<stdin>',cls_nat__add__left__cancel__less_0) ).

fof(c_0_119_120,axiom,
    ! [X20,X16,X17,X18] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X18)
      | c_lessequals(c_HOL_Otimes__class_Otimes(X20,X17,X18),c_HOL_Otimes__class_Otimes(X20,X16,X18),X18)
      | ~ c_lessequals(X16,X17,X18)
      | ~ c_HOL_Oord__class_Oless(X20,c_HOL_Ozero__class_Ozero(X18),X18) ),
    file('<stdin>',cls_mult__le__cancel__left__neg_1) ).

fof(c_0_120_121,axiom,
    ! [X20,X16,X17,X18] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X18)
      | c_lessequals(c_HOL_Otimes__class_Otimes(X20,X17,X18),c_HOL_Otimes__class_Otimes(X20,X16,X18),X18)
      | ~ c_lessequals(X17,X16,X18)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X18),X20,X18) ),
    file('<stdin>',cls_mult__le__cancel__left__pos_1) ).

fof(c_0_121_122,axiom,
    ! [X20,X16,X17,X18] :
      ( ~ class_Ring__and__Field_Opordered__ring(X18)
      | c_lessequals(c_HOL_Otimes__class_Otimes(X17,X20,X18),c_HOL_Otimes__class_Otimes(X16,X20,X18),X18)
      | ~ c_lessequals(X20,c_HOL_Ozero__class_Ozero(X18),X18)
      | ~ c_lessequals(X16,X17,X18) ),
    file('<stdin>',cls_mult__right__mono__neg_0) ).

fof(c_0_122_123,axiom,
    ! [X20,X16,X17,X18] :
      ( ~ class_Ring__and__Field_Opordered__ring(X18)
      | c_lessequals(c_HOL_Otimes__class_Otimes(X20,X17,X18),c_HOL_Otimes__class_Otimes(X20,X16,X18),X18)
      | ~ c_lessequals(X20,c_HOL_Ozero__class_Ozero(X18),X18)
      | ~ c_lessequals(X16,X17,X18) ),
    file('<stdin>',cls_mult__left__mono__neg_0) ).

fof(c_0_123_124,axiom,
    ! [X20,X16,X17,X18] :
      ( ~ class_Ring__and__Field_Omult__mono(X18)
      | c_lessequals(c_HOL_Otimes__class_Otimes(X17,X20,X18),c_HOL_Otimes__class_Otimes(X16,X20,X18),X18)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X18),X20,X18)
      | ~ c_lessequals(X17,X16,X18) ),
    file('<stdin>',cls_mult__right__mono_0) ).

fof(c_0_124_125,axiom,
    ! [X20,X16,X17,X18] :
      ( ~ class_Ring__and__Field_Omult__mono(X18)
      | c_lessequals(c_HOL_Otimes__class_Otimes(X20,X17,X18),c_HOL_Otimes__class_Otimes(X20,X16,X18),X18)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X18),X20,X18)
      | ~ c_lessequals(X17,X16,X18) ),
    file('<stdin>',cls_mult__left__mono_0) ).

fof(c_0_125_126,axiom,
    ! [X20,X16,X17,X18] :
      ( ~ class_Ring__and__Field_Omult__mono1(X18)
      | c_lessequals(c_HOL_Otimes__class_Otimes(X20,X17,X18),c_HOL_Otimes__class_Otimes(X20,X16,X18),X18)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X18),X20,X18)
      | ~ c_lessequals(X17,X16,X18) ),
    file('<stdin>',cls_mult__mono1_0) ).

fof(c_0_126_127,axiom,
    ! [X20,X16,X17,X18] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X18)
      | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X20,X17,X18),c_HOL_Otimes__class_Otimes(X20,X16,X18),X18)
      | ~ c_HOL_Oord__class_Oless(X16,X17,X18)
      | ~ c_HOL_Oord__class_Oless(X20,c_HOL_Ozero__class_Ozero(X18),X18) ),
    file('<stdin>',cls_mult__less__cancel__left__neg_1) ).

fof(c_0_127_128,axiom,
    ! [X20,X16,X17,X18] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X18)
      | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X20,X17,X18),c_HOL_Otimes__class_Otimes(X20,X16,X18),X18)
      | ~ c_HOL_Oord__class_Oless(X17,X16,X18)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X18),X20,X18) ),
    file('<stdin>',cls_mult__less__cancel__left__pos_1) ).

fof(c_0_128_129,axiom,
    ! [X20,X16,X17,X18] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X18)
      | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X20,X17,X18),c_HOL_Otimes__class_Otimes(X20,X16,X18),X18)
      | ~ c_HOL_Oord__class_Oless(X20,c_HOL_Ozero__class_Ozero(X18),X18)
      | ~ c_HOL_Oord__class_Oless(X16,X17,X18) ),
    file('<stdin>',cls_mult__strict__left__mono__neg_0) ).

fof(c_0_129_130,axiom,
    ! [X20,X16,X17,X18] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X18)
      | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X20,X17,X18),c_HOL_Otimes__class_Otimes(X20,X16,X18),X18)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X18),X20,X18)
      | ~ c_HOL_Oord__class_Oless(X17,X16,X18) ),
    file('<stdin>',cls_mult__strict__left__mono_0) ).

fof(c_0_130_131,axiom,
    ! [X20,X16,X17,X18] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X18)
      | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X20,X17,X18),c_HOL_Otimes__class_Otimes(X20,X16,X18),X18)
      | ~ c_HOL_Oord__class_Oless(X17,X16,X18)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X18),X20,X18) ),
    file('<stdin>',cls_mult__less__cancel__left__disj_4) ).

fof(c_0_131_132,axiom,
    ! [X20,X16,X17,X18] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X18)
      | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X20,X17,X18),c_HOL_Otimes__class_Otimes(X20,X16,X18),X18)
      | ~ c_HOL_Oord__class_Oless(X16,X17,X18)
      | ~ c_HOL_Oord__class_Oless(X20,c_HOL_Ozero__class_Ozero(X18),X18) ),
    file('<stdin>',cls_mult__less__cancel__left__disj_5) ).

fof(c_0_132_133,axiom,
    ! [X20,X16,X17,X18] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X18)
      | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X17,X20,X18),c_HOL_Otimes__class_Otimes(X16,X20,X18),X18)
      | ~ c_HOL_Oord__class_Oless(X20,c_HOL_Ozero__class_Ozero(X18),X18)
      | ~ c_HOL_Oord__class_Oless(X16,X17,X18) ),
    file('<stdin>',cls_mult__strict__right__mono__neg_0) ).

fof(c_0_133_134,axiom,
    ! [X20,X16,X17,X18] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X18)
      | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X17,X20,X18),c_HOL_Otimes__class_Otimes(X16,X20,X18),X18)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X18),X20,X18)
      | ~ c_HOL_Oord__class_Oless(X17,X16,X18) ),
    file('<stdin>',cls_mult__strict__right__mono_0) ).

fof(c_0_134_135,axiom,
    ! [X20,X16,X17,X18] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X18)
      | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X17,X20,X18),c_HOL_Otimes__class_Otimes(X16,X20,X18),X18)
      | ~ c_HOL_Oord__class_Oless(X17,X16,X18)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X18),X20,X18) ),
    file('<stdin>',cls_mult__less__cancel__right__disj_4) ).

fof(c_0_135_136,axiom,
    ! [X20,X16,X17,X18] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X18)
      | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X17,X20,X18),c_HOL_Otimes__class_Otimes(X16,X20,X18),X18)
      | ~ c_HOL_Oord__class_Oless(X16,X17,X18)
      | ~ c_HOL_Oord__class_Oless(X20,c_HOL_Ozero__class_Ozero(X18),X18) ),
    file('<stdin>',cls_mult__less__cancel__right__disj_5) ).

fof(c_0_136_137,axiom,
    ! [X20,X16,X17,X18] :
      ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X18)
      | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X20,X17,X18),c_HOL_Otimes__class_Otimes(X20,X16,X18),X18)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X18),X20,X18)
      | ~ c_HOL_Oord__class_Oless(X17,X16,X18) ),
    file('<stdin>',cls_mult__strict__left__mono__comm_0) ).

fof(c_0_137_138,axiom,
    ! [X9,X3,X18] :
      ( ~ class_Ring__and__Field_Oordered__idom(X18)
      | c_lessequals(c_HOL_Otimes__class_Otimes(X3,X9,X18),X3,X18)
      | ~ c_lessequals(X9,c_HOL_Oone__class_Oone(X18),X18)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X18),X9,X18)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X18),X3,X18) ),
    file('<stdin>',cls_mult__right__le__one__le_0) ).

fof(c_0_138_139,axiom,
    ! [X9,X3,X18] :
      ( ~ class_Ring__and__Field_Oordered__idom(X18)
      | c_lessequals(c_HOL_Otimes__class_Otimes(X9,X3,X18),X3,X18)
      | ~ c_lessequals(X9,c_HOL_Oone__class_Oone(X18),X18)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X18),X9,X18)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X18),X3,X18) ),
    file('<stdin>',cls_mult__left__le__one__le_0) ).

fof(c_0_139_140,axiom,
    ! [X1,X2,X7] :
      ( c_lessequals(X2,c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),X7,tc_nat),tc_nat)
      | ~ c_lessequals(X7,X1,tc_nat) ),
    file('<stdin>',cls_le__add__diff_0) ).

fof(c_0_140_141,axiom,
    ! [X27,X20,X16,X17,X18] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X18)
      | c_lessequals(c_HOL_Oplus__class_Oplus(X17,X20,X18),c_HOL_Oplus__class_Oplus(X16,X27,X18),X18)
      | ~ c_lessequals(X20,X27,X18)
      | ~ c_lessequals(X17,X16,X18) ),
    file('<stdin>',cls_add__mono_0) ).

fof(c_0_141_142,axiom,
    ! [X27,X20,X16,X17,X18] :
      ( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X18)
      | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X17,X20,X18),c_HOL_Oplus__class_Oplus(X16,X27,X18),X18)
      | ~ c_HOL_Oord__class_Oless(X20,X27,X18)
      | ~ c_HOL_Oord__class_Oless(X17,X16,X18) ),
    file('<stdin>',cls_add__strict__mono_0) ).

fof(c_0_142_143,axiom,
    ! [X27,X20,X16,X17,X18] :
      ( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X18)
      | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X17,X20,X18),c_HOL_Oplus__class_Oplus(X16,X27,X18),X18)
      | ~ c_HOL_Oord__class_Oless(X20,X27,X18)
      | ~ c_lessequals(X17,X16,X18) ),
    file('<stdin>',cls_add__le__less__mono_0) ).

fof(c_0_143_144,axiom,
    ! [X27,X20,X16,X17,X18] :
      ( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X18)
      | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X17,X20,X18),c_HOL_Oplus__class_Oplus(X16,X27,X18),X18)
      | ~ c_lessequals(X20,X27,X18)
      | ~ c_HOL_Oord__class_Oless(X17,X16,X18) ),
    file('<stdin>',cls_add__less__le__mono_0) ).

fof(c_0_144_145,axiom,
    ! [X9,X3,X18] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X18)
      | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X3,X18),c_HOL_Otimes__class_Otimes(X9,X9,X18),X18) != c_HOL_Ozero__class_Ozero(X18)
      | X9 = c_HOL_Ozero__class_Ozero(X18) ),
    file('<stdin>',cls_sum__squares__eq__zero__iff_1) ).

fof(c_0_145_146,axiom,
    ! [X9,X3,X18] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X18)
      | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X3,X18),c_HOL_Otimes__class_Otimes(X9,X9,X18),X18) != c_HOL_Ozero__class_Ozero(X18)
      | X3 = c_HOL_Ozero__class_Ozero(X18) ),
    file('<stdin>',cls_sum__squares__eq__zero__iff_0) ).

fof(c_0_146_147,axiom,
    ! [X19,X9,X3,X18] :
      ( ~ class_Orderings_Olinorder(X18)
      | c_Orderings_Oord__class_Omin(c_Orderings_Oord__class_Omax(X9,X19,X18),X3,X18) = c_Orderings_Oord__class_Omax(c_Orderings_Oord__class_Omin(X9,X3,X18),c_Orderings_Oord__class_Omin(X19,X3,X18),X18) ),
    file('<stdin>',cls_min__max_Oinf__sup__distrib2_0) ).

fof(c_0_147_148,axiom,
    ! [X19,X9,X3,X18] :
      ( ~ class_Orderings_Olinorder(X18)
      | c_Orderings_Oord__class_Omin(X3,c_Orderings_Oord__class_Omax(X9,X19,X18),X18) = c_Orderings_Oord__class_Omax(c_Orderings_Oord__class_Omin(X3,X9,X18),c_Orderings_Oord__class_Omin(X3,X19,X18),X18) ),
    file('<stdin>',cls_min__max_Oinf__sup__distrib1_0) ).

fof(c_0_148_149,axiom,
    ! [X19,X9,X3,X18] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add(X18)
      | c_HOL_Ominus__class_Ominus(c_Orderings_Oord__class_Omin(X3,X9,X18),X19,X18) = c_Orderings_Oord__class_Omin(c_HOL_Ominus__class_Ominus(X3,X19,X18),c_HOL_Ominus__class_Ominus(X9,X19,X18),X18) ),
    file('<stdin>',cls_min__diff__distrib__left_0) ).

fof(c_0_149_150,axiom,
    ! [X19,X9,X3,X18] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add(X18)
      | c_HOL_Ominus__class_Ominus(c_Orderings_Oord__class_Omax(X3,X9,X18),X19,X18) = c_Orderings_Oord__class_Omax(c_HOL_Ominus__class_Ominus(X3,X19,X18),c_HOL_Ominus__class_Ominus(X9,X19,X18),X18) ),
    file('<stdin>',cls_max__diff__distrib__left_0) ).

fof(c_0_150_151,axiom,
    ! [X19,X9,X3,X18] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X18)
      | c_HOL_Oplus__class_Oplus(c_Orderings_Oord__class_Omin(X3,X9,X18),X19,X18) = c_Orderings_Oord__class_Omin(c_HOL_Oplus__class_Oplus(X3,X19,X18),c_HOL_Oplus__class_Oplus(X9,X19,X18),X18) ),
    file('<stdin>',cls_min__add__distrib__left_0) ).

fof(c_0_151_152,axiom,
    ! [X19,X9,X3,X18] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X18)
      | c_HOL_Oplus__class_Oplus(c_Orderings_Oord__class_Omax(X3,X9,X18),X19,X18) = c_Orderings_Oord__class_Omax(c_HOL_Oplus__class_Oplus(X3,X19,X18),c_HOL_Oplus__class_Oplus(X9,X19,X18),X18) ),
    file('<stdin>',cls_max__add__distrib__left_0) ).

fof(c_0_152_153,axiom,
    ! [X20,X16,X17,X18] :
      ( ~ class_Divides_Osemiring__div(X18)
      | c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X17,c_HOL_Otimes__class_Otimes(X20,X16,X18),X18),X16,X18) = c_Divides_Odiv__class_Omod(X17,X16,X18) ),
    file('<stdin>',cls_mod__mult__self1_0) ).

fof(c_0_153_154,axiom,
    ! [X20,X16,X17,X18] :
      ( ~ class_Divides_Osemiring__div(X18)
      | c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X17,c_HOL_Otimes__class_Otimes(X16,X20,X18),X18),X16,X18) = c_Divides_Odiv__class_Omod(X17,X16,X18) ),
    file('<stdin>',cls_mod__mult__self2_0) ).

fof(c_0_154_155,axiom,
    ! [X2,X16,X17,X18] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X18)
      | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X17,X2,X18),c_HOL_Otimes__class_Otimes(X16,X2,X18),X18) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X17,X16,X18),X2,X18) ),
    file('<stdin>',cls_class__semiring_Osemiring__rules_I1_J_0) ).

fof(c_0_155_156,axiom,
    ! [X19,X9,X3,X18] :
      ( ~ class_Orderings_Olinorder(X18)
      | c_Orderings_Oord__class_Omax(c_Orderings_Oord__class_Omin(X9,X19,X18),X3,X18) = c_Orderings_Oord__class_Omin(c_Orderings_Oord__class_Omax(X9,X3,X18),c_Orderings_Oord__class_Omax(X19,X3,X18),X18) ),
    file('<stdin>',cls_min__max_Osup__inf__distrib2_0) ).

fof(c_0_156_157,axiom,
    ! [X19,X9,X3,X18] :
      ( ~ class_Orderings_Olinorder(X18)
      | c_Orderings_Oord__class_Omax(X3,c_Orderings_Oord__class_Omin(X9,X19,X18),X18) = c_Orderings_Oord__class_Omin(c_Orderings_Oord__class_Omax(X3,X9,X18),c_Orderings_Oord__class_Omax(X3,X19,X18),X18) ),
    file('<stdin>',cls_min__max_Osup__inf__distrib1_0) ).

fof(c_0_157_158,axiom,
    ! [X20,X16,X17,X18] :
      ( ~ class_Divides_Osemiring__div(X18)
      | c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X17,X20,X18),c_HOL_Otimes__class_Otimes(X16,X20,X18),X18) = c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(X17,X16,X18),X20,X18) ),
    file('<stdin>',cls_mod__mult__mult2_0) ).

fof(c_0_158_159,axiom,
    ! [X20,X16,X17,X18] :
      ( ~ class_Divides_Osemiring__div(X18)
      | c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X20,X17,X18),c_HOL_Otimes__class_Otimes(X20,X16,X18),X18) = c_HOL_Otimes__class_Otimes(X20,c_Divides_Odiv__class_Omod(X17,X16,X18),X18) ),
    file('<stdin>',cls_mod__mult__mult1_0) ).

fof(c_0_159_160,axiom,
    ! [X20,X16,X17,X18] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X18)
      | c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X17,X16,X18),X20,X18) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X17,X20,X18),c_HOL_Otimes__class_Otimes(X16,X20,X18),X18) ),
    file('<stdin>',cls_class__semiring_Osemiring__rules_I8_J_0) ).

fof(c_0_160_161,axiom,
    ! [X20,X16,X17,X18] :
      ( ~ class_Ring__and__Field_Ocomm__semiring(X18)
      | c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X17,X16,X18),X20,X18) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X17,X20,X18),c_HOL_Otimes__class_Otimes(X16,X20,X18),X18) ),
    file('<stdin>',cls_comm__semiring__class_Odistrib_0) ).

fof(c_0_161_162,axiom,
    ! [X19,X9,X3,X18] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X18)
      | c_HOL_Otimes__class_Otimes(X3,c_HOL_Oplus__class_Oplus(X9,X19,X18),X18) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X9,X18),c_HOL_Otimes__class_Otimes(X3,X19,X18),X18) ),
    file('<stdin>',cls_class__semiring_Omul__d_0) ).

fof(c_0_162_163,axiom,
    ! [X1,X2,X7] :
      ( c_lessequals(c_HOL_Otimes__class_Otimes(X7,X2,tc_nat),c_HOL_Otimes__class_Otimes(X7,X1,tc_nat),tc_nat)
      | ~ c_lessequals(X2,X1,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X7,tc_nat) ),
    file('<stdin>',cls_nat__mult__le__cancel1_1) ).

fof(c_0_163_164,axiom,
    ! [X1,X2,X7] :
      ( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X7,tc_nat),c_HOL_Otimes__class_Otimes(X1,X7,tc_nat),tc_nat)
      | ~ c_HOL_Oord__class_Oless(X2,X1,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X7,tc_nat) ),
    file('<stdin>',cls_mult__less__cancel2_2) ).

fof(c_0_164_165,axiom,
    ! [X1,X2,X7] :
      ( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X7,X2,tc_nat),c_HOL_Otimes__class_Otimes(X7,X1,tc_nat),tc_nat)
      | ~ c_HOL_Oord__class_Oless(X2,X1,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X7,tc_nat) ),
    file('<stdin>',cls_mult__less__cancel1_2) ).

fof(c_0_165_166,axiom,
    ! [X7,X14,X8] :
      ( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X7,X8,tc_nat),c_HOL_Otimes__class_Otimes(X7,X14,tc_nat),tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X7,tc_nat)
      | ~ c_HOL_Oord__class_Oless(X8,X14,tc_nat) ),
    file('<stdin>',cls_mult__less__mono2_0) ).

fof(c_0_166_167,axiom,
    ! [X7,X14,X8] :
      ( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X8,X7,tc_nat),c_HOL_Otimes__class_Otimes(X14,X7,tc_nat),tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X7,tc_nat)
      | ~ c_HOL_Oord__class_Oless(X8,X14,tc_nat) ),
    file('<stdin>',cls_mult__less__mono1_0) ).

fof(c_0_167_168,axiom,
    ! [X1,X2,X7] :
      ( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X7,X2,tc_nat),c_HOL_Otimes__class_Otimes(X7,X1,tc_nat),tc_nat)
      | ~ c_HOL_Oord__class_Oless(X2,X1,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X7,tc_nat) ),
    file('<stdin>',cls_nat__mult__less__cancel1_1) ).

fof(c_0_168_169,axiom,
    ! [X1,X2] :
      ( c_HOL_Otimes__class_Otimes(X2,X1,tc_nat) = c_HOL_Oplus__class_Oplus(X1,c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X1,tc_nat),tc_nat)
      | X2 = c_HOL_Ozero__class_Ozero(tc_nat) ),
    file('<stdin>',cls_mult__eq__if_1) ).

fof(c_0_169_170,axiom,
    ! [X1,X2,X28] :
      ( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X28,X1,tc_nat),c_HOL_Ominus__class_Ominus(X28,X2,tc_nat),tc_nat)
      | ~ c_HOL_Oord__class_Oless(X2,X28,tc_nat)
      | ~ c_HOL_Oord__class_Oless(X2,X1,tc_nat) ),
    file('<stdin>',cls_diff__less__mono2_0) ).

fof(c_0_170_171,axiom,
    ! [X28,X7,X14,X8] :
      ( c_lessequals(c_HOL_Oplus__class_Oplus(X8,X7,tc_nat),c_HOL_Oplus__class_Oplus(X14,X28,tc_nat),tc_nat)
      | ~ c_lessequals(X7,X28,tc_nat)
      | ~ c_lessequals(X8,X14,tc_nat) ),
    file('<stdin>',cls_add__le__mono_0) ).

fof(c_0_171_172,axiom,
    ! [X20,X16,X17] :
      ( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X17,X20,tc_nat),c_HOL_Ominus__class_Ominus(X16,X20,tc_nat),tc_nat)
      | ~ c_lessequals(X20,X17,tc_nat)
      | ~ c_HOL_Oord__class_Oless(X17,X16,tc_nat) ),
    file('<stdin>',cls_diff__less__mono_0) ).

fof(c_0_172_173,axiom,
    ! [X28,X7,X14,X8] :
      ( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X8,X7,tc_nat),c_HOL_Oplus__class_Oplus(X14,X28,tc_nat),tc_nat)
      | ~ c_HOL_Oord__class_Oless(X7,X28,tc_nat)
      | ~ c_HOL_Oord__class_Oless(X8,X14,tc_nat) ),
    file('<stdin>',cls_add__less__mono_0) ).

fof(c_0_173_174,axiom,
    ! [X28,X7,X14,X8] :
      ( c_lessequals(c_HOL_Otimes__class_Otimes(X8,X7,tc_nat),c_HOL_Otimes__class_Otimes(X14,X28,tc_nat),tc_nat)
      | ~ c_lessequals(X7,X28,tc_nat)
      | ~ c_lessequals(X8,X14,tc_nat) ),
    file('<stdin>',cls_mult__le__mono_0) ).

fof(c_0_174_175,axiom,
    ! [X16,X17,X18] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X18)
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X18),X16,X18)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X18),X17,X18)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X18),c_HOL_Otimes__class_Otimes(X16,X17,X18),X18) ),
    file('<stdin>',cls_zero__less__mult__pos2_0) ).

fof(c_0_175_176,axiom,
    ! [X16,X17,X18] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X18)
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X18),X16,X18)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X18),X17,X18)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X18),c_HOL_Otimes__class_Otimes(X17,X16,X18),X18) ),
    file('<stdin>',cls_zero__less__mult__pos_0) ).

fof(c_0_176_177,axiom,
    ! [X7,X8] :
      ( ~ c_lessequals(X8,c_HOL_Oplus__class_Oplus(X7,X8,tc_nat),tc_nat)
      | c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X7,X8,tc_nat),X8,tc_nat) = X7 ),
    file('<stdin>',cls_le__imp__diff__is__add_1) ).

fof(c_0_177_178,axiom,
    ! [X7,X14,X8] :
      ( c_lessequals(X14,c_HOL_Oplus__class_Oplus(X8,X7,tc_nat),tc_nat)
      | ~ c_lessequals(c_HOL_Ominus__class_Ominus(X14,X7,tc_nat),X8,tc_nat) ),
    file('<stdin>',cls_le__diff__conv_0) ).

fof(c_0_178_179,axiom,
    ! [X7,X14,X8] :
      ( c_lessequals(c_HOL_Ominus__class_Ominus(X14,X7,tc_nat),X8,tc_nat)
      | ~ c_lessequals(X14,c_HOL_Oplus__class_Oplus(X8,X7,tc_nat),tc_nat) ),
    file('<stdin>',cls_le__diff__conv_1) ).

fof(c_0_179_180,axiom,
    ! [X7,X14,X8] :
      ( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X8,X7,tc_nat),X14,tc_nat)
      | ~ c_HOL_Oord__class_Oless(X8,c_HOL_Ominus__class_Ominus(X14,X7,tc_nat),tc_nat) ),
    file('<stdin>',cls_less__diff__conv_0) ).

fof(c_0_180_181,axiom,
    ! [X7,X14,X8] :
      ( c_HOL_Oord__class_Oless(X8,c_HOL_Ominus__class_Ominus(X14,X7,tc_nat),tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X8,X7,tc_nat),X14,tc_nat) ),
    file('<stdin>',cls_less__diff__conv_1) ).

fof(c_0_181_182,axiom,
    ! [X19,X9,X3,X15,X18] :
      ( ~ class_OrderedGroup_Oab__group__add(X18)
      | c_HOL_Oplus__class_Oplus(X3,c_HOL_Oplus__class_Oplus(X9,X19,X18),X18) != c_HOL_Oplus__class_Oplus(X9,X15,X18)
      | c_HOL_Oplus__class_Oplus(X3,X19,X18) = X15 ),
    file('<stdin>',cls_add__cancel__21_0) ).

fof(c_0_182_183,axiom,
    ! [X7,X14,X8] :
      ( c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X8,X14,tc_nat),X7,tc_nat) = c_HOL_Oplus__class_Oplus(X8,c_HOL_Ominus__class_Ominus(X14,X7,tc_nat),tc_nat)
      | ~ c_lessequals(X7,X14,tc_nat) ),
    file('<stdin>',cls_diff__add__assoc_0) ).

fof(c_0_183_184,axiom,
    ! [X7,X14,X8] :
      ( c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X14,X8,tc_nat),X7,tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X14,X7,tc_nat),X8,tc_nat)
      | ~ c_lessequals(X7,X14,tc_nat) ),
    file('<stdin>',cls_diff__add__assoc2_0) ).

fof(c_0_184_185,axiom,
    ! [X7,X14,X8] :
      ( c_HOL_Ominus__class_Ominus(X8,c_HOL_Ominus__class_Ominus(X14,X7,tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X8,X7,tc_nat),X14,tc_nat)
      | ~ c_lessequals(X7,X14,tc_nat) ),
    file('<stdin>',cls_diff__diff__right_0) ).

fof(c_0_185_186,axiom,
    ! [X7,X14,X8] :
      ( c_HOL_Oplus__class_Oplus(X8,c_HOL_Ominus__class_Ominus(X14,X7,tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X8,X14,tc_nat),X7,tc_nat)
      | ~ c_lessequals(X7,X14,tc_nat) ),
    file('<stdin>',cls_add__diff__assoc_0) ).

fof(c_0_186_187,axiom,
    ! [X7,X14,X8] :
      ( c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X14,X7,tc_nat),X8,tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X14,X8,tc_nat),X7,tc_nat)
      | ~ c_lessequals(X7,X14,tc_nat) ),
    file('<stdin>',cls_add__diff__assoc2_0) ).

fof(c_0_187_188,axiom,
    ! [X16,X17,X18] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X18)
      | c_lessequals(c_HOL_Ozero__class_Ozero(X18),X16,X18)
      | c_lessequals(X16,c_HOL_Ozero__class_Ozero(X18),X18)
      | ~ c_lessequals(c_HOL_Otimes__class_Otimes(X17,X16,X18),c_HOL_Ozero__class_Ozero(X18),X18) ),
    file('<stdin>',cls_mult__le__0__iff_3) ).

fof(c_0_188_189,axiom,
    ! [X16,X17,X18] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X18)
      | c_lessequals(X17,c_HOL_Ozero__class_Ozero(X18),X18)
      | c_lessequals(X16,c_HOL_Ozero__class_Ozero(X18),X18)
      | ~ c_lessequals(c_HOL_Otimes__class_Otimes(X17,X16,X18),c_HOL_Ozero__class_Ozero(X18),X18) ),
    file('<stdin>',cls_mult__le__0__iff_2) ).

fof(c_0_189_190,axiom,
    ! [X16,X17,X18] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X18)
      | c_lessequals(c_HOL_Ozero__class_Ozero(X18),X16,X18)
      | c_lessequals(c_HOL_Ozero__class_Ozero(X18),X17,X18)
      | ~ c_lessequals(c_HOL_Otimes__class_Otimes(X17,X16,X18),c_HOL_Ozero__class_Ozero(X18),X18) ),
    file('<stdin>',cls_mult__le__0__iff_1) ).

fof(c_0_190_191,axiom,
    ! [X16,X17,X18] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X18)
      | c_lessequals(X17,c_HOL_Ozero__class_Ozero(X18),X18)
      | c_lessequals(c_HOL_Ozero__class_Ozero(X18),X17,X18)
      | ~ c_lessequals(c_HOL_Otimes__class_Otimes(X17,X16,X18),c_HOL_Ozero__class_Ozero(X18),X18) ),
    file('<stdin>',cls_mult__le__0__iff_0) ).

fof(c_0_191_192,axiom,
    ! [X16,X17,X18] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X18)
      | c_lessequals(X17,c_HOL_Ozero__class_Ozero(X18),X18)
      | c_lessequals(c_HOL_Ozero__class_Ozero(X18),X17,X18)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X18),c_HOL_Otimes__class_Otimes(X17,X16,X18),X18) ),
    file('<stdin>',cls_zero__le__mult__iff_0) ).

fof(c_0_192_193,axiom,
    ! [X16,X17,X18] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X18)
      | c_lessequals(X16,c_HOL_Ozero__class_Ozero(X18),X18)
      | c_lessequals(c_HOL_Ozero__class_Ozero(X18),X17,X18)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X18),c_HOL_Otimes__class_Otimes(X17,X16,X18),X18) ),
    file('<stdin>',cls_zero__le__mult__iff_1) ).

fof(c_0_193_194,axiom,
    ! [X16,X17,X18] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X18)
      | c_lessequals(X17,c_HOL_Ozero__class_Ozero(X18),X18)
      | c_lessequals(c_HOL_Ozero__class_Ozero(X18),X16,X18)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X18),c_HOL_Otimes__class_Otimes(X17,X16,X18),X18) ),
    file('<stdin>',cls_zero__le__mult__iff_2) ).

fof(c_0_194_195,axiom,
    ! [X16,X17,X18] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X18)
      | c_lessequals(X16,c_HOL_Ozero__class_Ozero(X18),X18)
      | c_lessequals(c_HOL_Ozero__class_Ozero(X18),X16,X18)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X18),c_HOL_Otimes__class_Otimes(X17,X16,X18),X18) ),
    file('<stdin>',cls_zero__le__mult__iff_3) ).

fof(c_0_195_196,axiom,
    ! [X1,X2] :
      ( c_HOL_Oplus__class_Oplus(X2,X1,tc_nat) = c_Suc(c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X2,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X1,tc_nat))
      | X2 = c_HOL_Ozero__class_Ozero(tc_nat) ),
    file('<stdin>',cls_add__eq__if_1) ).

fof(c_0_196_197,axiom,
    ! [X1,X2] :
      ( 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)
      | ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X1,tc_nat) ),
    file('<stdin>',cls_one__less__mult_0) ).

fof(c_0_197_198,axiom,
    ! [X1,X2] :
      ( c_lessequals(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Otimes__class_Otimes(X2,X1,tc_nat),tc_nat)
      | ~ c_lessequals(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X1,tc_nat)
      | ~ c_lessequals(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X2,tc_nat) ),
    file('<stdin>',cls_one__le__mult__iff_2) ).

fof(c_0_198_199,axiom,
    ! [X19,X9,X3,X18] :
      ( ~ class_Orderings_Olinorder(X18)
      | c_lessequals(X19,X9,X18)
      | c_lessequals(X19,X3,X18)
      | ~ c_lessequals(X19,c_Orderings_Oord__class_Omax(X3,X9,X18),X18) ),
    file('<stdin>',cls_le__max__iff__disj_0) ).

fof(c_0_199_200,axiom,
    ! [X19,X9,X3,X18] :
      ( ~ class_Orderings_Olinorder(X18)
      | c_lessequals(X9,X19,X18)
      | c_lessequals(X3,X19,X18)
      | ~ c_lessequals(c_Orderings_Oord__class_Omin(X3,X9,X18),X19,X18) ),
    file('<stdin>',cls_min__le__iff__disj_0) ).

fof(c_0_200_201,axiom,
    ! [X19,X9,X3,X18] :
      ( ~ class_Orderings_Olinorder(X18)
      | c_HOL_Oord__class_Oless(X19,X9,X18)
      | c_HOL_Oord__class_Oless(X19,X3,X18)
      | ~ c_HOL_Oord__class_Oless(X19,c_Orderings_Oord__class_Omax(X3,X9,X18),X18) ),
    file('<stdin>',cls_less__max__iff__disj_0) ).

fof(c_0_201_202,axiom,
    ! [X19,X9,X3,X18] :
      ( ~ class_Orderings_Olinorder(X18)
      | c_HOL_Oord__class_Oless(X9,X19,X18)
      | c_HOL_Oord__class_Oless(X3,X19,X18)
      | ~ c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omin(X3,X9,X18),X19,X18) ),
    file('<stdin>',cls_min__less__iff__disj_0) ).

fof(c_0_202_203,axiom,
    ! [X1,X2,X7] :
      ( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Suc(X7),X2,tc_nat),c_HOL_Otimes__class_Otimes(c_Suc(X7),X1,tc_nat),tc_nat)
      | ~ c_HOL_Oord__class_Oless(X2,X1,tc_nat) ),
    file('<stdin>',cls_Suc__mult__less__cancel1_1) ).

fof(c_0_203_204,axiom,
    ! [X1,X2,X7] :
      ( c_lessequals(c_HOL_Otimes__class_Otimes(c_Suc(X7),X2,tc_nat),c_HOL_Otimes__class_Otimes(c_Suc(X7),X1,tc_nat),tc_nat)
      | ~ c_lessequals(X2,X1,tc_nat) ),
    file('<stdin>',cls_Suc__mult__le__cancel1_1) ).

fof(c_0_204_205,axiom,
    ! [X16,X17,X18] :
      ( ~ class_OrderedGroup_Opordered__comm__monoid__add(X18)
      | c_lessequals(c_HOL_Ozero__class_Ozero(X18),c_HOL_Oplus__class_Oplus(X17,X16,X18),X18)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X18),X16,X18)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X18),X17,X18) ),
    file('<stdin>',cls_add__nonneg__nonneg_0) ).

fof(c_0_205_206,axiom,
    ! [X16,X17,X18] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X18)
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X18),c_HOL_Otimes__class_Otimes(X17,X16,X18),X18)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X18),X16,X18)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X18),X17,X18) ),
    file('<stdin>',cls_mult__pos__pos_0) ).

fof(c_0_206_207,axiom,
    ! [X16,X17,X18] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X18)
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X18),c_HOL_Otimes__class_Otimes(X17,X16,X18),X18)
      | ~ c_HOL_Oord__class_Oless(X16,c_HOL_Ozero__class_Ozero(X18),X18)
      | ~ c_HOL_Oord__class_Oless(X17,c_HOL_Ozero__class_Ozero(X18),X18) ),
    file('<stdin>',cls_mult__neg__neg_0) ).

fof(c_0_207_208,axiom,
    ! [X16,X17,X18] :
      ( ~ class_OrderedGroup_Opordered__comm__monoid__add(X18)
      | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X17,X16,X18),c_HOL_Ozero__class_Ozero(X18),X18)
      | ~ c_HOL_Oord__class_Oless(X16,c_HOL_Ozero__class_Ozero(X18),X18)
      | ~ c_lessequals(X17,c_HOL_Ozero__class_Ozero(X18),X18) ),
    file('<stdin>',cls_add__nonpos__neg_0) ).

fof(c_0_208_209,axiom,
    ! [X16,X17,X18] :
      ( ~ class_OrderedGroup_Opordered__comm__monoid__add(X18)
      | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X17,X16,X18),c_HOL_Ozero__class_Ozero(X18),X18)
      | ~ c_lessequals(X16,c_HOL_Ozero__class_Ozero(X18),X18)
      | ~ c_HOL_Oord__class_Oless(X17,c_HOL_Ozero__class_Ozero(X18),X18) ),
    file('<stdin>',cls_add__neg__nonpos_0) ).

fof(c_0_209_210,axiom,
    ! [X16,X17,X18] :
      ( ~ class_OrderedGroup_Opordered__comm__monoid__add(X18)
      | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X17,X16,X18),c_HOL_Ozero__class_Ozero(X18),X18)
      | ~ c_HOL_Oord__class_Oless(X16,c_HOL_Ozero__class_Ozero(X18),X18)
      | ~ c_HOL_Oord__class_Oless(X17,c_HOL_Ozero__class_Ozero(X18),X18) ),
    file('<stdin>',cls_add__neg__neg_0) ).

fof(c_0_210_211,axiom,
    ! [X16,X17,X18] :
      ( ~ class_OrderedGroup_Opordered__comm__monoid__add(X18)
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X18),c_HOL_Oplus__class_Oplus(X17,X16,X18),X18)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X18),X16,X18)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X18),X17,X18) ),
    file('<stdin>',cls_add__nonneg__pos_0) ).

fof(c_0_211_212,axiom,
    ! [X16,X17,X18] :
      ( ~ class_OrderedGroup_Opordered__comm__monoid__add(X18)
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X18),c_HOL_Oplus__class_Oplus(X17,X16,X18),X18)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X18),X16,X18)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X18),X17,X18) ),
    file('<stdin>',cls_add__pos__nonneg_0) ).

fof(c_0_212_213,axiom,
    ! [X16,X17,X18] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X18)
      | c_lessequals(c_HOL_Otimes__class_Otimes(X17,X16,X18),c_HOL_Ozero__class_Ozero(X18),X18)
      | ~ c_lessequals(X16,c_HOL_Ozero__class_Ozero(X18),X18)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X18),X17,X18) ),
    file('<stdin>',cls_mult__le__0__iff_4) ).

fof(c_0_213_214,axiom,
    ! [X16,X17,X18] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X18)
      | c_lessequals(c_HOL_Otimes__class_Otimes(X17,X16,X18),c_HOL_Ozero__class_Ozero(X18),X18)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X18),X16,X18)
      | ~ c_lessequals(X17,c_HOL_Ozero__class_Ozero(X18),X18) ),
    file('<stdin>',cls_mult__le__0__iff_5) ).

fof(c_0_214_215,axiom,
    ! [X16,X17,X18] :
      ( ~ class_Ring__and__Field_Opordered__cancel__semiring(X18)
      | c_lessequals(c_HOL_Otimes__class_Otimes(X17,X16,X18),c_HOL_Ozero__class_Ozero(X18),X18)
      | ~ c_lessequals(X16,c_HOL_Ozero__class_Ozero(X18),X18)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X18),X17,X18) ),
    file('<stdin>',cls_split__mult__neg__le_0) ).

fof(c_0_215_216,axiom,
    ! [X16,X17,X18] :
      ( ~ class_Ring__and__Field_Opordered__cancel__semiring(X18)
      | c_lessequals(c_HOL_Otimes__class_Otimes(X17,X16,X18),c_HOL_Ozero__class_Ozero(X18),X18)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X18),X16,X18)
      | ~ c_lessequals(X17,c_HOL_Ozero__class_Ozero(X18),X18) ),
    file('<stdin>',cls_split__mult__neg__le_1) ).

fof(c_0_216_217,axiom,
    ! [X16,X17,X18] :
      ( ~ class_Ring__and__Field_Opordered__cancel__semiring(X18)
      | c_lessequals(c_HOL_Otimes__class_Otimes(X17,X16,X18),c_HOL_Ozero__class_Ozero(X18),X18)
      | ~ c_lessequals(X16,c_HOL_Ozero__class_Ozero(X18),X18)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X18),X17,X18) ),
    file('<stdin>',cls_mult__nonneg__nonpos_0) ).

fof(c_0_217_218,axiom,
    ! [X16,X17,X18] :
      ( ~ class_Ring__and__Field_Opordered__cancel__semiring(X18)
      | c_lessequals(c_HOL_Otimes__class_Otimes(X17,X16,X18),c_HOL_Ozero__class_Ozero(X18),X18)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X18),X16,X18)
      | ~ c_lessequals(X17,c_HOL_Ozero__class_Ozero(X18),X18) ),
    file('<stdin>',cls_mult__nonpos__nonneg_0) ).

fof(c_0_218_219,axiom,
    ! [X16,X17,X18] :
      ( ~ class_Ring__and__Field_Opordered__cancel__semiring(X18)
      | c_lessequals(c_HOL_Otimes__class_Otimes(X16,X17,X18),c_HOL_Ozero__class_Ozero(X18),X18)
      | ~ c_lessequals(X16,c_HOL_Ozero__class_Ozero(X18),X18)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X18),X17,X18) ),
    file('<stdin>',cls_mult__nonneg__nonpos2_0) ).

fof(c_0_219_220,axiom,
    ! [X16,X17,X18] :
      ( ~ class_OrderedGroup_Opordered__comm__monoid__add(X18)
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X18),c_HOL_Oplus__class_Oplus(X17,X16,X18),X18)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X18),X16,X18)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X18),X17,X18) ),
    file('<stdin>',cls_add__pos__pos_0) ).

fof(c_0_220_221,axiom,
    ! [X16,X17,X18] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X18)
      | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X16,X17,X18),c_HOL_Ozero__class_Ozero(X18),X18)
      | ~ c_HOL_Oord__class_Oless(X16,c_HOL_Ozero__class_Ozero(X18),X18)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X18),X17,X18) ),
    file('<stdin>',cls_mult__pos__neg2_0) ).

fof(c_0_221_222,axiom,
    ! [X16,X17,X18] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X18)
      | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X17,X16,X18),c_HOL_Ozero__class_Ozero(X18),X18)
      | ~ c_HOL_Oord__class_Oless(X16,c_HOL_Ozero__class_Ozero(X18),X18)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X18),X17,X18) ),
    file('<stdin>',cls_mult__pos__neg_0) ).

fof(c_0_222_223,axiom,
    ! [X16,X17,X18] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X18)
      | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X17,X16,X18),c_HOL_Ozero__class_Ozero(X18),X18)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X18),X16,X18)
      | ~ c_HOL_Oord__class_Oless(X17,c_HOL_Ozero__class_Ozero(X18),X18) ),
    file('<stdin>',cls_mult__neg__pos_0) ).

fof(c_0_223_224,axiom,
    ! [X1,X2,X18] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X18)
      | c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X18),c_HOL_Otimes__class_Otimes(X2,X1,X18),X18)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X18),X1,X18)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X18),X2,X18) ),
    file('<stdin>',cls_less__1__mult_0) ).

fof(c_0_224_225,axiom,
    ! [X16,X17,X18] :
      ( ~ class_OrderedGroup_Opordered__comm__monoid__add(X18)
      | c_lessequals(c_HOL_Oplus__class_Oplus(X17,X16,X18),c_HOL_Ozero__class_Ozero(X18),X18)
      | ~ c_lessequals(X16,c_HOL_Ozero__class_Ozero(X18),X18)
      | ~ c_lessequals(X17,c_HOL_Ozero__class_Ozero(X18),X18) ),
    file('<stdin>',cls_add__nonpos__nonpos_0) ).

fof(c_0_225_226,axiom,
    ! [X16,X17,X18] :
      ( ~ class_Ring__and__Field_Opordered__cancel__semiring(X18)
      | c_lessequals(c_HOL_Ozero__class_Ozero(X18),c_HOL_Otimes__class_Otimes(X17,X16,X18),X18)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X18),X16,X18)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X18),X17,X18) ),
    file('<stdin>',cls_mult__nonneg__nonneg_0) ).

fof(c_0_226_227,axiom,
    ! [X16,X17,X18] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X18)
      | c_lessequals(c_HOL_Ozero__class_Ozero(X18),c_HOL_Otimes__class_Otimes(X17,X16,X18),X18)
      | ~ c_lessequals(X16,c_HOL_Ozero__class_Ozero(X18),X18)
      | ~ c_lessequals(X17,c_HOL_Ozero__class_Ozero(X18),X18) ),
    file('<stdin>',cls_zero__le__mult__iff_5) ).

fof(c_0_227_228,axiom,
    ! [X16,X17,X18] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X18)
      | c_lessequals(c_HOL_Ozero__class_Ozero(X18),c_HOL_Otimes__class_Otimes(X17,X16,X18),X18)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X18),X16,X18)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X18),X17,X18) ),
    file('<stdin>',cls_zero__le__mult__iff_4) ).

fof(c_0_228_229,axiom,
    ! [X16,X17,X18] :
      ( ~ class_Ring__and__Field_Opordered__ring(X18)
      | c_lessequals(c_HOL_Ozero__class_Ozero(X18),c_HOL_Otimes__class_Otimes(X17,X16,X18),X18)
      | ~ c_lessequals(X16,c_HOL_Ozero__class_Ozero(X18),X18)
      | ~ c_lessequals(X17,c_HOL_Ozero__class_Ozero(X18),X18) ),
    file('<stdin>',cls_mult__nonpos__nonpos_0) ).

fof(c_0_229_230,axiom,
    ! [X16,X17,X18] :
      ( ~ class_Ring__and__Field_Opordered__ring(X18)
      | c_lessequals(c_HOL_Ozero__class_Ozero(X18),c_HOL_Otimes__class_Otimes(X17,X16,X18),X18)
      | ~ c_lessequals(X16,c_HOL_Ozero__class_Ozero(X18),X18)
      | ~ c_lessequals(X17,c_HOL_Ozero__class_Ozero(X18),X18) ),
    file('<stdin>',cls_split__mult__pos__le_1) ).

fof(c_0_230_231,axiom,
    ! [X16,X17,X18] :
      ( ~ class_Ring__and__Field_Opordered__ring(X18)
      | c_lessequals(c_HOL_Ozero__class_Ozero(X18),c_HOL_Otimes__class_Otimes(X17,X16,X18),X18)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X18),X16,X18)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X18),X17,X18) ),
    file('<stdin>',cls_split__mult__pos__le_0) ).

fof(c_0_231_232,axiom,
    ! [X1,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(tc_nat),X2,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oplus__class_Oplus(X2,X1,tc_nat),tc_nat) ),
    file('<stdin>',cls_add__gr__0_0) ).

fof(c_0_232_233,axiom,
    ! [X1,X2] :
      ( 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)
      | ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X1,tc_nat) ),
    file('<stdin>',cls_n__less__m__mult__n_0) ).

fof(c_0_233_234,axiom,
    ! [X1,X2] :
      ( 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)
      | ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X1,tc_nat) ),
    file('<stdin>',cls_n__less__n__mult__m_0) ).

fof(c_0_234_235,axiom,
    ! [X20,X16,X17,X18] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X18)
      | c_lessequals(c_HOL_Oplus__class_Oplus(X17,X20,X18),c_HOL_Oplus__class_Oplus(X16,X20,X18),X18)
      | ~ c_lessequals(X17,X16,X18) ),
    file('<stdin>',cls_add__le__cancel__right_1) ).

fof(c_0_235_236,axiom,
    ! [X20,X16,X17,X18] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X18)
      | c_lessequals(c_HOL_Oplus__class_Oplus(X20,X17,X18),c_HOL_Oplus__class_Oplus(X20,X16,X18),X18)
      | ~ c_lessequals(X17,X16,X18) ),
    file('<stdin>',cls_add__le__cancel__left_1) ).

fof(c_0_236_237,axiom,
    ! [X20,X16,X17,X18] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X18)
      | c_lessequals(c_HOL_Oplus__class_Oplus(X17,X20,X18),c_HOL_Oplus__class_Oplus(X16,X20,X18),X18)
      | ~ c_lessequals(X17,X16,X18) ),
    file('<stdin>',cls_add__right__mono_0) ).

fof(c_0_237_238,axiom,
    ! [X20,X16,X17,X18] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X18)
      | c_lessequals(c_HOL_Oplus__class_Oplus(X20,X17,X18),c_HOL_Oplus__class_Oplus(X20,X16,X18),X18)
      | ~ c_lessequals(X17,X16,X18) ),
    file('<stdin>',cls_add__left__mono_0) ).

fof(c_0_238_239,axiom,
    ! [X20,X16,X17,X18] :
      ( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X18)
      | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X17,X20,X18),c_HOL_Oplus__class_Oplus(X16,X20,X18),X18)
      | ~ c_HOL_Oord__class_Oless(X17,X16,X18) ),
    file('<stdin>',cls_add__strict__right__mono_0) ).

fof(c_0_239_240,axiom,
    ! [X20,X16,X17,X18] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X18)
      | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X17,X20,X18),c_HOL_Oplus__class_Oplus(X16,X20,X18),X18)
      | ~ c_HOL_Oord__class_Oless(X17,X16,X18) ),
    file('<stdin>',cls_add__less__cancel__right_1) ).

fof(c_0_240_241,axiom,
    ! [X20,X16,X17,X18] :
      ( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X18)
      | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X20,X17,X18),c_HOL_Oplus__class_Oplus(X20,X16,X18),X18)
      | ~ c_HOL_Oord__class_Oless(X17,X16,X18) ),
    file('<stdin>',cls_add__strict__left__mono_0) ).

fof(c_0_241_242,axiom,
    ! [X20,X16,X17,X18] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X18)
      | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X20,X17,X18),c_HOL_Oplus__class_Oplus(X20,X16,X18),X18)
      | ~ c_HOL_Oord__class_Oless(X17,X16,X18) ),
    file('<stdin>',cls_add__less__cancel__left_1) ).

fof(c_0_242_243,axiom,
    ! [X20,X16,X17,X18] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X18)
      | ~ class_OrderedGroup_Ocomm__monoid__add(X18)
      | c_lessequals(X16,c_HOL_Oplus__class_Oplus(X17,X20,X18),X18)
      | ~ c_lessequals(X16,X20,X18)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X18),X17,X18) ),
    file('<stdin>',cls_add__increasing_0) ).

fof(c_0_243_244,axiom,
    ! [X20,X16,X17,X18] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X18)
      | ~ class_OrderedGroup_Ocomm__monoid__add(X18)
      | c_lessequals(X16,c_HOL_Oplus__class_Oplus(X17,X20,X18),X18)
      | ~ c_lessequals(X16,X17,X18)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X18),X20,X18) ),
    file('<stdin>',cls_add__increasing2_0) ).

fof(c_0_244_245,axiom,
    ! [X20,X16,X17,X18] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X18)
      | ~ class_OrderedGroup_Ocomm__monoid__add(X18)
      | c_HOL_Oord__class_Oless(X16,c_HOL_Oplus__class_Oplus(X17,X20,X18),X18)
      | ~ c_lessequals(X16,X20,X18)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X18),X17,X18) ),
    file('<stdin>',cls_add__strict__increasing_0) ).

fof(c_0_245_246,axiom,
    ! [X20,X16,X17,X18] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X18)
      | ~ class_OrderedGroup_Ocomm__monoid__add(X18)
      | c_HOL_Oord__class_Oless(X16,c_HOL_Oplus__class_Oplus(X17,X20,X18),X18)
      | ~ c_HOL_Oord__class_Oless(X16,X20,X18)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X18),X17,X18) ),
    file('<stdin>',cls_add__strict__increasing2_0) ).

fof(c_0_246_247,axiom,
    ! [X2,X7] :
      ( c_Divides_Odiv__class_Omod(c_Suc(c_HOL_Otimes__class_Otimes(X7,X2,tc_nat)),X7,tc_nat) = c_HOL_Oone__class_Oone(tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),X7,tc_nat) ),
    file('<stdin>',cls_Suc__times__mod__eq_0) ).

fof(c_0_247_248,axiom,
    ! [X20,X16,X17,X18] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X18)
      | c_HOL_Oord__class_Oless(X16,c_HOL_Oplus__class_Oplus(X17,X20,X18),X18)
      | ~ c_HOL_Oord__class_Oless(X16,X20,X18)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X18),X17,X18) ),
    file('<stdin>',cls_pos__add__strict_0) ).

fof(c_0_248_249,axiom,
    ! [X1,X2,X28] :
      ( c_lessequals(c_HOL_Ominus__class_Ominus(X28,X1,tc_nat),c_HOL_Ominus__class_Ominus(X28,X2,tc_nat),tc_nat)
      | ~ c_lessequals(X2,X1,tc_nat) ),
    file('<stdin>',cls_diff__le__mono2_0) ).

fof(c_0_249_250,axiom,
    ! [X1,X2,X28] :
      ( c_lessequals(c_HOL_Ominus__class_Ominus(X2,X28,tc_nat),c_HOL_Ominus__class_Ominus(X1,X28,tc_nat),tc_nat)
      | ~ c_lessequals(X2,X1,tc_nat) ),
    file('<stdin>',cls_diff__le__mono_0) ).

fof(c_0_250_251,axiom,
    ! [X7,X14,X8] :
      ( c_lessequals(c_HOL_Oplus__class_Oplus(X8,X7,tc_nat),c_HOL_Oplus__class_Oplus(X14,X7,tc_nat),tc_nat)
      | ~ c_lessequals(X8,X14,tc_nat) ),
    file('<stdin>',cls_add__le__mono1_0) ).

fof(c_0_251_252,axiom,
    ! [X1,X2,X7] :
      ( c_lessequals(c_HOL_Oplus__class_Oplus(X7,X2,tc_nat),c_HOL_Oplus__class_Oplus(X7,X1,tc_nat),tc_nat)
      | ~ c_lessequals(X2,X1,tc_nat) ),
    file('<stdin>',cls_nat__add__left__cancel__le_1) ).

fof(c_0_252_253,axiom,
    ! [X7,X14,X8] :
      ( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X8,X7,tc_nat),c_HOL_Oplus__class_Oplus(X14,X7,tc_nat),tc_nat)
      | ~ c_HOL_Oord__class_Oless(X8,X14,tc_nat) ),
    file('<stdin>',cls_add__less__mono1_0) ).

fof(c_0_253_254,axiom,
    ! [X1,X2,X7] :
      ( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X7,X2,tc_nat),c_HOL_Oplus__class_Oplus(X7,X1,tc_nat),tc_nat)
      | ~ c_HOL_Oord__class_Oless(X2,X1,tc_nat) ),
    file('<stdin>',cls_nat__add__left__cancel__less_1) ).

fof(c_0_254_255,axiom,
    ! [X7,X14,X8] :
      ( c_lessequals(c_HOL_Otimes__class_Otimes(X8,X7,tc_nat),c_HOL_Otimes__class_Otimes(X14,X7,tc_nat),tc_nat)
      | ~ c_lessequals(X8,X14,tc_nat) ),
    file('<stdin>',cls_mult__le__mono1_0) ).

fof(c_0_255_256,axiom,
    ! [X7,X14,X8] :
      ( c_lessequals(c_HOL_Otimes__class_Otimes(X7,X8,tc_nat),c_HOL_Otimes__class_Otimes(X7,X14,tc_nat),tc_nat)
      | ~ c_lessequals(X8,X14,tc_nat) ),
    file('<stdin>',cls_mult__le__mono2_0) ).

fof(c_0_256_257,axiom,
    ! [X1,X2,X7] :
      ( c_lessequals(c_HOL_Otimes__class_Otimes(X7,X2,tc_nat),c_HOL_Otimes__class_Otimes(X7,X1,tc_nat),tc_nat)
      | ~ c_lessequals(X2,X1,tc_nat) ),
    file('<stdin>',cls_mult__le__cancel1_2) ).

fof(c_0_257_258,axiom,
    ! [X1,X2,X7] :
      ( c_lessequals(c_HOL_Otimes__class_Otimes(X2,X7,tc_nat),c_HOL_Otimes__class_Otimes(X1,X7,tc_nat),tc_nat)
      | ~ c_lessequals(X2,X1,tc_nat) ),
    file('<stdin>',cls_mult__le__cancel2_2) ).

fof(c_0_258_259,axiom,
    ! [X4,X7,X8] :
      ( c_Lambda_Olift(c_Lambda_Olift(X4,X8),c_Suc(X7)) = c_Lambda_Olift(c_Lambda_Olift(X4,X7),X8)
      | ~ c_HOL_Oord__class_Oless(X8,c_HOL_Oplus__class_Oplus(X7,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat) ),
    file('<stdin>',cls_lift__lift_0) ).

fof(c_0_259_260,axiom,
    ! [X2,X17,X18] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X18)
      | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X17,X2,X18),X2,X18) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X17,c_HOL_Oone__class_Oone(X18),X18),X2,X18) ),
    file('<stdin>',cls_class__semiring_Osemiring__rules_I2_J_0) ).

fof(c_0_260_261,axiom,
    ! [X2,X17,X18] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X18)
      | c_HOL_Oplus__class_Oplus(X2,c_HOL_Otimes__class_Otimes(X17,X2,X18),X18) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X17,c_HOL_Oone__class_Oone(X18),X18),X2,X18) ),
    file('<stdin>',cls_class__semiring_Osemiring__rules_I3_J_0) ).

fof(c_0_261_262,axiom,
    ! [X19,X9,X3,X18] :
      ( ~ class_Orderings_Olinorder(X18)
      | c_lessequals(c_Orderings_Oord__class_Omax(X3,X9,X18),X19,X18)
      | ~ c_lessequals(X9,X19,X18)
      | ~ c_lessequals(X3,X19,X18) ),
    file('<stdin>',cls_min__max_Ole__sup__iff_2) ).

fof(c_0_262_263,axiom,
    ! [X19,X9,X3,X18] :
      ( ~ class_Orderings_Olinorder(X18)
      | c_lessequals(c_Orderings_Oord__class_Omax(X9,X19,X18),X3,X18)
      | ~ c_lessequals(X19,X3,X18)
      | ~ c_lessequals(X9,X3,X18) ),
    file('<stdin>',cls_min__max_Osup__least_0) ).

fof(c_0_263_264,axiom,
    ! [X3,X16,X17,X18] :
      ( ~ class_Orderings_Olinorder(X18)
      | c_lessequals(c_Orderings_Oord__class_Omax(X17,X16,X18),X3,X18)
      | ~ c_lessequals(X16,X3,X18)
      | ~ c_lessequals(X17,X3,X18) ),
    file('<stdin>',cls_min__max_Ole__supI_0) ).

fof(c_0_264_265,axiom,
    ! [X3,X16,X17,X18] :
      ( ~ class_Orderings_Olinorder(X18)
      | c_lessequals(X3,c_Orderings_Oord__class_Omin(X17,X16,X18),X18)
      | ~ c_lessequals(X3,X16,X18)
      | ~ c_lessequals(X3,X17,X18) ),
    file('<stdin>',cls_min__max_Ole__infI_0) ).

fof(c_0_265_266,axiom,
    ! [X19,X9,X3,X18] :
      ( ~ class_Orderings_Olinorder(X18)
      | c_lessequals(X3,c_Orderings_Oord__class_Omin(X9,X19,X18),X18)
      | ~ c_lessequals(X3,X19,X18)
      | ~ c_lessequals(X3,X9,X18) ),
    file('<stdin>',cls_min__max_Ole__inf__iff_2) ).

fof(c_0_266_267,axiom,
    ! [X19,X9,X3,X18] :
      ( ~ class_Orderings_Olinorder(X18)
      | c_lessequals(X3,c_Orderings_Oord__class_Omin(X9,X19,X18),X18)
      | ~ c_lessequals(X3,X19,X18)
      | ~ c_lessequals(X3,X9,X18) ),
    file('<stdin>',cls_min__max_Oinf__greatest_0) ).

fof(c_0_267_268,axiom,
    ! [X19,X9,X3,X18] :
      ( ~ class_Orderings_Olinorder(X18)
      | c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omax(X3,X9,X18),X19,X18)
      | ~ c_HOL_Oord__class_Oless(X9,X19,X18)
      | ~ c_HOL_Oord__class_Oless(X3,X19,X18) ),
    file('<stdin>',cls_max__less__iff__conj_2) ).

fof(c_0_268_269,axiom,
    ! [X19,X9,X3,X18] :
      ( ~ class_Orderings_Olinorder(X18)
      | c_HOL_Oord__class_Oless(X19,c_Orderings_Oord__class_Omin(X3,X9,X18),X18)
      | ~ c_HOL_Oord__class_Oless(X19,X9,X18)
      | ~ c_HOL_Oord__class_Oless(X19,X3,X18) ),
    file('<stdin>',cls_min__less__iff__conj_2) ).

fof(c_0_269_270,axiom,
    ! [X1,X2] :
      ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Otimes__class_Otimes(X2,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(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat) ),
    file('<stdin>',cls_nat__0__less__mult__iff_2) ).

fof(c_0_270_271,axiom,
    ! [X1,X2,X7] :
      ( c_HOL_Ominus__class_Ominus(X2,X7,tc_nat) != c_HOL_Ominus__class_Ominus(X1,X7,tc_nat)
      | ~ c_lessequals(X7,X1,tc_nat)
      | ~ c_lessequals(X7,X2,tc_nat)
      | X2 = X1 ),
    file('<stdin>',cls_eq__diff__iff_0) ).

fof(c_0_271_272,axiom,
    ! [X1,X2] :
      ( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),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) ),
    file('<stdin>',cls_diff__less_0) ).

fof(c_0_272_273,axiom,
    ! [X17,X18] :
      ( ~ class_OrderedGroup_Olordered__ab__group__add(X18)
      | c_lessequals(c_HOL_Ozero__class_Ozero(X18),X17,X18)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X18),c_HOL_Oplus__class_Oplus(X17,X17,X18),X18) ),
    file('<stdin>',cls_zero__le__double__add__iff__zero__le__single__add_0) ).

fof(c_0_273_274,axiom,
    ! [X17,X18] :
      ( ~ class_OrderedGroup_Olordered__ab__group__add(X18)
      | c_HOL_Oord__class_Oless(X17,c_HOL_Ozero__class_Ozero(X18),X18)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X17,X17,X18),c_HOL_Ozero__class_Ozero(X18),X18) ),
    file('<stdin>',cls_double__add__less__zero__iff__single__less__zero_0) ).

fof(c_0_274_275,axiom,
    ! [X17,X18] :
      ( ~ class_Ring__and__Field_Oordered__idom(X18)
      | c_HOL_Oord__class_Oless(X17,c_HOL_Ozero__class_Ozero(X18),X18)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X17,X17,X18),c_HOL_Ozero__class_Ozero(X18),X18) ),
    file('<stdin>',cls_even__less__0__iff_0) ).

fof(c_0_275_276,axiom,
    ! [X17,X18] :
      ( ~ class_OrderedGroup_Olordered__ab__group__add(X18)
      | c_lessequals(X17,c_HOL_Ozero__class_Ozero(X18),X18)
      | ~ c_lessequals(c_HOL_Oplus__class_Oplus(X17,X17,X18),c_HOL_Ozero__class_Ozero(X18),X18) ),
    file('<stdin>',cls_double__add__le__zero__iff__single__add__le__zero_0) ).

fof(c_0_276_277,axiom,
    ! [X17,X18] :
      ( ~ class_OrderedGroup_Olordered__ab__group__add(X18)
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X18),X17,X18)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X18),c_HOL_Oplus__class_Oplus(X17,X17,X18),X18) ),
    file('<stdin>',cls_zero__less__double__add__iff__zero__less__single__add_0) ).

fof(c_0_277_278,axiom,
    ! [X1,X2] :
      ( c_lessequals(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X1,tc_nat)
      | ~ c_lessequals(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Otimes__class_Otimes(X2,X1,tc_nat),tc_nat) ),
    file('<stdin>',cls_one__le__mult__iff_1) ).

fof(c_0_278_279,axiom,
    ! [X1,X2] :
      ( c_lessequals(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X2,tc_nat)
      | ~ c_lessequals(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Otimes__class_Otimes(X2,X1,tc_nat),tc_nat) ),
    file('<stdin>',cls_one__le__mult__iff_0) ).

fof(c_0_279_280,axiom,
    ! [X19,X9,X3,X18] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X18)
      | c_HOL_Oplus__class_Oplus(X3,c_HOL_Oplus__class_Oplus(X9,X19,X18),X18) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X3,X9,X18),X19,X18) ),
    file('<stdin>',cls_class__semiring_Oadd__a_0) ).

fof(c_0_280_281,axiom,
    ! [X19,X9,X3,X18] :
      ( ~ class_OrderedGroup_Oab__group__add(X18)
      | c_HOL_Oplus__class_Oplus(X3,c_HOL_Oplus__class_Oplus(X9,X19,X18),X18) = c_HOL_Oplus__class_Oplus(X9,c_HOL_Oplus__class_Oplus(X3,X19,X18),X18) ),
    file('<stdin>',cls_add__cancel__21_1) ).

fof(c_0_281_282,axiom,
    ! [X20,X16,X17,X18] :
      ( ~ class_OrderedGroup_Ocomm__monoid__add(X18)
      | c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X17,X16,X18),X20,X18) = c_HOL_Oplus__class_Oplus(X17,c_HOL_Oplus__class_Oplus(X16,X20,X18),X18) ),
    file('<stdin>',cls_comm__monoid__add_Omult__assoc_0) ).

fof(c_0_282_283,axiom,
    ! [X20,X16,X17,X18] :
      ( ~ class_OrderedGroup_Ocomm__monoid__add(X18)
      | c_HOL_Oplus__class_Oplus(X17,c_HOL_Oplus__class_Oplus(X16,X20,X18),X18) = c_HOL_Oplus__class_Oplus(X16,c_HOL_Oplus__class_Oplus(X17,X20,X18),X18) ),
    file('<stdin>',cls_comm__monoid__add_Omult__left__commute_0) ).

fof(c_0_283_284,axiom,
    ! [X20,X16,X17,X18] :
      ( ~ class_OrderedGroup_Oab__semigroup__add(X18)
      | c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X17,X16,X18),X20,X18) = c_HOL_Oplus__class_Oplus(X17,c_HOL_Oplus__class_Oplus(X16,X20,X18),X18) ),
    file('<stdin>',cls_ab__semigroup__add__class_Oadd__ac_I1_J_0) ).

fof(c_0_284_285,axiom,
    ! [X27,X20,X17,X18] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X18)
      | c_HOL_Oplus__class_Oplus(X17,c_HOL_Oplus__class_Oplus(X20,X27,X18),X18) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X17,X20,X18),X27,X18) ),
    file('<stdin>',cls_class__semiring_Osemiring__rules_I25_J_0) ).

fof(c_0_285_286,axiom,
    ! [X20,X16,X17,X18] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X18)
      | c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X17,X16,X18),X20,X18) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X17,X20,X18),X16,X18) ),
    file('<stdin>',cls_class__semiring_Osemiring__rules_I23_J_0) ).

fof(c_0_286_287,axiom,
    ! [X27,X20,X17,X18] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X18)
      | c_HOL_Oplus__class_Oplus(X17,c_HOL_Oplus__class_Oplus(X20,X27,X18),X18) = c_HOL_Oplus__class_Oplus(X20,c_HOL_Oplus__class_Oplus(X17,X27,X18),X18) ),
    file('<stdin>',cls_class__semiring_Osemiring__rules_I22_J_0) ).

fof(c_0_287_288,axiom,
    ! [X20,X16,X17,X18] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X18)
      | c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X17,X16,X18),X20,X18) = c_HOL_Oplus__class_Oplus(X17,c_HOL_Oplus__class_Oplus(X16,X20,X18),X18) ),
    file('<stdin>',cls_class__semiring_Osemiring__rules_I21_J_0) ).

fof(c_0_288_289,axiom,
    ! [X19,X9,X3,X18] :
      ( ~ class_Orderings_Olinorder(X18)
      | c_Orderings_Oord__class_Omin(c_Orderings_Oord__class_Omin(X3,X9,X18),X19,X18) = c_Orderings_Oord__class_Omin(X3,c_Orderings_Oord__class_Omin(X9,X19,X18),X18) ),
    file('<stdin>',cls_min__max_Oinf__assoc_0) ).

fof(c_0_289_290,axiom,
    ! [X19,X9,X3,X18] :
      ( ~ class_Orderings_Olinorder(X18)
      | c_Orderings_Oord__class_Omin(X3,c_Orderings_Oord__class_Omin(X9,X19,X18),X18) = c_Orderings_Oord__class_Omin(X9,c_Orderings_Oord__class_Omin(X3,X19,X18),X18) ),
    file('<stdin>',cls_min__max_Oinf__left__commute_0) ).

fof(c_0_290_291,axiom,
    ! [X19,X9,X3,X18] :
      ( ~ class_Orderings_Olinorder(X18)
      | c_Orderings_Oord__class_Omax(c_Orderings_Oord__class_Omax(X3,X9,X18),X19,X18) = c_Orderings_Oord__class_Omax(X3,c_Orderings_Oord__class_Omax(X9,X19,X18),X18) ),
    file('<stdin>',cls_min__max_Osup__assoc_0) ).

fof(c_0_291_292,axiom,
    ! [X19,X9,X3,X18] :
      ( ~ class_Orderings_Olinorder(X18)
      | c_Orderings_Oord__class_Omax(X3,c_Orderings_Oord__class_Omax(X9,X19,X18),X18) = c_Orderings_Oord__class_Omax(X9,c_Orderings_Oord__class_Omax(X3,X19,X18),X18) ),
    file('<stdin>',cls_min__max_Osup__left__commute_0) ).

fof(c_0_292_293,axiom,
    ! [X20,X16,X17,X18] :
      ( ~ class_OrderedGroup_Oab__semigroup__mult(X18)
      | c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X17,X16,X18),X20,X18) = c_HOL_Otimes__class_Otimes(X17,c_HOL_Otimes__class_Otimes(X16,X20,X18),X18) ),
    file('<stdin>',cls_ab__semigroup__mult__class_Omult__ac_I1_J_0) ).

fof(c_0_293_294,axiom,
    ! [X22,X24,X23,X18] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X18)
      | c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X23,X24,X18),X22,X18) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X23,X22,X18),X24,X18) ),
    file('<stdin>',cls_class__semiring_Osemiring__rules_I16_J_0) ).

fof(c_0_294_295,axiom,
    ! [X22,X24,X23,X18] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X18)
      | c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X23,X24,X18),X22,X18) = c_HOL_Otimes__class_Otimes(X23,c_HOL_Otimes__class_Otimes(X24,X22,X18),X18) ),
    file('<stdin>',cls_class__semiring_Osemiring__rules_I17_J_0) ).

fof(c_0_295_296,axiom,
    ! [X21,X22,X23,X18] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X18)
      | c_HOL_Otimes__class_Otimes(X23,c_HOL_Otimes__class_Otimes(X22,X21,X18),X18) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X23,X22,X18),X21,X18) ),
    file('<stdin>',cls_class__semiring_Osemiring__rules_I18_J_0) ).

fof(c_0_296_297,axiom,
    ! [X21,X22,X23,X18] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X18)
      | c_HOL_Otimes__class_Otimes(X23,c_HOL_Otimes__class_Otimes(X22,X21,X18),X18) = c_HOL_Otimes__class_Otimes(X22,c_HOL_Otimes__class_Otimes(X23,X21,X18),X18) ),
    file('<stdin>',cls_class__semiring_Osemiring__rules_I19_J_0) ).

fof(c_0_297_298,axiom,
    ! [X19,X9,X3,X18] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X18)
      | c_HOL_Otimes__class_Otimes(X3,c_HOL_Otimes__class_Otimes(X9,X19,X18),X18) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X3,X9,X18),X19,X18) ),
    file('<stdin>',cls_class__semiring_Omul__a_0) ).

fof(c_0_298_299,axiom,
    ! [X1,X2,X7] :
      ( c_HOL_Oord__class_Oless(X2,c_HOL_Oplus__class_Oplus(X1,X7,tc_nat),tc_nat)
      | ~ c_lessequals(X2,X1,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X7,tc_nat) ),
    file('<stdin>',cls_lem0_0) ).

fof(c_0_299_300,axiom,
    ! [X18] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X18)
      | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X18),c_HOL_Ozero__class_Ozero(X18),X18),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X18),c_HOL_Ozero__class_Ozero(X18),X18),X18) = c_HOL_Ozero__class_Ozero(X18) ),
    file('<stdin>',cls_sum__squares__eq__zero__iff_2) ).

fof(c_0_300_301,axiom,
    ! [X16,X17,X18] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add(X18)
      | c_lessequals(X17,X16,X18)
      | ~ c_lessequals(c_HOL_Ominus__class_Ominus(X17,X16,X18),c_HOL_Ozero__class_Ozero(X18),X18) ),
    file('<stdin>',cls_le__iff__diff__le__0_1) ).

fof(c_0_301_302,axiom,
    ! [X16,X17,X18] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add(X18)
      | c_HOL_Oord__class_Oless(X17,X16,X18)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X17,X16,X18),c_HOL_Ozero__class_Ozero(X18),X18) ),
    file('<stdin>',cls_less__iff__diff__less__0_1) ).

fof(c_0_302_303,axiom,
    ! [X25,X9,X26,X3,X18] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add(X18)
      | c_HOL_Ominus__class_Ominus(X3,X9,X18) != c_HOL_Ominus__class_Ominus(X26,X25,X18)
      | c_lessequals(X25,X26,X18)
      | ~ c_lessequals(X9,X3,X18) ),
    file('<stdin>',cls_le__eqI_0) ).

fof(c_0_303_304,axiom,
    ! [X25,X9,X26,X3,X18] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add(X18)
      | c_HOL_Ominus__class_Ominus(X3,X9,X18) != c_HOL_Ominus__class_Ominus(X26,X25,X18)
      | c_lessequals(X9,X3,X18)
      | ~ c_lessequals(X25,X26,X18) ),
    file('<stdin>',cls_le__eqI_1) ).

fof(c_0_304_305,axiom,
    ! [X25,X9,X26,X3,X18] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add(X18)
      | c_HOL_Ominus__class_Ominus(X3,X9,X18) != c_HOL_Ominus__class_Ominus(X26,X25,X18)
      | c_HOL_Oord__class_Oless(X26,X25,X18)
      | ~ c_HOL_Oord__class_Oless(X3,X9,X18) ),
    file('<stdin>',cls_less__eqI_0) ).

fof(c_0_305_306,axiom,
    ! [X25,X9,X26,X3,X18] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add(X18)
      | c_HOL_Ominus__class_Ominus(X3,X9,X18) != c_HOL_Ominus__class_Ominus(X26,X25,X18)
      | c_HOL_Oord__class_Oless(X3,X9,X18)
      | ~ c_HOL_Oord__class_Oless(X26,X25,X18) ),
    file('<stdin>',cls_less__eqI_1) ).

fof(c_0_306_307,axiom,
    ! [X1,X2,X7] :
      ( c_lessequals(c_HOL_Otimes__class_Otimes(X2,X7,tc_nat),c_HOL_Otimes__class_Otimes(X1,X7,tc_nat),tc_nat)
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X7,tc_nat) ),
    file('<stdin>',cls_mult__le__cancel2_1) ).

fof(c_0_307_308,axiom,
    ! [X1,X2,X7] :
      ( c_lessequals(c_HOL_Otimes__class_Otimes(X7,X2,tc_nat),c_HOL_Otimes__class_Otimes(X7,X1,tc_nat),tc_nat)
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X7,tc_nat) ),
    file('<stdin>',cls_mult__le__cancel1_1) ).

fof(c_0_308_309,axiom,
    ! [X19,X9,X3,X18] :
      ( ~ class_Orderings_Olinorder(X18)
      | c_lessequals(X3,X19,X18)
      | ~ c_lessequals(X3,c_Orderings_Oord__class_Omin(X9,X19,X18),X18) ),
    file('<stdin>',cls_min__max_Ole__inf__iff_1) ).

fof(c_0_309_310,axiom,
    ! [X19,X9,X3,X18] :
      ( ~ class_Orderings_Olinorder(X18)
      | c_lessequals(X3,X9,X18)
      | ~ c_lessequals(X3,c_Orderings_Oord__class_Omin(X9,X19,X18),X18) ),
    file('<stdin>',cls_min__max_Ole__inf__iff_0) ).

fof(c_0_310_311,axiom,
    ! [X3,X16,X17,X18] :
      ( ~ class_Orderings_Olinorder(X18)
      | c_lessequals(X3,X16,X18)
      | ~ c_lessequals(X3,c_Orderings_Oord__class_Omin(X17,X16,X18),X18) ),
    file('<stdin>',cls_min__max_Ole__infE_1) ).

fof(c_0_311_312,axiom,
    ! [X3,X16,X17,X18] :
      ( ~ class_Orderings_Olinorder(X18)
      | c_lessequals(X3,X17,X18)
      | ~ c_lessequals(X3,c_Orderings_Oord__class_Omin(X17,X16,X18),X18) ),
    file('<stdin>',cls_min__max_Ole__infE_0) ).

fof(c_0_312_313,axiom,
    ! [X19,X9,X3,X18] :
      ( ~ class_Orderings_Olinorder(X18)
      | c_lessequals(X9,X19,X18)
      | ~ c_lessequals(c_Orderings_Oord__class_Omax(X3,X9,X18),X19,X18) ),
    file('<stdin>',cls_min__max_Ole__sup__iff_1) ).

fof(c_0_313_314,axiom,
    ! [X19,X9,X3,X18] :
      ( ~ class_Orderings_Olinorder(X18)
      | c_lessequals(X3,X19,X18)
      | ~ c_lessequals(c_Orderings_Oord__class_Omax(X3,X9,X18),X19,X18) ),
    file('<stdin>',cls_min__max_Ole__sup__iff_0) ).

fof(c_0_314_315,axiom,
    ! [X3,X16,X17,X18] :
      ( ~ class_Orderings_Olinorder(X18)
      | c_lessequals(X16,X3,X18)
      | ~ c_lessequals(c_Orderings_Oord__class_Omax(X17,X16,X18),X3,X18) ),
    file('<stdin>',cls_min__max_Ole__supE_1) ).

fof(c_0_315_316,axiom,
    ! [X3,X16,X17,X18] :
      ( ~ class_Orderings_Olinorder(X18)
      | c_lessequals(X17,X3,X18)
      | ~ c_lessequals(c_Orderings_Oord__class_Omax(X17,X16,X18),X3,X18) ),
    file('<stdin>',cls_min__max_Ole__supE_0) ).

fof(c_0_316_317,axiom,
    ! [X19,X9,X3,X18] :
      ( ~ class_Orderings_Olinorder(X18)
      | c_HOL_Oord__class_Oless(X3,X19,X18)
      | ~ c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omax(X3,X9,X18),X19,X18) ),
    file('<stdin>',cls_max__less__iff__conj_0) ).

fof(c_0_317_318,axiom,
    ! [X19,X9,X3,X18] :
      ( ~ class_Orderings_Olinorder(X18)
      | c_HOL_Oord__class_Oless(X9,X19,X18)
      | ~ c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omax(X3,X9,X18),X19,X18) ),
    file('<stdin>',cls_max__less__iff__conj_1) ).

fof(c_0_318_319,axiom,
    ! [X19,X9,X3,X18] :
      ( ~ class_Orderings_Olinorder(X18)
      | c_HOL_Oord__class_Oless(X19,X3,X18)
      | ~ c_HOL_Oord__class_Oless(X19,c_Orderings_Oord__class_Omin(X3,X9,X18),X18) ),
    file('<stdin>',cls_min__less__iff__conj_0) ).

fof(c_0_319_320,axiom,
    ! [X19,X9,X3,X18] :
      ( ~ class_Orderings_Olinorder(X18)
      | c_HOL_Oord__class_Oless(X19,X9,X18)
      | ~ c_HOL_Oord__class_Oless(X19,c_Orderings_Oord__class_Omin(X3,X9,X18),X18) ),
    file('<stdin>',cls_min__less__iff__conj_1) ).

fof(c_0_320_321,axiom,
    ! [X1,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(tc_nat),c_HOL_Otimes__class_Otimes(X2,X1,tc_nat),tc_nat) ),
    file('<stdin>',cls_nat__0__less__mult__iff_1) ).

fof(c_0_321_322,axiom,
    ! [X1,X2] :
      ( 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(X2,X1,tc_nat),tc_nat) ),
    file('<stdin>',cls_nat__0__less__mult__iff_0) ).

fof(c_0_322_323,axiom,
    ! [X1,X2] :
      ( c_HOL_Oord__class_Oless(X2,X1,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),tc_nat) ),
    file('<stdin>',cls_zero__less__diff_0) ).

fof(c_0_323_324,axiom,
    ! [X1,X2,X28,X7] :
      ( c_HOL_Oplus__class_Oplus(X2,X28,tc_nat) != c_HOL_Oplus__class_Oplus(X7,X1,tc_nat)
      | ~ c_HOL_Oord__class_Oless(X7,X28,tc_nat)
      | c_HOL_Oord__class_Oless(X2,X1,tc_nat) ),
    file('<stdin>',cls_less__add__eq__less_0) ).

fof(c_0_324_325,axiom,
    ! [X7,X14,X8] :
      ( c_HOL_Oord__class_Oless(X8,X7,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X8,X14,tc_nat),X7,tc_nat) ),
    file('<stdin>',cls_add__lessD1_0) ).

fof(c_0_325_326,axiom,
    ! [X1,X2,X7] :
      ( c_lessequals(X7,X1,tc_nat)
      | ~ c_lessequals(c_HOL_Oplus__class_Oplus(X2,X7,tc_nat),X1,tc_nat) ),
    file('<stdin>',cls_add__leE_1) ).

fof(c_0_326_327,axiom,
    ! [X1,X2,X7] :
      ( c_lessequals(X2,X1,tc_nat)
      | ~ c_lessequals(c_HOL_Oplus__class_Oplus(X2,X7,tc_nat),X1,tc_nat) ),
    file('<stdin>',cls_add__leE_0) ).

fof(c_0_327_328,axiom,
    ! [X9,X3,X18] :
      ( ~ class_OrderedGroup_Opordered__comm__monoid__add(X18)
      | c_HOL_Oplus__class_Oplus(X3,X9,X18) != c_HOL_Ozero__class_Ozero(X18)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X18),X9,X18)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X18),X3,X18)
      | X9 = c_HOL_Ozero__class_Ozero(X18) ),
    file('<stdin>',cls_add__nonneg__eq__0__iff_1) ).

fof(c_0_328_329,axiom,
    ! [X9,X3,X18] :
      ( ~ class_OrderedGroup_Opordered__comm__monoid__add(X18)
      | c_HOL_Oplus__class_Oplus(X3,X9,X18) != c_HOL_Ozero__class_Ozero(X18)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X18),X9,X18)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X18),X3,X18)
      | X3 = c_HOL_Ozero__class_Ozero(X18) ),
    file('<stdin>',cls_add__nonneg__eq__0__iff_0) ).

fof(c_0_329_330,axiom,
    ! [X1,X2] :
      ( c_Divides_Odiv__class_Omod(X2,X1,tc_nat) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),X1,tc_nat)
      | ~ c_lessequals(X1,X2,tc_nat) ),
    file('<stdin>',cls_le__mod__geq_0) ).

fof(c_0_330_331,axiom,
    ! [X18] :
      ( ~ class_OrderedGroup_Opordered__comm__monoid__add(X18)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X18),c_HOL_Ozero__class_Ozero(X18),X18)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X18),c_HOL_Ozero__class_Ozero(X18),X18)
      | c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X18),c_HOL_Ozero__class_Ozero(X18),X18) = c_HOL_Ozero__class_Ozero(X18) ),
    file('<stdin>',cls_add__nonneg__eq__0__iff_2) ).

fof(c_0_331_332,axiom,
    ! [X1,X2] :
      ( c_Divides_Odiv__class_Omod(c_Suc(X2),X1,tc_nat) = c_Suc(c_Divides_Odiv__class_Omod(X2,X1,tc_nat))
      | c_Suc(c_Divides_Odiv__class_Omod(X2,X1,tc_nat)) = X1 ),
    file('<stdin>',cls_mod__Suc_1) ).

fof(c_0_332_333,axiom,
    ! [X17,X18] :
      ( ~ class_OrderedGroup_Olordered__ab__group__add(X18)
      | c_lessequals(c_HOL_Ozero__class_Ozero(X18),c_HOL_Oplus__class_Oplus(X17,X17,X18),X18)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X18),X17,X18) ),
    file('<stdin>',cls_zero__le__double__add__iff__zero__le__single__add_1) ).

fof(c_0_333_334,axiom,
    ! [X17,X18] :
      ( ~ class_OrderedGroup_Olordered__ab__group__add(X18)
      | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X17,X17,X18),c_HOL_Ozero__class_Ozero(X18),X18)
      | ~ c_HOL_Oord__class_Oless(X17,c_HOL_Ozero__class_Ozero(X18),X18) ),
    file('<stdin>',cls_double__add__less__zero__iff__single__less__zero_1) ).

fof(c_0_334_335,axiom,
    ! [X17,X18] :
      ( ~ class_Ring__and__Field_Oordered__idom(X18)
      | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X17,X17,X18),c_HOL_Ozero__class_Ozero(X18),X18)
      | ~ c_HOL_Oord__class_Oless(X17,c_HOL_Ozero__class_Ozero(X18),X18) ),
    file('<stdin>',cls_even__less__0__iff_1) ).

fof(c_0_335_336,axiom,
    ! [X17,X18] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X18)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X17,X17,X18),c_HOL_Ozero__class_Ozero(X18),X18) ),
    file('<stdin>',cls_not__square__less__zero_0) ).

fof(c_0_336_337,axiom,
    ! [X17,X18] :
      ( ~ class_OrderedGroup_Olordered__ab__group__add(X18)
      | c_lessequals(c_HOL_Oplus__class_Oplus(X17,X17,X18),c_HOL_Ozero__class_Ozero(X18),X18)
      | ~ c_lessequals(X17,c_HOL_Ozero__class_Ozero(X18),X18) ),
    file('<stdin>',cls_double__add__le__zero__iff__single__add__le__zero_1) ).

fof(c_0_337_338,axiom,
    ! [X17,X18] :
      ( ~ class_OrderedGroup_Olordered__ab__group__add(X18)
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X18),c_HOL_Oplus__class_Oplus(X17,X17,X18),X18)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X18),X17,X18) ),
    file('<stdin>',cls_zero__less__double__add__iff__zero__less__single__add_1) ).

fof(c_0_338_339,axiom,
    ! [X1,X2] :
      ( c_Divides_Odiv__class_Omod(X2,X1,tc_nat) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),X1,tc_nat)
      | c_HOL_Oord__class_Oless(X2,X1,tc_nat) ),
    file('<stdin>',cls_mod__if_1) ).

fof(c_0_339_340,axiom,
    ! [X16,X17,X18] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add(X18)
      | c_lessequals(c_HOL_Ominus__class_Ominus(X17,X16,X18),c_HOL_Ozero__class_Ozero(X18),X18)
      | ~ c_lessequals(X17,X16,X18) ),
    file('<stdin>',cls_le__iff__diff__le__0_0) ).

fof(c_0_340_341,axiom,
    ! [X16,X17,X18] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add(X18)
      | c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X17,X16,X18),c_HOL_Ozero__class_Ozero(X18),X18)
      | ~ c_HOL_Oord__class_Oless(X17,X16,X18) ),
    file('<stdin>',cls_less__iff__diff__less__0_0) ).

fof(c_0_341_342,axiom,
    ! [X5,X7,X8] :
      ( c_Lambda_Osubst(c_Lambda_OdB_OVar(X8),X5,X7) = c_Lambda_OdB_OVar(c_HOL_Ominus__class_Ominus(X8,c_HOL_Oone__class_Oone(tc_nat),tc_nat))
      | ~ c_HOL_Oord__class_Oless(X7,X8,tc_nat) ),
    file('<stdin>',cls_subst__Var_0) ).

fof(c_0_342_343,axiom,
    ! [X15,X14,X8] :
      ( c_Lambda_Osubst(c_Lambda_OdB_OVar(X14),X15,X8) = c_Lambda_OdB_OVar(c_HOL_Ominus__class_Ominus(X14,c_HOL_Oone__class_Oone(tc_nat),tc_nat))
      | ~ c_HOL_Oord__class_Oless(X8,X14,tc_nat) ),
    file('<stdin>',cls_subst__gt_0) ).

fof(c_0_343_344,axiom,
    ! [X1,X8] :
      ( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,c_Suc(X8),tc_nat),X1,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
    file('<stdin>',cls_diff__Suc__less_0) ).

fof(c_0_344_345,axiom,
    ! [X1,X2,X7] :
      ( c_HOL_Otimes__class_Otimes(X7,X2,tc_nat) != c_HOL_Otimes__class_Otimes(X7,X1,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X7,tc_nat)
      | X2 = X1 ),
    file('<stdin>',cls_nat__mult__eq__cancel1_0) ).

fof(c_0_345_346,axiom,
    ! [X19,X9,X3,X18] :
      ( ~ class_Orderings_Olinorder(X18)
      | c_lessequals(c_Orderings_Oord__class_Omin(X3,X9,X18),X19,X18)
      | ~ c_lessequals(X9,X19,X18) ),
    file('<stdin>',cls_min__le__iff__disj_2) ).

fof(c_0_346_347,axiom,
    ! [X19,X9,X3,X18] :
      ( ~ class_Orderings_Olinorder(X18)
      | c_lessequals(c_Orderings_Oord__class_Omin(X3,X9,X18),X19,X18)
      | ~ c_lessequals(X3,X19,X18) ),
    file('<stdin>',cls_min__le__iff__disj_1) ).

fof(c_0_347_348,axiom,
    ! [X3,X16,X17,X18] :
      ( ~ class_Orderings_Olinorder(X18)
      | c_lessequals(c_Orderings_Oord__class_Omin(X17,X16,X18),X3,X18)
      | ~ c_lessequals(X16,X3,X18) ),
    file('<stdin>',cls_min__max_Ole__infI2_0) ).

fof(c_0_348_349,axiom,
    ! [X3,X16,X17,X18] :
      ( ~ class_Orderings_Olinorder(X18)
      | c_lessequals(c_Orderings_Oord__class_Omin(X17,X16,X18),X3,X18)
      | ~ c_lessequals(X17,X3,X18) ),
    file('<stdin>',cls_min__max_Ole__infI1_0) ).

fof(c_0_349_350,axiom,
    ! [X19,X9,X3,X18] :
      ( ~ class_Orderings_Olinorder(X18)
      | c_lessequals(X19,c_Orderings_Oord__class_Omax(X3,X9,X18),X18)
      | ~ c_lessequals(X19,X9,X18) ),
    file('<stdin>',cls_le__max__iff__disj_2) ).

fof(c_0_350_351,axiom,
    ! [X19,X9,X3,X18] :
      ( ~ class_Orderings_Olinorder(X18)
      | c_lessequals(X19,c_Orderings_Oord__class_Omax(X3,X9,X18),X18)
      | ~ c_lessequals(X19,X3,X18) ),
    file('<stdin>',cls_le__max__iff__disj_1) ).

fof(c_0_351_352,axiom,
    ! [X3,X16,X17,X18] :
      ( ~ class_Orderings_Olinorder(X18)
      | c_lessequals(X3,c_Orderings_Oord__class_Omax(X17,X16,X18),X18)
      | ~ c_lessequals(X3,X16,X18) ),
    file('<stdin>',cls_min__max_Ole__supI2_0) ).

fof(c_0_352_353,axiom,
    ! [X3,X16,X17,X18] :
      ( ~ class_Orderings_Olinorder(X18)
      | c_lessequals(X3,c_Orderings_Oord__class_Omax(X17,X16,X18),X18)
      | ~ c_lessequals(X3,X17,X18) ),
    file('<stdin>',cls_min__max_Ole__supI1_0) ).

fof(c_0_353_354,axiom,
    ! [X3,X16,X17,X18] :
      ( ~ class_Orderings_Olinorder(X18)
      | c_HOL_Oord__class_Oless(X3,c_Orderings_Oord__class_Omax(X17,X16,X18),X18)
      | ~ c_HOL_Oord__class_Oless(X3,X17,X18) ),
    file('<stdin>',cls_min__max_Oless__supI1_0) ).

fof(c_0_354_355,axiom,
    ! [X3,X16,X17,X18] :
      ( ~ class_Orderings_Olinorder(X18)
      | c_HOL_Oord__class_Oless(X3,c_Orderings_Oord__class_Omax(X17,X16,X18),X18)
      | ~ c_HOL_Oord__class_Oless(X3,X16,X18) ),
    file('<stdin>',cls_min__max_Oless__supI2_0) ).

fof(c_0_355_356,axiom,
    ! [X19,X9,X3,X18] :
      ( ~ class_Orderings_Olinorder(X18)
      | c_HOL_Oord__class_Oless(X19,c_Orderings_Oord__class_Omax(X3,X9,X18),X18)
      | ~ c_HOL_Oord__class_Oless(X19,X3,X18) ),
    file('<stdin>',cls_less__max__iff__disj_1) ).

fof(c_0_356_357,axiom,
    ! [X19,X9,X3,X18] :
      ( ~ class_Orderings_Olinorder(X18)
      | c_HOL_Oord__class_Oless(X19,c_Orderings_Oord__class_Omax(X3,X9,X18),X18)
      | ~ c_HOL_Oord__class_Oless(X19,X9,X18) ),
    file('<stdin>',cls_less__max__iff__disj_2) ).

fof(c_0_357_358,axiom,
    ! [X3,X16,X17,X18] :
      ( ~ class_Orderings_Olinorder(X18)
      | c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omin(X17,X16,X18),X3,X18)
      | ~ c_HOL_Oord__class_Oless(X17,X3,X18) ),
    file('<stdin>',cls_min__max_Oless__infI1_0) ).

fof(c_0_358_359,axiom,
    ! [X3,X16,X17,X18] :
      ( ~ class_Orderings_Olinorder(X18)
      | c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omin(X17,X16,X18),X3,X18)
      | ~ c_HOL_Oord__class_Oless(X16,X3,X18) ),
    file('<stdin>',cls_min__max_Oless__infI2_0) ).

fof(c_0_359_360,axiom,
    ! [X19,X9,X3,X18] :
      ( ~ class_Orderings_Olinorder(X18)
      | c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omin(X3,X9,X18),X19,X18)
      | ~ c_HOL_Oord__class_Oless(X3,X19,X18) ),
    file('<stdin>',cls_min__less__iff__disj_1) ).

fof(c_0_360_361,axiom,
    ! [X19,X9,X3,X18] :
      ( ~ class_Orderings_Olinorder(X18)
      | c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omin(X3,X9,X18),X19,X18)
      | ~ c_HOL_Oord__class_Oless(X9,X19,X18) ),
    file('<stdin>',cls_min__less__iff__disj_2) ).

fof(c_0_361_362,axiom,
    ! [X1,X2] :
      ( c_HOL_Ominus__class_Ominus(c_Suc(X2),X1,tc_nat) = c_Suc(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat))
      | ~ c_lessequals(X1,X2,tc_nat) ),
    file('<stdin>',cls_Suc__diff__le_0) ).

fof(c_0_362_363,axiom,
    ! [X4,X5,X6,X8] :
      ( c_Lambda_Obeta(c_Lambda_Osubst(X6,X4,X8),c_Lambda_Osubst(X5,X4,X8))
      | ~ c_Lambda_Obeta(X6,X5) ),
    file('<stdin>',cls_subst__preserves__beta_0) ).

fof(c_0_363_364,axiom,
    ! [X1,X2] :
      ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oplus__class_Oplus(X2,X1,tc_nat),tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
    file('<stdin>',cls_add__gr__0_2) ).

fof(c_0_364_365,axiom,
    ! [X1,X2] :
      ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oplus__class_Oplus(X2,X1,tc_nat),tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat) ),
    file('<stdin>',cls_add__gr__0_1) ).

fof(c_0_365_366,axiom,
    ! [X2,X18] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X18)
      | c_HOL_Oplus__class_Oplus(X2,X2,X18) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(X18),c_HOL_Oone__class_Oone(X18),X18),X2,X18) ),
    file('<stdin>',cls_class__semiring_Osemiring__rules_I4_J_0) ).

fof(c_0_366_367,axiom,
    ! [X1,X2] :
      ( c_lessequals(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) ),
    file('<stdin>',cls_mod__le__divisor_0) ).

fof(c_0_367_368,axiom,
    ! [X1,X2] :
      ( 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) ),
    file('<stdin>',cls_mod__less__divisor_0) ).

fof(c_0_368_369,axiom,
    ! [X1,X2] :
      ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),tc_nat)
      | ~ c_HOL_Oord__class_Oless(X2,X1,tc_nat) ),
    file('<stdin>',cls_zero__less__diff_1) ).

fof(c_0_369_370,axiom,
    ! [X14,X8] :
      ( ~ c_lessequals(X8,X14,tc_nat)
      | X14 = c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X14,X8,tc_nat),X8,tc_nat) ),
    file('<stdin>',cls_le__imp__diff__is__add_0) ).

fof(c_0_370_371,axiom,
    ! [X1,X2] :
      ( c_HOL_Oplus__class_Oplus(X1,c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),tc_nat) = X2
      | ~ c_lessequals(X1,X2,tc_nat) ),
    file('<stdin>',cls_le__add__diff__inverse_0) ).

fof(c_0_371_372,axiom,
    ! [X1,X2] :
      ( c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),X1,tc_nat) = X2
      | ~ c_lessequals(X1,X2,tc_nat) ),
    file('<stdin>',cls_le__add__diff__inverse2_0) ).

fof(c_0_372_373,axiom,
    ! [X1,X8] :
      ( c_HOL_Ominus__class_Ominus(X1,c_HOL_Ominus__class_Ominus(X1,X8,tc_nat),tc_nat) = X8
      | ~ c_lessequals(X8,X1,tc_nat) ),
    file('<stdin>',cls_diff__diff__cancel_0) ).

fof(c_0_373_374,axiom,
    ! [X19,X9,X3] :
      ( c_HOL_Oord__class_Oless(X3,c_HOL_Oplus__class_Oplus(X9,X19,tc_nat),tc_nat)
      | ~ c_HOL_Oord__class_Oless(X3,X9,tc_nat) ),
    file('<stdin>',cls_termination__basic__simps_I1_J_0) ).

fof(c_0_374_375,axiom,
    ! [X19,X9,X3] :
      ( c_HOL_Oord__class_Oless(X3,c_HOL_Oplus__class_Oplus(X9,X19,tc_nat),tc_nat)
      | ~ c_HOL_Oord__class_Oless(X3,X19,tc_nat) ),
    file('<stdin>',cls_termination__basic__simps_I2_J_0) ).

fof(c_0_375_376,axiom,
    ! [X2,X14,X8] :
      ( c_HOL_Oord__class_Oless(X8,c_HOL_Oplus__class_Oplus(X14,X2,tc_nat),tc_nat)
      | ~ c_HOL_Oord__class_Oless(X8,X14,tc_nat) ),
    file('<stdin>',cls_trans__less__add1_0) ).

fof(c_0_376_377,axiom,
    ! [X2,X14,X8] :
      ( c_HOL_Oord__class_Oless(X8,c_HOL_Oplus__class_Oplus(X2,X14,tc_nat),tc_nat)
      | ~ c_HOL_Oord__class_Oless(X8,X14,tc_nat) ),
    file('<stdin>',cls_trans__less__add2_0) ).

fof(c_0_377_378,axiom,
    ! [X2,X14,X8] :
      ( c_lessequals(X8,c_HOL_Oplus__class_Oplus(X2,X14,tc_nat),tc_nat)
      | ~ c_lessequals(X8,X14,tc_nat) ),
    file('<stdin>',cls_trans__le__add2_0) ).

fof(c_0_378_379,axiom,
    ! [X2,X14,X8] :
      ( c_lessequals(X8,c_HOL_Oplus__class_Oplus(X14,X2,tc_nat),tc_nat)
      | ~ c_lessequals(X8,X14,tc_nat) ),
    file('<stdin>',cls_trans__le__add1_0) ).

fof(c_0_379_380,axiom,
    ! [X19,X9,X3] :
      ( c_lessequals(X3,c_HOL_Oplus__class_Oplus(X9,X19,tc_nat),tc_nat)
      | ~ c_lessequals(X3,X19,tc_nat) ),
    file('<stdin>',cls_termination__basic__simps_I4_J_0) ).

fof(c_0_380_381,axiom,
    ! [X19,X9,X3] :
      ( c_lessequals(X3,c_HOL_Oplus__class_Oplus(X9,X19,tc_nat),tc_nat)
      | ~ c_lessequals(X3,X9,tc_nat) ),
    file('<stdin>',cls_termination__basic__simps_I3_J_0) ).

fof(c_0_381_382,axiom,
    ! [X1,X7,X14] :
      ( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X14,X1,tc_nat),X7,tc_nat)
      | ~ c_HOL_Oord__class_Oless(X14,X7,tc_nat) ),
    file('<stdin>',cls_less__imp__diff__less_0) ).

fof(c_0_382_383,axiom,
    ! [X19,X9,X3,X18] :
      ( ~ class_Orderings_Opreorder(X18)
      | c_HOL_Oord__class_Oless(X3,X19,X18)
      | ~ c_HOL_Oord__class_Oless(X9,X19,X18)
      | ~ c_HOL_Oord__class_Oless(X3,X9,X18) ),
    file('<stdin>',cls_order__less__trans_0) ).

fof(c_0_383_384,axiom,
    ! [X19,X9,X3,X18] :
      ( ~ class_Orderings_Oorder(X18)
      | c_HOL_Oord__class_Oless(X19,X3,X18)
      | ~ c_HOL_Oord__class_Oless(X19,X9,X18)
      | ~ c_HOL_Oord__class_Oless(X9,X3,X18) ),
    file('<stdin>',cls_xt1_I10_J_0) ).

fof(c_0_384_385,axiom,
    ! [X19,X9,X3,X18] :
      ( ~ class_Orderings_Oorder(X18)
      | c_lessequals(X19,X3,X18)
      | ~ c_lessequals(X19,X9,X18)
      | ~ c_lessequals(X9,X3,X18) ),
    file('<stdin>',cls_xt1_I6_J_0) ).

fof(c_0_385_386,axiom,
    ! [X19,X9,X3,X18] :
      ( ~ class_Orderings_Oorder(X18)
      | c_HOL_Oord__class_Oless(X19,X3,X18)
      | ~ c_lessequals(X19,X9,X18)
      | ~ c_HOL_Oord__class_Oless(X9,X3,X18) ),
    file('<stdin>',cls_xt1_I7_J_0) ).

fof(c_0_386_387,axiom,
    ! [X19,X9,X3,X18] :
      ( ~ class_Orderings_Oorder(X18)
      | c_HOL_Oord__class_Oless(X19,X3,X18)
      | ~ c_HOL_Oord__class_Oless(X19,X9,X18)
      | ~ c_lessequals(X9,X3,X18) ),
    file('<stdin>',cls_xt1_I8_J_0) ).

fof(c_0_387_388,axiom,
    ! [X19,X9,X3,X18] :
      ( ~ class_Orderings_Opreorder(X18)
      | c_lessequals(X3,X19,X18)
      | ~ c_lessequals(X9,X19,X18)
      | ~ c_lessequals(X3,X9,X18) ),
    file('<stdin>',cls_order__trans_0) ).

fof(c_0_388_389,axiom,
    ! [X19,X9,X3,X18] :
      ( ~ class_Orderings_Opreorder(X18)
      | c_HOL_Oord__class_Oless(X3,X19,X18)
      | ~ c_HOL_Oord__class_Oless(X9,X19,X18)
      | ~ c_lessequals(X3,X9,X18) ),
    file('<stdin>',cls_order__le__less__trans_0) ).

fof(c_0_389_390,axiom,
    ! [X19,X9,X3,X18] :
      ( ~ class_Orderings_Opreorder(X18)
      | c_HOL_Oord__class_Oless(X3,X19,X18)
      | ~ c_lessequals(X9,X19,X18)
      | ~ c_HOL_Oord__class_Oless(X3,X9,X18) ),
    file('<stdin>',cls_order__less__le__trans_0) ).

fof(c_0_390_391,axiom,
    ! [X1,X2] :
      ( c_Suc(c_Divides_Odiv__class_Omod(X2,X1,tc_nat)) != X1
      | c_Divides_Odiv__class_Omod(c_Suc(X2),X1,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat) ),
    file('<stdin>',cls_mod__Suc_0) ).

fof(c_0_391_392,axiom,
    ! [X7,X14,X8] :
      ( c_HOL_Oord__class_Oless(c_Suc(X8),X7,tc_nat)
      | ~ c_HOL_Oord__class_Oless(X14,X7,tc_nat)
      | ~ c_HOL_Oord__class_Oless(X8,X14,tc_nat) ),
    file('<stdin>',cls_less__trans__Suc_0) ).

fof(c_0_392_393,axiom,
    ! [X16,X17,X18] :
      ( ~ class_Divides_Osemiring__div(X18)
      | c_Divides_Odiv__class_Omod(c_Divides_Odiv__class_Omod(X17,X16,X18),X16,X18) = c_Divides_Odiv__class_Omod(X17,X16,X18) ),
    file('<stdin>',cls_mod__mod__trivial_0) ).

fof(c_0_393_394,axiom,
    ! [X9,X3,X18] :
      ( ~ class_Orderings_Olinorder(X18)
      | c_Orderings_Oord__class_Omin(X3,c_Orderings_Oord__class_Omin(X3,X9,X18),X18) = c_Orderings_Oord__class_Omin(X3,X9,X18) ),
    file('<stdin>',cls_min__max_Oinf__left__idem_0) ).

fof(c_0_394_395,axiom,
    ! [X9,X3,X18] :
      ( ~ class_OrderedGroup_Oab__semigroup__idem__mult(X18)
      | c_HOL_Otimes__class_Otimes(X3,c_HOL_Otimes__class_Otimes(X3,X9,X18),X18) = c_HOL_Otimes__class_Otimes(X3,X9,X18) ),
    file('<stdin>',cls_mult__left__idem_0) ).

fof(c_0_395_396,axiom,
    ! [X16,X17,X18] :
      ( ~ class_Divides_Osemiring__div(X18)
      | c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X17,X16,X18),X16,X18) = c_Divides_Odiv__class_Omod(X17,X16,X18) ),
    file('<stdin>',cls_mod__add__self2_0) ).

fof(c_0_396_397,axiom,
    ! [X16,X17,X18] :
      ( ~ class_Divides_Osemiring__div(X18)
      | c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X16,X17,X18),X16,X18) = c_Divides_Odiv__class_Omod(X17,X16,X18) ),
    file('<stdin>',cls_mod__add__self1_0) ).

fof(c_0_397_398,axiom,
    ! [X9,X3,X18] :
      ( ~ class_Orderings_Olinorder(X18)
      | c_Orderings_Oord__class_Omax(X3,c_Orderings_Oord__class_Omax(X3,X9,X18),X18) = c_Orderings_Oord__class_Omax(X3,X9,X18) ),
    file('<stdin>',cls_min__max_Osup__left__idem_0) ).

fof(c_0_398_399,axiom,
    ! [X1] :
      ( c_Suc(c_HOL_Ominus__class_Ominus(X1,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat)) = X1
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
    file('<stdin>',cls_Suc__pred_0) ).

fof(c_0_399_400,axiom,
    ! [X7,X14,X8] :
      ( c_lessequals(X8,X7,tc_nat)
      | ~ c_lessequals(X14,X7,tc_nat)
      | ~ c_lessequals(X8,X14,tc_nat) ),
    file('<stdin>',cls_le__trans_0) ).

fof(c_0_400_401,axiom,
    ! [X1,X2] :
      ( c_HOL_Oplus__class_Oplus(X1,c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),tc_nat) = X2
      | c_HOL_Oord__class_Oless(X2,X1,tc_nat) ),
    file('<stdin>',cls_add__diff__inverse_0) ).

fof(c_0_401_402,axiom,
    ! [X1] :
      ( c_Suc(c_HOL_Ominus__class_Ominus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat)) = X1
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
    file('<stdin>',cls_Suc__diff__1_0) ).

fof(c_0_402_403,axiom,
    ! [X1] :
      ( X1 = c_Suc(c_HOL_Ominus__class_Ominus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat))
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
    file('<stdin>',cls_Suc__pred_H_0) ).

fof(c_0_403_404,axiom,
    ! [X9,X3,X18] :
      ( ~ class_Orderings_Opreorder(X18)
      | c_HOL_Oord__class_Oless(X3,X9,X18)
      | c_lessequals(X9,X3,X18)
      | ~ c_lessequals(X3,X9,X18) ),
    file('<stdin>',cls_less__le__not__le_2) ).

fof(c_0_404_405,axiom,
    ! [X18] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X18)
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X18),c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(X18),c_HOL_Oone__class_Oone(X18),X18),X18) ),
    file('<stdin>',cls_zero__less__two_0) ).

fof(c_0_405_406,axiom,
    ! [X19,X9,X3,X18] :
      ( ~ class_Ring__and__Field_Oidom(X18)
      | ~ class_Int_Onumber__ring(X18)
      | c_HOL_Oplus__class_Oplus(X3,X9,X18) != c_HOL_Oplus__class_Oplus(X3,X19,X18)
      | X9 = X19 ),
    file('<stdin>',cls_class__ringb_Oadd__cancel_0) ).

fof(c_0_406_407,axiom,
    ! [X1,X2,X7] :
      ( c_HOL_Otimes__class_Otimes(c_Suc(X7),X2,tc_nat) != c_HOL_Otimes__class_Otimes(c_Suc(X7),X1,tc_nat)
      | X2 = X1 ),
    file('<stdin>',cls_Suc__mult__cancel1_0) ).

fof(c_0_407_408,axiom,
    ! [X7,X8] :
      ( c_Lambda_Olift(c_Lambda_OdB_OVar(X8),X7) = c_Lambda_OdB_OVar(c_HOL_Oplus__class_Oplus(X8,c_HOL_Oone__class_Oone(tc_nat),tc_nat))
      | c_HOL_Oord__class_Oless(X8,X7,tc_nat) ),
    file('<stdin>',cls_lift_Osimps_I1_J_1) ).

fof(c_0_408_409,axiom,
    ! [X9,X3,X18] :
      ( ~ class_Orderings_Oorder(X18)
      | X3 = X9
      | ~ c_lessequals(X9,X3,X18)
      | ~ c_lessequals(X3,X9,X18) ),
    file('<stdin>',cls_order__eq__iff_2) ).

fof(c_0_409_410,axiom,
    ! [X9,X3,X18] :
      ( ~ class_Orderings_Oorder(X18)
      | X3 = X9
      | ~ c_lessequals(X9,X3,X18)
      | ~ c_lessequals(X3,X9,X18) ),
    file('<stdin>',cls_order__antisym_0) ).

fof(c_0_410_411,axiom,
    ! [X9,X3,X18] :
      ( ~ class_Orderings_Oorder(X18)
      | X3 = X9
      | ~ c_lessequals(X3,X9,X18)
      | ~ c_lessequals(X9,X3,X18) ),
    file('<stdin>',cls_order__antisym__conv_0) ).

fof(c_0_411_412,axiom,
    ! [X17,X18] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X18)
      | c_HOL_Oord__class_Oless(X17,c_HOL_Oplus__class_Oplus(X17,c_HOL_Oone__class_Oone(X18),X18),X18) ),
    file('<stdin>',cls_less__add__one_0) ).

fof(c_0_412_413,axiom,
    ! [X9,X32,X3,X18] :
      ( ~ class_OrderedGroup_Oab__group__add(X18)
      | c_HOL_Ominus__class_Ominus(X32,X9,X18) != c_HOL_Ominus__class_Ominus(X3,X3,X18)
      | X32 = X9 ),
    file('<stdin>',cls_eq__eqI_1) ).

fof(c_0_413_414,axiom,
    ! [X25,X26,X3,X18] :
      ( ~ class_OrderedGroup_Oab__group__add(X18)
      | c_HOL_Ominus__class_Ominus(X3,X3,X18) != c_HOL_Ominus__class_Ominus(X26,X25,X18)
      | X26 = X25 ),
    file('<stdin>',cls_eq__eqI_0) ).

fof(c_0_414_415,axiom,
    ! [X20,X16,X17,X18] :
      ( ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X18)
      | c_HOL_Oplus__class_Oplus(X17,X16,X18) != c_HOL_Oplus__class_Oplus(X17,X20,X18)
      | X16 = X20 ),
    file('<stdin>',cls_add__imp__eq_0) ).

fof(c_0_415_416,axiom,
    ! [X20,X16,X17,X18] :
      ( ~ class_OrderedGroup_Ocancel__semigroup__add(X18)
      | c_HOL_Oplus__class_Oplus(X17,X16,X18) != c_HOL_Oplus__class_Oplus(X17,X20,X18)
      | X16 = X20 ),
    file('<stdin>',cls_add__left__cancel_0) ).

fof(c_0_416_417,axiom,
    ! [X20,X16,X17,X18] :
      ( ~ class_OrderedGroup_Ocancel__semigroup__add(X18)
      | c_HOL_Oplus__class_Oplus(X16,X17,X18) != c_HOL_Oplus__class_Oplus(X20,X17,X18)
      | X16 = X20 ),
    file('<stdin>',cls_add__right__cancel_0) ).

fof(c_0_417_418,axiom,
    ! [X3,X18] :
      ( ~ class_Orderings_Olinorder(X18)
      | ~ c_lessequals(X3,X3,X18)
      | ~ c_HOL_Oord__class_Oless(X3,X3,X18) ),
    file('<stdin>',cls_linorder__antisym__conv2_1) ).

fof(c_0_418_419,axiom,
    ! [X9,X3,X18] :
      ( ~ class_Orderings_Olinorder(X18)
      | ~ c_HOL_Oord__class_Oless(X3,X9,X18)
      | ~ c_lessequals(X9,X3,X18) ),
    file('<stdin>',cls_linorder__not__less_1) ).

fof(c_0_419_420,axiom,
    ! [X9,X3,X18] :
      ( ~ class_Orderings_Olinorder(X18)
      | ~ c_lessequals(X3,X9,X18)
      | ~ c_HOL_Oord__class_Oless(X9,X3,X18) ),
    file('<stdin>',cls_linorder__not__le_1) ).

fof(c_0_420_421,axiom,
    ! [X9,X3,X18] :
      ( ~ class_Orderings_Opreorder(X18)
      | ~ c_lessequals(X9,X3,X18)
      | ~ c_HOL_Oord__class_Oless(X3,X9,X18) ),
    file('<stdin>',cls_less__le__not__le_1) ).

fof(c_0_421_422,axiom,
    ! [X16,X17,X18] :
      ( ~ class_Orderings_Oorder(X18)
      | ~ c_HOL_Oord__class_Oless(X17,X16,X18)
      | ~ c_HOL_Oord__class_Oless(X16,X17,X18) ),
    file('<stdin>',cls_xt1_I9_J_0) ).

fof(c_0_422_423,axiom,
    ! [X9,X3,X18] :
      ( ~ class_Orderings_Olinorder(X18)
      | ~ c_HOL_Oord__class_Oless(X3,X9,X18)
      | ~ c_HOL_Oord__class_Oless(X9,X3,X18) ),
    file('<stdin>',cls_not__less__iff__gr__or__eq_1) ).

fof(c_0_423_424,axiom,
    ! [X9,X3,X18] :
      ( ~ class_Orderings_Opreorder(X18)
      | ~ c_HOL_Oord__class_Oless(X9,X3,X18)
      | ~ c_HOL_Oord__class_Oless(X3,X9,X18) ),
    file('<stdin>',cls_order__less__asym_0) ).

fof(c_0_424_425,axiom,
    ! [X16,X17,X18] :
      ( ~ class_Orderings_Opreorder(X18)
      | ~ c_HOL_Oord__class_Oless(X16,X17,X18)
      | ~ c_HOL_Oord__class_Oless(X17,X16,X18) ),
    file('<stdin>',cls_order__less__asym_H_0) ).

fof(c_0_425_426,axiom,
    ! [X1,X2] :
      ( X1 = X2
      | ~ c_HOL_Oord__class_Oless(X1,c_Suc(X2),tc_nat)
      | ~ c_lessequals(X2,X1,tc_nat) ),
    file('<stdin>',cls_le__less__Suc__eq_0) ).

fof(c_0_426_427,axiom,
    ! [X1,X2] :
      ( ~ c_lessequals(X2,X1,tc_nat)
      | ~ c_lessequals(c_Suc(X1),X2,tc_nat) ),
    file('<stdin>',cls_not__less__eq__eq_1) ).

fof(c_0_427_428,axiom,
    ! [X1,X2] :
      ( ~ c_HOL_Oord__class_Oless(X2,X1,tc_nat)
      | ~ c_HOL_Oord__class_Oless(X1,c_Suc(X2),tc_nat) ),
    file('<stdin>',cls_not__less__eq_1) ).

fof(c_0_428_429,axiom,
    ! [X1,X2] :
      ( c_HOL_Ominus__class_Ominus(X1,X2,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)
      | c_HOL_Ominus__class_Ominus(X2,X1,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)
      | X2 = X1 ),
    file('<stdin>',cls_diffs0__imp__equal_0) ).

fof(c_0_429_430,axiom,
    ! [X17,X18] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X18)
      | c_lessequals(c_HOL_Ozero__class_Ozero(X18),c_HOL_Otimes__class_Otimes(X17,X17,X18),X18) ),
    file('<stdin>',cls_zero__le__square_0) ).

fof(c_0_430_431,axiom,
    ! [X1,X2,X7] :
      ( c_HOL_Otimes__class_Otimes(X7,X2,tc_nat) != c_HOL_Otimes__class_Otimes(X7,X1,tc_nat)
      | X2 = X1
      | X7 = c_HOL_Ozero__class_Ozero(tc_nat) ),
    file('<stdin>',cls_nat__mult__eq__cancel__disj_0) ).

fof(c_0_431_432,axiom,
    ! [X1,X2,X7] :
      ( c_HOL_Otimes__class_Otimes(X7,X2,tc_nat) != c_HOL_Otimes__class_Otimes(X7,X1,tc_nat)
      | X7 = c_HOL_Ozero__class_Ozero(tc_nat)
      | X2 = X1 ),
    file('<stdin>',cls_mult__cancel1_0) ).

fof(c_0_432_433,axiom,
    ! [X1,X2,X7] :
      ( c_HOL_Otimes__class_Otimes(X2,X7,tc_nat) != c_HOL_Otimes__class_Otimes(X1,X7,tc_nat)
      | X7 = c_HOL_Ozero__class_Ozero(tc_nat)
      | X2 = X1 ),
    file('<stdin>',cls_mult__cancel2_0) ).

fof(c_0_433_434,axiom,
    ! [X16,X17,X18] :
      ( ~ class_Divides_Osemiring__div(X18)
      | c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X17,X16,X18),X16,X18) = c_HOL_Ozero__class_Ozero(X18) ),
    file('<stdin>',cls_mod__mult__self2__is__0_0) ).

fof(c_0_434_435,axiom,
    ! [X16,X17,X18] :
      ( ~ class_Divides_Osemiring__div(X18)
      | c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X16,X17,X18),X16,X18) = c_HOL_Ozero__class_Ozero(X18) ),
    file('<stdin>',cls_mod__mult__self1__is__0_0) ).

fof(c_0_435_436,axiom,
    ! [X1,X2] :
      ( X2 = X1
      | ~ c_lessequals(X1,X2,tc_nat)
      | ~ c_lessequals(X2,X1,tc_nat) ),
    file('<stdin>',cls_le__antisym_0) ).

fof(c_0_436_437,axiom,
    ! [X16,X17,X18] :
      ( ~ class_OrderedGroup_Ogroup__add(X18)
      | c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X17,X16,X18),X16,X18) = X17 ),
    file('<stdin>',cls_diff__add__cancel_0) ).

fof(c_0_437_438,axiom,
    ! [X9,X3,X18] :
      ( ~ class_Orderings_Olinorder(X18)
      | c_Orderings_Oord__class_Omin(X3,c_Orderings_Oord__class_Omax(X3,X9,X18),X18) = X3 ),
    file('<stdin>',cls_min__max_Oinf__sup__absorb_0) ).

fof(c_0_438_439,axiom,
    ! [X9,X3,X18] :
      ( ~ class_Orderings_Olinorder(X18)
      | c_Orderings_Oord__class_Omax(X3,c_Orderings_Oord__class_Omin(X3,X9,X18),X18) = X3 ),
    file('<stdin>',cls_min__max_Osup__inf__absorb_0) ).

fof(c_0_439_440,axiom,
    ! [X16,X17,X18] :
      ( ~ class_OrderedGroup_Ogroup__add(X18)
      | c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X17,X16,X18),X16,X18) = X17 ),
    file('<stdin>',cls_add__diff__cancel_0) ).

fof(c_0_440_441,axiom,
    ! [X9,X3,X18] :
      ( ~ class_Orderings_Olinorder(X18)
      | c_lessequals(X3,c_Orderings_Oord__class_Omax(X3,X9,X18),X18) ),
    file('<stdin>',cls_le__maxI1_0) ).

fof(c_0_441_442,axiom,
    ! [X9,X3,X18] :
      ( ~ class_Orderings_Olinorder(X18)
      | c_lessequals(X9,c_Orderings_Oord__class_Omax(X3,X9,X18),X18) ),
    file('<stdin>',cls_le__maxI2_0) ).

fof(c_0_442_443,axiom,
    ! [X9,X3,X18] :
      ( ~ class_Orderings_Olinorder(X18)
      | c_lessequals(c_Orderings_Oord__class_Omin(X3,X9,X18),X3,X18) ),
    file('<stdin>',cls_min__max_Oinf__le1_0) ).

fof(c_0_443_444,axiom,
    ! [X9,X3,X18] :
      ( ~ class_Orderings_Olinorder(X18)
      | c_lessequals(c_Orderings_Oord__class_Omin(X3,X9,X18),X9,X18) ),
    file('<stdin>',cls_min__max_Oinf__le2_0) ).

fof(c_0_444_445,axiom,
    ! [X19,X9,X3] :
      ( c_HOL_Oplus__class_Oplus(X3,X9,tc_nat) != c_HOL_Oplus__class_Oplus(X3,X19,tc_nat)
      | X9 = X19 ),
    file('<stdin>',cls_natgb_Oadd__cancel_0) ).

fof(c_0_445_446,axiom,
    ! [X1,X2,X7] :
      ( c_HOL_Oplus__class_Oplus(X2,X7,tc_nat) != c_HOL_Oplus__class_Oplus(X1,X7,tc_nat)
      | X2 = X1 ),
    file('<stdin>',cls_nat__add__right__cancel_0) ).

fof(c_0_446_447,axiom,
    ! [X1,X2,X7] :
      ( c_HOL_Oplus__class_Oplus(X7,X2,tc_nat) != c_HOL_Oplus__class_Oplus(X7,X1,tc_nat)
      | X2 = X1 ),
    file('<stdin>',cls_nat__add__left__cancel_0) ).

fof(c_0_447_448,axiom,
    ! [X1,X2] :
      ( c_lessequals(X1,X2,tc_nat)
      | ~ c_lessequals(c_Suc(X1),c_Suc(X2),tc_nat) ),
    file('<stdin>',cls_Suc__le__mono_0) ).

fof(c_0_448_449,axiom,
    ! [X1,X2] :
      ( c_HOL_Oord__class_Oless(X2,X1,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_Suc(X2),c_Suc(X1),tc_nat) ),
    file('<stdin>',cls_Suc__less__eq_0) ).

fof(c_0_449_450,axiom,
    ! [X1,X2] :
      ( X2 = c_Suc(X1)
      | c_lessequals(X2,X1,tc_nat)
      | ~ c_lessequals(X2,c_Suc(X1),tc_nat) ),
    file('<stdin>',cls_le__SucE_0) ).

fof(c_0_450_451,axiom,
    ! [X16,X17,X18] :
      ( ~ class_Orderings_Oorder(X18)
      | c_HOL_Oord__class_Oless(X16,X17,X18)
      | X17 = X16
      | ~ c_lessequals(X16,X17,X18) ),
    file('<stdin>',cls_xt1_I11_J_0) ).

fof(c_0_451_452,axiom,
    ! [X16,X17,X18] :
      ( ~ class_Orderings_Oorder(X18)
      | c_HOL_Oord__class_Oless(X16,X17,X18)
      | ~ c_lessequals(X16,X17,X18)
      | X17 = X16 ),
    file('<stdin>',cls_xt1_I12_J_0) ).

fof(c_0_452_453,axiom,
    ! [X9,X3,X18] :
      ( ~ class_Orderings_Oorder(X18)
      | X3 = X9
      | c_HOL_Oord__class_Oless(X3,X9,X18)
      | ~ c_lessequals(X3,X9,X18) ),
    file('<stdin>',cls_order__le__less_0) ).

fof(c_0_453_454,axiom,
    ! [X9,X3,X18] :
      ( ~ class_Orderings_Oorder(X18)
      | c_HOL_Oord__class_Oless(X3,X9,X18)
      | X3 = X9
      | ~ c_lessequals(X3,X9,X18) ),
    file('<stdin>',cls_order__less__le_2) ).

fof(c_0_454_455,axiom,
    ! [X16,X17,X18] :
      ( ~ class_Orderings_Oorder(X18)
      | c_HOL_Oord__class_Oless(X17,X16,X18)
      | X17 = X16
      | ~ c_lessequals(X17,X16,X18) ),
    file('<stdin>',cls_order__le__neq__trans_0) ).

fof(c_0_455_456,axiom,
    ! [X16,X17,X18] :
      ( ~ class_Orderings_Oorder(X18)
      | c_HOL_Oord__class_Oless(X17,X16,X18)
      | ~ c_lessequals(X17,X16,X18)
      | X17 = X16 ),
    file('<stdin>',cls_order__neq__le__trans_0) ).

fof(c_0_456_457,axiom,
    ! [X9,X3,X18] :
      ( ~ class_Orderings_Olinorder(X18)
      | X3 = X9
      | ~ c_lessequals(X3,X9,X18)
      | c_HOL_Oord__class_Oless(X3,X9,X18) ),
    file('<stdin>',cls_linorder__antisym__conv1_0) ).

fof(c_0_457_458,axiom,
    ! [X9,X3,X18] :
      ( ~ class_Orderings_Olinorder(X18)
      | X3 = X9
      | c_HOL_Oord__class_Oless(X3,X9,X18)
      | ~ c_lessequals(X3,X9,X18) ),
    file('<stdin>',cls_linorder__antisym__conv2_0) ).

fof(c_0_458_459,axiom,
    ! [X9,X3,X18] :
      ( ~ class_Orderings_Olinorder(X18)
      | c_Orderings_Oord__class_Omax(X3,X9,X18) != X9
      | c_lessequals(X3,X9,X18) ),
    file('<stdin>',cls_min__max_Ole__iff__sup_1) ).

fof(c_0_459_460,axiom,
    ! [X9,X3,X18] :
      ( ~ class_Orderings_Olinorder(X18)
      | c_Orderings_Oord__class_Omin(X3,X9,X18) != X3
      | c_lessequals(X3,X9,X18) ),
    file('<stdin>',cls_min__max_Ole__iff__inf_1) ).

fof(c_0_460_461,axiom,
    ! [X1,X2] :
      ( c_lessequals(c_Suc(X1),c_Suc(X2),tc_nat)
      | ~ c_lessequals(X1,X2,tc_nat) ),
    file('<stdin>',cls_Suc__le__mono_1) ).

fof(c_0_461_462,axiom,
    ! [X3,X1] :
      ( c_HOL_Oord__class_Oless(c_Suc(X3),c_Suc(X1),tc_nat)
      | ~ c_HOL_Oord__class_Oless(X3,X1,tc_nat) ),
    file('<stdin>',cls_less__Suc__eq__0__disj_3) ).

fof(c_0_462_463,axiom,
    ! [X1,X2] :
      ( c_HOL_Oord__class_Oless(c_Suc(X2),c_Suc(X1),tc_nat)
      | ~ c_HOL_Oord__class_Oless(X2,X1,tc_nat) ),
    file('<stdin>',cls_Suc__mono_0) ).

fof(c_0_463_464,axiom,
    ! [X9,X3,X18] :
      ( ~ class_Orderings_Olinorder(X18)
      | c_Orderings_Oord__class_Omax(X3,X9,X18) = X9
      | ~ c_lessequals(X3,X9,X18) ),
    file('<stdin>',cls_min__max_Ole__iff__sup_0) ).

fof(c_0_464_465,axiom,
    ! [X9,X3,X18] :
      ( ~ class_Orderings_Olinorder(X18)
      | c_Orderings_Oord__class_Omax(X3,X9,X18) = X3
      | ~ c_lessequals(X9,X3,X18) ),
    file('<stdin>',cls_min__max_Osup__absorb1_0) ).

fof(c_0_465_466,axiom,
    ! [X9,X3,X18] :
      ( ~ class_Orderings_Olinorder(X18)
      | c_Orderings_Oord__class_Omin(X3,X9,X18) = X3
      | ~ c_lessequals(X3,X9,X18) ),
    file('<stdin>',cls_min__max_Ole__iff__inf_0) ).

fof(c_0_466_467,axiom,
    ! [X9,X3,X18] :
      ( ~ class_Orderings_Olinorder(X18)
      | c_Orderings_Oord__class_Omin(X3,X9,X18) = X9
      | ~ c_lessequals(X9,X3,X18) ),
    file('<stdin>',cls_min__max_Oinf__absorb2_0) ).

fof(c_0_467_468,axiom,
    ! [X1,X2] :
      ( X1 = X2
      | ~ c_HOL_Oord__class_Oless(X1,c_Suc(X2),tc_nat)
      | c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
    file('<stdin>',cls_not__less__less__Suc__eq_0) ).

fof(c_0_468_469,axiom,
    ! [X1,X2] :
      ( X2 = X1
      | ~ c_HOL_Oord__class_Oless(X1,c_Suc(X2),tc_nat)
      | c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
    file('<stdin>',cls_less__antisym_0) ).

fof(c_0_469_470,axiom,
    ! [X1,X2] :
      ( X2 = X1
      | c_HOL_Oord__class_Oless(X2,X1,tc_nat)
      | ~ c_HOL_Oord__class_Oless(X2,c_Suc(X1),tc_nat) ),
    file('<stdin>',cls_less__SucE_0) ).

fof(c_0_470_471,axiom,
    ! [X15,X14,X8] :
      ( c_Lambda_Osubst(c_Lambda_OdB_OVar(X14),X15,X8) = c_Lambda_OdB_OVar(X14)
      | ~ c_HOL_Oord__class_Oless(X14,X8,tc_nat) ),
    file('<stdin>',cls_subst__lt_0) ).

fof(c_0_471_472,axiom,
    ! [X1,X2] :
      ( c_HOL_Oord__class_Oless(c_Suc(X2),X1,tc_nat)
      | c_Suc(X2) = X1
      | ~ c_HOL_Oord__class_Oless(X2,X1,tc_nat) ),
    file('<stdin>',cls_Suc__lessI_0) ).

fof(c_0_472_473,axiom,
    ! [X9,X3,X18] :
      ( ~ class_Orderings_Oorder(X18)
      | c_lessequals(X3,X9,X18)
      | ~ c_HOL_Oord__class_Oless(X3,X9,X18) ),
    file('<stdin>',cls_order__le__less_1) ).

fof(c_0_473_474,axiom,
    ! [X9,X3,X18] :
      ( ~ class_Orderings_Opreorder(X18)
      | c_lessequals(X3,X9,X18)
      | ~ c_HOL_Oord__class_Oless(X3,X9,X18) ),
    file('<stdin>',cls_order__less__imp__le_0) ).

fof(c_0_474_475,axiom,
    ! [X1,X2] :
      ( c_HOL_Oord__class_Oless(X2,X1,tc_nat)
      | ~ c_lessequals(c_Suc(X2),X1,tc_nat) ),
    file('<stdin>',cls_Suc__le__eq_0) ).

fof(c_0_475_476,axiom,
    ! [X1,X2] :
      ( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
      | ~ c_lessequals(c_Suc(X1),X2,tc_nat) ),
    file('<stdin>',cls_less__eq__Suc__le_1) ).

fof(c_0_476_477,axiom,
    ! [X1,X2] :
      ( c_lessequals(X2,X1,tc_nat)
      | ~ c_HOL_Oord__class_Oless(X2,c_Suc(X1),tc_nat) ),
    file('<stdin>',cls_less__Suc__eq__le_0) ).

fof(c_0_477_478,axiom,
    ! [X1,X2] :
      ( c_HOL_Oord__class_Oless(X2,X1,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_Suc(X2),X1,tc_nat) ),
    file('<stdin>',cls_Suc__lessD_0) ).

fof(c_0_478_479,axiom,
    ! [X1,X2] :
      ( c_lessequals(X2,X1,tc_nat)
      | ~ c_lessequals(c_Suc(X2),X1,tc_nat) ),
    file('<stdin>',cls_Suc__leD_0) ).

fof(c_0_479_480,axiom,
    ! [X1,X2] :
      ( c_lessequals(c_Suc(X2),X1,tc_nat)
      | ~ c_HOL_Oord__class_Oless(X2,X1,tc_nat) ),
    file('<stdin>',cls_Suc__leI_0) ).

fof(c_0_480_481,axiom,
    ! [X1,X2] :
      ( c_lessequals(c_Suc(X1),X2,tc_nat)
      | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
    file('<stdin>',cls_less__eq__Suc__le_0) ).

fof(c_0_481_482,axiom,
    ! [X1,X2] :
      ( c_HOL_Oord__class_Oless(X2,c_Suc(X1),tc_nat)
      | ~ c_lessequals(X2,X1,tc_nat) ),
    file('<stdin>',cls_less__Suc__eq__le_1) ).

fof(c_0_482_483,axiom,
    ! [X3] :
      ( ~ c_lessequals(X3,X3,tc_nat)
      | c_HOL_Oord__class_Oless(X3,c_Suc(X3),tc_nat) ),
    file('<stdin>',cls_le__less__Suc__eq_1) ).

fof(c_0_483_484,axiom,
    ! [X1,X2] :
      ( c_HOL_Oord__class_Oless(X2,c_Suc(X1),tc_nat)
      | ~ c_HOL_Oord__class_Oless(X2,X1,tc_nat) ),
    file('<stdin>',cls_less__SucI_0) ).

fof(c_0_484_485,axiom,
    ! [X1,X2] :
      ( c_lessequals(X2,c_Suc(X1),tc_nat)
      | ~ c_lessequals(X2,X1,tc_nat) ),
    file('<stdin>',cls_le__SucI_0) ).

fof(c_0_485_486,axiom,
    ! [X1,X2] :
      ( c_HOL_Ominus__class_Ominus(X2,X1,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)
      | c_lessequals(X2,X1,tc_nat) ),
    file('<stdin>',cls_diff__is__0__eq_0) ).

fof(c_0_486_487,axiom,
    ! [X1,X2] :
      ( c_HOL_Ominus__class_Ominus(X2,X1,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat)
      | ~ c_lessequals(X2,X1,tc_nat) ),
    file('<stdin>',cls_diff__is__0__eq_1) ).

fof(c_0_487_488,axiom,
    ! [X1,X2] :
      ( c_HOL_Oord__class_Oless(X2,X1,tc_nat)
      | X2 = X1
      | ~ c_lessequals(X2,X1,tc_nat) ),
    file('<stdin>',cls_nat__less__le_2) ).

fof(c_0_488_489,axiom,
    ! [X1,X2] :
      ( X2 = X1
      | c_HOL_Oord__class_Oless(X2,X1,tc_nat)
      | ~ c_lessequals(X2,X1,tc_nat) ),
    file('<stdin>',cls_le__eq__less__or__eq_0) ).

fof(c_0_489_490,axiom,
    ! [X1,X2] :
      ( c_HOL_Oord__class_Oless(X2,X1,tc_nat)
      | X2 = X1
      | ~ c_lessequals(X2,X1,tc_nat) ),
    file('<stdin>',cls_le__neq__implies__less_0) ).

fof(c_0_490_491,axiom,
    ! [X1,X2] :
      ( c_Divides_Odiv__class_Omod(X2,X1,tc_nat) = X2
      | ~ c_HOL_Oord__class_Oless(X2,X1,tc_nat) ),
    file('<stdin>',cls_mod__if_0) ).

fof(c_0_491_492,axiom,
    ! [X9,X3] :
      ( c_lessequals(X3,X9,tc_nat)
      | ~ c_HOL_Oord__class_Oless(X3,X9,tc_nat) ),
    file('<stdin>',cls_termination__basic__simps_I5_J_0) ).

fof(c_0_492_493,axiom,
    ! [X1,X2] :
      ( c_lessequals(X2,X1,tc_nat)
      | ~ c_HOL_Oord__class_Oless(X2,X1,tc_nat) ),
    file('<stdin>',cls_nat__less__le_0) ).

fof(c_0_493_494,axiom,
    ! [X5,X7,X8] :
      ( c_Lambda_Osubst(c_Lambda_OdB_OVar(X8),X5,X7) = c_Lambda_OdB_OVar(X8)
      | X8 = X7
      | c_HOL_Oord__class_Oless(X7,X8,tc_nat) ),
    file('<stdin>',cls_subst__Var_2) ).

fof(c_0_494_495,axiom,
    ! [X9,X3,X18] :
      ( ~ class_Ring__and__Field_Oordered__idom(X18)
      | c_HOL_Oord__class_Oless(X9,X3,X18)
      | c_HOL_Oord__class_Oless(X3,X9,X18)
      | X3 = X9 ),
    file('<stdin>',cls_linorder__neqE__ordered__idom_0) ).

fof(c_0_495_496,axiom,
    ! [X9,X3,X18] :
      ( ~ class_Orderings_Olinorder(X18)
      | X3 = X9
      | c_HOL_Oord__class_Oless(X9,X3,X18)
      | c_HOL_Oord__class_Oless(X3,X9,X18) ),
    file('<stdin>',cls_not__less__iff__gr__or__eq_0) ).

fof(c_0_496_497,axiom,
    ! [X9,X3,X18] :
      ( ~ class_Orderings_Olinorder(X18)
      | c_HOL_Oord__class_Oless(X9,X3,X18)
      | c_HOL_Oord__class_Oless(X3,X9,X18)
      | X3 = X9 ),
    file('<stdin>',cls_linorder__neqE_0) ).

fof(c_0_497_498,axiom,
    ! [X9,X3,X18] :
      ( ~ class_Orderings_Olinorder(X18)
      | c_HOL_Oord__class_Oless(X9,X3,X18)
      | X3 = X9
      | c_HOL_Oord__class_Oless(X3,X9,X18) ),
    file('<stdin>',cls_linorder__less__linear_0) ).

fof(c_0_498_499,axiom,
    ! [X9,X3,X18] :
      ( ~ class_Orderings_Olinorder(X18)
      | X3 = X9
      | c_HOL_Oord__class_Oless(X3,X9,X18)
      | c_HOL_Oord__class_Oless(X9,X3,X18) ),
    file('<stdin>',cls_linorder__antisym__conv3_0) ).

fof(c_0_499_500,axiom,
    ! [X9,X3,X18] :
      ( ~ class_Orderings_Olinorder(X18)
      | c_HOL_Oord__class_Oless(X3,X9,X18)
      | c_lessequals(X9,X3,X18) ),
    file('<stdin>',cls_not__leE_0) ).

fof(c_0_500_501,axiom,
    ! [X3,X18] :
      ( ~ class_Orderings_Olinorder(X18)
      | c_HOL_Oord__class_Oless(X3,X3,X18)
      | c_lessequals(X3,X3,X18) ),
    file('<stdin>',cls_linorder__antisym__conv1_1) ).

fof(c_0_501_502,axiom,
    ! [X9,X3,X18] :
      ( ~ class_Orderings_Olinorder(X18)
      | c_lessequals(X9,X3,X18)
      | c_HOL_Oord__class_Oless(X3,X9,X18) ),
    file('<stdin>',cls_linorder__not__less_0) ).

fof(c_0_502_503,axiom,
    ! [X9,X3,X18] :
      ( ~ class_Orderings_Olinorder(X18)
      | c_HOL_Oord__class_Oless(X9,X3,X18)
      | c_lessequals(X3,X9,X18) ),
    file('<stdin>',cls_linorder__not__le_0) ).

fof(c_0_503_504,axiom,
    ! [X9,X3,X18] :
      ( ~ class_Orderings_Olinorder(X18)
      | c_lessequals(X9,X3,X18)
      | c_lessequals(X3,X9,X18) ),
    file('<stdin>',cls_linorder__linear_0) ).

fof(c_0_504_505,axiom,
    ! [X20,X17,X18] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X18)
      | c_HOL_Oplus__class_Oplus(X17,X20,X18) = c_HOL_Oplus__class_Oplus(X20,X17,X18) ),
    file('<stdin>',cls_class__semiring_Osemiring__rules_I24_J_0) ).

fof(c_0_505_506,axiom,
    ! [X16,X17,X18] :
      ( ~ class_OrderedGroup_Ocomm__monoid__add(X18)
      | c_HOL_Oplus__class_Oplus(X17,X16,X18) = c_HOL_Oplus__class_Oplus(X16,X17,X18) ),
    file('<stdin>',cls_comm__monoid__add_Omult__commute_0) ).

fof(c_0_506_507,axiom,
    ! [X9,X3,X18] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X18)
      | c_HOL_Oplus__class_Oplus(X3,X9,X18) = c_HOL_Oplus__class_Oplus(X9,X3,X18) ),
    file('<stdin>',cls_class__semiring_Oadd__c_0) ).

fof(c_0_507_508,axiom,
    ! [X9,X3,X18] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X18)
      | c_HOL_Otimes__class_Otimes(X3,X9,X18) = c_HOL_Otimes__class_Otimes(X9,X3,X18) ),
    file('<stdin>',cls_class__semiring_Omul__c_0) ).

fof(c_0_508_509,axiom,
    ! [X16,X17,X18] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X18)
      | c_HOL_Otimes__class_Otimes(X17,X16,X18) = c_HOL_Otimes__class_Otimes(X16,X17,X18) ),
    file('<stdin>',cls_class__semiring_Osemiring__rules_I7_J_0) ).

fof(c_0_509_510,axiom,
    ! [X9,X3,X18] :
      ( ~ class_Orderings_Olinorder(X18)
      | c_Orderings_Oord__class_Omin(X3,X9,X18) = c_Orderings_Oord__class_Omin(X9,X3,X18) ),
    file('<stdin>',cls_min__max_Oinf__commute_0) ).

fof(c_0_510_511,axiom,
    ! [X9,X3,X18] :
      ( ~ class_Orderings_Olinorder(X18)
      | c_Orderings_Oord__class_Omax(X3,X9,X18) = c_Orderings_Oord__class_Omax(X9,X3,X18) ),
    file('<stdin>',cls_min__max_Osup__commute_0) ).

fof(c_0_511_512,axiom,
    ! [X3,X5] :
      ( c_HOL_Oord__class_Oless(X3,X3,tc_nat)
      | c_Lambda_Osubst(c_Lambda_OdB_OVar(X3),X5,X3) = X5 ),
    file('<stdin>',cls_subst__Var_1) ).

fof(c_0_512_513,axiom,
    ! [X1,X2] :
      ( c_lessequals(c_Suc(X1),X2,tc_nat)
      | c_lessequals(X2,X1,tc_nat) ),
    file('<stdin>',cls_not__less__eq__eq_0) ).

fof(c_0_513_514,axiom,
    ! [X3] :
      ( c_HOL_Oord__class_Oless(X3,X3,tc_nat)
      | c_HOL_Oord__class_Oless(X3,c_Suc(X3),tc_nat) ),
    file('<stdin>',cls_not__less__less__Suc__eq_1) ).

fof(c_0_514_515,axiom,
    ! [X1,X2] :
      ( c_HOL_Oord__class_Oless(X1,c_Suc(X2),tc_nat)
      | c_HOL_Oord__class_Oless(X2,X1,tc_nat) ),
    file('<stdin>',cls_not__less__eq_0) ).

fof(c_0_515_516,axiom,
    ! [X18] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X18)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X18),c_HOL_Ozero__class_Ozero(X18),X18) ),
    file('<stdin>',cls_not__one__less__zero_0) ).

fof(c_0_516_517,axiom,
    ! [X18] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X18)
      | ~ c_lessequals(c_HOL_Oone__class_Oone(X18),c_HOL_Ozero__class_Ozero(X18),X18) ),
    file('<stdin>',cls_not__one__le__zero_0) ).

fof(c_0_517_518,axiom,
    ! [X1,X2] :
      ( c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != c_HOL_Oplus__class_Oplus(X2,X1,tc_nat)
      | X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
      | X2 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
    file('<stdin>',cls_one__is__add_1) ).

fof(c_0_518_519,axiom,
    ! [X1,X2] :
      ( c_HOL_Oplus__class_Oplus(X2,X1,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
      | X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
      | X2 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
    file('<stdin>',cls_add__is__1_1) ).

fof(c_0_519_520,axiom,
    ! [X16,X17,X18] :
      ( ~ class_Ring__and__Field_Oring__no__zero__divisors(X18)
      | c_HOL_Otimes__class_Otimes(X17,X16,X18) != c_HOL_Ozero__class_Ozero(X18)
      | X16 = c_HOL_Ozero__class_Ozero(X18)
      | X17 = c_HOL_Ozero__class_Ozero(X18) ),
    file('<stdin>',cls_mult__eq__0__iff_0) ).

fof(c_0_520_521,axiom,
    ! [X16,X17,X18] :
      ( ~ class_Ring__and__Field_Ono__zero__divisors(X18)
      | c_HOL_Otimes__class_Otimes(X17,X16,X18) != c_HOL_Ozero__class_Ozero(X18)
      | X16 = c_HOL_Ozero__class_Ozero(X18)
      | X17 = c_HOL_Ozero__class_Ozero(X18) ),
    file('<stdin>',cls_no__zero__divisors_0) ).

fof(c_0_521_522,axiom,
    ! [X16,X17,X18] :
      ( ~ class_Ring__and__Field_Ono__zero__divisors(X18)
      | c_HOL_Otimes__class_Otimes(X17,X16,X18) != c_HOL_Ozero__class_Ozero(X18)
      | X17 = c_HOL_Ozero__class_Ozero(X18)
      | X16 = c_HOL_Ozero__class_Ozero(X18) ),
    file('<stdin>',cls_no__zero__divirors__neq0_0) ).

fof(c_0_522_523,axiom,
    ! [X1,X2] :
      ( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
      | c_HOL_Oord__class_Oless(X2,X1,tc_nat)
      | X2 = X1 ),
    file('<stdin>',cls_nat__neq__iff_0) ).

fof(c_0_523_524,axiom,
    ! [X9,X3] :
      ( c_HOL_Oord__class_Oless(X9,X3,tc_nat)
      | c_HOL_Oord__class_Oless(X3,X9,tc_nat)
      | X3 = X9 ),
    file('<stdin>',cls_linorder__neqE__nat_0) ).

fof(c_0_524_525,axiom,
    ! [X9,X3,X18] :
      ( ~ class_Ring__and__Field_Oidom(X18)
      | ~ class_Int_Onumber__ring(X18)
      | c_HOL_Ominus__class_Ominus(X3,X9,X18) != c_HOL_Ozero__class_Ozero(X18)
      | X3 = X9 ),
    file('<stdin>',cls_class__ringb_Osubr0__iff_0) ).

fof(c_0_525_526,axiom,
    ! [X7,X8] :
      ( c_Lambda_Olift(c_Lambda_OdB_OVar(X8),X7) = c_Lambda_OdB_OVar(X8)
      | ~ c_HOL_Oord__class_Oless(X8,X7,tc_nat) ),
    file('<stdin>',cls_lift_Osimps_I1_J_0) ).

fof(c_0_526_527,axiom,
    ! [X3,X17,X18] :
      ( ~ class_Ring__and__Field_Oidom(X18)
      | ~ class_Int_Onumber__ring(X18)
      | X3 != c_HOL_Oplus__class_Oplus(X3,X17,X18)
      | X17 = c_HOL_Ozero__class_Ozero(X18) ),
    file('<stdin>',cls_class__ringb_Oadd__r0__iff_0) ).

fof(c_0_527_528,axiom,
    ! [X1] :
      ( 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) ),
    file('<stdin>',cls_less__Suc0_0) ).

fof(c_0_528_529,axiom,
    ! [X1,X2] :
      ( c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != c_HOL_Oplus__class_Oplus(X2,X1,tc_nat)
      | X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
      | X1 = c_HOL_Ozero__class_Ozero(tc_nat) ),
    file('<stdin>',cls_one__is__add_3) ).

fof(c_0_529_530,axiom,
    ! [X1,X2] :
      ( c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != c_HOL_Oplus__class_Oplus(X2,X1,tc_nat)
      | X2 = c_HOL_Ozero__class_Ozero(tc_nat)
      | X2 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
    file('<stdin>',cls_one__is__add_0) ).

fof(c_0_530_531,axiom,
    ! [X1,X2] :
      ( c_HOL_Oplus__class_Oplus(X2,X1,tc_nat) != 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) ),
    file('<stdin>',cls_add__is__1_3) ).

fof(c_0_531_532,axiom,
    ! [X1,X2] :
      ( c_HOL_Oplus__class_Oplus(X2,X1,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
      | X2 = c_HOL_Ozero__class_Ozero(tc_nat)
      | X2 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
    file('<stdin>',cls_add__is__1_0) ).

fof(c_0_532_533,axiom,
    ! [X1,X2] :
      ( c_lessequals(X1,X2,tc_nat)
      | c_lessequals(X2,X1,tc_nat) ),
    file('<stdin>',cls_nat__le__linear_0) ).

fof(c_0_533_534,axiom,
    ! [X17,X18] :
      ( ~ class_OrderedGroup_Olordered__ab__group__add(X18)
      | c_HOL_Oplus__class_Oplus(X17,X17,X18) != c_HOL_Ozero__class_Ozero(X18)
      | X17 = c_HOL_Ozero__class_Ozero(X18) ),
    file('<stdin>',cls_double__eq__0__iff_0) ).

fof(c_0_534_535,axiom,
    ! [X1,X2] :
      ( c_HOL_Otimes__class_Otimes(X2,X1,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
      | X2 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
    file('<stdin>',cls_mult__eq__1__iff_0) ).

fof(c_0_535_536,axiom,
    ! [X1,X2] :
      ( 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)) ),
    file('<stdin>',cls_mult__eq__1__iff_1) ).

fof(c_0_536_537,axiom,
    ! [X1,X2] :
      ( c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != c_HOL_Oplus__class_Oplus(X2,X1,tc_nat)
      | X2 = c_HOL_Ozero__class_Ozero(tc_nat)
      | X1 = c_HOL_Ozero__class_Ozero(tc_nat) ),
    file('<stdin>',cls_one__is__add_2) ).

fof(c_0_537_538,axiom,
    ! [X1,X2] :
      ( c_HOL_Oplus__class_Oplus(X2,X1,tc_nat) != 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) ),
    file('<stdin>',cls_add__is__1_2) ).

fof(c_0_538_539,axiom,
    ! [X16,X17,X18] :
      ( ~ class_OrderedGroup_Ogroup__add(X18)
      | c_HOL_Ominus__class_Ominus(X17,X16,X18) != c_HOL_Ozero__class_Ozero(X18)
      | X17 = X16 ),
    file('<stdin>',cls_right__minus__eq_0) ).

fof(c_0_539_540,axiom,
    ! [X16,X17,X18] :
      ( ~ class_OrderedGroup_Oab__group__add(X18)
      | c_HOL_Ominus__class_Ominus(X17,X16,X18) != c_HOL_Ozero__class_Ozero(X18)
      | X17 = X16 ),
    file('<stdin>',cls_eq__iff__diff__eq__0_1) ).

fof(c_0_540_541,axiom,
    ! [X1,X2] :
      ( c_HOL_Otimes__class_Otimes(X2,X1,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)
      | X1 = c_HOL_Ozero__class_Ozero(tc_nat)
      | X2 = c_HOL_Ozero__class_Ozero(tc_nat) ),
    file('<stdin>',cls_mult__is__0_0) ).

fof(c_0_541_542,axiom,
    ! [X3,X18] :
      ( ~ class_Orderings_Oorder(X18)
      | ~ c_HOL_Oord__class_Oless(X3,X3,X18) ),
    file('<stdin>',cls_order__less__le_1) ).

fof(c_0_542_543,axiom,
    ! [X3,X18] :
      ( ~ class_Orderings_Olinorder(X18)
      | ~ c_HOL_Oord__class_Oless(X3,X3,X18) ),
    file('<stdin>',cls_linorder__neq__iff_1) ).

fof(c_0_543_544,axiom,
    ! [X3,X18] :
      ( ~ class_Orderings_Opreorder(X18)
      | ~ c_HOL_Oord__class_Oless(X3,X3,X18) ),
    file('<stdin>',cls_order__less__irrefl_0) ).

fof(c_0_544_545,axiom,
    ! [X1,X2] :
      ( X2 != c_HOL_Otimes__class_Otimes(X2,X1,tc_nat)
      | X2 = c_HOL_Ozero__class_Ozero(tc_nat)
      | X1 = c_HOL_Oone__class_Oone(tc_nat) ),
    file('<stdin>',cls_mult__eq__self__implies__10_0) ).

fof(c_0_545_546,axiom,
    ! [X1] :
      ( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
      | ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ),
    file('<stdin>',cls_le__0__eq_0) ).

fof(c_0_546_547,axiom,
    ! [X1,X2] :
      ( c_HOL_Oplus__class_Oplus(X2,X1,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)
      | X2 = c_HOL_Ozero__class_Ozero(tc_nat) ),
    file('<stdin>',cls_add__is__0_0) ).

fof(c_0_547_548,axiom,
    ! [X1,X2] :
      ( c_HOL_Oplus__class_Oplus(X2,X1,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)
      | X1 = c_HOL_Ozero__class_Ozero(tc_nat) ),
    file('<stdin>',cls_add__is__0_1) ).

fof(c_0_548_549,axiom,
    ! [X1,X2] :
      ( c_HOL_Otimes__class_Otimes(X2,X1,tc_nat) != c_HOL_Oone__class_Oone(tc_nat)
      | X1 = c_HOL_Oone__class_Oone(tc_nat) ),
    file('<stdin>',cls_nat__mult__eq__1__iff_1) ).

fof(c_0_549_550,axiom,
    ! [X1,X2] :
      ( c_HOL_Otimes__class_Otimes(X2,X1,tc_nat) != c_HOL_Oone__class_Oone(tc_nat)
      | X2 = c_HOL_Oone__class_Oone(tc_nat) ),
    file('<stdin>',cls_nat__mult__eq__1__iff_0) ).

fof(c_0_550_551,axiom,
    ! [X1,X2] :
      ( c_HOL_Oone__class_Oone(tc_nat) != c_HOL_Otimes__class_Otimes(X2,X1,tc_nat)
      | X2 = c_HOL_Oone__class_Oone(tc_nat) ),
    file('<stdin>',cls_nat__1__eq__mult__iff_0) ).

fof(c_0_551_552,axiom,
    ! [X1,X2] :
      ( c_HOL_Oone__class_Oone(tc_nat) != c_HOL_Otimes__class_Otimes(X2,X1,tc_nat)
      | X1 = c_HOL_Oone__class_Oone(tc_nat) ),
    file('<stdin>',cls_nat__1__eq__mult__iff_1) ).

fof(c_0_552_553,axiom,
    ! [X15,X4,X5] :
      ( c_Lambda_Obeta(c_Lambda_OdB_OApp(X15,X5),c_Lambda_OdB_OApp(X15,X4))
      | ~ c_Lambda_Obeta(X5,X4) ),
    file('<stdin>',cls_appR_0) ).

fof(c_0_553_554,axiom,
    ! [X15,X4,X5] :
      ( c_Lambda_Obeta(c_Lambda_OdB_OApp(X5,X15),c_Lambda_OdB_OApp(X4,X15))
      | ~ c_Lambda_Obeta(X5,X4) ),
    file('<stdin>',cls_appL_0) ).

fof(c_0_554_555,axiom,
    ! [X5,X6,X8] :
      ( c_Lambda_Obeta(c_Lambda_Olift(X6,X8),c_Lambda_Olift(X5,X8))
      | ~ c_Lambda_Obeta(X6,X5) ),
    file('<stdin>',cls_lift__preserves__beta_0) ).

fof(c_0_555_556,axiom,
    ! [X1,X2] :
      ( c_HOL_Oplus__class_Oplus(X2,X1,tc_nat) != X2
      | X1 = c_HOL_Ozero__class_Ozero(tc_nat) ),
    file('<stdin>',cls_add__eq__self__zero_0) ).

fof(c_0_556_557,axiom,
    ! [X3,X17] :
      ( X3 != c_HOL_Oplus__class_Oplus(X3,X17,tc_nat)
      | X17 = c_HOL_Ozero__class_Ozero(tc_nat) ),
    file('<stdin>',cls_natgb_Oadd__r0__iff_0) ).

fof(c_0_557_558,axiom,
    ! [X18] :
      ( ~ class_OrderedGroup_Olordered__ab__group__add(X18)
      | c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X18),c_HOL_Ozero__class_Ozero(X18),X18) = c_HOL_Ozero__class_Ozero(X18) ),
    file('<stdin>',cls_double__eq__0__iff_1) ).

fof(c_0_558_559,axiom,
    ! [X3,X18] :
      ( ~ class_Ring__and__Field_Oidom(X18)
      | ~ class_Int_Onumber__ring(X18)
      | X3 = c_HOL_Oplus__class_Oplus(X3,c_HOL_Ozero__class_Ozero(X18),X18) ),
    file('<stdin>',cls_class__ringb_Oadd__r0__iff_1) ).

fof(c_0_559_560,axiom,
    ! [X18] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X18)
      | c_lessequals(c_HOL_Ozero__class_Ozero(X18),c_HOL_Oone__class_Oone(X18),X18) ),
    file('<stdin>',cls_zero__le__one_0) ).

fof(c_0_560_561,axiom,
    ! [X18] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X18)
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X18),c_HOL_Oone__class_Oone(X18),X18) ),
    file('<stdin>',cls_zero__less__one_0) ).

fof(c_0_561_562,axiom,
    ! [X3,X18] :
      ( ~ class_Ring__and__Field_Oidom(X18)
      | ~ class_Int_Onumber__ring(X18)
      | c_HOL_Ominus__class_Ominus(X3,X3,X18) = c_HOL_Ozero__class_Ozero(X18) ),
    file('<stdin>',cls_class__ringb_Osubr0__iff_1) ).

fof(c_0_562_563,axiom,
    ! [X17,X18] :
      ( ~ class_Divides_Osemiring__div(X18)
      | c_Divides_Odiv__class_Omod(c_HOL_Ozero__class_Ozero(X18),X17,X18) = c_HOL_Ozero__class_Ozero(X18) ),
    file('<stdin>',cls_mod__0_0) ).

fof(c_0_563_564,axiom,
    ! [X17,X18] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X18)
      | c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X18),X17,X18) = c_HOL_Ozero__class_Ozero(X18) ),
    file('<stdin>',cls_class__semiring_Osemiring__rules_I9_J_0) ).

fof(c_0_564_565,axiom,
    ! [X17,X18] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X18)
      | c_HOL_Otimes__class_Otimes(X17,c_HOL_Ozero__class_Ozero(X18),X18) = c_HOL_Ozero__class_Ozero(X18) ),
    file('<stdin>',cls_class__semiring_Osemiring__rules_I10_J_0) ).

fof(c_0_565_566,axiom,
    ! [X17,X18] :
      ( ~ class_Ring__and__Field_Oring__no__zero__divisors(X18)
      | c_HOL_Otimes__class_Otimes(X17,c_HOL_Ozero__class_Ozero(X18),X18) = c_HOL_Ozero__class_Ozero(X18) ),
    file('<stdin>',cls_mult__eq__0__iff_2) ).

fof(c_0_566_567,axiom,
    ! [X16,X18] :
      ( ~ class_Ring__and__Field_Oring__no__zero__divisors(X18)
      | c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X18),X16,X18) = c_HOL_Ozero__class_Ozero(X18) ),
    file('<stdin>',cls_mult__eq__0__iff_1) ).

fof(c_0_567_568,axiom,
    ! [X17,X18] :
      ( ~ class_Ring__and__Field_Omult__zero(X18)
      | c_HOL_Otimes__class_Otimes(X17,c_HOL_Ozero__class_Ozero(X18),X18) = c_HOL_Ozero__class_Ozero(X18) ),
    file('<stdin>',cls_mult__zero__right_0) ).

fof(c_0_568_569,axiom,
    ! [X17,X18] :
      ( ~ class_Ring__and__Field_Omult__zero(X18)
      | c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X18),X17,X18) = c_HOL_Ozero__class_Ozero(X18) ),
    file('<stdin>',cls_mult__zero__left_0) ).

fof(c_0_569_570,axiom,
    ! [X3,X18] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X18)
      | c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X18),X3,X18) = c_HOL_Ozero__class_Ozero(X18) ),
    file('<stdin>',cls_class__semiring_Omul__0_0) ).

fof(c_0_570_571,axiom,
    ! [X17,X18] :
      ( ~ class_Divides_Osemiring__div(X18)
      | c_Divides_Odiv__class_Omod(X17,c_HOL_Oone__class_Oone(X18),X18) = c_HOL_Ozero__class_Ozero(X18) ),
    file('<stdin>',cls_mod__by__1_0) ).

fof(c_0_571_572,axiom,
    ! [X17,X18] :
      ( ~ class_Divides_Osemiring__div(X18)
      | c_Divides_Odiv__class_Omod(X17,c_HOL_Ozero__class_Ozero(X18),X18) = X17 ),
    file('<stdin>',cls_mod__by__0_0) ).

fof(c_0_572_573,axiom,
    ! [X17,X18] :
      ( ~ class_OrderedGroup_Ogroup__add(X18)
      | c_HOL_Ominus__class_Ominus(X17,c_HOL_Ozero__class_Ozero(X18),X18) = X17 ),
    file('<stdin>',cls_diff__0__right_0) ).

fof(c_0_573_574,axiom,
    ! [X3,X18] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X18)
      | c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(X18),X3,X18) = X3 ),
    file('<stdin>',cls_class__semiring_Omul__1_0) ).

fof(c_0_574_575,axiom,
    ! [X17,X18] :
      ( ~ class_OrderedGroup_Ocomm__monoid__mult(X18)
      | c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(X18),X17,X18) = X17 ),
    file('<stdin>',cls_mult__1_0) ).

fof(c_0_575_576,axiom,
    ! [X17,X18] :
      ( ~ class_OrderedGroup_Omonoid__mult(X18)
      | c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(X18),X17,X18) = X17 ),
    file('<stdin>',cls_mult__1__left_0) ).

fof(c_0_576_577,axiom,
    ! [X17,X18] :
      ( ~ class_OrderedGroup_Omonoid__mult(X18)
      | c_HOL_Otimes__class_Otimes(X17,c_HOL_Oone__class_Oone(X18),X18) = X17 ),
    file('<stdin>',cls_mult__1__right_0) ).

fof(c_0_577_578,axiom,
    ! [X17,X18] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X18)
      | c_HOL_Otimes__class_Otimes(X17,c_HOL_Oone__class_Oone(X18),X18) = X17 ),
    file('<stdin>',cls_class__semiring_Osemiring__rules_I12_J_0) ).

fof(c_0_578_579,axiom,
    ! [X17,X18] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X18)
      | c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(X18),X17,X18) = X17 ),
    file('<stdin>',cls_class__semiring_Osemiring__rules_I11_J_0) ).

fof(c_0_579_580,axiom,
    ! [X3,X18] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X18)
      | c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X18),X3,X18) = X3 ),
    file('<stdin>',cls_class__semiring_Oadd__0_0) ).

fof(c_0_580_581,axiom,
    ! [X17,X18] :
      ( ~ class_OrderedGroup_Ocomm__monoid__add(X18)
      | c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X18),X17,X18) = X17 ),
    file('<stdin>',cls_comm__monoid__add_Omult__1_0) ).

fof(c_0_581_582,axiom,
    ! [X17,X18] :
      ( ~ class_OrderedGroup_Ocomm__monoid__add(X18)
      | c_HOL_Oplus__class_Oplus(X17,c_HOL_Ozero__class_Ozero(X18),X18) = X17 ),
    file('<stdin>',cls_comm__monoid__add_Omult__1__right_0) ).

fof(c_0_582_583,axiom,
    ! [X17,X18] :
      ( ~ class_OrderedGroup_Omonoid__add(X18)
      | c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X18),X17,X18) = X17 ),
    file('<stdin>',cls_add__0__left_0) ).

fof(c_0_583_584,axiom,
    ! [X17,X18] :
      ( ~ class_OrderedGroup_Omonoid__add(X18)
      | c_HOL_Oplus__class_Oplus(X17,c_HOL_Ozero__class_Ozero(X18),X18) = X17 ),
    file('<stdin>',cls_monoid__add__class_Oadd__0__right_0) ).

fof(c_0_584_585,axiom,
    ! [X17,X18] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X18)
      | c_HOL_Oplus__class_Oplus(X17,c_HOL_Ozero__class_Ozero(X18),X18) = X17 ),
    file('<stdin>',cls_class__semiring_Osemiring__rules_I6_J_0) ).

fof(c_0_585_586,axiom,
    ! [X17,X18] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X18)
      | c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X18),X17,X18) = X17 ),
    file('<stdin>',cls_class__semiring_Osemiring__rules_I5_J_0) ).

fof(c_0_586_587,axiom,
    ! [X17,X18] :
      ( ~ class_Divides_Osemiring__div(X18)
      | c_Divides_Odiv__class_Omod(X17,X17,X18) = c_HOL_Ozero__class_Ozero(X18) ),
    file('<stdin>',cls_mod__self_0) ).

fof(c_0_587_588,axiom,
    ! [X3,X18] :
      ( ~ class_OrderedGroup_Oab__group__add(X18)
      | c_HOL_Ominus__class_Ominus(X3,X3,X18) = c_HOL_Ozero__class_Ozero(X18) ),
    file('<stdin>',cls_eq__iff__diff__eq__0_0) ).

fof(c_0_588_589,axiom,
    ! [X3,X18] :
      ( ~ class_OrderedGroup_Ogroup__add(X18)
      | c_HOL_Ominus__class_Ominus(X3,X3,X18) = c_HOL_Ozero__class_Ozero(X18) ),
    file('<stdin>',cls_right__minus__eq_1) ).

fof(c_0_589_590,axiom,
    ! [X17,X18] :
      ( ~ class_OrderedGroup_Ogroup__add(X18)
      | c_HOL_Ominus__class_Ominus(X17,X17,X18) = c_HOL_Ozero__class_Ozero(X18) ),
    file('<stdin>',cls_diff__self_0) ).

fof(c_0_590_591,axiom,
    ! [X3,X18] :
      ( ~ class_Orderings_Olinorder(X18)
      | c_Orderings_Oord__class_Omin(X3,X3,X18) = X3 ),
    file('<stdin>',cls_min__max_Oinf__idem_0) ).

fof(c_0_591_592,axiom,
    ! [X3,X18] :
      ( ~ class_Orderings_Olinorder(X18)
      | c_Orderings_Oord__class_Omax(X3,X3,X18) = X3 ),
    file('<stdin>',cls_min__max_Osup__idem_0) ).

fof(c_0_592_593,axiom,
    ! [X3,X18] :
      ( ~ class_OrderedGroup_Oab__semigroup__idem__mult(X18)
      | c_HOL_Otimes__class_Otimes(X3,X3,X18) = X3 ),
    file('<stdin>',cls_mult__idem_0) ).

fof(c_0_593_594,axiom,
    ! [X3,X18] :
      ( ~ class_Orderings_Oorder(X18)
      | c_lessequals(X3,X3,X18) ),
    file('<stdin>',cls_order__eq__iff_0) ).

fof(c_0_594_595,axiom,
    ! [X3,X18] :
      ( ~ class_Orderings_Opreorder(X18)
      | c_lessequals(X3,X3,X18) ),
    file('<stdin>',cls_order__eq__refl_0) ).

fof(c_0_595_596,axiom,
    ! [X1] :
      ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
      | X1 = c_HOL_Ozero__class_Ozero(tc_nat) ),
    file('<stdin>',cls_gr0I_0) ).

fof(c_0_596_597,axiom,
    ! [X4,X5] :
      ( c_Lambda_Obeta(c_Lambda_OdB_OAbs(X5),c_Lambda_OdB_OAbs(X4))
      | ~ c_Lambda_Obeta(X5,X4) ),
    file('<stdin>',cls_abs_0) ).

fof(c_0_597_598,axiom,
    ! [X33,X34,X35,X36] :
      ( c_Lambda_OdB_OApp(X36,X34) != c_Lambda_OdB_OApp(X35,X33)
      | X34 = X33 ),
    file('<stdin>',cls_dB_Osimps_I2_J_1) ).

fof(c_0_598_599,axiom,
    ! [X33,X34,X35,X36] :
      ( c_Lambda_OdB_OApp(X36,X34) != c_Lambda_OdB_OApp(X35,X33)
      | X36 = X35 ),
    file('<stdin>',cls_dB_Osimps_I2_J_0) ).

fof(c_0_599_600,axiom,
    ! [X4,X8] :
      ( c_InductTermi_OIT(c_Lambda_Olift(X4,X8))
      | ~ c_InductTermi_OIT(X4) ),
    file('<stdin>',cls_lift__IT_0) ).

fof(c_0_600_601,axiom,
    ! [X18] :
      ( ~ class_Ring__and__Field_Ozero__neq__one(X18)
      | c_HOL_Oone__class_Oone(X18) != c_HOL_Ozero__class_Ozero(X18) ),
    file('<stdin>',cls_one__neq__zero_0) ).

fof(c_0_601_602,axiom,
    ! [X18] :
      ( ~ class_Ring__and__Field_Ozero__neq__one(X18)
      | c_HOL_Ozero__class_Ozero(X18) != c_HOL_Oone__class_Oone(X18) ),
    file('<stdin>',cls_zero__neq__one_0) ).

fof(c_0_602_603,axiom,
    ! [X6] :
      ( c_InductTermi_OIT(c_Lambda_OdB_OAbs(X6))
      | ~ c_InductTermi_OIT(X6) ),
    file('<stdin>',cls_Lambda_0) ).

fof(c_0_603_604,axiom,
    ! [X10,X11] :
      ( c_Lambda_OdB_OVar(X11) != c_Lambda_OdB_OVar(X10)
      | X11 = X10 ),
    file('<stdin>',cls_dB_Osimps_I1_J_0) ).

fof(c_0_604_605,axiom,
    ! [X12,X13] :
      ( c_Lambda_OdB_OAbs(X13) != c_Lambda_OdB_OAbs(X12)
      | X13 = X12 ),
    file('<stdin>',cls_dB_Osimps_I3_J_0) ).

fof(c_0_605_606,axiom,
    ! [X10,X11] :
      ( c_Suc(X11) != c_Suc(X10)
      | X11 = X10 ),
    file('<stdin>',cls_nat_Oinject_0) ).

fof(c_0_606_607,axiom,
    ! [X9,X3] :
      ( c_Suc(X3) != c_Suc(X9)
      | X3 = X9 ),
    file('<stdin>',cls_Suc__inject_0) ).

fof(c_0_607_608,plain,
    ! [X15,X1,X2,X14,X8] :
      ( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X8,X15,tc_nat),X2,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X14,X15,tc_nat),X1,tc_nat),tc_nat)
      | ~ c_HOL_Oord__class_Oless(X2,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X14,X8,tc_nat),X15,tc_nat),X1,tc_nat),tc_nat)
      | ~ c_lessequals(X8,X14,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_0]) ).

fof(c_0_608_609,plain,
    ! [X15,X1,X2,X14,X8] :
      ( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X8,X15,tc_nat),X2,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X14,X15,tc_nat),X1,tc_nat),tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X8,X14,tc_nat),X15,tc_nat),X2,tc_nat),X1,tc_nat)
      | ~ c_lessequals(X14,X8,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_1]) ).

fof(c_0_609_610,plain,
    ! [X15,X1,X2,X14,X8] :
      ( c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X8,X15,tc_nat),X2,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X14,X15,tc_nat),X1,tc_nat),tc_nat)
      | ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X8,X14,tc_nat),X15,tc_nat),X2,tc_nat),X1,tc_nat)
      | ~ c_lessequals(X14,X8,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_2]) ).

fof(c_0_610_611,plain,
    ! [X15,X1,X2,X14,X8] :
      ( c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X8,X15,tc_nat),X2,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X14,X15,tc_nat),X1,tc_nat),tc_nat)
      | ~ c_lessequals(X2,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X14,X8,tc_nat),X15,tc_nat),X1,tc_nat),tc_nat)
      | ~ c_lessequals(X8,X14,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_3]) ).

fof(c_0_611_612,plain,
    ! [X39,X27,X20,X16,X17,X18] :
      ( ~ class_Ring__and__Field_Opordered__ring(X18)
      | c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X17,X39,X18),X20,X18),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X16,X39,X18),X27,X18),X18)
      | ~ c_lessequals(X20,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X16,X17,X18),X39,X18),X27,X18),X18) ),
    inference(fof_simplification,[status(thm)],[c_0_4]) ).

fof(c_0_612_613,plain,
    ! [X39,X27,X20,X16,X17,X18] :
      ( ~ class_Ring__and__Field_Opordered__ring(X18)
      | c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X17,X39,X18),X20,X18),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X16,X39,X18),X27,X18),X18)
      | ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X17,X16,X18),X39,X18),X20,X18),X27,X18) ),
    inference(fof_simplification,[status(thm)],[c_0_5]) ).

fof(c_0_613_614,plain,
    ! [X39,X27,X20,X16,X17,X18] :
      ( ~ class_Ring__and__Field_Opordered__ring(X18)
      | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X17,X39,X18),X20,X18),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X16,X39,X18),X27,X18),X18)
      | ~ c_HOL_Oord__class_Oless(X20,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X16,X17,X18),X39,X18),X27,X18),X18) ),
    inference(fof_simplification,[status(thm)],[c_0_6]) ).

fof(c_0_614_615,plain,
    ! [X39,X27,X20,X16,X17,X18] :
      ( ~ class_Ring__and__Field_Opordered__ring(X18)
      | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X17,X39,X18),X20,X18),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X16,X39,X18),X27,X18),X18)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X17,X16,X18),X39,X18),X20,X18),X27,X18) ),
    inference(fof_simplification,[status(thm)],[c_0_7]) ).

fof(c_0_615_616,plain,
    ! [X15,X1,X2,X14,X8] :
      ( c_HOL_Oord__class_Oless(X2,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X14,X8,tc_nat),X15,tc_nat),X1,tc_nat),tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X8,X15,tc_nat),X2,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X14,X15,tc_nat),X1,tc_nat),tc_nat)
      | ~ c_lessequals(X8,X14,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_8]) ).

fof(c_0_616_617,plain,
    ! [X15,X1,X2,X14,X8] :
      ( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X8,X14,tc_nat),X15,tc_nat),X2,tc_nat),X1,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X8,X15,tc_nat),X2,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X14,X15,tc_nat),X1,tc_nat),tc_nat)
      | ~ c_lessequals(X14,X8,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_9]) ).

fof(c_0_617_618,plain,
    ! [X15,X1,X2,X14,X8] :
      ( c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X8,X14,tc_nat),X15,tc_nat),X2,tc_nat),X1,tc_nat)
      | ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X8,X15,tc_nat),X2,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X14,X15,tc_nat),X1,tc_nat),tc_nat)
      | ~ c_lessequals(X14,X8,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_10]) ).

fof(c_0_618_619,plain,
    ! [X15,X1,X2,X14,X8] :
      ( c_lessequals(X2,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X14,X8,tc_nat),X15,tc_nat),X1,tc_nat),tc_nat)
      | ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X8,X15,tc_nat),X2,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X14,X15,tc_nat),X1,tc_nat),tc_nat)
      | ~ c_lessequals(X8,X14,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_11]) ).

fof(c_0_619_620,plain,
    ! [X39,X27,X20,X16,X17,X18] :
      ( ~ class_Ring__and__Field_Opordered__ring(X18)
      | c_lessequals(X20,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X16,X17,X18),X39,X18),X27,X18),X18)
      | ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X17,X39,X18),X20,X18),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X16,X39,X18),X27,X18),X18) ),
    inference(fof_simplification,[status(thm)],[c_0_12]) ).

fof(c_0_620_621,plain,
    ! [X39,X27,X20,X16,X17,X18] :
      ( ~ class_Ring__and__Field_Opordered__ring(X18)
      | c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X17,X16,X18),X39,X18),X20,X18),X27,X18)
      | ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X17,X39,X18),X20,X18),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X16,X39,X18),X27,X18),X18) ),
    inference(fof_simplification,[status(thm)],[c_0_13]) ).

fof(c_0_621_622,plain,
    ! [X39,X27,X20,X16,X17,X18] :
      ( ~ class_Ring__and__Field_Opordered__ring(X18)
      | c_HOL_Oord__class_Oless(X20,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X16,X17,X18),X39,X18),X27,X18),X18)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X17,X39,X18),X20,X18),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X16,X39,X18),X27,X18),X18) ),
    inference(fof_simplification,[status(thm)],[c_0_14]) ).

fof(c_0_622_623,plain,
    ! [X39,X27,X20,X16,X17,X18] :
      ( ~ class_Ring__and__Field_Opordered__ring(X18)
      | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X17,X16,X18),X39,X18),X20,X18),X27,X18)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X17,X39,X18),X20,X18),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X16,X39,X18),X27,X18),X18) ),
    inference(fof_simplification,[status(thm)],[c_0_15]) ).

fof(c_0_623_624,plain,
    ! [X15,X1,X2,X14,X8] :
      ( c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X8,X15,tc_nat),X2,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X14,X15,tc_nat),X1,tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(X2,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X14,X8,tc_nat),X15,tc_nat),X1,tc_nat),tc_nat)
      | ~ c_lessequals(X8,X14,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_16]) ).

fof(c_0_624_625,plain,
    ! [X15,X1,X2,X14,X8] :
      ( c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X8,X15,tc_nat),X2,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X14,X15,tc_nat),X1,tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X8,X14,tc_nat),X15,tc_nat),X2,tc_nat),X1,tc_nat)
      | ~ c_lessequals(X14,X8,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_17]) ).

fof(c_0_625_626,plain,
    ! [X15,X2,X14,X8] :
      ( ~ c_lessequals(X14,X8,tc_nat)
      | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X8,X15,tc_nat),X2,tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X14,X15,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X8,X14,tc_nat),X15,tc_nat),X2,tc_nat),tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_18]) ).

fof(c_0_626_627,plain,
    ! [X15,X1,X14,X8] :
      ( ~ c_lessequals(X8,X14,tc_nat)
      | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X8,X15,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X14,X8,tc_nat),X15,tc_nat),X1,tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X14,X15,tc_nat),X1,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_19]) ).

fof(c_0_627_628,plain,
    ! [X18] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X18)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X18),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X18),c_HOL_Ozero__class_Ozero(X18),X18),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X18),c_HOL_Ozero__class_Ozero(X18),X18),X18),X18) ),
    inference(fof_simplification,[status(thm)],[c_0_20]) ).

fof(c_0_628_629,plain,
    ! [X39,X27,X16,X17,X18] :
      ( ~ class_Ring__and__Field_Oring(X18)
      | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X17,X39,X18),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X16,X17,X18),X39,X18),X27,X18),X18) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X16,X39,X18),X27,X18) ),
    inference(fof_simplification,[status(thm)],[c_0_21]) ).

fof(c_0_629_630,plain,
    ! [X39,X20,X16,X17,X18] :
      ( ~ class_Ring__and__Field_Oring(X18)
      | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X17,X39,X18),X20,X18) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X16,X39,X18),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X17,X16,X18),X39,X18),X20,X18),X18) ),
    inference(fof_simplification,[status(thm)],[c_0_22]) ).

fof(c_0_630_631,plain,
    ! [X6,X30,X20,X16] :
      ( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X16,c_Divides_Odiv__class_Omod(X30,X20,tc_nat),tc_nat),X6,tc_nat),c_HOL_Otimes__class_Otimes(X16,X20,tc_nat),tc_nat)
      | ~ c_HOL_Oord__class_Oless(X6,X16,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X20,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_23]) ).

fof(c_0_631_632,plain,
    ! [X9,X3,X18] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X18)
      | X3 = c_HOL_Ozero__class_Ozero(X18)
      | ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X3,X18),c_HOL_Otimes__class_Otimes(X9,X9,X18),X18),c_HOL_Ozero__class_Ozero(X18),X18) ),
    inference(fof_simplification,[status(thm)],[c_0_24]) ).

fof(c_0_632_633,plain,
    ! [X9,X3,X18] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X18)
      | X9 = c_HOL_Ozero__class_Ozero(X18)
      | ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X3,X18),c_HOL_Otimes__class_Otimes(X9,X9,X18),X18),c_HOL_Ozero__class_Ozero(X18),X18) ),
    inference(fof_simplification,[status(thm)],[c_0_25]) ).

fof(c_0_633_634,plain,
    ! [X9,X3,X18] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X18)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X3,X18),c_HOL_Otimes__class_Otimes(X9,X9,X18),X18),c_HOL_Ozero__class_Ozero(X18),X18) ),
    inference(fof_simplification,[status(thm)],[c_0_26]) ).

fof(c_0_634_635,plain,
    ! [X15,X1,X2,X14,X8] :
      ( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X8,X15,tc_nat),X2,tc_nat) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X14,X15,tc_nat),X1,tc_nat)
      | ~ c_lessequals(X14,X8,tc_nat)
      | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X8,X14,tc_nat),X15,tc_nat),X2,tc_nat) = X1 ),
    inference(fof_simplification,[status(thm)],[c_0_27]) ).

fof(c_0_635_636,plain,
    ! [X15,X1,X2,X14,X8] :
      ( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X8,X15,tc_nat),X2,tc_nat) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X14,X15,tc_nat),X1,tc_nat)
      | ~ c_lessequals(X8,X14,tc_nat)
      | X2 = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X14,X8,tc_nat),X15,tc_nat),X1,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_28]) ).

fof(c_0_636_637,plain,
    ! [X19,X9,X3,X18] :
      ( ~ class_Orderings_Olinorder(X18)
      | c_lessequals(c_Orderings_Oord__class_Omax(c_Orderings_Oord__class_Omin(X3,X9,X18),c_Orderings_Oord__class_Omin(X3,X19,X18),X18),c_Orderings_Oord__class_Omin(X3,c_Orderings_Oord__class_Omax(X9,X19,X18),X18),X18) ),
    inference(fof_simplification,[status(thm)],[c_0_29]) ).

fof(c_0_637_638,plain,
    ! [X19,X9,X3,X18] :
      ( ~ class_Orderings_Olinorder(X18)
      | c_lessequals(c_Orderings_Oord__class_Omax(X3,c_Orderings_Oord__class_Omin(X9,X19,X18),X18),c_Orderings_Oord__class_Omin(c_Orderings_Oord__class_Omax(X3,X9,X18),c_Orderings_Oord__class_Omax(X3,X19,X18),X18),X18) ),
    inference(fof_simplification,[status(thm)],[c_0_30]) ).

fof(c_0_638_639,plain,
    ! [X39,X27,X20,X16,X17,X18] :
      ( ~ class_Ring__and__Field_Oring(X18)
      | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X17,X39,X18),X20,X18) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X16,X39,X18),X27,X18)
      | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X17,X16,X18),X39,X18),X20,X18) = X27 ),
    inference(fof_simplification,[status(thm)],[c_0_31]) ).

fof(c_0_639_640,plain,
    ! [X39,X27,X20,X16,X17,X18] :
      ( ~ class_Ring__and__Field_Oring(X18)
      | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X17,X39,X18),X20,X18) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X16,X39,X18),X27,X18)
      | X20 = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X16,X17,X18),X39,X18),X27,X18) ),
    inference(fof_simplification,[status(thm)],[c_0_32]) ).

fof(c_0_640_641,plain,
    ! [X39,X20,X16,X17,X18] :
      ( ~ class_Ring__and__Field_Osemiring(X18)
      | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X17,X39,X18),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X16,X39,X18),X20,X18),X18) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X17,X16,X18),X39,X18),X20,X18) ),
    inference(fof_simplification,[status(thm)],[c_0_33]) ).

fof(c_0_641_642,plain,
    ! [X19,X9,X3,X40,X18] :
      ( ~ class_Ring__and__Field_Oidom(X18)
      | ~ class_Int_Onumber__ring(X18)
      | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X40,X9,X18),c_HOL_Otimes__class_Otimes(X3,X19,X18),X18) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X40,X19,X18),c_HOL_Otimes__class_Otimes(X3,X9,X18),X18)
      | X9 = X19
      | X40 = X3 ),
    inference(fof_simplification,[status(thm)],[c_0_34]) ).

fof(c_0_642_643,plain,
    ! [X27,X20,X16,X17,X18] :
      ( ~ class_Ring__and__Field_Oidom(X18)
      | ~ class_Int_Onumber__ring(X18)
      | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X17,X20,X18),c_HOL_Otimes__class_Otimes(X16,X27,X18),X18) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X17,X27,X18),c_HOL_Otimes__class_Otimes(X16,X20,X18),X18)
      | X20 = X27
      | X17 = X16 ),
    inference(fof_simplification,[status(thm)],[c_0_35]) ).

fof(c_0_643_644,axiom,
    ! [X27,X20,X16,X17] :
      ( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X17,X20,tc_nat),c_HOL_Otimes__class_Otimes(X16,X27,tc_nat),tc_nat) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X17,X27,tc_nat),c_HOL_Otimes__class_Otimes(X16,X20,tc_nat),tc_nat)
      | X20 = X27
      | X17 = X16 ),
    c_0_36 ).

fof(c_0_644_645,axiom,
    ! [X19,X9,X3,X40] :
      ( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X40,X9,tc_nat),c_HOL_Otimes__class_Otimes(X3,X19,tc_nat),tc_nat) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X40,X19,tc_nat),c_HOL_Otimes__class_Otimes(X3,X9,tc_nat),tc_nat)
      | X9 = X19
      | X40 = X3 ),
    c_0_37 ).

fof(c_0_645_646,plain,
    ! [X20,X16,X17,X18] :
      ( ~ class_Divides_Osemiring__div(X18)
      | c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X17,X16,X18),X20,X18) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(X17,X20,X18),c_Divides_Odiv__class_Omod(X16,X20,X18),X18),X20,X18) ),
    inference(fof_simplification,[status(thm)],[c_0_38]) ).

fof(c_0_646_647,plain,
    ! [X20,X16,X17,X18] :
      ( ~ class_Divides_Osemiring__div(X18)
      | c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X17,X16,X18),X20,X18) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(X17,X20,X18),c_Divides_Odiv__class_Omod(X16,X20,X18),X18),X20,X18) ),
    inference(fof_simplification,[status(thm)],[c_0_39]) ).

fof(c_0_647_648,plain,
    ! [X20,X16,X17,X18] :
      ( ~ class_Divides_Oring__div(X18)
      | c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X17,X16,X18),X20,X18) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(c_Divides_Odiv__class_Omod(X17,X20,X18),c_Divides_Odiv__class_Omod(X16,X20,X18),X18),X20,X18) ),
    inference(fof_simplification,[status(thm)],[c_0_40]) ).

fof(c_0_648_649,plain,
    ! [X29,X15,X4,X14,X8] :
      ( c_Lambda_Osubst(c_Lambda_Osubst(X4,c_Lambda_Olift(X29,X8),c_Suc(X14)),c_Lambda_Osubst(X15,X29,X14),X8) = c_Lambda_Osubst(c_Lambda_Osubst(X4,X15,X8),X29,X14)
      | ~ c_HOL_Oord__class_Oless(X8,c_HOL_Oplus__class_Oplus(X14,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_41]) ).

fof(c_0_649_650,plain,
    ! [X4,X5,X14,X8] :
      ( c_Lambda_Olift(c_Lambda_Osubst(X4,X5,X14),X8) = c_Lambda_Osubst(c_Lambda_Olift(X4,c_HOL_Oplus__class_Oplus(X8,c_HOL_Oone__class_Oone(tc_nat),tc_nat)),c_Lambda_Olift(X5,X8),X14)
      | ~ c_HOL_Oord__class_Oless(X14,c_HOL_Oplus__class_Oplus(X8,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_42]) ).

fof(c_0_650_651,plain,
    ! [X18] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X18)
      | c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X18),c_HOL_Ozero__class_Ozero(X18),X18),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X18),c_HOL_Ozero__class_Ozero(X18),X18),X18),c_HOL_Ozero__class_Ozero(X18),X18) ),
    inference(fof_simplification,[status(thm)],[c_0_43]) ).

fof(c_0_651_652,plain,
    ! [X20,X37,X16,X38,X17,X18] :
      ( ~ class_Divides_Osemiring__div(X18)
      | c_Divides_Odiv__class_Omod(X16,X20,X18) != c_Divides_Odiv__class_Omod(X37,X20,X18)
      | c_Divides_Odiv__class_Omod(X17,X20,X18) != c_Divides_Odiv__class_Omod(X38,X20,X18)
      | c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X17,X16,X18),X20,X18) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X38,X37,X18),X20,X18) ),
    inference(fof_simplification,[status(thm)],[c_0_44]) ).

fof(c_0_652_653,plain,
    ! [X20,X37,X16,X38,X17,X18] :
      ( ~ class_Divides_Osemiring__div(X18)
      | c_Divides_Odiv__class_Omod(X16,X20,X18) != c_Divides_Odiv__class_Omod(X37,X20,X18)
      | c_Divides_Odiv__class_Omod(X17,X20,X18) != c_Divides_Odiv__class_Omod(X38,X20,X18)
      | c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X17,X16,X18),X20,X18) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X38,X37,X18),X20,X18) ),
    inference(fof_simplification,[status(thm)],[c_0_45]) ).

fof(c_0_653_654,plain,
    ! [X20,X37,X16,X38,X17,X18] :
      ( ~ class_Divides_Oring__div(X18)
      | c_Divides_Odiv__class_Omod(X16,X20,X18) != c_Divides_Odiv__class_Omod(X37,X20,X18)
      | c_Divides_Odiv__class_Omod(X17,X20,X18) != c_Divides_Odiv__class_Omod(X38,X20,X18)
      | c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X17,X16,X18),X20,X18) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X38,X37,X18),X20,X18) ),
    inference(fof_simplification,[status(thm)],[c_0_46]) ).

fof(c_0_654_655,plain,
    ! [X21,X22,X24,X23,X18] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X18)
      | c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X23,X24,X18),c_HOL_Otimes__class_Otimes(X22,X21,X18),X18) = c_HOL_Otimes__class_Otimes(X23,c_HOL_Otimes__class_Otimes(X24,c_HOL_Otimes__class_Otimes(X22,X21,X18),X18),X18) ),
    inference(fof_simplification,[status(thm)],[c_0_47]) ).

fof(c_0_655_656,plain,
    ! [X21,X22,X24,X23,X18] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X18)
      | c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X23,X24,X18),c_HOL_Otimes__class_Otimes(X22,X21,X18),X18) = c_HOL_Otimes__class_Otimes(X22,c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X23,X24,X18),X21,X18),X18) ),
    inference(fof_simplification,[status(thm)],[c_0_48]) ).

fof(c_0_656_657,plain,
    ! [X27,X20,X16,X17,X18] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X18)
      | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X17,X20,X18),c_HOL_Otimes__class_Otimes(X16,X27,X18),X18)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X18),X20,X18)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X18),X16,X18)
      | ~ c_HOL_Oord__class_Oless(X20,X27,X18)
      | ~ c_HOL_Oord__class_Oless(X17,X16,X18) ),
    inference(fof_simplification,[status(thm)],[c_0_49]) ).

fof(c_0_657_658,plain,
    ! [X27,X20,X16,X17,X18] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X18)
      | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X17,X20,X18),c_HOL_Otimes__class_Otimes(X16,X27,X18),X18)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X18),X20,X18)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X18),X17,X18)
      | ~ c_lessequals(X20,X27,X18)
      | ~ c_HOL_Oord__class_Oless(X17,X16,X18) ),
    inference(fof_simplification,[status(thm)],[c_0_50]) ).

fof(c_0_658_659,plain,
    ! [X27,X20,X16,X17,X18] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X18)
      | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X17,X20,X18),c_HOL_Otimes__class_Otimes(X16,X27,X18),X18)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X18),X20,X18)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X18),X17,X18)
      | ~ c_HOL_Oord__class_Oless(X20,X27,X18)
      | ~ c_lessequals(X17,X16,X18) ),
    inference(fof_simplification,[status(thm)],[c_0_51]) ).

fof(c_0_659_660,plain,
    ! [X27,X20,X16,X17,X18] :
      ( ~ class_Ring__and__Field_Opordered__semiring(X18)
      | c_lessequals(c_HOL_Otimes__class_Otimes(X17,X20,X18),c_HOL_Otimes__class_Otimes(X16,X27,X18),X18)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X18),X20,X18)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X18),X16,X18)
      | ~ c_lessequals(X20,X27,X18)
      | ~ c_lessequals(X17,X16,X18) ),
    inference(fof_simplification,[status(thm)],[c_0_52]) ).

fof(c_0_660_661,plain,
    ! [X27,X20,X16,X17,X18] :
      ( ~ class_Ring__and__Field_Opordered__semiring(X18)
      | c_lessequals(c_HOL_Otimes__class_Otimes(X17,X20,X18),c_HOL_Otimes__class_Otimes(X16,X27,X18),X18)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X18),X20,X18)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X18),X17,X18)
      | ~ c_lessequals(X20,X27,X18)
      | ~ c_lessequals(X17,X16,X18) ),
    inference(fof_simplification,[status(thm)],[c_0_53]) ).

fof(c_0_661_662,plain,
    ! [X27,X20,X16,X17,X18] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X18)
      | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X17,X20,X18),c_HOL_Otimes__class_Otimes(X16,X27,X18),X18)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X18),X20,X18)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X18),X17,X18)
      | ~ c_HOL_Oord__class_Oless(X20,X27,X18)
      | ~ c_HOL_Oord__class_Oless(X17,X16,X18) ),
    inference(fof_simplification,[status(thm)],[c_0_54]) ).

fof(c_0_662_663,plain,
    ! [X1,X2,X7] :
      ( c_lessequals(X2,X1,tc_nat)
      | ~ c_lessequals(c_HOL_Ominus__class_Ominus(X2,X7,tc_nat),c_HOL_Ominus__class_Ominus(X1,X7,tc_nat),tc_nat)
      | ~ c_lessequals(X7,X1,tc_nat)
      | ~ c_lessequals(X7,X2,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_55]) ).

fof(c_0_663_664,plain,
    ! [X1,X2,X7] :
      ( c_HOL_Oord__class_Oless(X2,X1,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X2,X7,tc_nat),c_HOL_Ominus__class_Ominus(X1,X7,tc_nat),tc_nat)
      | ~ c_lessequals(X7,X1,tc_nat)
      | ~ c_lessequals(X7,X2,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_56]) ).

fof(c_0_664_665,plain,
    ! [X9,X3,X18] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X18)
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X18),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X3,X18),c_HOL_Otimes__class_Otimes(X9,X9,X18),X18),X18)
      | X3 = c_HOL_Ozero__class_Ozero(X18) ),
    inference(fof_simplification,[status(thm)],[c_0_57]) ).

fof(c_0_665_666,plain,
    ! [X9,X3,X18] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X18)
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X18),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X3,X18),c_HOL_Otimes__class_Otimes(X9,X9,X18),X18),X18)
      | X9 = c_HOL_Ozero__class_Ozero(X18) ),
    inference(fof_simplification,[status(thm)],[c_0_58]) ).

fof(c_0_666_667,plain,
    ! [X9,X3,X18] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X18)
      | c_lessequals(c_HOL_Ozero__class_Ozero(X18),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X3,X18),c_HOL_Otimes__class_Otimes(X9,X9,X18),X18),X18) ),
    inference(fof_simplification,[status(thm)],[c_0_59]) ).

fof(c_0_667_668,axiom,
    ! [X9,X31,X32,X3,X1] :
      ( c_HOL_Oplus__class_Oplus(X3,c_HOL_Otimes__class_Otimes(X1,X32,tc_nat),tc_nat) != c_HOL_Oplus__class_Oplus(X9,c_HOL_Otimes__class_Otimes(X1,X31,tc_nat),tc_nat)
      | c_Divides_Odiv__class_Omod(X3,X1,tc_nat) = c_Divides_Odiv__class_Omod(X9,X1,tc_nat) ),
    c_0_60 ).

fof(c_0_668_669,plain,
    ! [X4,X5,X14,X8] :
      ( c_Lambda_Olift(c_Lambda_Osubst(X4,X5,X14),X8) = c_Lambda_Osubst(c_Lambda_Olift(X4,X8),c_Lambda_Olift(X5,X8),c_HOL_Oplus__class_Oplus(X14,c_HOL_Oone__class_Oone(tc_nat),tc_nat))
      | ~ c_HOL_Oord__class_Oless(X8,c_HOL_Oplus__class_Oplus(X14,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_61]) ).

fof(c_0_669_670,plain,
    ! [X20,X16,X17,X18] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X18)
      | c_HOL_Oord__class_Oless(X17,X16,X18)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X18),X20,X18)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X17,X20,X18),c_HOL_Otimes__class_Otimes(X16,X20,X18),X18) ),
    inference(fof_simplification,[status(thm)],[c_0_62]) ).

fof(c_0_670_671,plain,
    ! [X20,X16,X17,X18] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X18)
      | c_HOL_Oord__class_Oless(X17,X16,X18)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X18),X20,X18)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X20,X17,X18),c_HOL_Otimes__class_Otimes(X20,X16,X18),X18) ),
    inference(fof_simplification,[status(thm)],[c_0_63]) ).

fof(c_0_671_672,plain,
    ! [X20,X16,X17,X18] :
      ( ~ class_Ring__and__Field_Oordered__semiring(X18)
      | c_HOL_Oord__class_Oless(X17,X16,X18)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X18),X20,X18)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X17,X20,X18),c_HOL_Otimes__class_Otimes(X16,X20,X18),X18) ),
    inference(fof_simplification,[status(thm)],[c_0_64]) ).

fof(c_0_672_673,plain,
    ! [X20,X16,X17,X18] :
      ( ~ class_Ring__and__Field_Oordered__semiring(X18)
      | c_HOL_Oord__class_Oless(X17,X16,X18)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X18),X20,X18)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X20,X17,X18),c_HOL_Otimes__class_Otimes(X20,X16,X18),X18) ),
    inference(fof_simplification,[status(thm)],[c_0_65]) ).

fof(c_0_673_674,plain,
    ! [X20,X16,X17,X18] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X18)
      | c_lessequals(X16,X17,X18)
      | ~ c_lessequals(c_HOL_Otimes__class_Otimes(X20,X17,X18),c_HOL_Otimes__class_Otimes(X20,X16,X18),X18)
      | ~ c_HOL_Oord__class_Oless(X20,c_HOL_Ozero__class_Ozero(X18),X18) ),
    inference(fof_simplification,[status(thm)],[c_0_66]) ).

fof(c_0_674_675,plain,
    ! [X20,X16,X17,X18] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X18)
      | c_lessequals(X17,X16,X18)
      | ~ c_lessequals(c_HOL_Otimes__class_Otimes(X20,X17,X18),c_HOL_Otimes__class_Otimes(X20,X16,X18),X18)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X18),X20,X18) ),
    inference(fof_simplification,[status(thm)],[c_0_67]) ).

fof(c_0_675_676,plain,
    ! [X20,X16,X17,X18] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X18)
      | c_lessequals(X17,X16,X18)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X18),X20,X18)
      | ~ c_lessequals(c_HOL_Otimes__class_Otimes(X20,X17,X18),c_HOL_Otimes__class_Otimes(X20,X16,X18),X18) ),
    inference(fof_simplification,[status(thm)],[c_0_68]) ).

fof(c_0_676_677,plain,
    ! [X20,X16,X17,X18] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X18)
      | c_lessequals(X17,X16,X18)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X18),X20,X18)
      | ~ c_lessequals(c_HOL_Otimes__class_Otimes(X17,X20,X18),c_HOL_Otimes__class_Otimes(X16,X20,X18),X18) ),
    inference(fof_simplification,[status(thm)],[c_0_69]) ).

fof(c_0_677_678,plain,
    ! [X20,X16,X17,X18] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X18)
      | c_HOL_Oord__class_Oless(X16,X17,X18)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X20,X17,X18),c_HOL_Otimes__class_Otimes(X20,X16,X18),X18)
      | ~ c_HOL_Oord__class_Oless(X20,c_HOL_Ozero__class_Ozero(X18),X18) ),
    inference(fof_simplification,[status(thm)],[c_0_70]) ).

fof(c_0_678_679,plain,
    ! [X20,X16,X17,X18] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X18)
      | c_HOL_Oord__class_Oless(X17,X16,X18)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X20,X17,X18),c_HOL_Otimes__class_Otimes(X20,X16,X18),X18)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X18),X20,X18) ),
    inference(fof_simplification,[status(thm)],[c_0_71]) ).

fof(c_0_679_680,plain,
    ! [X1,X2,X7] :
      ( c_lessequals(X2,X1,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X7,tc_nat)
      | ~ c_lessequals(c_HOL_Otimes__class_Otimes(X2,X7,tc_nat),c_HOL_Otimes__class_Otimes(X1,X7,tc_nat),tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_72]) ).

fof(c_0_680_681,plain,
    ! [X1,X2,X7] :
      ( c_lessequals(X2,X1,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X7,tc_nat)
      | ~ c_lessequals(c_HOL_Otimes__class_Otimes(X7,X2,tc_nat),c_HOL_Otimes__class_Otimes(X7,X1,tc_nat),tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_73]) ).

fof(c_0_681_682,plain,
    ! [X1,X2,X7] :
      ( c_lessequals(X2,X1,tc_nat)
      | ~ c_lessequals(c_HOL_Otimes__class_Otimes(X7,X2,tc_nat),c_HOL_Otimes__class_Otimes(X7,X1,tc_nat),tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X7,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_74]) ).

fof(c_0_682_683,plain,
    ! [X1,X2,X7] :
      ( c_HOL_Oord__class_Oless(X2,X1,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X7,X2,tc_nat),c_HOL_Otimes__class_Otimes(X7,X1,tc_nat),tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X7,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_75]) ).

fof(c_0_683_684,plain,
    ! [X20,X16,X17,X18] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X18)
      | c_HOL_Oord__class_Oless(X20,c_HOL_Ozero__class_Ozero(X18),X18)
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X18),X20,X18)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X20,X17,X18),c_HOL_Otimes__class_Otimes(X20,X16,X18),X18) ),
    inference(fof_simplification,[status(thm)],[c_0_76]) ).

fof(c_0_684_685,plain,
    ! [X20,X16,X17,X18] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X18)
      | c_HOL_Oord__class_Oless(X20,c_HOL_Ozero__class_Ozero(X18),X18)
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X18),X20,X18)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X17,X20,X18),c_HOL_Otimes__class_Otimes(X16,X20,X18),X18) ),
    inference(fof_simplification,[status(thm)],[c_0_77]) ).

fof(c_0_685_686,plain,
    ! [X3,X27,X20,X18] :
      ( ~ class_Ring__and__Field_Oidom(X18)
      | ~ class_Int_Onumber__ring(X18)
      | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X20,X18),c_HOL_Otimes__class_Otimes(X3,X27,X18),X18) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X27,X18),c_HOL_Otimes__class_Otimes(X3,X20,X18),X18) ),
    inference(fof_simplification,[status(thm)],[c_0_78]) ).

fof(c_0_686_687,plain,
    ! [X19,X9,X3,X18] :
      ( ~ class_Ring__and__Field_Oidom(X18)
      | ~ class_Int_Onumber__ring(X18)
      | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X9,X18),c_HOL_Otimes__class_Otimes(X3,X19,X18),X18) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X19,X18),c_HOL_Otimes__class_Otimes(X3,X9,X18),X18) ),
    inference(fof_simplification,[status(thm)],[c_0_79]) ).

fof(c_0_687_688,plain,
    ! [X20,X16,X17,X18] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X18)
      | c_HOL_Oord__class_Oless(X20,c_HOL_Ozero__class_Ozero(X18),X18)
      | c_HOL_Oord__class_Oless(X17,X16,X18)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X17,X20,X18),c_HOL_Otimes__class_Otimes(X16,X20,X18),X18) ),
    inference(fof_simplification,[status(thm)],[c_0_80]) ).

fof(c_0_688_689,plain,
    ! [X20,X16,X17,X18] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X18)
      | c_HOL_Oord__class_Oless(X16,X17,X18)
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X18),X20,X18)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X17,X20,X18),c_HOL_Otimes__class_Otimes(X16,X20,X18),X18) ),
    inference(fof_simplification,[status(thm)],[c_0_81]) ).

fof(c_0_689_690,plain,
    ! [X20,X16,X17,X18] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X18)
      | c_HOL_Oord__class_Oless(X20,c_HOL_Ozero__class_Ozero(X18),X18)
      | c_HOL_Oord__class_Oless(X17,X16,X18)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X20,X17,X18),c_HOL_Otimes__class_Otimes(X20,X16,X18),X18) ),
    inference(fof_simplification,[status(thm)],[c_0_82]) ).

fof(c_0_690_691,plain,
    ! [X20,X16,X17,X18] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X18)
      | c_HOL_Oord__class_Oless(X16,X17,X18)
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X18),X20,X18)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X20,X17,X18),c_HOL_Otimes__class_Otimes(X20,X16,X18),X18) ),
    inference(fof_simplification,[status(thm)],[c_0_83]) ).

fof(c_0_691_692,plain,
    ! [X20,X16,X17,X18] :
      ( ~ class_Divides_Osemiring__div(X18)
      | c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(X17,X20,X18),X16,X18),X20,X18) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X17,X16,X18),X20,X18) ),
    inference(fof_simplification,[status(thm)],[c_0_84]) ).

fof(c_0_692_693,plain,
    ! [X20,X16,X17,X18] :
      ( ~ class_Divides_Oring__div(X18)
      | c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X17,X16,X18),X20,X18) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(c_Divides_Odiv__class_Omod(X17,X20,X18),X16,X18),X20,X18) ),
    inference(fof_simplification,[status(thm)],[c_0_85]) ).

fof(c_0_693_694,plain,
    ! [X20,X16,X17,X18] :
      ( ~ class_Divides_Oring__div(X18)
      | c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X17,X16,X18),X20,X18) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X17,c_Divides_Odiv__class_Omod(X16,X20,X18),X18),X20,X18) ),
    inference(fof_simplification,[status(thm)],[c_0_86]) ).

fof(c_0_694_695,plain,
    ! [X21,X22,X24,X23,X18] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X18)
      | c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X23,X24,X18),c_HOL_Otimes__class_Otimes(X22,X21,X18),X18) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X23,X22,X18),c_HOL_Otimes__class_Otimes(X24,X21,X18),X18) ),
    inference(fof_simplification,[status(thm)],[c_0_87]) ).

fof(c_0_695_696,plain,
    ! [X20,X16,X17,X18] :
      ( ~ class_Divides_Osemiring__div(X18)
      | c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X17,X16,X18),X20,X18) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(X17,X20,X18),X16,X18),X20,X18) ),
    inference(fof_simplification,[status(thm)],[c_0_88]) ).

fof(c_0_696_697,plain,
    ! [X20,X16,X17,X18] :
      ( ~ class_Divides_Osemiring__div(X18)
      | c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X17,X16,X18),X20,X18) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X17,c_Divides_Odiv__class_Omod(X16,X20,X18),X18),X20,X18) ),
    inference(fof_simplification,[status(thm)],[c_0_89]) ).

fof(c_0_697_698,plain,
    ! [X20,X16,X17,X18] :
      ( ~ class_Divides_Osemiring__div(X18)
      | c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X17,X16,X18),X20,X18) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(X17,X20,X18),X16,X18),X20,X18) ),
    inference(fof_simplification,[status(thm)],[c_0_90]) ).

fof(c_0_698_699,plain,
    ! [X20,X16,X17,X18] :
      ( ~ class_Divides_Osemiring__div(X18)
      | c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X17,X16,X18),X20,X18) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X17,c_Divides_Odiv__class_Omod(X16,X20,X18),X18),X20,X18) ),
    inference(fof_simplification,[status(thm)],[c_0_91]) ).

fof(c_0_699_700,plain,
    ! [X27,X20,X16,X17,X18] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X18)
      | c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X17,X16,X18),c_HOL_Oplus__class_Oplus(X20,X27,X18),X18) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X17,X20,X18),c_HOL_Oplus__class_Oplus(X16,X27,X18),X18) ),
    inference(fof_simplification,[status(thm)],[c_0_92]) ).

fof(c_0_700_701,plain,
    ! [X20,X16,X17,X18] :
      ( ~ class_Divides_Osemiring__div(X18)
      | c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(X17,X20,X18),X16,X18),X20,X18) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X17,X16,X18),X20,X18) ),
    inference(fof_simplification,[status(thm)],[c_0_93]) ).

fof(c_0_701_702,plain,
    ! [X20,X16,X17,X18] :
      ( ~ class_Divides_Osemiring__div(X18)
      | c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X17,c_Divides_Odiv__class_Omod(X16,X20,X18),X18),X20,X18) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X17,X16,X18),X20,X18) ),
    inference(fof_simplification,[status(thm)],[c_0_94]) ).

fof(c_0_702_703,plain,
    ! [X20,X16,X17,X18] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X18)
      | c_HOL_Oord__class_Oless(X16,X17,X18)
      | c_HOL_Oord__class_Oless(X17,X16,X18)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X20,X17,X18),c_HOL_Otimes__class_Otimes(X20,X16,X18),X18) ),
    inference(fof_simplification,[status(thm)],[c_0_95]) ).

fof(c_0_703_704,plain,
    ! [X20,X16,X17,X18] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X18)
      | c_HOL_Oord__class_Oless(X16,X17,X18)
      | c_HOL_Oord__class_Oless(X17,X16,X18)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X17,X20,X18),c_HOL_Otimes__class_Otimes(X16,X20,X18),X18) ),
    inference(fof_simplification,[status(thm)],[c_0_96]) ).

fof(c_0_704_705,plain,
    ! [X3,X6,X27,X20,X18] :
      ( ~ class_Ring__and__Field_Oidom(X18)
      | ~ class_Int_Onumber__ring(X18)
      | c_HOL_Oplus__class_Oplus(X3,c_HOL_Otimes__class_Otimes(X6,X20,X18),X18) != c_HOL_Oplus__class_Oplus(X3,c_HOL_Otimes__class_Otimes(X6,X27,X18),X18)
      | X20 = X27
      | X6 = c_HOL_Ozero__class_Ozero(X18) ),
    inference(fof_simplification,[status(thm)],[c_0_97]) ).

fof(c_0_705_706,plain,
    ! [X2,X7,X14] :
      ( c_HOL_Ominus__class_Ominus(c_Suc(c_HOL_Ominus__class_Ominus(X14,X7,tc_nat)),X2,tc_nat) = c_HOL_Ominus__class_Ominus(c_Suc(X14),c_HOL_Oplus__class_Oplus(X7,X2,tc_nat),tc_nat)
      | ~ c_lessequals(X7,X14,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_98]) ).

fof(c_0_706_707,plain,
    ! [X2,X7,X14] :
      ( c_HOL_Ominus__class_Ominus(X2,c_Suc(c_HOL_Ominus__class_Ominus(X14,X7,tc_nat)),tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X2,X7,tc_nat),c_Suc(X14),tc_nat)
      | ~ c_lessequals(X7,X14,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_99]) ).

fof(c_0_707_708,plain,
    ! [X1,X2,X7] :
      ( c_lessequals(c_HOL_Ominus__class_Ominus(X2,X7,tc_nat),c_HOL_Ominus__class_Ominus(X1,X7,tc_nat),tc_nat)
      | ~ c_lessequals(X2,X1,tc_nat)
      | ~ c_lessequals(X7,X1,tc_nat)
      | ~ c_lessequals(X7,X2,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_100]) ).

fof(c_0_708_709,plain,
    ! [X1,X2,X7] :
      ( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X2,X7,tc_nat),c_HOL_Ominus__class_Ominus(X1,X7,tc_nat),tc_nat)
      | ~ c_HOL_Oord__class_Oless(X2,X1,tc_nat)
      | ~ c_lessequals(X7,X1,tc_nat)
      | ~ c_lessequals(X7,X2,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_101]) ).

fof(c_0_709_710,plain,
    ! [X27,X20,X16,X17,X18] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add(X18)
      | c_lessequals(X17,c_HOL_Oplus__class_Oplus(X16,X27,X18),X18)
      | ~ c_lessequals(X20,X27,X18)
      | ~ c_lessequals(X17,c_HOL_Oplus__class_Oplus(X16,X20,X18),X18) ),
    inference(fof_simplification,[status(thm)],[c_0_102]) ).

fof(c_0_710_711,plain,
    ! [X1,X2,X7] :
      ( c_HOL_Oord__class_Oless(X2,X1,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Suc(X7),X2,tc_nat),c_HOL_Otimes__class_Otimes(c_Suc(X7),X1,tc_nat),tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_103]) ).

fof(c_0_711_712,plain,
    ! [X1,X2,X7] :
      ( c_lessequals(X2,X1,tc_nat)
      | ~ c_lessequals(c_HOL_Otimes__class_Otimes(c_Suc(X7),X2,tc_nat),c_HOL_Otimes__class_Otimes(c_Suc(X7),X1,tc_nat),tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_104]) ).

fof(c_0_712_713,axiom,
    ! [X3,X6,X27,X20] :
      ( c_HOL_Oplus__class_Oplus(X3,c_HOL_Otimes__class_Otimes(X6,X20,tc_nat),tc_nat) != c_HOL_Oplus__class_Oplus(X3,c_HOL_Otimes__class_Otimes(X6,X27,tc_nat),tc_nat)
      | X20 = X27
      | X6 = c_HOL_Ozero__class_Ozero(tc_nat) ),
    c_0_105 ).

fof(c_0_713_714,plain,
    ! [X7,X14,X8] :
      ( c_lessequals(X8,c_HOL_Ominus__class_Ominus(X14,X7,tc_nat),tc_nat)
      | ~ c_lessequals(c_HOL_Oplus__class_Oplus(X8,X7,tc_nat),X14,tc_nat)
      | ~ c_lessequals(X7,X14,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_106]) ).

fof(c_0_714_715,plain,
    ! [X7,X14,X8] :
      ( c_lessequals(c_HOL_Oplus__class_Oplus(X8,X7,tc_nat),X14,tc_nat)
      | ~ c_lessequals(X8,c_HOL_Ominus__class_Ominus(X14,X7,tc_nat),tc_nat)
      | ~ c_lessequals(X7,X14,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_107]) ).

fof(c_0_715_716,plain,
    ! [X20,X16,X17,X18] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X18)
      | c_lessequals(X17,X16,X18)
      | ~ c_lessequals(c_HOL_Oplus__class_Oplus(X17,X20,X18),c_HOL_Oplus__class_Oplus(X16,X20,X18),X18) ),
    inference(fof_simplification,[status(thm)],[c_0_108]) ).

fof(c_0_716_717,plain,
    ! [X20,X16,X17,X18] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X18)
      | c_lessequals(X17,X16,X18)
      | ~ c_lessequals(c_HOL_Oplus__class_Oplus(X20,X17,X18),c_HOL_Oplus__class_Oplus(X20,X16,X18),X18) ),
    inference(fof_simplification,[status(thm)],[c_0_109]) ).

fof(c_0_717_718,plain,
    ! [X20,X16,X17,X18] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X18)
      | c_HOL_Oord__class_Oless(X17,X16,X18)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X17,X20,X18),c_HOL_Oplus__class_Oplus(X16,X20,X18),X18) ),
    inference(fof_simplification,[status(thm)],[c_0_110]) ).

fof(c_0_718_719,plain,
    ! [X20,X16,X17,X18] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X18)
      | c_HOL_Oord__class_Oless(X17,X16,X18)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X20,X17,X18),c_HOL_Oplus__class_Oplus(X20,X16,X18),X18) ),
    inference(fof_simplification,[status(thm)],[c_0_111]) ).

fof(c_0_719_720,plain,
    ! [X1,X2,X7] :
      ( c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X2,X7,tc_nat),c_HOL_Ominus__class_Ominus(X1,X7,tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(X2,X1,tc_nat)
      | ~ c_lessequals(X7,X1,tc_nat)
      | ~ c_lessequals(X7,X2,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_112]) ).

fof(c_0_720_721,plain,
    ! [X1,X2,X7] :
      ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X7,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X7,tc_nat),c_HOL_Otimes__class_Otimes(X1,X7,tc_nat),tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_113]) ).

fof(c_0_721_722,plain,
    ! [X1,X2,X7] :
      ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X7,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X7,X2,tc_nat),c_HOL_Otimes__class_Otimes(X7,X1,tc_nat),tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_114]) ).

fof(c_0_722_723,plain,
    ! [X1,X2,X7] :
      ( c_lessequals(X2,X1,tc_nat)
      | ~ c_lessequals(c_HOL_Oplus__class_Oplus(X7,X2,tc_nat),c_HOL_Oplus__class_Oplus(X7,X1,tc_nat),tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_115]) ).

fof(c_0_723_724,plain,
    ! [X1,X2,X7] :
      ( c_HOL_Oord__class_Oless(X2,X1,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X7,X2,tc_nat),c_HOL_Otimes__class_Otimes(X7,X1,tc_nat),tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_116]) ).

fof(c_0_724_725,plain,
    ! [X1,X2,X7] :
      ( c_HOL_Oord__class_Oless(X2,X1,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X7,tc_nat),c_HOL_Otimes__class_Otimes(X1,X7,tc_nat),tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_117]) ).

fof(c_0_725,plain,
    ! [X1,X2,X7] :
      ( c_HOL_Oord__class_Oless(X2,X1,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X7,X2,tc_nat),c_HOL_Oplus__class_Oplus(X7,X1,tc_nat),tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_118]) ).

fof(c_0_726,plain,
    ! [X20,X16,X17,X18] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X18)
      | c_lessequals(c_HOL_Otimes__class_Otimes(X20,X17,X18),c_HOL_Otimes__class_Otimes(X20,X16,X18),X18)
      | ~ c_lessequals(X16,X17,X18)
      | ~ c_HOL_Oord__class_Oless(X20,c_HOL_Ozero__class_Ozero(X18),X18) ),
    inference(fof_simplification,[status(thm)],[c_0_119]) ).

fof(c_0_727,plain,
    ! [X20,X16,X17,X18] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X18)
      | c_lessequals(c_HOL_Otimes__class_Otimes(X20,X17,X18),c_HOL_Otimes__class_Otimes(X20,X16,X18),X18)
      | ~ c_lessequals(X17,X16,X18)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X18),X20,X18) ),
    inference(fof_simplification,[status(thm)],[c_0_120]) ).

fof(c_0_728,plain,
    ! [X20,X16,X17,X18] :
      ( ~ class_Ring__and__Field_Opordered__ring(X18)
      | c_lessequals(c_HOL_Otimes__class_Otimes(X17,X20,X18),c_HOL_Otimes__class_Otimes(X16,X20,X18),X18)
      | ~ c_lessequals(X20,c_HOL_Ozero__class_Ozero(X18),X18)
      | ~ c_lessequals(X16,X17,X18) ),
    inference(fof_simplification,[status(thm)],[c_0_121]) ).

fof(c_0_729,plain,
    ! [X20,X16,X17,X18] :
      ( ~ class_Ring__and__Field_Opordered__ring(X18)
      | c_lessequals(c_HOL_Otimes__class_Otimes(X20,X17,X18),c_HOL_Otimes__class_Otimes(X20,X16,X18),X18)
      | ~ c_lessequals(X20,c_HOL_Ozero__class_Ozero(X18),X18)
      | ~ c_lessequals(X16,X17,X18) ),
    inference(fof_simplification,[status(thm)],[c_0_122]) ).

fof(c_0_730,plain,
    ! [X20,X16,X17,X18] :
      ( ~ class_Ring__and__Field_Omult__mono(X18)
      | c_lessequals(c_HOL_Otimes__class_Otimes(X17,X20,X18),c_HOL_Otimes__class_Otimes(X16,X20,X18),X18)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X18),X20,X18)
      | ~ c_lessequals(X17,X16,X18) ),
    inference(fof_simplification,[status(thm)],[c_0_123]) ).

fof(c_0_731,plain,
    ! [X20,X16,X17,X18] :
      ( ~ class_Ring__and__Field_Omult__mono(X18)
      | c_lessequals(c_HOL_Otimes__class_Otimes(X20,X17,X18),c_HOL_Otimes__class_Otimes(X20,X16,X18),X18)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X18),X20,X18)
      | ~ c_lessequals(X17,X16,X18) ),
    inference(fof_simplification,[status(thm)],[c_0_124]) ).

fof(c_0_732,plain,
    ! [X20,X16,X17,X18] :
      ( ~ class_Ring__and__Field_Omult__mono1(X18)
      | c_lessequals(c_HOL_Otimes__class_Otimes(X20,X17,X18),c_HOL_Otimes__class_Otimes(X20,X16,X18),X18)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X18),X20,X18)
      | ~ c_lessequals(X17,X16,X18) ),
    inference(fof_simplification,[status(thm)],[c_0_125]) ).

fof(c_0_733,plain,
    ! [X20,X16,X17,X18] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X18)
      | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X20,X17,X18),c_HOL_Otimes__class_Otimes(X20,X16,X18),X18)
      | ~ c_HOL_Oord__class_Oless(X16,X17,X18)
      | ~ c_HOL_Oord__class_Oless(X20,c_HOL_Ozero__class_Ozero(X18),X18) ),
    inference(fof_simplification,[status(thm)],[c_0_126]) ).

fof(c_0_734,plain,
    ! [X20,X16,X17,X18] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X18)
      | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X20,X17,X18),c_HOL_Otimes__class_Otimes(X20,X16,X18),X18)
      | ~ c_HOL_Oord__class_Oless(X17,X16,X18)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X18),X20,X18) ),
    inference(fof_simplification,[status(thm)],[c_0_127]) ).

fof(c_0_735,plain,
    ! [X20,X16,X17,X18] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X18)
      | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X20,X17,X18),c_HOL_Otimes__class_Otimes(X20,X16,X18),X18)
      | ~ c_HOL_Oord__class_Oless(X20,c_HOL_Ozero__class_Ozero(X18),X18)
      | ~ c_HOL_Oord__class_Oless(X16,X17,X18) ),
    inference(fof_simplification,[status(thm)],[c_0_128]) ).

fof(c_0_736,plain,
    ! [X20,X16,X17,X18] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X18)
      | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X20,X17,X18),c_HOL_Otimes__class_Otimes(X20,X16,X18),X18)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X18),X20,X18)
      | ~ c_HOL_Oord__class_Oless(X17,X16,X18) ),
    inference(fof_simplification,[status(thm)],[c_0_129]) ).

fof(c_0_737,plain,
    ! [X20,X16,X17,X18] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X18)
      | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X20,X17,X18),c_HOL_Otimes__class_Otimes(X20,X16,X18),X18)
      | ~ c_HOL_Oord__class_Oless(X17,X16,X18)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X18),X20,X18) ),
    inference(fof_simplification,[status(thm)],[c_0_130]) ).

fof(c_0_738,plain,
    ! [X20,X16,X17,X18] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X18)
      | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X20,X17,X18),c_HOL_Otimes__class_Otimes(X20,X16,X18),X18)
      | ~ c_HOL_Oord__class_Oless(X16,X17,X18)
      | ~ c_HOL_Oord__class_Oless(X20,c_HOL_Ozero__class_Ozero(X18),X18) ),
    inference(fof_simplification,[status(thm)],[c_0_131]) ).

fof(c_0_739,plain,
    ! [X20,X16,X17,X18] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X18)
      | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X17,X20,X18),c_HOL_Otimes__class_Otimes(X16,X20,X18),X18)
      | ~ c_HOL_Oord__class_Oless(X20,c_HOL_Ozero__class_Ozero(X18),X18)
      | ~ c_HOL_Oord__class_Oless(X16,X17,X18) ),
    inference(fof_simplification,[status(thm)],[c_0_132]) ).

fof(c_0_740,plain,
    ! [X20,X16,X17,X18] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X18)
      | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X17,X20,X18),c_HOL_Otimes__class_Otimes(X16,X20,X18),X18)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X18),X20,X18)
      | ~ c_HOL_Oord__class_Oless(X17,X16,X18) ),
    inference(fof_simplification,[status(thm)],[c_0_133]) ).

fof(c_0_741,plain,
    ! [X20,X16,X17,X18] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X18)
      | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X17,X20,X18),c_HOL_Otimes__class_Otimes(X16,X20,X18),X18)
      | ~ c_HOL_Oord__class_Oless(X17,X16,X18)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X18),X20,X18) ),
    inference(fof_simplification,[status(thm)],[c_0_134]) ).

fof(c_0_742,plain,
    ! [X20,X16,X17,X18] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X18)
      | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X17,X20,X18),c_HOL_Otimes__class_Otimes(X16,X20,X18),X18)
      | ~ c_HOL_Oord__class_Oless(X16,X17,X18)
      | ~ c_HOL_Oord__class_Oless(X20,c_HOL_Ozero__class_Ozero(X18),X18) ),
    inference(fof_simplification,[status(thm)],[c_0_135]) ).

fof(c_0_743,plain,
    ! [X20,X16,X17,X18] :
      ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X18)
      | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X20,X17,X18),c_HOL_Otimes__class_Otimes(X20,X16,X18),X18)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X18),X20,X18)
      | ~ c_HOL_Oord__class_Oless(X17,X16,X18) ),
    inference(fof_simplification,[status(thm)],[c_0_136]) ).

fof(c_0_744,plain,
    ! [X9,X3,X18] :
      ( ~ class_Ring__and__Field_Oordered__idom(X18)
      | c_lessequals(c_HOL_Otimes__class_Otimes(X3,X9,X18),X3,X18)
      | ~ c_lessequals(X9,c_HOL_Oone__class_Oone(X18),X18)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X18),X9,X18)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X18),X3,X18) ),
    inference(fof_simplification,[status(thm)],[c_0_137]) ).

fof(c_0_745,plain,
    ! [X9,X3,X18] :
      ( ~ class_Ring__and__Field_Oordered__idom(X18)
      | c_lessequals(c_HOL_Otimes__class_Otimes(X9,X3,X18),X3,X18)
      | ~ c_lessequals(X9,c_HOL_Oone__class_Oone(X18),X18)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X18),X9,X18)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X18),X3,X18) ),
    inference(fof_simplification,[status(thm)],[c_0_138]) ).

fof(c_0_746,plain,
    ! [X1,X2,X7] :
      ( c_lessequals(X2,c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),X7,tc_nat),tc_nat)
      | ~ c_lessequals(X7,X1,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_139]) ).

fof(c_0_747,plain,
    ! [X27,X20,X16,X17,X18] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X18)
      | c_lessequals(c_HOL_Oplus__class_Oplus(X17,X20,X18),c_HOL_Oplus__class_Oplus(X16,X27,X18),X18)
      | ~ c_lessequals(X20,X27,X18)
      | ~ c_lessequals(X17,X16,X18) ),
    inference(fof_simplification,[status(thm)],[c_0_140]) ).

fof(c_0_748,plain,
    ! [X27,X20,X16,X17,X18] :
      ( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X18)
      | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X17,X20,X18),c_HOL_Oplus__class_Oplus(X16,X27,X18),X18)
      | ~ c_HOL_Oord__class_Oless(X20,X27,X18)
      | ~ c_HOL_Oord__class_Oless(X17,X16,X18) ),
    inference(fof_simplification,[status(thm)],[c_0_141]) ).

fof(c_0_749,plain,
    ! [X27,X20,X16,X17,X18] :
      ( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X18)
      | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X17,X20,X18),c_HOL_Oplus__class_Oplus(X16,X27,X18),X18)
      | ~ c_HOL_Oord__class_Oless(X20,X27,X18)
      | ~ c_lessequals(X17,X16,X18) ),
    inference(fof_simplification,[status(thm)],[c_0_142]) ).

fof(c_0_750,plain,
    ! [X27,X20,X16,X17,X18] :
      ( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X18)
      | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X17,X20,X18),c_HOL_Oplus__class_Oplus(X16,X27,X18),X18)
      | ~ c_lessequals(X20,X27,X18)
      | ~ c_HOL_Oord__class_Oless(X17,X16,X18) ),
    inference(fof_simplification,[status(thm)],[c_0_143]) ).

fof(c_0_751,plain,
    ! [X9,X3,X18] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X18)
      | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X3,X18),c_HOL_Otimes__class_Otimes(X9,X9,X18),X18) != c_HOL_Ozero__class_Ozero(X18)
      | X9 = c_HOL_Ozero__class_Ozero(X18) ),
    inference(fof_simplification,[status(thm)],[c_0_144]) ).

fof(c_0_752,plain,
    ! [X9,X3,X18] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X18)
      | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X3,X18),c_HOL_Otimes__class_Otimes(X9,X9,X18),X18) != c_HOL_Ozero__class_Ozero(X18)
      | X3 = c_HOL_Ozero__class_Ozero(X18) ),
    inference(fof_simplification,[status(thm)],[c_0_145]) ).

fof(c_0_753,plain,
    ! [X19,X9,X3,X18] :
      ( ~ class_Orderings_Olinorder(X18)
      | c_Orderings_Oord__class_Omin(c_Orderings_Oord__class_Omax(X9,X19,X18),X3,X18) = c_Orderings_Oord__class_Omax(c_Orderings_Oord__class_Omin(X9,X3,X18),c_Orderings_Oord__class_Omin(X19,X3,X18),X18) ),
    inference(fof_simplification,[status(thm)],[c_0_146]) ).

fof(c_0_754,plain,
    ! [X19,X9,X3,X18] :
      ( ~ class_Orderings_Olinorder(X18)
      | c_Orderings_Oord__class_Omin(X3,c_Orderings_Oord__class_Omax(X9,X19,X18),X18) = c_Orderings_Oord__class_Omax(c_Orderings_Oord__class_Omin(X3,X9,X18),c_Orderings_Oord__class_Omin(X3,X19,X18),X18) ),
    inference(fof_simplification,[status(thm)],[c_0_147]) ).

fof(c_0_755,plain,
    ! [X19,X9,X3,X18] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add(X18)
      | c_HOL_Ominus__class_Ominus(c_Orderings_Oord__class_Omin(X3,X9,X18),X19,X18) = c_Orderings_Oord__class_Omin(c_HOL_Ominus__class_Ominus(X3,X19,X18),c_HOL_Ominus__class_Ominus(X9,X19,X18),X18) ),
    inference(fof_simplification,[status(thm)],[c_0_148]) ).

fof(c_0_756,plain,
    ! [X19,X9,X3,X18] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add(X18)
      | c_HOL_Ominus__class_Ominus(c_Orderings_Oord__class_Omax(X3,X9,X18),X19,X18) = c_Orderings_Oord__class_Omax(c_HOL_Ominus__class_Ominus(X3,X19,X18),c_HOL_Ominus__class_Ominus(X9,X19,X18),X18) ),
    inference(fof_simplification,[status(thm)],[c_0_149]) ).

fof(c_0_757,plain,
    ! [X19,X9,X3,X18] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X18)
      | c_HOL_Oplus__class_Oplus(c_Orderings_Oord__class_Omin(X3,X9,X18),X19,X18) = c_Orderings_Oord__class_Omin(c_HOL_Oplus__class_Oplus(X3,X19,X18),c_HOL_Oplus__class_Oplus(X9,X19,X18),X18) ),
    inference(fof_simplification,[status(thm)],[c_0_150]) ).

fof(c_0_758,plain,
    ! [X19,X9,X3,X18] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X18)
      | c_HOL_Oplus__class_Oplus(c_Orderings_Oord__class_Omax(X3,X9,X18),X19,X18) = c_Orderings_Oord__class_Omax(c_HOL_Oplus__class_Oplus(X3,X19,X18),c_HOL_Oplus__class_Oplus(X9,X19,X18),X18) ),
    inference(fof_simplification,[status(thm)],[c_0_151]) ).

fof(c_0_759,plain,
    ! [X20,X16,X17,X18] :
      ( ~ class_Divides_Osemiring__div(X18)
      | c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X17,c_HOL_Otimes__class_Otimes(X20,X16,X18),X18),X16,X18) = c_Divides_Odiv__class_Omod(X17,X16,X18) ),
    inference(fof_simplification,[status(thm)],[c_0_152]) ).

fof(c_0_760,plain,
    ! [X20,X16,X17,X18] :
      ( ~ class_Divides_Osemiring__div(X18)
      | c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X17,c_HOL_Otimes__class_Otimes(X16,X20,X18),X18),X16,X18) = c_Divides_Odiv__class_Omod(X17,X16,X18) ),
    inference(fof_simplification,[status(thm)],[c_0_153]) ).

fof(c_0_761,plain,
    ! [X2,X16,X17,X18] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X18)
      | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X17,X2,X18),c_HOL_Otimes__class_Otimes(X16,X2,X18),X18) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X17,X16,X18),X2,X18) ),
    inference(fof_simplification,[status(thm)],[c_0_154]) ).

fof(c_0_762,plain,
    ! [X19,X9,X3,X18] :
      ( ~ class_Orderings_Olinorder(X18)
      | c_Orderings_Oord__class_Omax(c_Orderings_Oord__class_Omin(X9,X19,X18),X3,X18) = c_Orderings_Oord__class_Omin(c_Orderings_Oord__class_Omax(X9,X3,X18),c_Orderings_Oord__class_Omax(X19,X3,X18),X18) ),
    inference(fof_simplification,[status(thm)],[c_0_155]) ).

fof(c_0_763,plain,
    ! [X19,X9,X3,X18] :
      ( ~ class_Orderings_Olinorder(X18)
      | c_Orderings_Oord__class_Omax(X3,c_Orderings_Oord__class_Omin(X9,X19,X18),X18) = c_Orderings_Oord__class_Omin(c_Orderings_Oord__class_Omax(X3,X9,X18),c_Orderings_Oord__class_Omax(X3,X19,X18),X18) ),
    inference(fof_simplification,[status(thm)],[c_0_156]) ).

fof(c_0_764,plain,
    ! [X20,X16,X17,X18] :
      ( ~ class_Divides_Osemiring__div(X18)
      | c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X17,X20,X18),c_HOL_Otimes__class_Otimes(X16,X20,X18),X18) = c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(X17,X16,X18),X20,X18) ),
    inference(fof_simplification,[status(thm)],[c_0_157]) ).

fof(c_0_765,plain,
    ! [X20,X16,X17,X18] :
      ( ~ class_Divides_Osemiring__div(X18)
      | c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X20,X17,X18),c_HOL_Otimes__class_Otimes(X20,X16,X18),X18) = c_HOL_Otimes__class_Otimes(X20,c_Divides_Odiv__class_Omod(X17,X16,X18),X18) ),
    inference(fof_simplification,[status(thm)],[c_0_158]) ).

fof(c_0_766,plain,
    ! [X20,X16,X17,X18] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X18)
      | c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X17,X16,X18),X20,X18) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X17,X20,X18),c_HOL_Otimes__class_Otimes(X16,X20,X18),X18) ),
    inference(fof_simplification,[status(thm)],[c_0_159]) ).

fof(c_0_767,plain,
    ! [X20,X16,X17,X18] :
      ( ~ class_Ring__and__Field_Ocomm__semiring(X18)
      | c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X17,X16,X18),X20,X18) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X17,X20,X18),c_HOL_Otimes__class_Otimes(X16,X20,X18),X18) ),
    inference(fof_simplification,[status(thm)],[c_0_160]) ).

fof(c_0_768,plain,
    ! [X19,X9,X3,X18] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X18)
      | c_HOL_Otimes__class_Otimes(X3,c_HOL_Oplus__class_Oplus(X9,X19,X18),X18) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X9,X18),c_HOL_Otimes__class_Otimes(X3,X19,X18),X18) ),
    inference(fof_simplification,[status(thm)],[c_0_161]) ).

fof(c_0_769,plain,
    ! [X1,X2,X7] :
      ( c_lessequals(c_HOL_Otimes__class_Otimes(X7,X2,tc_nat),c_HOL_Otimes__class_Otimes(X7,X1,tc_nat),tc_nat)
      | ~ c_lessequals(X2,X1,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X7,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_162]) ).

fof(c_0_770,plain,
    ! [X1,X2,X7] :
      ( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X7,tc_nat),c_HOL_Otimes__class_Otimes(X1,X7,tc_nat),tc_nat)
      | ~ c_HOL_Oord__class_Oless(X2,X1,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X7,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_163]) ).

fof(c_0_771,plain,
    ! [X1,X2,X7] :
      ( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X7,X2,tc_nat),c_HOL_Otimes__class_Otimes(X7,X1,tc_nat),tc_nat)
      | ~ c_HOL_Oord__class_Oless(X2,X1,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X7,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_164]) ).

fof(c_0_772,plain,
    ! [X7,X14,X8] :
      ( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X7,X8,tc_nat),c_HOL_Otimes__class_Otimes(X7,X14,tc_nat),tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X7,tc_nat)
      | ~ c_HOL_Oord__class_Oless(X8,X14,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_165]) ).

fof(c_0_773,plain,
    ! [X7,X14,X8] :
      ( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X8,X7,tc_nat),c_HOL_Otimes__class_Otimes(X14,X7,tc_nat),tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X7,tc_nat)
      | ~ c_HOL_Oord__class_Oless(X8,X14,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_166]) ).

fof(c_0_774,plain,
    ! [X1,X2,X7] :
      ( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X7,X2,tc_nat),c_HOL_Otimes__class_Otimes(X7,X1,tc_nat),tc_nat)
      | ~ c_HOL_Oord__class_Oless(X2,X1,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X7,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_167]) ).

fof(c_0_775,axiom,
    ! [X1,X2] :
      ( c_HOL_Otimes__class_Otimes(X2,X1,tc_nat) = c_HOL_Oplus__class_Oplus(X1,c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X1,tc_nat),tc_nat)
      | X2 = c_HOL_Ozero__class_Ozero(tc_nat) ),
    c_0_168 ).

fof(c_0_776,plain,
    ! [X1,X2,X28] :
      ( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X28,X1,tc_nat),c_HOL_Ominus__class_Ominus(X28,X2,tc_nat),tc_nat)
      | ~ c_HOL_Oord__class_Oless(X2,X28,tc_nat)
      | ~ c_HOL_Oord__class_Oless(X2,X1,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_169]) ).

fof(c_0_777,plain,
    ! [X28,X7,X14,X8] :
      ( c_lessequals(c_HOL_Oplus__class_Oplus(X8,X7,tc_nat),c_HOL_Oplus__class_Oplus(X14,X28,tc_nat),tc_nat)
      | ~ c_lessequals(X7,X28,tc_nat)
      | ~ c_lessequals(X8,X14,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_170]) ).

fof(c_0_778,plain,
    ! [X20,X16,X17] :
      ( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X17,X20,tc_nat),c_HOL_Ominus__class_Ominus(X16,X20,tc_nat),tc_nat)
      | ~ c_lessequals(X20,X17,tc_nat)
      | ~ c_HOL_Oord__class_Oless(X17,X16,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_171]) ).

fof(c_0_779,plain,
    ! [X28,X7,X14,X8] :
      ( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X8,X7,tc_nat),c_HOL_Oplus__class_Oplus(X14,X28,tc_nat),tc_nat)
      | ~ c_HOL_Oord__class_Oless(X7,X28,tc_nat)
      | ~ c_HOL_Oord__class_Oless(X8,X14,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_172]) ).

fof(c_0_780,plain,
    ! [X28,X7,X14,X8] :
      ( c_lessequals(c_HOL_Otimes__class_Otimes(X8,X7,tc_nat),c_HOL_Otimes__class_Otimes(X14,X28,tc_nat),tc_nat)
      | ~ c_lessequals(X7,X28,tc_nat)
      | ~ c_lessequals(X8,X14,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_173]) ).

fof(c_0_781,plain,
    ! [X16,X17,X18] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X18)
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X18),X16,X18)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X18),X17,X18)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X18),c_HOL_Otimes__class_Otimes(X16,X17,X18),X18) ),
    inference(fof_simplification,[status(thm)],[c_0_174]) ).

fof(c_0_782,plain,
    ! [X16,X17,X18] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X18)
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X18),X16,X18)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X18),X17,X18)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X18),c_HOL_Otimes__class_Otimes(X17,X16,X18),X18) ),
    inference(fof_simplification,[status(thm)],[c_0_175]) ).

fof(c_0_783,plain,
    ! [X7,X8] :
      ( ~ c_lessequals(X8,c_HOL_Oplus__class_Oplus(X7,X8,tc_nat),tc_nat)
      | c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X7,X8,tc_nat),X8,tc_nat) = X7 ),
    inference(fof_simplification,[status(thm)],[c_0_176]) ).

fof(c_0_784,plain,
    ! [X7,X14,X8] :
      ( c_lessequals(X14,c_HOL_Oplus__class_Oplus(X8,X7,tc_nat),tc_nat)
      | ~ c_lessequals(c_HOL_Ominus__class_Ominus(X14,X7,tc_nat),X8,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_177]) ).

fof(c_0_785,plain,
    ! [X7,X14,X8] :
      ( c_lessequals(c_HOL_Ominus__class_Ominus(X14,X7,tc_nat),X8,tc_nat)
      | ~ c_lessequals(X14,c_HOL_Oplus__class_Oplus(X8,X7,tc_nat),tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_178]) ).

fof(c_0_786,plain,
    ! [X7,X14,X8] :
      ( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X8,X7,tc_nat),X14,tc_nat)
      | ~ c_HOL_Oord__class_Oless(X8,c_HOL_Ominus__class_Ominus(X14,X7,tc_nat),tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_179]) ).

fof(c_0_787,plain,
    ! [X7,X14,X8] :
      ( c_HOL_Oord__class_Oless(X8,c_HOL_Ominus__class_Ominus(X14,X7,tc_nat),tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X8,X7,tc_nat),X14,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_180]) ).

fof(c_0_788,plain,
    ! [X19,X9,X3,X15,X18] :
      ( ~ class_OrderedGroup_Oab__group__add(X18)
      | c_HOL_Oplus__class_Oplus(X3,c_HOL_Oplus__class_Oplus(X9,X19,X18),X18) != c_HOL_Oplus__class_Oplus(X9,X15,X18)
      | c_HOL_Oplus__class_Oplus(X3,X19,X18) = X15 ),
    inference(fof_simplification,[status(thm)],[c_0_181]) ).

fof(c_0_789,plain,
    ! [X7,X14,X8] :
      ( c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X8,X14,tc_nat),X7,tc_nat) = c_HOL_Oplus__class_Oplus(X8,c_HOL_Ominus__class_Ominus(X14,X7,tc_nat),tc_nat)
      | ~ c_lessequals(X7,X14,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_182]) ).

fof(c_0_790,plain,
    ! [X7,X14,X8] :
      ( c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X14,X8,tc_nat),X7,tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X14,X7,tc_nat),X8,tc_nat)
      | ~ c_lessequals(X7,X14,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_183]) ).

fof(c_0_791,plain,
    ! [X7,X14,X8] :
      ( c_HOL_Ominus__class_Ominus(X8,c_HOL_Ominus__class_Ominus(X14,X7,tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X8,X7,tc_nat),X14,tc_nat)
      | ~ c_lessequals(X7,X14,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_184]) ).

fof(c_0_792,plain,
    ! [X7,X14,X8] :
      ( c_HOL_Oplus__class_Oplus(X8,c_HOL_Ominus__class_Ominus(X14,X7,tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X8,X14,tc_nat),X7,tc_nat)
      | ~ c_lessequals(X7,X14,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_185]) ).

fof(c_0_793,plain,
    ! [X7,X14,X8] :
      ( c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X14,X7,tc_nat),X8,tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X14,X8,tc_nat),X7,tc_nat)
      | ~ c_lessequals(X7,X14,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_186]) ).

fof(c_0_794,plain,
    ! [X16,X17,X18] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X18)
      | c_lessequals(c_HOL_Ozero__class_Ozero(X18),X16,X18)
      | c_lessequals(X16,c_HOL_Ozero__class_Ozero(X18),X18)
      | ~ c_lessequals(c_HOL_Otimes__class_Otimes(X17,X16,X18),c_HOL_Ozero__class_Ozero(X18),X18) ),
    inference(fof_simplification,[status(thm)],[c_0_187]) ).

fof(c_0_795,plain,
    ! [X16,X17,X18] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X18)
      | c_lessequals(X17,c_HOL_Ozero__class_Ozero(X18),X18)
      | c_lessequals(X16,c_HOL_Ozero__class_Ozero(X18),X18)
      | ~ c_lessequals(c_HOL_Otimes__class_Otimes(X17,X16,X18),c_HOL_Ozero__class_Ozero(X18),X18) ),
    inference(fof_simplification,[status(thm)],[c_0_188]) ).

fof(c_0_796,plain,
    ! [X16,X17,X18] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X18)
      | c_lessequals(c_HOL_Ozero__class_Ozero(X18),X16,X18)
      | c_lessequals(c_HOL_Ozero__class_Ozero(X18),X17,X18)
      | ~ c_lessequals(c_HOL_Otimes__class_Otimes(X17,X16,X18),c_HOL_Ozero__class_Ozero(X18),X18) ),
    inference(fof_simplification,[status(thm)],[c_0_189]) ).

fof(c_0_797,plain,
    ! [X16,X17,X18] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X18)
      | c_lessequals(X17,c_HOL_Ozero__class_Ozero(X18),X18)
      | c_lessequals(c_HOL_Ozero__class_Ozero(X18),X17,X18)
      | ~ c_lessequals(c_HOL_Otimes__class_Otimes(X17,X16,X18),c_HOL_Ozero__class_Ozero(X18),X18) ),
    inference(fof_simplification,[status(thm)],[c_0_190]) ).

fof(c_0_798,plain,
    ! [X16,X17,X18] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X18)
      | c_lessequals(X17,c_HOL_Ozero__class_Ozero(X18),X18)
      | c_lessequals(c_HOL_Ozero__class_Ozero(X18),X17,X18)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X18),c_HOL_Otimes__class_Otimes(X17,X16,X18),X18) ),
    inference(fof_simplification,[status(thm)],[c_0_191]) ).

fof(c_0_799,plain,
    ! [X16,X17,X18] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X18)
      | c_lessequals(X16,c_HOL_Ozero__class_Ozero(X18),X18)
      | c_lessequals(c_HOL_Ozero__class_Ozero(X18),X17,X18)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X18),c_HOL_Otimes__class_Otimes(X17,X16,X18),X18) ),
    inference(fof_simplification,[status(thm)],[c_0_192]) ).

fof(c_0_800,plain,
    ! [X16,X17,X18] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X18)
      | c_lessequals(X17,c_HOL_Ozero__class_Ozero(X18),X18)
      | c_lessequals(c_HOL_Ozero__class_Ozero(X18),X16,X18)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X18),c_HOL_Otimes__class_Otimes(X17,X16,X18),X18) ),
    inference(fof_simplification,[status(thm)],[c_0_193]) ).

fof(c_0_801,plain,
    ! [X16,X17,X18] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X18)
      | c_lessequals(X16,c_HOL_Ozero__class_Ozero(X18),X18)
      | c_lessequals(c_HOL_Ozero__class_Ozero(X18),X16,X18)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X18),c_HOL_Otimes__class_Otimes(X17,X16,X18),X18) ),
    inference(fof_simplification,[status(thm)],[c_0_194]) ).

fof(c_0_802,axiom,
    ! [X1,X2] :
      ( c_HOL_Oplus__class_Oplus(X2,X1,tc_nat) = c_Suc(c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X2,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X1,tc_nat))
      | X2 = c_HOL_Ozero__class_Ozero(tc_nat) ),
    c_0_195 ).

fof(c_0_803,plain,
    ! [X1,X2] :
      ( 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)
      | ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X1,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_196]) ).

fof(c_0_804,plain,
    ! [X1,X2] :
      ( c_lessequals(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Otimes__class_Otimes(X2,X1,tc_nat),tc_nat)
      | ~ c_lessequals(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X1,tc_nat)
      | ~ c_lessequals(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X2,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_197]) ).

fof(c_0_805,plain,
    ! [X19,X9,X3,X18] :
      ( ~ class_Orderings_Olinorder(X18)
      | c_lessequals(X19,X9,X18)
      | c_lessequals(X19,X3,X18)
      | ~ c_lessequals(X19,c_Orderings_Oord__class_Omax(X3,X9,X18),X18) ),
    inference(fof_simplification,[status(thm)],[c_0_198]) ).

fof(c_0_806,plain,
    ! [X19,X9,X3,X18] :
      ( ~ class_Orderings_Olinorder(X18)
      | c_lessequals(X9,X19,X18)
      | c_lessequals(X3,X19,X18)
      | ~ c_lessequals(c_Orderings_Oord__class_Omin(X3,X9,X18),X19,X18) ),
    inference(fof_simplification,[status(thm)],[c_0_199]) ).

fof(c_0_807,plain,
    ! [X19,X9,X3,X18] :
      ( ~ class_Orderings_Olinorder(X18)
      | c_HOL_Oord__class_Oless(X19,X9,X18)
      | c_HOL_Oord__class_Oless(X19,X3,X18)
      | ~ c_HOL_Oord__class_Oless(X19,c_Orderings_Oord__class_Omax(X3,X9,X18),X18) ),
    inference(fof_simplification,[status(thm)],[c_0_200]) ).

fof(c_0_808,plain,
    ! [X19,X9,X3,X18] :
      ( ~ class_Orderings_Olinorder(X18)
      | c_HOL_Oord__class_Oless(X9,X19,X18)
      | c_HOL_Oord__class_Oless(X3,X19,X18)
      | ~ c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omin(X3,X9,X18),X19,X18) ),
    inference(fof_simplification,[status(thm)],[c_0_201]) ).

fof(c_0_809,plain,
    ! [X1,X2,X7] :
      ( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Suc(X7),X2,tc_nat),c_HOL_Otimes__class_Otimes(c_Suc(X7),X1,tc_nat),tc_nat)
      | ~ c_HOL_Oord__class_Oless(X2,X1,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_202]) ).

fof(c_0_810,plain,
    ! [X1,X2,X7] :
      ( c_lessequals(c_HOL_Otimes__class_Otimes(c_Suc(X7),X2,tc_nat),c_HOL_Otimes__class_Otimes(c_Suc(X7),X1,tc_nat),tc_nat)
      | ~ c_lessequals(X2,X1,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_203]) ).

fof(c_0_811,plain,
    ! [X16,X17,X18] :
      ( ~ class_OrderedGroup_Opordered__comm__monoid__add(X18)
      | c_lessequals(c_HOL_Ozero__class_Ozero(X18),c_HOL_Oplus__class_Oplus(X17,X16,X18),X18)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X18),X16,X18)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X18),X17,X18) ),
    inference(fof_simplification,[status(thm)],[c_0_204]) ).

fof(c_0_812,plain,
    ! [X16,X17,X18] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X18)
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X18),c_HOL_Otimes__class_Otimes(X17,X16,X18),X18)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X18),X16,X18)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X18),X17,X18) ),
    inference(fof_simplification,[status(thm)],[c_0_205]) ).

fof(c_0_813,plain,
    ! [X16,X17,X18] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X18)
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X18),c_HOL_Otimes__class_Otimes(X17,X16,X18),X18)
      | ~ c_HOL_Oord__class_Oless(X16,c_HOL_Ozero__class_Ozero(X18),X18)
      | ~ c_HOL_Oord__class_Oless(X17,c_HOL_Ozero__class_Ozero(X18),X18) ),
    inference(fof_simplification,[status(thm)],[c_0_206]) ).

fof(c_0_814,plain,
    ! [X16,X17,X18] :
      ( ~ class_OrderedGroup_Opordered__comm__monoid__add(X18)
      | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X17,X16,X18),c_HOL_Ozero__class_Ozero(X18),X18)
      | ~ c_HOL_Oord__class_Oless(X16,c_HOL_Ozero__class_Ozero(X18),X18)
      | ~ c_lessequals(X17,c_HOL_Ozero__class_Ozero(X18),X18) ),
    inference(fof_simplification,[status(thm)],[c_0_207]) ).

fof(c_0_815,plain,
    ! [X16,X17,X18] :
      ( ~ class_OrderedGroup_Opordered__comm__monoid__add(X18)
      | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X17,X16,X18),c_HOL_Ozero__class_Ozero(X18),X18)
      | ~ c_lessequals(X16,c_HOL_Ozero__class_Ozero(X18),X18)
      | ~ c_HOL_Oord__class_Oless(X17,c_HOL_Ozero__class_Ozero(X18),X18) ),
    inference(fof_simplification,[status(thm)],[c_0_208]) ).

fof(c_0_816,plain,
    ! [X16,X17,X18] :
      ( ~ class_OrderedGroup_Opordered__comm__monoid__add(X18)
      | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X17,X16,X18),c_HOL_Ozero__class_Ozero(X18),X18)
      | ~ c_HOL_Oord__class_Oless(X16,c_HOL_Ozero__class_Ozero(X18),X18)
      | ~ c_HOL_Oord__class_Oless(X17,c_HOL_Ozero__class_Ozero(X18),X18) ),
    inference(fof_simplification,[status(thm)],[c_0_209]) ).

fof(c_0_817,plain,
    ! [X16,X17,X18] :
      ( ~ class_OrderedGroup_Opordered__comm__monoid__add(X18)
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X18),c_HOL_Oplus__class_Oplus(X17,X16,X18),X18)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X18),X16,X18)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X18),X17,X18) ),
    inference(fof_simplification,[status(thm)],[c_0_210]) ).

fof(c_0_818,plain,
    ! [X16,X17,X18] :
      ( ~ class_OrderedGroup_Opordered__comm__monoid__add(X18)
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X18),c_HOL_Oplus__class_Oplus(X17,X16,X18),X18)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X18),X16,X18)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X18),X17,X18) ),
    inference(fof_simplification,[status(thm)],[c_0_211]) ).

fof(c_0_819,plain,
    ! [X16,X17,X18] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X18)
      | c_lessequals(c_HOL_Otimes__class_Otimes(X17,X16,X18),c_HOL_Ozero__class_Ozero(X18),X18)
      | ~ c_lessequals(X16,c_HOL_Ozero__class_Ozero(X18),X18)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X18),X17,X18) ),
    inference(fof_simplification,[status(thm)],[c_0_212]) ).

fof(c_0_820,plain,
    ! [X16,X17,X18] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X18)
      | c_lessequals(c_HOL_Otimes__class_Otimes(X17,X16,X18),c_HOL_Ozero__class_Ozero(X18),X18)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X18),X16,X18)
      | ~ c_lessequals(X17,c_HOL_Ozero__class_Ozero(X18),X18) ),
    inference(fof_simplification,[status(thm)],[c_0_213]) ).

fof(c_0_821,plain,
    ! [X16,X17,X18] :
      ( ~ class_Ring__and__Field_Opordered__cancel__semiring(X18)
      | c_lessequals(c_HOL_Otimes__class_Otimes(X17,X16,X18),c_HOL_Ozero__class_Ozero(X18),X18)
      | ~ c_lessequals(X16,c_HOL_Ozero__class_Ozero(X18),X18)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X18),X17,X18) ),
    inference(fof_simplification,[status(thm)],[c_0_214]) ).

fof(c_0_822,plain,
    ! [X16,X17,X18] :
      ( ~ class_Ring__and__Field_Opordered__cancel__semiring(X18)
      | c_lessequals(c_HOL_Otimes__class_Otimes(X17,X16,X18),c_HOL_Ozero__class_Ozero(X18),X18)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X18),X16,X18)
      | ~ c_lessequals(X17,c_HOL_Ozero__class_Ozero(X18),X18) ),
    inference(fof_simplification,[status(thm)],[c_0_215]) ).

fof(c_0_823,plain,
    ! [X16,X17,X18] :
      ( ~ class_Ring__and__Field_Opordered__cancel__semiring(X18)
      | c_lessequals(c_HOL_Otimes__class_Otimes(X17,X16,X18),c_HOL_Ozero__class_Ozero(X18),X18)
      | ~ c_lessequals(X16,c_HOL_Ozero__class_Ozero(X18),X18)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X18),X17,X18) ),
    inference(fof_simplification,[status(thm)],[c_0_216]) ).

fof(c_0_824,plain,
    ! [X16,X17,X18] :
      ( ~ class_Ring__and__Field_Opordered__cancel__semiring(X18)
      | c_lessequals(c_HOL_Otimes__class_Otimes(X17,X16,X18),c_HOL_Ozero__class_Ozero(X18),X18)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X18),X16,X18)
      | ~ c_lessequals(X17,c_HOL_Ozero__class_Ozero(X18),X18) ),
    inference(fof_simplification,[status(thm)],[c_0_217]) ).

fof(c_0_825,plain,
    ! [X16,X17,X18] :
      ( ~ class_Ring__and__Field_Opordered__cancel__semiring(X18)
      | c_lessequals(c_HOL_Otimes__class_Otimes(X16,X17,X18),c_HOL_Ozero__class_Ozero(X18),X18)
      | ~ c_lessequals(X16,c_HOL_Ozero__class_Ozero(X18),X18)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X18),X17,X18) ),
    inference(fof_simplification,[status(thm)],[c_0_218]) ).

fof(c_0_826,plain,
    ! [X16,X17,X18] :
      ( ~ class_OrderedGroup_Opordered__comm__monoid__add(X18)
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X18),c_HOL_Oplus__class_Oplus(X17,X16,X18),X18)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X18),X16,X18)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X18),X17,X18) ),
    inference(fof_simplification,[status(thm)],[c_0_219]) ).

fof(c_0_827,plain,
    ! [X16,X17,X18] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X18)
      | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X16,X17,X18),c_HOL_Ozero__class_Ozero(X18),X18)
      | ~ c_HOL_Oord__class_Oless(X16,c_HOL_Ozero__class_Ozero(X18),X18)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X18),X17,X18) ),
    inference(fof_simplification,[status(thm)],[c_0_220]) ).

fof(c_0_828,plain,
    ! [X16,X17,X18] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X18)
      | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X17,X16,X18),c_HOL_Ozero__class_Ozero(X18),X18)
      | ~ c_HOL_Oord__class_Oless(X16,c_HOL_Ozero__class_Ozero(X18),X18)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X18),X17,X18) ),
    inference(fof_simplification,[status(thm)],[c_0_221]) ).

fof(c_0_829,plain,
    ! [X16,X17,X18] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X18)
      | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X17,X16,X18),c_HOL_Ozero__class_Ozero(X18),X18)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X18),X16,X18)
      | ~ c_HOL_Oord__class_Oless(X17,c_HOL_Ozero__class_Ozero(X18),X18) ),
    inference(fof_simplification,[status(thm)],[c_0_222]) ).

fof(c_0_830,plain,
    ! [X1,X2,X18] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X18)
      | c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X18),c_HOL_Otimes__class_Otimes(X2,X1,X18),X18)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X18),X1,X18)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X18),X2,X18) ),
    inference(fof_simplification,[status(thm)],[c_0_223]) ).

fof(c_0_831,plain,
    ! [X16,X17,X18] :
      ( ~ class_OrderedGroup_Opordered__comm__monoid__add(X18)
      | c_lessequals(c_HOL_Oplus__class_Oplus(X17,X16,X18),c_HOL_Ozero__class_Ozero(X18),X18)
      | ~ c_lessequals(X16,c_HOL_Ozero__class_Ozero(X18),X18)
      | ~ c_lessequals(X17,c_HOL_Ozero__class_Ozero(X18),X18) ),
    inference(fof_simplification,[status(thm)],[c_0_224]) ).

fof(c_0_832,plain,
    ! [X16,X17,X18] :
      ( ~ class_Ring__and__Field_Opordered__cancel__semiring(X18)
      | c_lessequals(c_HOL_Ozero__class_Ozero(X18),c_HOL_Otimes__class_Otimes(X17,X16,X18),X18)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X18),X16,X18)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X18),X17,X18) ),
    inference(fof_simplification,[status(thm)],[c_0_225]) ).

fof(c_0_833,plain,
    ! [X16,X17,X18] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X18)
      | c_lessequals(c_HOL_Ozero__class_Ozero(X18),c_HOL_Otimes__class_Otimes(X17,X16,X18),X18)
      | ~ c_lessequals(X16,c_HOL_Ozero__class_Ozero(X18),X18)
      | ~ c_lessequals(X17,c_HOL_Ozero__class_Ozero(X18),X18) ),
    inference(fof_simplification,[status(thm)],[c_0_226]) ).

fof(c_0_834,plain,
    ! [X16,X17,X18] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X18)
      | c_lessequals(c_HOL_Ozero__class_Ozero(X18),c_HOL_Otimes__class_Otimes(X17,X16,X18),X18)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X18),X16,X18)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X18),X17,X18) ),
    inference(fof_simplification,[status(thm)],[c_0_227]) ).

fof(c_0_835,plain,
    ! [X16,X17,X18] :
      ( ~ class_Ring__and__Field_Opordered__ring(X18)
      | c_lessequals(c_HOL_Ozero__class_Ozero(X18),c_HOL_Otimes__class_Otimes(X17,X16,X18),X18)
      | ~ c_lessequals(X16,c_HOL_Ozero__class_Ozero(X18),X18)
      | ~ c_lessequals(X17,c_HOL_Ozero__class_Ozero(X18),X18) ),
    inference(fof_simplification,[status(thm)],[c_0_228]) ).

fof(c_0_836,plain,
    ! [X16,X17,X18] :
      ( ~ class_Ring__and__Field_Opordered__ring(X18)
      | c_lessequals(c_HOL_Ozero__class_Ozero(X18),c_HOL_Otimes__class_Otimes(X17,X16,X18),X18)
      | ~ c_lessequals(X16,c_HOL_Ozero__class_Ozero(X18),X18)
      | ~ c_lessequals(X17,c_HOL_Ozero__class_Ozero(X18),X18) ),
    inference(fof_simplification,[status(thm)],[c_0_229]) ).

fof(c_0_837,plain,
    ! [X16,X17,X18] :
      ( ~ class_Ring__and__Field_Opordered__ring(X18)
      | c_lessequals(c_HOL_Ozero__class_Ozero(X18),c_HOL_Otimes__class_Otimes(X17,X16,X18),X18)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X18),X16,X18)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X18),X17,X18) ),
    inference(fof_simplification,[status(thm)],[c_0_230]) ).

fof(c_0_838,plain,
    ! [X1,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(tc_nat),X2,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oplus__class_Oplus(X2,X1,tc_nat),tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_231]) ).

fof(c_0_839,plain,
    ! [X1,X2] :
      ( 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)
      | ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X1,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_232]) ).

fof(c_0_840,plain,
    ! [X1,X2] :
      ( 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)
      | ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X1,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_233]) ).

fof(c_0_841,plain,
    ! [X20,X16,X17,X18] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X18)
      | c_lessequals(c_HOL_Oplus__class_Oplus(X17,X20,X18),c_HOL_Oplus__class_Oplus(X16,X20,X18),X18)
      | ~ c_lessequals(X17,X16,X18) ),
    inference(fof_simplification,[status(thm)],[c_0_234]) ).

fof(c_0_842,plain,
    ! [X20,X16,X17,X18] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X18)
      | c_lessequals(c_HOL_Oplus__class_Oplus(X20,X17,X18),c_HOL_Oplus__class_Oplus(X20,X16,X18),X18)
      | ~ c_lessequals(X17,X16,X18) ),
    inference(fof_simplification,[status(thm)],[c_0_235]) ).

fof(c_0_843,plain,
    ! [X20,X16,X17,X18] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X18)
      | c_lessequals(c_HOL_Oplus__class_Oplus(X17,X20,X18),c_HOL_Oplus__class_Oplus(X16,X20,X18),X18)
      | ~ c_lessequals(X17,X16,X18) ),
    inference(fof_simplification,[status(thm)],[c_0_236]) ).

fof(c_0_844,plain,
    ! [X20,X16,X17,X18] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X18)
      | c_lessequals(c_HOL_Oplus__class_Oplus(X20,X17,X18),c_HOL_Oplus__class_Oplus(X20,X16,X18),X18)
      | ~ c_lessequals(X17,X16,X18) ),
    inference(fof_simplification,[status(thm)],[c_0_237]) ).

fof(c_0_845,plain,
    ! [X20,X16,X17,X18] :
      ( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X18)
      | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X17,X20,X18),c_HOL_Oplus__class_Oplus(X16,X20,X18),X18)
      | ~ c_HOL_Oord__class_Oless(X17,X16,X18) ),
    inference(fof_simplification,[status(thm)],[c_0_238]) ).

fof(c_0_846,plain,
    ! [X20,X16,X17,X18] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X18)
      | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X17,X20,X18),c_HOL_Oplus__class_Oplus(X16,X20,X18),X18)
      | ~ c_HOL_Oord__class_Oless(X17,X16,X18) ),
    inference(fof_simplification,[status(thm)],[c_0_239]) ).

fof(c_0_847,plain,
    ! [X20,X16,X17,X18] :
      ( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X18)
      | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X20,X17,X18),c_HOL_Oplus__class_Oplus(X20,X16,X18),X18)
      | ~ c_HOL_Oord__class_Oless(X17,X16,X18) ),
    inference(fof_simplification,[status(thm)],[c_0_240]) ).

fof(c_0_848,plain,
    ! [X20,X16,X17,X18] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X18)
      | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X20,X17,X18),c_HOL_Oplus__class_Oplus(X20,X16,X18),X18)
      | ~ c_HOL_Oord__class_Oless(X17,X16,X18) ),
    inference(fof_simplification,[status(thm)],[c_0_241]) ).

fof(c_0_849,plain,
    ! [X20,X16,X17,X18] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X18)
      | ~ class_OrderedGroup_Ocomm__monoid__add(X18)
      | c_lessequals(X16,c_HOL_Oplus__class_Oplus(X17,X20,X18),X18)
      | ~ c_lessequals(X16,X20,X18)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X18),X17,X18) ),
    inference(fof_simplification,[status(thm)],[c_0_242]) ).

fof(c_0_850,plain,
    ! [X20,X16,X17,X18] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X18)
      | ~ class_OrderedGroup_Ocomm__monoid__add(X18)
      | c_lessequals(X16,c_HOL_Oplus__class_Oplus(X17,X20,X18),X18)
      | ~ c_lessequals(X16,X17,X18)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X18),X20,X18) ),
    inference(fof_simplification,[status(thm)],[c_0_243]) ).

fof(c_0_851,plain,
    ! [X20,X16,X17,X18] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X18)
      | ~ class_OrderedGroup_Ocomm__monoid__add(X18)
      | c_HOL_Oord__class_Oless(X16,c_HOL_Oplus__class_Oplus(X17,X20,X18),X18)
      | ~ c_lessequals(X16,X20,X18)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X18),X17,X18) ),
    inference(fof_simplification,[status(thm)],[c_0_244]) ).

fof(c_0_852,plain,
    ! [X20,X16,X17,X18] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X18)
      | ~ class_OrderedGroup_Ocomm__monoid__add(X18)
      | c_HOL_Oord__class_Oless(X16,c_HOL_Oplus__class_Oplus(X17,X20,X18),X18)
      | ~ c_HOL_Oord__class_Oless(X16,X20,X18)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X18),X17,X18) ),
    inference(fof_simplification,[status(thm)],[c_0_245]) ).

fof(c_0_853,plain,
    ! [X2,X7] :
      ( c_Divides_Odiv__class_Omod(c_Suc(c_HOL_Otimes__class_Otimes(X7,X2,tc_nat)),X7,tc_nat) = c_HOL_Oone__class_Oone(tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),X7,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_246]) ).

fof(c_0_854,plain,
    ! [X20,X16,X17,X18] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X18)
      | c_HOL_Oord__class_Oless(X16,c_HOL_Oplus__class_Oplus(X17,X20,X18),X18)
      | ~ c_HOL_Oord__class_Oless(X16,X20,X18)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X18),X17,X18) ),
    inference(fof_simplification,[status(thm)],[c_0_247]) ).

fof(c_0_855,plain,
    ! [X1,X2,X28] :
      ( c_lessequals(c_HOL_Ominus__class_Ominus(X28,X1,tc_nat),c_HOL_Ominus__class_Ominus(X28,X2,tc_nat),tc_nat)
      | ~ c_lessequals(X2,X1,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_248]) ).

fof(c_0_856,plain,
    ! [X1,X2,X28] :
      ( c_lessequals(c_HOL_Ominus__class_Ominus(X2,X28,tc_nat),c_HOL_Ominus__class_Ominus(X1,X28,tc_nat),tc_nat)
      | ~ c_lessequals(X2,X1,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_249]) ).

fof(c_0_857,plain,
    ! [X7,X14,X8] :
      ( c_lessequals(c_HOL_Oplus__class_Oplus(X8,X7,tc_nat),c_HOL_Oplus__class_Oplus(X14,X7,tc_nat),tc_nat)
      | ~ c_lessequals(X8,X14,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_250]) ).

fof(c_0_858,plain,
    ! [X1,X2,X7] :
      ( c_lessequals(c_HOL_Oplus__class_Oplus(X7,X2,tc_nat),c_HOL_Oplus__class_Oplus(X7,X1,tc_nat),tc_nat)
      | ~ c_lessequals(X2,X1,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_251]) ).

fof(c_0_859,plain,
    ! [X7,X14,X8] :
      ( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X8,X7,tc_nat),c_HOL_Oplus__class_Oplus(X14,X7,tc_nat),tc_nat)
      | ~ c_HOL_Oord__class_Oless(X8,X14,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_252]) ).

fof(c_0_860,plain,
    ! [X1,X2,X7] :
      ( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X7,X2,tc_nat),c_HOL_Oplus__class_Oplus(X7,X1,tc_nat),tc_nat)
      | ~ c_HOL_Oord__class_Oless(X2,X1,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_253]) ).

fof(c_0_861,plain,
    ! [X7,X14,X8] :
      ( c_lessequals(c_HOL_Otimes__class_Otimes(X8,X7,tc_nat),c_HOL_Otimes__class_Otimes(X14,X7,tc_nat),tc_nat)
      | ~ c_lessequals(X8,X14,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_254]) ).

fof(c_0_862,plain,
    ! [X7,X14,X8] :
      ( c_lessequals(c_HOL_Otimes__class_Otimes(X7,X8,tc_nat),c_HOL_Otimes__class_Otimes(X7,X14,tc_nat),tc_nat)
      | ~ c_lessequals(X8,X14,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_255]) ).

fof(c_0_863,plain,
    ! [X1,X2,X7] :
      ( c_lessequals(c_HOL_Otimes__class_Otimes(X7,X2,tc_nat),c_HOL_Otimes__class_Otimes(X7,X1,tc_nat),tc_nat)
      | ~ c_lessequals(X2,X1,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_256]) ).

fof(c_0_864,plain,
    ! [X1,X2,X7] :
      ( c_lessequals(c_HOL_Otimes__class_Otimes(X2,X7,tc_nat),c_HOL_Otimes__class_Otimes(X1,X7,tc_nat),tc_nat)
      | ~ c_lessequals(X2,X1,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_257]) ).

fof(c_0_865,plain,
    ! [X4,X7,X8] :
      ( c_Lambda_Olift(c_Lambda_Olift(X4,X8),c_Suc(X7)) = c_Lambda_Olift(c_Lambda_Olift(X4,X7),X8)
      | ~ c_HOL_Oord__class_Oless(X8,c_HOL_Oplus__class_Oplus(X7,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_258]) ).

fof(c_0_866,plain,
    ! [X2,X17,X18] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X18)
      | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X17,X2,X18),X2,X18) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X17,c_HOL_Oone__class_Oone(X18),X18),X2,X18) ),
    inference(fof_simplification,[status(thm)],[c_0_259]) ).

fof(c_0_867,plain,
    ! [X2,X17,X18] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X18)
      | c_HOL_Oplus__class_Oplus(X2,c_HOL_Otimes__class_Otimes(X17,X2,X18),X18) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X17,c_HOL_Oone__class_Oone(X18),X18),X2,X18) ),
    inference(fof_simplification,[status(thm)],[c_0_260]) ).

fof(c_0_868,plain,
    ! [X19,X9,X3,X18] :
      ( ~ class_Orderings_Olinorder(X18)
      | c_lessequals(c_Orderings_Oord__class_Omax(X3,X9,X18),X19,X18)
      | ~ c_lessequals(X9,X19,X18)
      | ~ c_lessequals(X3,X19,X18) ),
    inference(fof_simplification,[status(thm)],[c_0_261]) ).

fof(c_0_869,plain,
    ! [X19,X9,X3,X18] :
      ( ~ class_Orderings_Olinorder(X18)
      | c_lessequals(c_Orderings_Oord__class_Omax(X9,X19,X18),X3,X18)
      | ~ c_lessequals(X19,X3,X18)
      | ~ c_lessequals(X9,X3,X18) ),
    inference(fof_simplification,[status(thm)],[c_0_262]) ).

fof(c_0_870,plain,
    ! [X3,X16,X17,X18] :
      ( ~ class_Orderings_Olinorder(X18)
      | c_lessequals(c_Orderings_Oord__class_Omax(X17,X16,X18),X3,X18)
      | ~ c_lessequals(X16,X3,X18)
      | ~ c_lessequals(X17,X3,X18) ),
    inference(fof_simplification,[status(thm)],[c_0_263]) ).

fof(c_0_871,plain,
    ! [X3,X16,X17,X18] :
      ( ~ class_Orderings_Olinorder(X18)
      | c_lessequals(X3,c_Orderings_Oord__class_Omin(X17,X16,X18),X18)
      | ~ c_lessequals(X3,X16,X18)
      | ~ c_lessequals(X3,X17,X18) ),
    inference(fof_simplification,[status(thm)],[c_0_264]) ).

fof(c_0_872,plain,
    ! [X19,X9,X3,X18] :
      ( ~ class_Orderings_Olinorder(X18)
      | c_lessequals(X3,c_Orderings_Oord__class_Omin(X9,X19,X18),X18)
      | ~ c_lessequals(X3,X19,X18)
      | ~ c_lessequals(X3,X9,X18) ),
    inference(fof_simplification,[status(thm)],[c_0_265]) ).

fof(c_0_873,plain,
    ! [X19,X9,X3,X18] :
      ( ~ class_Orderings_Olinorder(X18)
      | c_lessequals(X3,c_Orderings_Oord__class_Omin(X9,X19,X18),X18)
      | ~ c_lessequals(X3,X19,X18)
      | ~ c_lessequals(X3,X9,X18) ),
    inference(fof_simplification,[status(thm)],[c_0_266]) ).

fof(c_0_874,plain,
    ! [X19,X9,X3,X18] :
      ( ~ class_Orderings_Olinorder(X18)
      | c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omax(X3,X9,X18),X19,X18)
      | ~ c_HOL_Oord__class_Oless(X9,X19,X18)
      | ~ c_HOL_Oord__class_Oless(X3,X19,X18) ),
    inference(fof_simplification,[status(thm)],[c_0_267]) ).

fof(c_0_875,plain,
    ! [X19,X9,X3,X18] :
      ( ~ class_Orderings_Olinorder(X18)
      | c_HOL_Oord__class_Oless(X19,c_Orderings_Oord__class_Omin(X3,X9,X18),X18)
      | ~ c_HOL_Oord__class_Oless(X19,X9,X18)
      | ~ c_HOL_Oord__class_Oless(X19,X3,X18) ),
    inference(fof_simplification,[status(thm)],[c_0_268]) ).

fof(c_0_876,plain,
    ! [X1,X2] :
      ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Otimes__class_Otimes(X2,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(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_269]) ).

fof(c_0_877,plain,
    ! [X1,X2,X7] :
      ( c_HOL_Ominus__class_Ominus(X2,X7,tc_nat) != c_HOL_Ominus__class_Ominus(X1,X7,tc_nat)
      | ~ c_lessequals(X7,X1,tc_nat)
      | ~ c_lessequals(X7,X2,tc_nat)
      | X2 = X1 ),
    inference(fof_simplification,[status(thm)],[c_0_270]) ).

fof(c_0_878,plain,
    ! [X1,X2] :
      ( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),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(fof_simplification,[status(thm)],[c_0_271]) ).

fof(c_0_879,plain,
    ! [X17,X18] :
      ( ~ class_OrderedGroup_Olordered__ab__group__add(X18)
      | c_lessequals(c_HOL_Ozero__class_Ozero(X18),X17,X18)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X18),c_HOL_Oplus__class_Oplus(X17,X17,X18),X18) ),
    inference(fof_simplification,[status(thm)],[c_0_272]) ).

fof(c_0_880,plain,
    ! [X17,X18] :
      ( ~ class_OrderedGroup_Olordered__ab__group__add(X18)
      | c_HOL_Oord__class_Oless(X17,c_HOL_Ozero__class_Ozero(X18),X18)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X17,X17,X18),c_HOL_Ozero__class_Ozero(X18),X18) ),
    inference(fof_simplification,[status(thm)],[c_0_273]) ).

fof(c_0_881,plain,
    ! [X17,X18] :
      ( ~ class_Ring__and__Field_Oordered__idom(X18)
      | c_HOL_Oord__class_Oless(X17,c_HOL_Ozero__class_Ozero(X18),X18)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X17,X17,X18),c_HOL_Ozero__class_Ozero(X18),X18) ),
    inference(fof_simplification,[status(thm)],[c_0_274]) ).

fof(c_0_882,plain,
    ! [X17,X18] :
      ( ~ class_OrderedGroup_Olordered__ab__group__add(X18)
      | c_lessequals(X17,c_HOL_Ozero__class_Ozero(X18),X18)
      | ~ c_lessequals(c_HOL_Oplus__class_Oplus(X17,X17,X18),c_HOL_Ozero__class_Ozero(X18),X18) ),
    inference(fof_simplification,[status(thm)],[c_0_275]) ).

fof(c_0_883,plain,
    ! [X17,X18] :
      ( ~ class_OrderedGroup_Olordered__ab__group__add(X18)
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X18),X17,X18)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X18),c_HOL_Oplus__class_Oplus(X17,X17,X18),X18) ),
    inference(fof_simplification,[status(thm)],[c_0_276]) ).

fof(c_0_884,plain,
    ! [X1,X2] :
      ( c_lessequals(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X1,tc_nat)
      | ~ c_lessequals(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Otimes__class_Otimes(X2,X1,tc_nat),tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_277]) ).

fof(c_0_885,plain,
    ! [X1,X2] :
      ( c_lessequals(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X2,tc_nat)
      | ~ c_lessequals(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Otimes__class_Otimes(X2,X1,tc_nat),tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_278]) ).

fof(c_0_886,plain,
    ! [X19,X9,X3,X18] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X18)
      | c_HOL_Oplus__class_Oplus(X3,c_HOL_Oplus__class_Oplus(X9,X19,X18),X18) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X3,X9,X18),X19,X18) ),
    inference(fof_simplification,[status(thm)],[c_0_279]) ).

fof(c_0_887,plain,
    ! [X19,X9,X3,X18] :
      ( ~ class_OrderedGroup_Oab__group__add(X18)
      | c_HOL_Oplus__class_Oplus(X3,c_HOL_Oplus__class_Oplus(X9,X19,X18),X18) = c_HOL_Oplus__class_Oplus(X9,c_HOL_Oplus__class_Oplus(X3,X19,X18),X18) ),
    inference(fof_simplification,[status(thm)],[c_0_280]) ).

fof(c_0_888,plain,
    ! [X20,X16,X17,X18] :
      ( ~ class_OrderedGroup_Ocomm__monoid__add(X18)
      | c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X17,X16,X18),X20,X18) = c_HOL_Oplus__class_Oplus(X17,c_HOL_Oplus__class_Oplus(X16,X20,X18),X18) ),
    inference(fof_simplification,[status(thm)],[c_0_281]) ).

fof(c_0_889,plain,
    ! [X20,X16,X17,X18] :
      ( ~ class_OrderedGroup_Ocomm__monoid__add(X18)
      | c_HOL_Oplus__class_Oplus(X17,c_HOL_Oplus__class_Oplus(X16,X20,X18),X18) = c_HOL_Oplus__class_Oplus(X16,c_HOL_Oplus__class_Oplus(X17,X20,X18),X18) ),
    inference(fof_simplification,[status(thm)],[c_0_282]) ).

fof(c_0_890,plain,
    ! [X20,X16,X17,X18] :
      ( ~ class_OrderedGroup_Oab__semigroup__add(X18)
      | c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X17,X16,X18),X20,X18) = c_HOL_Oplus__class_Oplus(X17,c_HOL_Oplus__class_Oplus(X16,X20,X18),X18) ),
    inference(fof_simplification,[status(thm)],[c_0_283]) ).

fof(c_0_891,plain,
    ! [X27,X20,X17,X18] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X18)
      | c_HOL_Oplus__class_Oplus(X17,c_HOL_Oplus__class_Oplus(X20,X27,X18),X18) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X17,X20,X18),X27,X18) ),
    inference(fof_simplification,[status(thm)],[c_0_284]) ).

fof(c_0_892,plain,
    ! [X20,X16,X17,X18] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X18)
      | c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X17,X16,X18),X20,X18) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X17,X20,X18),X16,X18) ),
    inference(fof_simplification,[status(thm)],[c_0_285]) ).

fof(c_0_893,plain,
    ! [X27,X20,X17,X18] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X18)
      | c_HOL_Oplus__class_Oplus(X17,c_HOL_Oplus__class_Oplus(X20,X27,X18),X18) = c_HOL_Oplus__class_Oplus(X20,c_HOL_Oplus__class_Oplus(X17,X27,X18),X18) ),
    inference(fof_simplification,[status(thm)],[c_0_286]) ).

fof(c_0_894,plain,
    ! [X20,X16,X17,X18] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X18)
      | c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X17,X16,X18),X20,X18) = c_HOL_Oplus__class_Oplus(X17,c_HOL_Oplus__class_Oplus(X16,X20,X18),X18) ),
    inference(fof_simplification,[status(thm)],[c_0_287]) ).

fof(c_0_895,plain,
    ! [X19,X9,X3,X18] :
      ( ~ class_Orderings_Olinorder(X18)
      | c_Orderings_Oord__class_Omin(c_Orderings_Oord__class_Omin(X3,X9,X18),X19,X18) = c_Orderings_Oord__class_Omin(X3,c_Orderings_Oord__class_Omin(X9,X19,X18),X18) ),
    inference(fof_simplification,[status(thm)],[c_0_288]) ).

fof(c_0_896,plain,
    ! [X19,X9,X3,X18] :
      ( ~ class_Orderings_Olinorder(X18)
      | c_Orderings_Oord__class_Omin(X3,c_Orderings_Oord__class_Omin(X9,X19,X18),X18) = c_Orderings_Oord__class_Omin(X9,c_Orderings_Oord__class_Omin(X3,X19,X18),X18) ),
    inference(fof_simplification,[status(thm)],[c_0_289]) ).

fof(c_0_897,plain,
    ! [X19,X9,X3,X18] :
      ( ~ class_Orderings_Olinorder(X18)
      | c_Orderings_Oord__class_Omax(c_Orderings_Oord__class_Omax(X3,X9,X18),X19,X18) = c_Orderings_Oord__class_Omax(X3,c_Orderings_Oord__class_Omax(X9,X19,X18),X18) ),
    inference(fof_simplification,[status(thm)],[c_0_290]) ).

fof(c_0_898,plain,
    ! [X19,X9,X3,X18] :
      ( ~ class_Orderings_Olinorder(X18)
      | c_Orderings_Oord__class_Omax(X3,c_Orderings_Oord__class_Omax(X9,X19,X18),X18) = c_Orderings_Oord__class_Omax(X9,c_Orderings_Oord__class_Omax(X3,X19,X18),X18) ),
    inference(fof_simplification,[status(thm)],[c_0_291]) ).

fof(c_0_899,plain,
    ! [X20,X16,X17,X18] :
      ( ~ class_OrderedGroup_Oab__semigroup__mult(X18)
      | c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X17,X16,X18),X20,X18) = c_HOL_Otimes__class_Otimes(X17,c_HOL_Otimes__class_Otimes(X16,X20,X18),X18) ),
    inference(fof_simplification,[status(thm)],[c_0_292]) ).

fof(c_0_900,plain,
    ! [X22,X24,X23,X18] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X18)
      | c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X23,X24,X18),X22,X18) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X23,X22,X18),X24,X18) ),
    inference(fof_simplification,[status(thm)],[c_0_293]) ).

fof(c_0_901,plain,
    ! [X22,X24,X23,X18] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X18)
      | c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X23,X24,X18),X22,X18) = c_HOL_Otimes__class_Otimes(X23,c_HOL_Otimes__class_Otimes(X24,X22,X18),X18) ),
    inference(fof_simplification,[status(thm)],[c_0_294]) ).

fof(c_0_902,plain,
    ! [X21,X22,X23,X18] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X18)
      | c_HOL_Otimes__class_Otimes(X23,c_HOL_Otimes__class_Otimes(X22,X21,X18),X18) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X23,X22,X18),X21,X18) ),
    inference(fof_simplification,[status(thm)],[c_0_295]) ).

fof(c_0_903,plain,
    ! [X21,X22,X23,X18] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X18)
      | c_HOL_Otimes__class_Otimes(X23,c_HOL_Otimes__class_Otimes(X22,X21,X18),X18) = c_HOL_Otimes__class_Otimes(X22,c_HOL_Otimes__class_Otimes(X23,X21,X18),X18) ),
    inference(fof_simplification,[status(thm)],[c_0_296]) ).

fof(c_0_904,plain,
    ! [X19,X9,X3,X18] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X18)
      | c_HOL_Otimes__class_Otimes(X3,c_HOL_Otimes__class_Otimes(X9,X19,X18),X18) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X3,X9,X18),X19,X18) ),
    inference(fof_simplification,[status(thm)],[c_0_297]) ).

fof(c_0_905,plain,
    ! [X1,X2,X7] :
      ( c_HOL_Oord__class_Oless(X2,c_HOL_Oplus__class_Oplus(X1,X7,tc_nat),tc_nat)
      | ~ c_lessequals(X2,X1,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X7,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_298]) ).

fof(c_0_906,plain,
    ! [X18] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X18)
      | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X18),c_HOL_Ozero__class_Ozero(X18),X18),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X18),c_HOL_Ozero__class_Ozero(X18),X18),X18) = c_HOL_Ozero__class_Ozero(X18) ),
    inference(fof_simplification,[status(thm)],[c_0_299]) ).

fof(c_0_907,plain,
    ! [X16,X17,X18] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add(X18)
      | c_lessequals(X17,X16,X18)
      | ~ c_lessequals(c_HOL_Ominus__class_Ominus(X17,X16,X18),c_HOL_Ozero__class_Ozero(X18),X18) ),
    inference(fof_simplification,[status(thm)],[c_0_300]) ).

fof(c_0_908,plain,
    ! [X16,X17,X18] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add(X18)
      | c_HOL_Oord__class_Oless(X17,X16,X18)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X17,X16,X18),c_HOL_Ozero__class_Ozero(X18),X18) ),
    inference(fof_simplification,[status(thm)],[c_0_301]) ).

fof(c_0_909,plain,
    ! [X25,X9,X26,X3,X18] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add(X18)
      | c_HOL_Ominus__class_Ominus(X3,X9,X18) != c_HOL_Ominus__class_Ominus(X26,X25,X18)
      | c_lessequals(X25,X26,X18)
      | ~ c_lessequals(X9,X3,X18) ),
    inference(fof_simplification,[status(thm)],[c_0_302]) ).

fof(c_0_910,plain,
    ! [X25,X9,X26,X3,X18] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add(X18)
      | c_HOL_Ominus__class_Ominus(X3,X9,X18) != c_HOL_Ominus__class_Ominus(X26,X25,X18)
      | c_lessequals(X9,X3,X18)
      | ~ c_lessequals(X25,X26,X18) ),
    inference(fof_simplification,[status(thm)],[c_0_303]) ).

fof(c_0_911,plain,
    ! [X25,X9,X26,X3,X18] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add(X18)
      | c_HOL_Ominus__class_Ominus(X3,X9,X18) != c_HOL_Ominus__class_Ominus(X26,X25,X18)
      | c_HOL_Oord__class_Oless(X26,X25,X18)
      | ~ c_HOL_Oord__class_Oless(X3,X9,X18) ),
    inference(fof_simplification,[status(thm)],[c_0_304]) ).

fof(c_0_912,plain,
    ! [X25,X9,X26,X3,X18] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add(X18)
      | c_HOL_Ominus__class_Ominus(X3,X9,X18) != c_HOL_Ominus__class_Ominus(X26,X25,X18)
      | c_HOL_Oord__class_Oless(X3,X9,X18)
      | ~ c_HOL_Oord__class_Oless(X26,X25,X18) ),
    inference(fof_simplification,[status(thm)],[c_0_305]) ).

fof(c_0_913,axiom,
    ! [X1,X2,X7] :
      ( c_lessequals(c_HOL_Otimes__class_Otimes(X2,X7,tc_nat),c_HOL_Otimes__class_Otimes(X1,X7,tc_nat),tc_nat)
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X7,tc_nat) ),
    c_0_306 ).

fof(c_0_914,axiom,
    ! [X1,X2,X7] :
      ( c_lessequals(c_HOL_Otimes__class_Otimes(X7,X2,tc_nat),c_HOL_Otimes__class_Otimes(X7,X1,tc_nat),tc_nat)
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X7,tc_nat) ),
    c_0_307 ).

fof(c_0_915,plain,
    ! [X19,X9,X3,X18] :
      ( ~ class_Orderings_Olinorder(X18)
      | c_lessequals(X3,X19,X18)
      | ~ c_lessequals(X3,c_Orderings_Oord__class_Omin(X9,X19,X18),X18) ),
    inference(fof_simplification,[status(thm)],[c_0_308]) ).

fof(c_0_916,plain,
    ! [X19,X9,X3,X18] :
      ( ~ class_Orderings_Olinorder(X18)
      | c_lessequals(X3,X9,X18)
      | ~ c_lessequals(X3,c_Orderings_Oord__class_Omin(X9,X19,X18),X18) ),
    inference(fof_simplification,[status(thm)],[c_0_309]) ).

fof(c_0_917,plain,
    ! [X3,X16,X17,X18] :
      ( ~ class_Orderings_Olinorder(X18)
      | c_lessequals(X3,X16,X18)
      | ~ c_lessequals(X3,c_Orderings_Oord__class_Omin(X17,X16,X18),X18) ),
    inference(fof_simplification,[status(thm)],[c_0_310]) ).

fof(c_0_918,plain,
    ! [X3,X16,X17,X18] :
      ( ~ class_Orderings_Olinorder(X18)
      | c_lessequals(X3,X17,X18)
      | ~ c_lessequals(X3,c_Orderings_Oord__class_Omin(X17,X16,X18),X18) ),
    inference(fof_simplification,[status(thm)],[c_0_311]) ).

fof(c_0_919,plain,
    ! [X19,X9,X3,X18] :
      ( ~ class_Orderings_Olinorder(X18)
      | c_lessequals(X9,X19,X18)
      | ~ c_lessequals(c_Orderings_Oord__class_Omax(X3,X9,X18),X19,X18) ),
    inference(fof_simplification,[status(thm)],[c_0_312]) ).

fof(c_0_920,plain,
    ! [X19,X9,X3,X18] :
      ( ~ class_Orderings_Olinorder(X18)
      | c_lessequals(X3,X19,X18)
      | ~ c_lessequals(c_Orderings_Oord__class_Omax(X3,X9,X18),X19,X18) ),
    inference(fof_simplification,[status(thm)],[c_0_313]) ).

fof(c_0_921,plain,
    ! [X3,X16,X17,X18] :
      ( ~ class_Orderings_Olinorder(X18)
      | c_lessequals(X16,X3,X18)
      | ~ c_lessequals(c_Orderings_Oord__class_Omax(X17,X16,X18),X3,X18) ),
    inference(fof_simplification,[status(thm)],[c_0_314]) ).

fof(c_0_922,plain,
    ! [X3,X16,X17,X18] :
      ( ~ class_Orderings_Olinorder(X18)
      | c_lessequals(X17,X3,X18)
      | ~ c_lessequals(c_Orderings_Oord__class_Omax(X17,X16,X18),X3,X18) ),
    inference(fof_simplification,[status(thm)],[c_0_315]) ).

fof(c_0_923,plain,
    ! [X19,X9,X3,X18] :
      ( ~ class_Orderings_Olinorder(X18)
      | c_HOL_Oord__class_Oless(X3,X19,X18)
      | ~ c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omax(X3,X9,X18),X19,X18) ),
    inference(fof_simplification,[status(thm)],[c_0_316]) ).

fof(c_0_924,plain,
    ! [X19,X9,X3,X18] :
      ( ~ class_Orderings_Olinorder(X18)
      | c_HOL_Oord__class_Oless(X9,X19,X18)
      | ~ c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omax(X3,X9,X18),X19,X18) ),
    inference(fof_simplification,[status(thm)],[c_0_317]) ).

fof(c_0_925,plain,
    ! [X19,X9,X3,X18] :
      ( ~ class_Orderings_Olinorder(X18)
      | c_HOL_Oord__class_Oless(X19,X3,X18)
      | ~ c_HOL_Oord__class_Oless(X19,c_Orderings_Oord__class_Omin(X3,X9,X18),X18) ),
    inference(fof_simplification,[status(thm)],[c_0_318]) ).

fof(c_0_926,plain,
    ! [X19,X9,X3,X18] :
      ( ~ class_Orderings_Olinorder(X18)
      | c_HOL_Oord__class_Oless(X19,X9,X18)
      | ~ c_HOL_Oord__class_Oless(X19,c_Orderings_Oord__class_Omin(X3,X9,X18),X18) ),
    inference(fof_simplification,[status(thm)],[c_0_319]) ).

fof(c_0_927,plain,
    ! [X1,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(tc_nat),c_HOL_Otimes__class_Otimes(X2,X1,tc_nat),tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_320]) ).

fof(c_0_928,plain,
    ! [X1,X2] :
      ( 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(X2,X1,tc_nat),tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_321]) ).

fof(c_0_929,plain,
    ! [X1,X2] :
      ( c_HOL_Oord__class_Oless(X2,X1,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_322]) ).

fof(c_0_930,plain,
    ! [X1,X2,X28,X7] :
      ( c_HOL_Oplus__class_Oplus(X2,X28,tc_nat) != c_HOL_Oplus__class_Oplus(X7,X1,tc_nat)
      | ~ c_HOL_Oord__class_Oless(X7,X28,tc_nat)
      | c_HOL_Oord__class_Oless(X2,X1,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_323]) ).

fof(c_0_931,plain,
    ! [X7,X14,X8] :
      ( c_HOL_Oord__class_Oless(X8,X7,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X8,X14,tc_nat),X7,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_324]) ).

fof(c_0_932,plain,
    ! [X1,X2,X7] :
      ( c_lessequals(X7,X1,tc_nat)
      | ~ c_lessequals(c_HOL_Oplus__class_Oplus(X2,X7,tc_nat),X1,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_325]) ).

fof(c_0_933,plain,
    ! [X1,X2,X7] :
      ( c_lessequals(X2,X1,tc_nat)
      | ~ c_lessequals(c_HOL_Oplus__class_Oplus(X2,X7,tc_nat),X1,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_326]) ).

fof(c_0_934,plain,
    ! [X9,X3,X18] :
      ( ~ class_OrderedGroup_Opordered__comm__monoid__add(X18)
      | c_HOL_Oplus__class_Oplus(X3,X9,X18) != c_HOL_Ozero__class_Ozero(X18)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X18),X9,X18)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X18),X3,X18)
      | X9 = c_HOL_Ozero__class_Ozero(X18) ),
    inference(fof_simplification,[status(thm)],[c_0_327]) ).

fof(c_0_935,plain,
    ! [X9,X3,X18] :
      ( ~ class_OrderedGroup_Opordered__comm__monoid__add(X18)
      | c_HOL_Oplus__class_Oplus(X3,X9,X18) != c_HOL_Ozero__class_Ozero(X18)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X18),X9,X18)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X18),X3,X18)
      | X3 = c_HOL_Ozero__class_Ozero(X18) ),
    inference(fof_simplification,[status(thm)],[c_0_328]) ).

fof(c_0_936,plain,
    ! [X1,X2] :
      ( c_Divides_Odiv__class_Omod(X2,X1,tc_nat) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),X1,tc_nat)
      | ~ c_lessequals(X1,X2,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_329]) ).

fof(c_0_937,plain,
    ! [X18] :
      ( ~ class_OrderedGroup_Opordered__comm__monoid__add(X18)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X18),c_HOL_Ozero__class_Ozero(X18),X18)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X18),c_HOL_Ozero__class_Ozero(X18),X18)
      | c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X18),c_HOL_Ozero__class_Ozero(X18),X18) = c_HOL_Ozero__class_Ozero(X18) ),
    inference(fof_simplification,[status(thm)],[c_0_330]) ).

fof(c_0_938,axiom,
    ! [X1,X2] :
      ( c_Divides_Odiv__class_Omod(c_Suc(X2),X1,tc_nat) = c_Suc(c_Divides_Odiv__class_Omod(X2,X1,tc_nat))
      | c_Suc(c_Divides_Odiv__class_Omod(X2,X1,tc_nat)) = X1 ),
    c_0_331 ).

fof(c_0_939,plain,
    ! [X17,X18] :
      ( ~ class_OrderedGroup_Olordered__ab__group__add(X18)
      | c_lessequals(c_HOL_Ozero__class_Ozero(X18),c_HOL_Oplus__class_Oplus(X17,X17,X18),X18)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X18),X17,X18) ),
    inference(fof_simplification,[status(thm)],[c_0_332]) ).

fof(c_0_940,plain,
    ! [X17,X18] :
      ( ~ class_OrderedGroup_Olordered__ab__group__add(X18)
      | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X17,X17,X18),c_HOL_Ozero__class_Ozero(X18),X18)
      | ~ c_HOL_Oord__class_Oless(X17,c_HOL_Ozero__class_Ozero(X18),X18) ),
    inference(fof_simplification,[status(thm)],[c_0_333]) ).

fof(c_0_941,plain,
    ! [X17,X18] :
      ( ~ class_Ring__and__Field_Oordered__idom(X18)
      | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X17,X17,X18),c_HOL_Ozero__class_Ozero(X18),X18)
      | ~ c_HOL_Oord__class_Oless(X17,c_HOL_Ozero__class_Ozero(X18),X18) ),
    inference(fof_simplification,[status(thm)],[c_0_334]) ).

fof(c_0_942,plain,
    ! [X17,X18] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X18)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X17,X17,X18),c_HOL_Ozero__class_Ozero(X18),X18) ),
    inference(fof_simplification,[status(thm)],[c_0_335]) ).

fof(c_0_943,plain,
    ! [X17,X18] :
      ( ~ class_OrderedGroup_Olordered__ab__group__add(X18)
      | c_lessequals(c_HOL_Oplus__class_Oplus(X17,X17,X18),c_HOL_Ozero__class_Ozero(X18),X18)
      | ~ c_lessequals(X17,c_HOL_Ozero__class_Ozero(X18),X18) ),
    inference(fof_simplification,[status(thm)],[c_0_336]) ).

fof(c_0_944,plain,
    ! [X17,X18] :
      ( ~ class_OrderedGroup_Olordered__ab__group__add(X18)
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X18),c_HOL_Oplus__class_Oplus(X17,X17,X18),X18)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X18),X17,X18) ),
    inference(fof_simplification,[status(thm)],[c_0_337]) ).

fof(c_0_945,axiom,
    ! [X1,X2] :
      ( c_Divides_Odiv__class_Omod(X2,X1,tc_nat) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),X1,tc_nat)
      | c_HOL_Oord__class_Oless(X2,X1,tc_nat) ),
    c_0_338 ).

fof(c_0_946,plain,
    ! [X16,X17,X18] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add(X18)
      | c_lessequals(c_HOL_Ominus__class_Ominus(X17,X16,X18),c_HOL_Ozero__class_Ozero(X18),X18)
      | ~ c_lessequals(X17,X16,X18) ),
    inference(fof_simplification,[status(thm)],[c_0_339]) ).

fof(c_0_947,plain,
    ! [X16,X17,X18] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add(X18)
      | c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X17,X16,X18),c_HOL_Ozero__class_Ozero(X18),X18)
      | ~ c_HOL_Oord__class_Oless(X17,X16,X18) ),
    inference(fof_simplification,[status(thm)],[c_0_340]) ).

fof(c_0_948,plain,
    ! [X5,X7,X8] :
      ( c_Lambda_Osubst(c_Lambda_OdB_OVar(X8),X5,X7) = c_Lambda_OdB_OVar(c_HOL_Ominus__class_Ominus(X8,c_HOL_Oone__class_Oone(tc_nat),tc_nat))
      | ~ c_HOL_Oord__class_Oless(X7,X8,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_341]) ).

fof(c_0_949,plain,
    ! [X15,X14,X8] :
      ( c_Lambda_Osubst(c_Lambda_OdB_OVar(X14),X15,X8) = c_Lambda_OdB_OVar(c_HOL_Ominus__class_Ominus(X14,c_HOL_Oone__class_Oone(tc_nat),tc_nat))
      | ~ c_HOL_Oord__class_Oless(X8,X14,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_342]) ).

fof(c_0_950,plain,
    ! [X1,X8] :
      ( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,c_Suc(X8),tc_nat),X1,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_343]) ).

fof(c_0_951,plain,
    ! [X1,X2,X7] :
      ( c_HOL_Otimes__class_Otimes(X7,X2,tc_nat) != c_HOL_Otimes__class_Otimes(X7,X1,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X7,tc_nat)
      | X2 = X1 ),
    inference(fof_simplification,[status(thm)],[c_0_344]) ).

fof(c_0_952,plain,
    ! [X19,X9,X3,X18] :
      ( ~ class_Orderings_Olinorder(X18)
      | c_lessequals(c_Orderings_Oord__class_Omin(X3,X9,X18),X19,X18)
      | ~ c_lessequals(X9,X19,X18) ),
    inference(fof_simplification,[status(thm)],[c_0_345]) ).

fof(c_0_953,plain,
    ! [X19,X9,X3,X18] :
      ( ~ class_Orderings_Olinorder(X18)
      | c_lessequals(c_Orderings_Oord__class_Omin(X3,X9,X18),X19,X18)
      | ~ c_lessequals(X3,X19,X18) ),
    inference(fof_simplification,[status(thm)],[c_0_346]) ).

fof(c_0_954,plain,
    ! [X3,X16,X17,X18] :
      ( ~ class_Orderings_Olinorder(X18)
      | c_lessequals(c_Orderings_Oord__class_Omin(X17,X16,X18),X3,X18)
      | ~ c_lessequals(X16,X3,X18) ),
    inference(fof_simplification,[status(thm)],[c_0_347]) ).

fof(c_0_955,plain,
    ! [X3,X16,X17,X18] :
      ( ~ class_Orderings_Olinorder(X18)
      | c_lessequals(c_Orderings_Oord__class_Omin(X17,X16,X18),X3,X18)
      | ~ c_lessequals(X17,X3,X18) ),
    inference(fof_simplification,[status(thm)],[c_0_348]) ).

fof(c_0_956,plain,
    ! [X19,X9,X3,X18] :
      ( ~ class_Orderings_Olinorder(X18)
      | c_lessequals(X19,c_Orderings_Oord__class_Omax(X3,X9,X18),X18)
      | ~ c_lessequals(X19,X9,X18) ),
    inference(fof_simplification,[status(thm)],[c_0_349]) ).

fof(c_0_957,plain,
    ! [X19,X9,X3,X18] :
      ( ~ class_Orderings_Olinorder(X18)
      | c_lessequals(X19,c_Orderings_Oord__class_Omax(X3,X9,X18),X18)
      | ~ c_lessequals(X19,X3,X18) ),
    inference(fof_simplification,[status(thm)],[c_0_350]) ).

fof(c_0_958,plain,
    ! [X3,X16,X17,X18] :
      ( ~ class_Orderings_Olinorder(X18)
      | c_lessequals(X3,c_Orderings_Oord__class_Omax(X17,X16,X18),X18)
      | ~ c_lessequals(X3,X16,X18) ),
    inference(fof_simplification,[status(thm)],[c_0_351]) ).

fof(c_0_959,plain,
    ! [X3,X16,X17,X18] :
      ( ~ class_Orderings_Olinorder(X18)
      | c_lessequals(X3,c_Orderings_Oord__class_Omax(X17,X16,X18),X18)
      | ~ c_lessequals(X3,X17,X18) ),
    inference(fof_simplification,[status(thm)],[c_0_352]) ).

fof(c_0_960,plain,
    ! [X3,X16,X17,X18] :
      ( ~ class_Orderings_Olinorder(X18)
      | c_HOL_Oord__class_Oless(X3,c_Orderings_Oord__class_Omax(X17,X16,X18),X18)
      | ~ c_HOL_Oord__class_Oless(X3,X17,X18) ),
    inference(fof_simplification,[status(thm)],[c_0_353]) ).

fof(c_0_961,plain,
    ! [X3,X16,X17,X18] :
      ( ~ class_Orderings_Olinorder(X18)
      | c_HOL_Oord__class_Oless(X3,c_Orderings_Oord__class_Omax(X17,X16,X18),X18)
      | ~ c_HOL_Oord__class_Oless(X3,X16,X18) ),
    inference(fof_simplification,[status(thm)],[c_0_354]) ).

fof(c_0_962,plain,
    ! [X19,X9,X3,X18] :
      ( ~ class_Orderings_Olinorder(X18)
      | c_HOL_Oord__class_Oless(X19,c_Orderings_Oord__class_Omax(X3,X9,X18),X18)
      | ~ c_HOL_Oord__class_Oless(X19,X3,X18) ),
    inference(fof_simplification,[status(thm)],[c_0_355]) ).

fof(c_0_963,plain,
    ! [X19,X9,X3,X18] :
      ( ~ class_Orderings_Olinorder(X18)
      | c_HOL_Oord__class_Oless(X19,c_Orderings_Oord__class_Omax(X3,X9,X18),X18)
      | ~ c_HOL_Oord__class_Oless(X19,X9,X18) ),
    inference(fof_simplification,[status(thm)],[c_0_356]) ).

fof(c_0_964,plain,
    ! [X3,X16,X17,X18] :
      ( ~ class_Orderings_Olinorder(X18)
      | c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omin(X17,X16,X18),X3,X18)
      | ~ c_HOL_Oord__class_Oless(X17,X3,X18) ),
    inference(fof_simplification,[status(thm)],[c_0_357]) ).

fof(c_0_965,plain,
    ! [X3,X16,X17,X18] :
      ( ~ class_Orderings_Olinorder(X18)
      | c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omin(X17,X16,X18),X3,X18)
      | ~ c_HOL_Oord__class_Oless(X16,X3,X18) ),
    inference(fof_simplification,[status(thm)],[c_0_358]) ).

fof(c_0_966,plain,
    ! [X19,X9,X3,X18] :
      ( ~ class_Orderings_Olinorder(X18)
      | c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omin(X3,X9,X18),X19,X18)
      | ~ c_HOL_Oord__class_Oless(X3,X19,X18) ),
    inference(fof_simplification,[status(thm)],[c_0_359]) ).

fof(c_0_967,plain,
    ! [X19,X9,X3,X18] :
      ( ~ class_Orderings_Olinorder(X18)
      | c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omin(X3,X9,X18),X19,X18)
      | ~ c_HOL_Oord__class_Oless(X9,X19,X18) ),
    inference(fof_simplification,[status(thm)],[c_0_360]) ).

fof(c_0_968,plain,
    ! [X1,X2] :
      ( c_HOL_Ominus__class_Ominus(c_Suc(X2),X1,tc_nat) = c_Suc(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat))
      | ~ c_lessequals(X1,X2,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_361]) ).

fof(c_0_969,plain,
    ! [X4,X5,X6,X8] :
      ( c_Lambda_Obeta(c_Lambda_Osubst(X6,X4,X8),c_Lambda_Osubst(X5,X4,X8))
      | ~ c_Lambda_Obeta(X6,X5) ),
    inference(fof_simplification,[status(thm)],[c_0_362]) ).

fof(c_0_970,plain,
    ! [X1,X2] :
      ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oplus__class_Oplus(X2,X1,tc_nat),tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_363]) ).

fof(c_0_971,plain,
    ! [X1,X2] :
      ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oplus__class_Oplus(X2,X1,tc_nat),tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_364]) ).

fof(c_0_972,plain,
    ! [X2,X18] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X18)
      | c_HOL_Oplus__class_Oplus(X2,X2,X18) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(X18),c_HOL_Oone__class_Oone(X18),X18),X2,X18) ),
    inference(fof_simplification,[status(thm)],[c_0_365]) ).

fof(c_0_973,plain,
    ! [X1,X2] :
      ( c_lessequals(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(fof_simplification,[status(thm)],[c_0_366]) ).

fof(c_0_974,plain,
    ! [X1,X2] :
      ( 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(fof_simplification,[status(thm)],[c_0_367]) ).

fof(c_0_975,plain,
    ! [X1,X2] :
      ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),tc_nat)
      | ~ c_HOL_Oord__class_Oless(X2,X1,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_368]) ).

fof(c_0_976,plain,
    ! [X14,X8] :
      ( ~ c_lessequals(X8,X14,tc_nat)
      | X14 = c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X14,X8,tc_nat),X8,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_369]) ).

fof(c_0_977,plain,
    ! [X1,X2] :
      ( c_HOL_Oplus__class_Oplus(X1,c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),tc_nat) = X2
      | ~ c_lessequals(X1,X2,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_370]) ).

fof(c_0_978,plain,
    ! [X1,X2] :
      ( c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),X1,tc_nat) = X2
      | ~ c_lessequals(X1,X2,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_371]) ).

fof(c_0_979,plain,
    ! [X1,X8] :
      ( c_HOL_Ominus__class_Ominus(X1,c_HOL_Ominus__class_Ominus(X1,X8,tc_nat),tc_nat) = X8
      | ~ c_lessequals(X8,X1,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_372]) ).

fof(c_0_980,plain,
    ! [X19,X9,X3] :
      ( c_HOL_Oord__class_Oless(X3,c_HOL_Oplus__class_Oplus(X9,X19,tc_nat),tc_nat)
      | ~ c_HOL_Oord__class_Oless(X3,X9,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_373]) ).

fof(c_0_981,plain,
    ! [X19,X9,X3] :
      ( c_HOL_Oord__class_Oless(X3,c_HOL_Oplus__class_Oplus(X9,X19,tc_nat),tc_nat)
      | ~ c_HOL_Oord__class_Oless(X3,X19,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_374]) ).

fof(c_0_982,plain,
    ! [X2,X14,X8] :
      ( c_HOL_Oord__class_Oless(X8,c_HOL_Oplus__class_Oplus(X14,X2,tc_nat),tc_nat)
      | ~ c_HOL_Oord__class_Oless(X8,X14,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_375]) ).

fof(c_0_983,plain,
    ! [X2,X14,X8] :
      ( c_HOL_Oord__class_Oless(X8,c_HOL_Oplus__class_Oplus(X2,X14,tc_nat),tc_nat)
      | ~ c_HOL_Oord__class_Oless(X8,X14,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_376]) ).

fof(c_0_984,plain,
    ! [X2,X14,X8] :
      ( c_lessequals(X8,c_HOL_Oplus__class_Oplus(X2,X14,tc_nat),tc_nat)
      | ~ c_lessequals(X8,X14,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_377]) ).

fof(c_0_985,plain,
    ! [X2,X14,X8] :
      ( c_lessequals(X8,c_HOL_Oplus__class_Oplus(X14,X2,tc_nat),tc_nat)
      | ~ c_lessequals(X8,X14,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_378]) ).

fof(c_0_986,plain,
    ! [X19,X9,X3] :
      ( c_lessequals(X3,c_HOL_Oplus__class_Oplus(X9,X19,tc_nat),tc_nat)
      | ~ c_lessequals(X3,X19,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_379]) ).

fof(c_0_987,plain,
    ! [X19,X9,X3] :
      ( c_lessequals(X3,c_HOL_Oplus__class_Oplus(X9,X19,tc_nat),tc_nat)
      | ~ c_lessequals(X3,X9,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_380]) ).

fof(c_0_988,plain,
    ! [X1,X7,X14] :
      ( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X14,X1,tc_nat),X7,tc_nat)
      | ~ c_HOL_Oord__class_Oless(X14,X7,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_381]) ).

fof(c_0_989,plain,
    ! [X19,X9,X3,X18] :
      ( ~ class_Orderings_Opreorder(X18)
      | c_HOL_Oord__class_Oless(X3,X19,X18)
      | ~ c_HOL_Oord__class_Oless(X9,X19,X18)
      | ~ c_HOL_Oord__class_Oless(X3,X9,X18) ),
    inference(fof_simplification,[status(thm)],[c_0_382]) ).

fof(c_0_990,plain,
    ! [X19,X9,X3,X18] :
      ( ~ class_Orderings_Oorder(X18)
      | c_HOL_Oord__class_Oless(X19,X3,X18)
      | ~ c_HOL_Oord__class_Oless(X19,X9,X18)
      | ~ c_HOL_Oord__class_Oless(X9,X3,X18) ),
    inference(fof_simplification,[status(thm)],[c_0_383]) ).

fof(c_0_991,plain,
    ! [X19,X9,X3,X18] :
      ( ~ class_Orderings_Oorder(X18)
      | c_lessequals(X19,X3,X18)
      | ~ c_lessequals(X19,X9,X18)
      | ~ c_lessequals(X9,X3,X18) ),
    inference(fof_simplification,[status(thm)],[c_0_384]) ).

fof(c_0_992,plain,
    ! [X19,X9,X3,X18] :
      ( ~ class_Orderings_Oorder(X18)
      | c_HOL_Oord__class_Oless(X19,X3,X18)
      | ~ c_lessequals(X19,X9,X18)
      | ~ c_HOL_Oord__class_Oless(X9,X3,X18) ),
    inference(fof_simplification,[status(thm)],[c_0_385]) ).

fof(c_0_993,plain,
    ! [X19,X9,X3,X18] :
      ( ~ class_Orderings_Oorder(X18)
      | c_HOL_Oord__class_Oless(X19,X3,X18)
      | ~ c_HOL_Oord__class_Oless(X19,X9,X18)
      | ~ c_lessequals(X9,X3,X18) ),
    inference(fof_simplification,[status(thm)],[c_0_386]) ).

fof(c_0_994,plain,
    ! [X19,X9,X3,X18] :
      ( ~ class_Orderings_Opreorder(X18)
      | c_lessequals(X3,X19,X18)
      | ~ c_lessequals(X9,X19,X18)
      | ~ c_lessequals(X3,X9,X18) ),
    inference(fof_simplification,[status(thm)],[c_0_387]) ).

fof(c_0_995,plain,
    ! [X19,X9,X3,X18] :
      ( ~ class_Orderings_Opreorder(X18)
      | c_HOL_Oord__class_Oless(X3,X19,X18)
      | ~ c_HOL_Oord__class_Oless(X9,X19,X18)
      | ~ c_lessequals(X3,X9,X18) ),
    inference(fof_simplification,[status(thm)],[c_0_388]) ).

fof(c_0_996,plain,
    ! [X19,X9,X3,X18] :
      ( ~ class_Orderings_Opreorder(X18)
      | c_HOL_Oord__class_Oless(X3,X19,X18)
      | ~ c_lessequals(X9,X19,X18)
      | ~ c_HOL_Oord__class_Oless(X3,X9,X18) ),
    inference(fof_simplification,[status(thm)],[c_0_389]) ).

fof(c_0_997,axiom,
    ! [X1,X2] :
      ( c_Suc(c_Divides_Odiv__class_Omod(X2,X1,tc_nat)) != X1
      | c_Divides_Odiv__class_Omod(c_Suc(X2),X1,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat) ),
    c_0_390 ).

fof(c_0_998,plain,
    ! [X7,X14,X8] :
      ( c_HOL_Oord__class_Oless(c_Suc(X8),X7,tc_nat)
      | ~ c_HOL_Oord__class_Oless(X14,X7,tc_nat)
      | ~ c_HOL_Oord__class_Oless(X8,X14,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_391]) ).

fof(c_0_999,plain,
    ! [X16,X17,X18] :
      ( ~ class_Divides_Osemiring__div(X18)
      | c_Divides_Odiv__class_Omod(c_Divides_Odiv__class_Omod(X17,X16,X18),X16,X18) = c_Divides_Odiv__class_Omod(X17,X16,X18) ),
    inference(fof_simplification,[status(thm)],[c_0_392]) ).

fof(c_0_1000,plain,
    ! [X9,X3,X18] :
      ( ~ class_Orderings_Olinorder(X18)
      | c_Orderings_Oord__class_Omin(X3,c_Orderings_Oord__class_Omin(X3,X9,X18),X18) = c_Orderings_Oord__class_Omin(X3,X9,X18) ),
    inference(fof_simplification,[status(thm)],[c_0_393]) ).

fof(c_0_1001,plain,
    ! [X9,X3,X18] :
      ( ~ class_OrderedGroup_Oab__semigroup__idem__mult(X18)
      | c_HOL_Otimes__class_Otimes(X3,c_HOL_Otimes__class_Otimes(X3,X9,X18),X18) = c_HOL_Otimes__class_Otimes(X3,X9,X18) ),
    inference(fof_simplification,[status(thm)],[c_0_394]) ).

fof(c_0_1002,plain,
    ! [X16,X17,X18] :
      ( ~ class_Divides_Osemiring__div(X18)
      | c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X17,X16,X18),X16,X18) = c_Divides_Odiv__class_Omod(X17,X16,X18) ),
    inference(fof_simplification,[status(thm)],[c_0_395]) ).

fof(c_0_1003,plain,
    ! [X16,X17,X18] :
      ( ~ class_Divides_Osemiring__div(X18)
      | c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X16,X17,X18),X16,X18) = c_Divides_Odiv__class_Omod(X17,X16,X18) ),
    inference(fof_simplification,[status(thm)],[c_0_396]) ).

fof(c_0_1004,plain,
    ! [X9,X3,X18] :
      ( ~ class_Orderings_Olinorder(X18)
      | c_Orderings_Oord__class_Omax(X3,c_Orderings_Oord__class_Omax(X3,X9,X18),X18) = c_Orderings_Oord__class_Omax(X3,X9,X18) ),
    inference(fof_simplification,[status(thm)],[c_0_397]) ).

fof(c_0_1005,plain,
    ! [X1] :
      ( c_Suc(c_HOL_Ominus__class_Ominus(X1,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat)) = X1
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_398]) ).

fof(c_0_1006,plain,
    ! [X7,X14,X8] :
      ( c_lessequals(X8,X7,tc_nat)
      | ~ c_lessequals(X14,X7,tc_nat)
      | ~ c_lessequals(X8,X14,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_399]) ).

fof(c_0_1007,axiom,
    ! [X1,X2] :
      ( c_HOL_Oplus__class_Oplus(X1,c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),tc_nat) = X2
      | c_HOL_Oord__class_Oless(X2,X1,tc_nat) ),
    c_0_400 ).

fof(c_0_1008,plain,
    ! [X1] :
      ( c_Suc(c_HOL_Ominus__class_Ominus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat)) = X1
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_401]) ).

fof(c_0_1009,plain,
    ! [X1] :
      ( X1 = c_Suc(c_HOL_Ominus__class_Ominus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat))
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_402]) ).

fof(c_0_1010,plain,
    ! [X9,X3,X18] :
      ( ~ class_Orderings_Opreorder(X18)
      | c_HOL_Oord__class_Oless(X3,X9,X18)
      | c_lessequals(X9,X3,X18)
      | ~ c_lessequals(X3,X9,X18) ),
    inference(fof_simplification,[status(thm)],[c_0_403]) ).

fof(c_0_1011,plain,
    ! [X18] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X18)
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X18),c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(X18),c_HOL_Oone__class_Oone(X18),X18),X18) ),
    inference(fof_simplification,[status(thm)],[c_0_404]) ).

fof(c_0_1012,plain,
    ! [X19,X9,X3,X18] :
      ( ~ class_Ring__and__Field_Oidom(X18)
      | ~ class_Int_Onumber__ring(X18)
      | c_HOL_Oplus__class_Oplus(X3,X9,X18) != c_HOL_Oplus__class_Oplus(X3,X19,X18)
      | X9 = X19 ),
    inference(fof_simplification,[status(thm)],[c_0_405]) ).

fof(c_0_1013,axiom,
    ! [X1,X2,X7] :
      ( c_HOL_Otimes__class_Otimes(c_Suc(X7),X2,tc_nat) != c_HOL_Otimes__class_Otimes(c_Suc(X7),X1,tc_nat)
      | X2 = X1 ),
    c_0_406 ).

fof(c_0_1014,axiom,
    ! [X7,X8] :
      ( c_Lambda_Olift(c_Lambda_OdB_OVar(X8),X7) = c_Lambda_OdB_OVar(c_HOL_Oplus__class_Oplus(X8,c_HOL_Oone__class_Oone(tc_nat),tc_nat))
      | c_HOL_Oord__class_Oless(X8,X7,tc_nat) ),
    c_0_407 ).

fof(c_0_1015,plain,
    ! [X9,X3,X18] :
      ( ~ class_Orderings_Oorder(X18)
      | X3 = X9
      | ~ c_lessequals(X9,X3,X18)
      | ~ c_lessequals(X3,X9,X18) ),
    inference(fof_simplification,[status(thm)],[c_0_408]) ).

fof(c_0_1016,plain,
    ! [X9,X3,X18] :
      ( ~ class_Orderings_Oorder(X18)
      | X3 = X9
      | ~ c_lessequals(X9,X3,X18)
      | ~ c_lessequals(X3,X9,X18) ),
    inference(fof_simplification,[status(thm)],[c_0_409]) ).

fof(c_0_1017,plain,
    ! [X9,X3,X18] :
      ( ~ class_Orderings_Oorder(X18)
      | X3 = X9
      | ~ c_lessequals(X3,X9,X18)
      | ~ c_lessequals(X9,X3,X18) ),
    inference(fof_simplification,[status(thm)],[c_0_410]) ).

fof(c_0_1018,plain,
    ! [X17,X18] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X18)
      | c_HOL_Oord__class_Oless(X17,c_HOL_Oplus__class_Oplus(X17,c_HOL_Oone__class_Oone(X18),X18),X18) ),
    inference(fof_simplification,[status(thm)],[c_0_411]) ).

fof(c_0_1019,plain,
    ! [X9,X32,X3,X18] :
      ( ~ class_OrderedGroup_Oab__group__add(X18)
      | c_HOL_Ominus__class_Ominus(X32,X9,X18) != c_HOL_Ominus__class_Ominus(X3,X3,X18)
      | X32 = X9 ),
    inference(fof_simplification,[status(thm)],[c_0_412]) ).

fof(c_0_1020,plain,
    ! [X25,X26,X3,X18] :
      ( ~ class_OrderedGroup_Oab__group__add(X18)
      | c_HOL_Ominus__class_Ominus(X3,X3,X18) != c_HOL_Ominus__class_Ominus(X26,X25,X18)
      | X26 = X25 ),
    inference(fof_simplification,[status(thm)],[c_0_413]) ).

fof(c_0_1021,plain,
    ! [X20,X16,X17,X18] :
      ( ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X18)
      | c_HOL_Oplus__class_Oplus(X17,X16,X18) != c_HOL_Oplus__class_Oplus(X17,X20,X18)
      | X16 = X20 ),
    inference(fof_simplification,[status(thm)],[c_0_414]) ).

fof(c_0_1022,plain,
    ! [X20,X16,X17,X18] :
      ( ~ class_OrderedGroup_Ocancel__semigroup__add(X18)
      | c_HOL_Oplus__class_Oplus(X17,X16,X18) != c_HOL_Oplus__class_Oplus(X17,X20,X18)
      | X16 = X20 ),
    inference(fof_simplification,[status(thm)],[c_0_415]) ).

fof(c_0_1023,plain,
    ! [X20,X16,X17,X18] :
      ( ~ class_OrderedGroup_Ocancel__semigroup__add(X18)
      | c_HOL_Oplus__class_Oplus(X16,X17,X18) != c_HOL_Oplus__class_Oplus(X20,X17,X18)
      | X16 = X20 ),
    inference(fof_simplification,[status(thm)],[c_0_416]) ).

fof(c_0_1024,plain,
    ! [X3,X18] :
      ( ~ class_Orderings_Olinorder(X18)
      | ~ c_lessequals(X3,X3,X18)
      | ~ c_HOL_Oord__class_Oless(X3,X3,X18) ),
    inference(fof_simplification,[status(thm)],[c_0_417]) ).

fof(c_0_1025,plain,
    ! [X9,X3,X18] :
      ( ~ class_Orderings_Olinorder(X18)
      | ~ c_HOL_Oord__class_Oless(X3,X9,X18)
      | ~ c_lessequals(X9,X3,X18) ),
    inference(fof_simplification,[status(thm)],[c_0_418]) ).

fof(c_0_1026,plain,
    ! [X9,X3,X18] :
      ( ~ class_Orderings_Olinorder(X18)
      | ~ c_lessequals(X3,X9,X18)
      | ~ c_HOL_Oord__class_Oless(X9,X3,X18) ),
    inference(fof_simplification,[status(thm)],[c_0_419]) ).

fof(c_0_1027,plain,
    ! [X9,X3,X18] :
      ( ~ class_Orderings_Opreorder(X18)
      | ~ c_lessequals(X9,X3,X18)
      | ~ c_HOL_Oord__class_Oless(X3,X9,X18) ),
    inference(fof_simplification,[status(thm)],[c_0_420]) ).

fof(c_0_1028,plain,
    ! [X16,X17,X18] :
      ( ~ class_Orderings_Oorder(X18)
      | ~ c_HOL_Oord__class_Oless(X17,X16,X18)
      | ~ c_HOL_Oord__class_Oless(X16,X17,X18) ),
    inference(fof_simplification,[status(thm)],[c_0_421]) ).

fof(c_0_1029,plain,
    ! [X9,X3,X18] :
      ( ~ class_Orderings_Olinorder(X18)
      | ~ c_HOL_Oord__class_Oless(X3,X9,X18)
      | ~ c_HOL_Oord__class_Oless(X9,X3,X18) ),
    inference(fof_simplification,[status(thm)],[c_0_422]) ).

fof(c_0_1030,plain,
    ! [X9,X3,X18] :
      ( ~ class_Orderings_Opreorder(X18)
      | ~ c_HOL_Oord__class_Oless(X9,X3,X18)
      | ~ c_HOL_Oord__class_Oless(X3,X9,X18) ),
    inference(fof_simplification,[status(thm)],[c_0_423]) ).

fof(c_0_1031,plain,
    ! [X16,X17,X18] :
      ( ~ class_Orderings_Opreorder(X18)
      | ~ c_HOL_Oord__class_Oless(X16,X17,X18)
      | ~ c_HOL_Oord__class_Oless(X17,X16,X18) ),
    inference(fof_simplification,[status(thm)],[c_0_424]) ).

fof(c_0_1032,plain,
    ! [X1,X2] :
      ( X1 = X2
      | ~ c_HOL_Oord__class_Oless(X1,c_Suc(X2),tc_nat)
      | ~ c_lessequals(X2,X1,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_425]) ).

fof(c_0_1033,plain,
    ! [X1,X2] :
      ( ~ c_lessequals(X2,X1,tc_nat)
      | ~ c_lessequals(c_Suc(X1),X2,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_426]) ).

fof(c_0_1034,plain,
    ! [X1,X2] :
      ( ~ c_HOL_Oord__class_Oless(X2,X1,tc_nat)
      | ~ c_HOL_Oord__class_Oless(X1,c_Suc(X2),tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_427]) ).

fof(c_0_1035,axiom,
    ! [X1,X2] :
      ( c_HOL_Ominus__class_Ominus(X1,X2,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)
      | c_HOL_Ominus__class_Ominus(X2,X1,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)
      | X2 = X1 ),
    c_0_428 ).

fof(c_0_1036,plain,
    ! [X17,X18] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X18)
      | c_lessequals(c_HOL_Ozero__class_Ozero(X18),c_HOL_Otimes__class_Otimes(X17,X17,X18),X18) ),
    inference(fof_simplification,[status(thm)],[c_0_429]) ).

fof(c_0_1037,axiom,
    ! [X1,X2,X7] :
      ( c_HOL_Otimes__class_Otimes(X7,X2,tc_nat) != c_HOL_Otimes__class_Otimes(X7,X1,tc_nat)
      | X2 = X1
      | X7 = c_HOL_Ozero__class_Ozero(tc_nat) ),
    c_0_430 ).

fof(c_0_1038,axiom,
    ! [X1,X2,X7] :
      ( c_HOL_Otimes__class_Otimes(X7,X2,tc_nat) != c_HOL_Otimes__class_Otimes(X7,X1,tc_nat)
      | X7 = c_HOL_Ozero__class_Ozero(tc_nat)
      | X2 = X1 ),
    c_0_431 ).

fof(c_0_1039,axiom,
    ! [X1,X2,X7] :
      ( c_HOL_Otimes__class_Otimes(X2,X7,tc_nat) != c_HOL_Otimes__class_Otimes(X1,X7,tc_nat)
      | X7 = c_HOL_Ozero__class_Ozero(tc_nat)
      | X2 = X1 ),
    c_0_432 ).

fof(c_0_1040,plain,
    ! [X16,X17,X18] :
      ( ~ class_Divides_Osemiring__div(X18)
      | c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X17,X16,X18),X16,X18) = c_HOL_Ozero__class_Ozero(X18) ),
    inference(fof_simplification,[status(thm)],[c_0_433]) ).

fof(c_0_1041,plain,
    ! [X16,X17,X18] :
      ( ~ class_Divides_Osemiring__div(X18)
      | c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X16,X17,X18),X16,X18) = c_HOL_Ozero__class_Ozero(X18) ),
    inference(fof_simplification,[status(thm)],[c_0_434]) ).

fof(c_0_1042,plain,
    ! [X1,X2] :
      ( X2 = X1
      | ~ c_lessequals(X1,X2,tc_nat)
      | ~ c_lessequals(X2,X1,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_435]) ).

fof(c_0_1043,plain,
    ! [X16,X17,X18] :
      ( ~ class_OrderedGroup_Ogroup__add(X18)
      | c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X17,X16,X18),X16,X18) = X17 ),
    inference(fof_simplification,[status(thm)],[c_0_436]) ).

fof(c_0_1044,plain,
    ! [X9,X3,X18] :
      ( ~ class_Orderings_Olinorder(X18)
      | c_Orderings_Oord__class_Omin(X3,c_Orderings_Oord__class_Omax(X3,X9,X18),X18) = X3 ),
    inference(fof_simplification,[status(thm)],[c_0_437]) ).

fof(c_0_1045,plain,
    ! [X9,X3,X18] :
      ( ~ class_Orderings_Olinorder(X18)
      | c_Orderings_Oord__class_Omax(X3,c_Orderings_Oord__class_Omin(X3,X9,X18),X18) = X3 ),
    inference(fof_simplification,[status(thm)],[c_0_438]) ).

fof(c_0_1046,plain,
    ! [X16,X17,X18] :
      ( ~ class_OrderedGroup_Ogroup__add(X18)
      | c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X17,X16,X18),X16,X18) = X17 ),
    inference(fof_simplification,[status(thm)],[c_0_439]) ).

fof(c_0_1047,plain,
    ! [X9,X3,X18] :
      ( ~ class_Orderings_Olinorder(X18)
      | c_lessequals(X3,c_Orderings_Oord__class_Omax(X3,X9,X18),X18) ),
    inference(fof_simplification,[status(thm)],[c_0_440]) ).

fof(c_0_1048,plain,
    ! [X9,X3,X18] :
      ( ~ class_Orderings_Olinorder(X18)
      | c_lessequals(X9,c_Orderings_Oord__class_Omax(X3,X9,X18),X18) ),
    inference(fof_simplification,[status(thm)],[c_0_441]) ).

fof(c_0_1049,plain,
    ! [X9,X3,X18] :
      ( ~ class_Orderings_Olinorder(X18)
      | c_lessequals(c_Orderings_Oord__class_Omin(X3,X9,X18),X3,X18) ),
    inference(fof_simplification,[status(thm)],[c_0_442]) ).

fof(c_0_1050,plain,
    ! [X9,X3,X18] :
      ( ~ class_Orderings_Olinorder(X18)
      | c_lessequals(c_Orderings_Oord__class_Omin(X3,X9,X18),X9,X18) ),
    inference(fof_simplification,[status(thm)],[c_0_443]) ).

fof(c_0_1051,axiom,
    ! [X19,X9,X3] :
      ( c_HOL_Oplus__class_Oplus(X3,X9,tc_nat) != c_HOL_Oplus__class_Oplus(X3,X19,tc_nat)
      | X9 = X19 ),
    c_0_444 ).

fof(c_0_1052,axiom,
    ! [X1,X2,X7] :
      ( c_HOL_Oplus__class_Oplus(X2,X7,tc_nat) != c_HOL_Oplus__class_Oplus(X1,X7,tc_nat)
      | X2 = X1 ),
    c_0_445 ).

fof(c_0_1053,axiom,
    ! [X1,X2,X7] :
      ( c_HOL_Oplus__class_Oplus(X7,X2,tc_nat) != c_HOL_Oplus__class_Oplus(X7,X1,tc_nat)
      | X2 = X1 ),
    c_0_446 ).

fof(c_0_1054,plain,
    ! [X1,X2] :
      ( c_lessequals(X1,X2,tc_nat)
      | ~ c_lessequals(c_Suc(X1),c_Suc(X2),tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_447]) ).

fof(c_0_1055,plain,
    ! [X1,X2] :
      ( c_HOL_Oord__class_Oless(X2,X1,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_Suc(X2),c_Suc(X1),tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_448]) ).

fof(c_0_1056,plain,
    ! [X1,X2] :
      ( X2 = c_Suc(X1)
      | c_lessequals(X2,X1,tc_nat)
      | ~ c_lessequals(X2,c_Suc(X1),tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_449]) ).

fof(c_0_1057,plain,
    ! [X16,X17,X18] :
      ( ~ class_Orderings_Oorder(X18)
      | c_HOL_Oord__class_Oless(X16,X17,X18)
      | X17 = X16
      | ~ c_lessequals(X16,X17,X18) ),
    inference(fof_simplification,[status(thm)],[c_0_450]) ).

fof(c_0_1058,plain,
    ! [X16,X17,X18] :
      ( ~ class_Orderings_Oorder(X18)
      | c_HOL_Oord__class_Oless(X16,X17,X18)
      | ~ c_lessequals(X16,X17,X18)
      | X17 = X16 ),
    inference(fof_simplification,[status(thm)],[c_0_451]) ).

fof(c_0_1059,plain,
    ! [X9,X3,X18] :
      ( ~ class_Orderings_Oorder(X18)
      | X3 = X9
      | c_HOL_Oord__class_Oless(X3,X9,X18)
      | ~ c_lessequals(X3,X9,X18) ),
    inference(fof_simplification,[status(thm)],[c_0_452]) ).

fof(c_0_1060,plain,
    ! [X9,X3,X18] :
      ( ~ class_Orderings_Oorder(X18)
      | c_HOL_Oord__class_Oless(X3,X9,X18)
      | X3 = X9
      | ~ c_lessequals(X3,X9,X18) ),
    inference(fof_simplification,[status(thm)],[c_0_453]) ).

fof(c_0_1061,plain,
    ! [X16,X17,X18] :
      ( ~ class_Orderings_Oorder(X18)
      | c_HOL_Oord__class_Oless(X17,X16,X18)
      | X17 = X16
      | ~ c_lessequals(X17,X16,X18) ),
    inference(fof_simplification,[status(thm)],[c_0_454]) ).

fof(c_0_1062,plain,
    ! [X16,X17,X18] :
      ( ~ class_Orderings_Oorder(X18)
      | c_HOL_Oord__class_Oless(X17,X16,X18)
      | ~ c_lessequals(X17,X16,X18)
      | X17 = X16 ),
    inference(fof_simplification,[status(thm)],[c_0_455]) ).

fof(c_0_1063,plain,
    ! [X9,X3,X18] :
      ( ~ class_Orderings_Olinorder(X18)
      | X3 = X9
      | ~ c_lessequals(X3,X9,X18)
      | c_HOL_Oord__class_Oless(X3,X9,X18) ),
    inference(fof_simplification,[status(thm)],[c_0_456]) ).

fof(c_0_1064,plain,
    ! [X9,X3,X18] :
      ( ~ class_Orderings_Olinorder(X18)
      | X3 = X9
      | c_HOL_Oord__class_Oless(X3,X9,X18)
      | ~ c_lessequals(X3,X9,X18) ),
    inference(fof_simplification,[status(thm)],[c_0_457]) ).

fof(c_0_1065,plain,
    ! [X9,X3,X18] :
      ( ~ class_Orderings_Olinorder(X18)
      | c_Orderings_Oord__class_Omax(X3,X9,X18) != X9
      | c_lessequals(X3,X9,X18) ),
    inference(fof_simplification,[status(thm)],[c_0_458]) ).

fof(c_0_1066,plain,
    ! [X9,X3,X18] :
      ( ~ class_Orderings_Olinorder(X18)
      | c_Orderings_Oord__class_Omin(X3,X9,X18) != X3
      | c_lessequals(X3,X9,X18) ),
    inference(fof_simplification,[status(thm)],[c_0_459]) ).

fof(c_0_1067,plain,
    ! [X1,X2] :
      ( c_lessequals(c_Suc(X1),c_Suc(X2),tc_nat)
      | ~ c_lessequals(X1,X2,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_460]) ).

fof(c_0_1068,plain,
    ! [X3,X1] :
      ( c_HOL_Oord__class_Oless(c_Suc(X3),c_Suc(X1),tc_nat)
      | ~ c_HOL_Oord__class_Oless(X3,X1,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_461]) ).

fof(c_0_1069,plain,
    ! [X1,X2] :
      ( c_HOL_Oord__class_Oless(c_Suc(X2),c_Suc(X1),tc_nat)
      | ~ c_HOL_Oord__class_Oless(X2,X1,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_462]) ).

fof(c_0_1070,plain,
    ! [X9,X3,X18] :
      ( ~ class_Orderings_Olinorder(X18)
      | c_Orderings_Oord__class_Omax(X3,X9,X18) = X9
      | ~ c_lessequals(X3,X9,X18) ),
    inference(fof_simplification,[status(thm)],[c_0_463]) ).

fof(c_0_1071,plain,
    ! [X9,X3,X18] :
      ( ~ class_Orderings_Olinorder(X18)
      | c_Orderings_Oord__class_Omax(X3,X9,X18) = X3
      | ~ c_lessequals(X9,X3,X18) ),
    inference(fof_simplification,[status(thm)],[c_0_464]) ).

fof(c_0_1072,plain,
    ! [X9,X3,X18] :
      ( ~ class_Orderings_Olinorder(X18)
      | c_Orderings_Oord__class_Omin(X3,X9,X18) = X3
      | ~ c_lessequals(X3,X9,X18) ),
    inference(fof_simplification,[status(thm)],[c_0_465]) ).

fof(c_0_1073,plain,
    ! [X9,X3,X18] :
      ( ~ class_Orderings_Olinorder(X18)
      | c_Orderings_Oord__class_Omin(X3,X9,X18) = X9
      | ~ c_lessequals(X9,X3,X18) ),
    inference(fof_simplification,[status(thm)],[c_0_466]) ).

fof(c_0_1074,plain,
    ! [X1,X2] :
      ( X1 = X2
      | ~ c_HOL_Oord__class_Oless(X1,c_Suc(X2),tc_nat)
      | c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_467]) ).

fof(c_0_1075,plain,
    ! [X1,X2] :
      ( X2 = X1
      | ~ c_HOL_Oord__class_Oless(X1,c_Suc(X2),tc_nat)
      | c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_468]) ).

fof(c_0_1076,plain,
    ! [X1,X2] :
      ( X2 = X1
      | c_HOL_Oord__class_Oless(X2,X1,tc_nat)
      | ~ c_HOL_Oord__class_Oless(X2,c_Suc(X1),tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_469]) ).

fof(c_0_1077,plain,
    ! [X15,X14,X8] :
      ( c_Lambda_Osubst(c_Lambda_OdB_OVar(X14),X15,X8) = c_Lambda_OdB_OVar(X14)
      | ~ c_HOL_Oord__class_Oless(X14,X8,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_470]) ).

fof(c_0_1078,plain,
    ! [X1,X2] :
      ( c_HOL_Oord__class_Oless(c_Suc(X2),X1,tc_nat)
      | c_Suc(X2) = X1
      | ~ c_HOL_Oord__class_Oless(X2,X1,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_471]) ).

fof(c_0_1079,plain,
    ! [X9,X3,X18] :
      ( ~ class_Orderings_Oorder(X18)
      | c_lessequals(X3,X9,X18)
      | ~ c_HOL_Oord__class_Oless(X3,X9,X18) ),
    inference(fof_simplification,[status(thm)],[c_0_472]) ).

fof(c_0_1080,plain,
    ! [X9,X3,X18] :
      ( ~ class_Orderings_Opreorder(X18)
      | c_lessequals(X3,X9,X18)
      | ~ c_HOL_Oord__class_Oless(X3,X9,X18) ),
    inference(fof_simplification,[status(thm)],[c_0_473]) ).

fof(c_0_1081,plain,
    ! [X1,X2] :
      ( c_HOL_Oord__class_Oless(X2,X1,tc_nat)
      | ~ c_lessequals(c_Suc(X2),X1,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_474]) ).

fof(c_0_1082,plain,
    ! [X1,X2] :
      ( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
      | ~ c_lessequals(c_Suc(X1),X2,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_475]) ).

fof(c_0_1083,plain,
    ! [X1,X2] :
      ( c_lessequals(X2,X1,tc_nat)
      | ~ c_HOL_Oord__class_Oless(X2,c_Suc(X1),tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_476]) ).

fof(c_0_1084,plain,
    ! [X1,X2] :
      ( c_HOL_Oord__class_Oless(X2,X1,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_Suc(X2),X1,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_477]) ).

fof(c_0_1085,plain,
    ! [X1,X2] :
      ( c_lessequals(X2,X1,tc_nat)
      | ~ c_lessequals(c_Suc(X2),X1,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_478]) ).

fof(c_0_1086,plain,
    ! [X1,X2] :
      ( c_lessequals(c_Suc(X2),X1,tc_nat)
      | ~ c_HOL_Oord__class_Oless(X2,X1,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_479]) ).

fof(c_0_1087,plain,
    ! [X1,X2] :
      ( c_lessequals(c_Suc(X1),X2,tc_nat)
      | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_480]) ).

fof(c_0_1088,plain,
    ! [X1,X2] :
      ( c_HOL_Oord__class_Oless(X2,c_Suc(X1),tc_nat)
      | ~ c_lessequals(X2,X1,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_481]) ).

fof(c_0_1089,plain,
    ! [X3] :
      ( ~ c_lessequals(X3,X3,tc_nat)
      | c_HOL_Oord__class_Oless(X3,c_Suc(X3),tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_482]) ).

fof(c_0_1090,plain,
    ! [X1,X2] :
      ( c_HOL_Oord__class_Oless(X2,c_Suc(X1),tc_nat)
      | ~ c_HOL_Oord__class_Oless(X2,X1,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_483]) ).

fof(c_0_1091,plain,
    ! [X1,X2] :
      ( c_lessequals(X2,c_Suc(X1),tc_nat)
      | ~ c_lessequals(X2,X1,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_484]) ).

fof(c_0_1092,axiom,
    ! [X1,X2] :
      ( c_HOL_Ominus__class_Ominus(X2,X1,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)
      | c_lessequals(X2,X1,tc_nat) ),
    c_0_485 ).

fof(c_0_1093,plain,
    ! [X1,X2] :
      ( c_HOL_Ominus__class_Ominus(X2,X1,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat)
      | ~ c_lessequals(X2,X1,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_486]) ).

fof(c_0_1094,plain,
    ! [X1,X2] :
      ( c_HOL_Oord__class_Oless(X2,X1,tc_nat)
      | X2 = X1
      | ~ c_lessequals(X2,X1,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_487]) ).

fof(c_0_1095,plain,
    ! [X1,X2] :
      ( X2 = X1
      | c_HOL_Oord__class_Oless(X2,X1,tc_nat)
      | ~ c_lessequals(X2,X1,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_488]) ).

fof(c_0_1096,plain,
    ! [X1,X2] :
      ( c_HOL_Oord__class_Oless(X2,X1,tc_nat)
      | X2 = X1
      | ~ c_lessequals(X2,X1,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_489]) ).

fof(c_0_1097,plain,
    ! [X1,X2] :
      ( c_Divides_Odiv__class_Omod(X2,X1,tc_nat) = X2
      | ~ c_HOL_Oord__class_Oless(X2,X1,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_490]) ).

fof(c_0_1098,plain,
    ! [X9,X3] :
      ( c_lessequals(X3,X9,tc_nat)
      | ~ c_HOL_Oord__class_Oless(X3,X9,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_491]) ).

fof(c_0_1099,plain,
    ! [X1,X2] :
      ( c_lessequals(X2,X1,tc_nat)
      | ~ c_HOL_Oord__class_Oless(X2,X1,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_492]) ).

fof(c_0_1100,axiom,
    ! [X5,X7,X8] :
      ( c_Lambda_Osubst(c_Lambda_OdB_OVar(X8),X5,X7) = c_Lambda_OdB_OVar(X8)
      | X8 = X7
      | c_HOL_Oord__class_Oless(X7,X8,tc_nat) ),
    c_0_493 ).

fof(c_0_1101,plain,
    ! [X9,X3,X18] :
      ( ~ class_Ring__and__Field_Oordered__idom(X18)
      | c_HOL_Oord__class_Oless(X9,X3,X18)
      | c_HOL_Oord__class_Oless(X3,X9,X18)
      | X3 = X9 ),
    inference(fof_simplification,[status(thm)],[c_0_494]) ).

fof(c_0_1102,plain,
    ! [X9,X3,X18] :
      ( ~ class_Orderings_Olinorder(X18)
      | X3 = X9
      | c_HOL_Oord__class_Oless(X9,X3,X18)
      | c_HOL_Oord__class_Oless(X3,X9,X18) ),
    inference(fof_simplification,[status(thm)],[c_0_495]) ).

fof(c_0_1103,plain,
    ! [X9,X3,X18] :
      ( ~ class_Orderings_Olinorder(X18)
      | c_HOL_Oord__class_Oless(X9,X3,X18)
      | c_HOL_Oord__class_Oless(X3,X9,X18)
      | X3 = X9 ),
    inference(fof_simplification,[status(thm)],[c_0_496]) ).

fof(c_0_1104,plain,
    ! [X9,X3,X18] :
      ( ~ class_Orderings_Olinorder(X18)
      | c_HOL_Oord__class_Oless(X9,X3,X18)
      | X3 = X9
      | c_HOL_Oord__class_Oless(X3,X9,X18) ),
    inference(fof_simplification,[status(thm)],[c_0_497]) ).

fof(c_0_1105,plain,
    ! [X9,X3,X18] :
      ( ~ class_Orderings_Olinorder(X18)
      | X3 = X9
      | c_HOL_Oord__class_Oless(X3,X9,X18)
      | c_HOL_Oord__class_Oless(X9,X3,X18) ),
    inference(fof_simplification,[status(thm)],[c_0_498]) ).

fof(c_0_1106,plain,
    ! [X9,X3,X18] :
      ( ~ class_Orderings_Olinorder(X18)
      | c_HOL_Oord__class_Oless(X3,X9,X18)
      | c_lessequals(X9,X3,X18) ),
    inference(fof_simplification,[status(thm)],[c_0_499]) ).

fof(c_0_1107,plain,
    ! [X3,X18] :
      ( ~ class_Orderings_Olinorder(X18)
      | c_HOL_Oord__class_Oless(X3,X3,X18)
      | c_lessequals(X3,X3,X18) ),
    inference(fof_simplification,[status(thm)],[c_0_500]) ).

fof(c_0_1108,plain,
    ! [X9,X3,X18] :
      ( ~ class_Orderings_Olinorder(X18)
      | c_lessequals(X9,X3,X18)
      | c_HOL_Oord__class_Oless(X3,X9,X18) ),
    inference(fof_simplification,[status(thm)],[c_0_501]) ).

fof(c_0_1109,plain,
    ! [X9,X3,X18] :
      ( ~ class_Orderings_Olinorder(X18)
      | c_HOL_Oord__class_Oless(X9,X3,X18)
      | c_lessequals(X3,X9,X18) ),
    inference(fof_simplification,[status(thm)],[c_0_502]) ).

fof(c_0_1110,plain,
    ! [X9,X3,X18] :
      ( ~ class_Orderings_Olinorder(X18)
      | c_lessequals(X9,X3,X18)
      | c_lessequals(X3,X9,X18) ),
    inference(fof_simplification,[status(thm)],[c_0_503]) ).

fof(c_0_1111,plain,
    ! [X20,X17,X18] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X18)
      | c_HOL_Oplus__class_Oplus(X17,X20,X18) = c_HOL_Oplus__class_Oplus(X20,X17,X18) ),
    inference(fof_simplification,[status(thm)],[c_0_504]) ).

fof(c_0_1112,plain,
    ! [X16,X17,X18] :
      ( ~ class_OrderedGroup_Ocomm__monoid__add(X18)
      | c_HOL_Oplus__class_Oplus(X17,X16,X18) = c_HOL_Oplus__class_Oplus(X16,X17,X18) ),
    inference(fof_simplification,[status(thm)],[c_0_505]) ).

fof(c_0_1113,plain,
    ! [X9,X3,X18] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X18)
      | c_HOL_Oplus__class_Oplus(X3,X9,X18) = c_HOL_Oplus__class_Oplus(X9,X3,X18) ),
    inference(fof_simplification,[status(thm)],[c_0_506]) ).

fof(c_0_1114,plain,
    ! [X9,X3,X18] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X18)
      | c_HOL_Otimes__class_Otimes(X3,X9,X18) = c_HOL_Otimes__class_Otimes(X9,X3,X18) ),
    inference(fof_simplification,[status(thm)],[c_0_507]) ).

fof(c_0_1115,plain,
    ! [X16,X17,X18] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X18)
      | c_HOL_Otimes__class_Otimes(X17,X16,X18) = c_HOL_Otimes__class_Otimes(X16,X17,X18) ),
    inference(fof_simplification,[status(thm)],[c_0_508]) ).

fof(c_0_1116,plain,
    ! [X9,X3,X18] :
      ( ~ class_Orderings_Olinorder(X18)
      | c_Orderings_Oord__class_Omin(X3,X9,X18) = c_Orderings_Oord__class_Omin(X9,X3,X18) ),
    inference(fof_simplification,[status(thm)],[c_0_509]) ).

fof(c_0_1117,plain,
    ! [X9,X3,X18] :
      ( ~ class_Orderings_Olinorder(X18)
      | c_Orderings_Oord__class_Omax(X3,X9,X18) = c_Orderings_Oord__class_Omax(X9,X3,X18) ),
    inference(fof_simplification,[status(thm)],[c_0_510]) ).

fof(c_0_1118,axiom,
    ! [X3,X5] :
      ( c_HOL_Oord__class_Oless(X3,X3,tc_nat)
      | c_Lambda_Osubst(c_Lambda_OdB_OVar(X3),X5,X3) = X5 ),
    c_0_511 ).

fof(c_0_1119,axiom,
    ! [X1,X2] :
      ( c_lessequals(c_Suc(X1),X2,tc_nat)
      | c_lessequals(X2,X1,tc_nat) ),
    c_0_512 ).

fof(c_0_1120,axiom,
    ! [X3] :
      ( c_HOL_Oord__class_Oless(X3,X3,tc_nat)
      | c_HOL_Oord__class_Oless(X3,c_Suc(X3),tc_nat) ),
    c_0_513 ).

fof(c_0_1121,axiom,
    ! [X1,X2] :
      ( c_HOL_Oord__class_Oless(X1,c_Suc(X2),tc_nat)
      | c_HOL_Oord__class_Oless(X2,X1,tc_nat) ),
    c_0_514 ).

fof(c_0_1122,plain,
    ! [X18] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X18)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X18),c_HOL_Ozero__class_Ozero(X18),X18) ),
    inference(fof_simplification,[status(thm)],[c_0_515]) ).

fof(c_0_1123,plain,
    ! [X18] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X18)
      | ~ c_lessequals(c_HOL_Oone__class_Oone(X18),c_HOL_Ozero__class_Ozero(X18),X18) ),
    inference(fof_simplification,[status(thm)],[c_0_516]) ).

fof(c_0_1124,axiom,
    ! [X1,X2] :
      ( c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != c_HOL_Oplus__class_Oplus(X2,X1,tc_nat)
      | X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
      | X2 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
    c_0_517 ).

fof(c_0_1125,axiom,
    ! [X1,X2] :
      ( c_HOL_Oplus__class_Oplus(X2,X1,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
      | X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
      | X2 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
    c_0_518 ).

fof(c_0_1126,plain,
    ! [X16,X17,X18] :
      ( ~ class_Ring__and__Field_Oring__no__zero__divisors(X18)
      | c_HOL_Otimes__class_Otimes(X17,X16,X18) != c_HOL_Ozero__class_Ozero(X18)
      | X16 = c_HOL_Ozero__class_Ozero(X18)
      | X17 = c_HOL_Ozero__class_Ozero(X18) ),
    inference(fof_simplification,[status(thm)],[c_0_519]) ).

fof(c_0_1127,plain,
    ! [X16,X17,X18] :
      ( ~ class_Ring__and__Field_Ono__zero__divisors(X18)
      | c_HOL_Otimes__class_Otimes(X17,X16,X18) != c_HOL_Ozero__class_Ozero(X18)
      | X16 = c_HOL_Ozero__class_Ozero(X18)
      | X17 = c_HOL_Ozero__class_Ozero(X18) ),
    inference(fof_simplification,[status(thm)],[c_0_520]) ).

fof(c_0_1128,plain,
    ! [X16,X17,X18] :
      ( ~ class_Ring__and__Field_Ono__zero__divisors(X18)
      | c_HOL_Otimes__class_Otimes(X17,X16,X18) != c_HOL_Ozero__class_Ozero(X18)
      | X17 = c_HOL_Ozero__class_Ozero(X18)
      | X16 = c_HOL_Ozero__class_Ozero(X18) ),
    inference(fof_simplification,[status(thm)],[c_0_521]) ).

fof(c_0_1129,axiom,
    ! [X1,X2] :
      ( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
      | c_HOL_Oord__class_Oless(X2,X1,tc_nat)
      | X2 = X1 ),
    c_0_522 ).

fof(c_0_1130,axiom,
    ! [X9,X3] :
      ( c_HOL_Oord__class_Oless(X9,X3,tc_nat)
      | c_HOL_Oord__class_Oless(X3,X9,tc_nat)
      | X3 = X9 ),
    c_0_523 ).

fof(c_0_1131,plain,
    ! [X9,X3,X18] :
      ( ~ class_Ring__and__Field_Oidom(X18)
      | ~ class_Int_Onumber__ring(X18)
      | c_HOL_Ominus__class_Ominus(X3,X9,X18) != c_HOL_Ozero__class_Ozero(X18)
      | X3 = X9 ),
    inference(fof_simplification,[status(thm)],[c_0_524]) ).

fof(c_0_1132,plain,
    ! [X7,X8] :
      ( c_Lambda_Olift(c_Lambda_OdB_OVar(X8),X7) = c_Lambda_OdB_OVar(X8)
      | ~ c_HOL_Oord__class_Oless(X8,X7,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_525]) ).

fof(c_0_1133,plain,
    ! [X3,X17,X18] :
      ( ~ class_Ring__and__Field_Oidom(X18)
      | ~ class_Int_Onumber__ring(X18)
      | X3 != c_HOL_Oplus__class_Oplus(X3,X17,X18)
      | X17 = c_HOL_Ozero__class_Ozero(X18) ),
    inference(fof_simplification,[status(thm)],[c_0_526]) ).

fof(c_0_1134,plain,
    ! [X1] :
      ( 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(fof_simplification,[status(thm)],[c_0_527]) ).

fof(c_0_1135,axiom,
    ! [X1,X2] :
      ( c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != c_HOL_Oplus__class_Oplus(X2,X1,tc_nat)
      | X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
      | X1 = c_HOL_Ozero__class_Ozero(tc_nat) ),
    c_0_528 ).

fof(c_0_1136,axiom,
    ! [X1,X2] :
      ( c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != c_HOL_Oplus__class_Oplus(X2,X1,tc_nat)
      | X2 = c_HOL_Ozero__class_Ozero(tc_nat)
      | X2 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
    c_0_529 ).

fof(c_0_1137,axiom,
    ! [X1,X2] :
      ( c_HOL_Oplus__class_Oplus(X2,X1,tc_nat) != 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) ),
    c_0_530 ).

fof(c_0_1138,axiom,
    ! [X1,X2] :
      ( c_HOL_Oplus__class_Oplus(X2,X1,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
      | X2 = c_HOL_Ozero__class_Ozero(tc_nat)
      | X2 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
    c_0_531 ).

fof(c_0_1139,axiom,
    ! [X1,X2] :
      ( c_lessequals(X1,X2,tc_nat)
      | c_lessequals(X2,X1,tc_nat) ),
    c_0_532 ).

fof(c_0_1140,plain,
    ! [X17,X18] :
      ( ~ class_OrderedGroup_Olordered__ab__group__add(X18)
      | c_HOL_Oplus__class_Oplus(X17,X17,X18) != c_HOL_Ozero__class_Ozero(X18)
      | X17 = c_HOL_Ozero__class_Ozero(X18) ),
    inference(fof_simplification,[status(thm)],[c_0_533]) ).

fof(c_0_1141,axiom,
    ! [X1,X2] :
      ( c_HOL_Otimes__class_Otimes(X2,X1,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
      | X2 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
    c_0_534 ).

fof(c_0_1142,axiom,
    ! [X1,X2] :
      ( 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)) ),
    c_0_535 ).

fof(c_0_1143,axiom,
    ! [X1,X2] :
      ( c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != c_HOL_Oplus__class_Oplus(X2,X1,tc_nat)
      | X2 = c_HOL_Ozero__class_Ozero(tc_nat)
      | X1 = c_HOL_Ozero__class_Ozero(tc_nat) ),
    c_0_536 ).

fof(c_0_1144,axiom,
    ! [X1,X2] :
      ( c_HOL_Oplus__class_Oplus(X2,X1,tc_nat) != 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) ),
    c_0_537 ).

fof(c_0_1145,plain,
    ! [X16,X17,X18] :
      ( ~ class_OrderedGroup_Ogroup__add(X18)
      | c_HOL_Ominus__class_Ominus(X17,X16,X18) != c_HOL_Ozero__class_Ozero(X18)
      | X17 = X16 ),
    inference(fof_simplification,[status(thm)],[c_0_538]) ).

fof(c_0_1146,plain,
    ! [X16,X17,X18] :
      ( ~ class_OrderedGroup_Oab__group__add(X18)
      | c_HOL_Ominus__class_Ominus(X17,X16,X18) != c_HOL_Ozero__class_Ozero(X18)
      | X17 = X16 ),
    inference(fof_simplification,[status(thm)],[c_0_539]) ).

fof(c_0_1147,axiom,
    ! [X1,X2] :
      ( c_HOL_Otimes__class_Otimes(X2,X1,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)
      | X1 = c_HOL_Ozero__class_Ozero(tc_nat)
      | X2 = c_HOL_Ozero__class_Ozero(tc_nat) ),
    c_0_540 ).

fof(c_0_1148,plain,
    ! [X3,X18] :
      ( ~ class_Orderings_Oorder(X18)
      | ~ c_HOL_Oord__class_Oless(X3,X3,X18) ),
    inference(fof_simplification,[status(thm)],[c_0_541]) ).

fof(c_0_1149,plain,
    ! [X3,X18] :
      ( ~ class_Orderings_Olinorder(X18)
      | ~ c_HOL_Oord__class_Oless(X3,X3,X18) ),
    inference(fof_simplification,[status(thm)],[c_0_542]) ).

fof(c_0_1150,plain,
    ! [X3,X18] :
      ( ~ class_Orderings_Opreorder(X18)
      | ~ c_HOL_Oord__class_Oless(X3,X3,X18) ),
    inference(fof_simplification,[status(thm)],[c_0_543]) ).

fof(c_0_1151,axiom,
    ! [X1,X2] :
      ( X2 != c_HOL_Otimes__class_Otimes(X2,X1,tc_nat)
      | X2 = c_HOL_Ozero__class_Ozero(tc_nat)
      | X1 = c_HOL_Oone__class_Oone(tc_nat) ),
    c_0_544 ).

fof(c_0_1152,plain,
    ! [X1] :
      ( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
      | ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_545]) ).

fof(c_0_1153,axiom,
    ! [X1,X2] :
      ( c_HOL_Oplus__class_Oplus(X2,X1,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)
      | X2 = c_HOL_Ozero__class_Ozero(tc_nat) ),
    c_0_546 ).

fof(c_0_1154,axiom,
    ! [X1,X2] :
      ( c_HOL_Oplus__class_Oplus(X2,X1,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)
      | X1 = c_HOL_Ozero__class_Ozero(tc_nat) ),
    c_0_547 ).

fof(c_0_1155,axiom,
    ! [X1,X2] :
      ( c_HOL_Otimes__class_Otimes(X2,X1,tc_nat) != c_HOL_Oone__class_Oone(tc_nat)
      | X1 = c_HOL_Oone__class_Oone(tc_nat) ),
    c_0_548 ).

fof(c_0_1156,axiom,
    ! [X1,X2] :
      ( c_HOL_Otimes__class_Otimes(X2,X1,tc_nat) != c_HOL_Oone__class_Oone(tc_nat)
      | X2 = c_HOL_Oone__class_Oone(tc_nat) ),
    c_0_549 ).

fof(c_0_1157,axiom,
    ! [X1,X2] :
      ( c_HOL_Oone__class_Oone(tc_nat) != c_HOL_Otimes__class_Otimes(X2,X1,tc_nat)
      | X2 = c_HOL_Oone__class_Oone(tc_nat) ),
    c_0_550 ).

fof(c_0_1158,axiom,
    ! [X1,X2] :
      ( c_HOL_Oone__class_Oone(tc_nat) != c_HOL_Otimes__class_Otimes(X2,X1,tc_nat)
      | X1 = c_HOL_Oone__class_Oone(tc_nat) ),
    c_0_551 ).

fof(c_0_1159,plain,
    ! [X15,X4,X5] :
      ( c_Lambda_Obeta(c_Lambda_OdB_OApp(X15,X5),c_Lambda_OdB_OApp(X15,X4))
      | ~ c_Lambda_Obeta(X5,X4) ),
    inference(fof_simplification,[status(thm)],[c_0_552]) ).

fof(c_0_1160,plain,
    ! [X15,X4,X5] :
      ( c_Lambda_Obeta(c_Lambda_OdB_OApp(X5,X15),c_Lambda_OdB_OApp(X4,X15))
      | ~ c_Lambda_Obeta(X5,X4) ),
    inference(fof_simplification,[status(thm)],[c_0_553]) ).

fof(c_0_1161,plain,
    ! [X5,X6,X8] :
      ( c_Lambda_Obeta(c_Lambda_Olift(X6,X8),c_Lambda_Olift(X5,X8))
      | ~ c_Lambda_Obeta(X6,X5) ),
    inference(fof_simplification,[status(thm)],[c_0_554]) ).

fof(c_0_1162,axiom,
    ! [X1,X2] :
      ( c_HOL_Oplus__class_Oplus(X2,X1,tc_nat) != X2
      | X1 = c_HOL_Ozero__class_Ozero(tc_nat) ),
    c_0_555 ).

fof(c_0_1163,axiom,
    ! [X3,X17] :
      ( X3 != c_HOL_Oplus__class_Oplus(X3,X17,tc_nat)
      | X17 = c_HOL_Ozero__class_Ozero(tc_nat) ),
    c_0_556 ).

fof(c_0_1164,plain,
    ! [X18] :
      ( ~ class_OrderedGroup_Olordered__ab__group__add(X18)
      | c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X18),c_HOL_Ozero__class_Ozero(X18),X18) = c_HOL_Ozero__class_Ozero(X18) ),
    inference(fof_simplification,[status(thm)],[c_0_557]) ).

fof(c_0_1165,plain,
    ! [X3,X18] :
      ( ~ class_Ring__and__Field_Oidom(X18)
      | ~ class_Int_Onumber__ring(X18)
      | X3 = c_HOL_Oplus__class_Oplus(X3,c_HOL_Ozero__class_Ozero(X18),X18) ),
    inference(fof_simplification,[status(thm)],[c_0_558]) ).

fof(c_0_1166,plain,
    ! [X18] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X18)
      | c_lessequals(c_HOL_Ozero__class_Ozero(X18),c_HOL_Oone__class_Oone(X18),X18) ),
    inference(fof_simplification,[status(thm)],[c_0_559]) ).

fof(c_0_1167,plain,
    ! [X18] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X18)
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X18),c_HOL_Oone__class_Oone(X18),X18) ),
    inference(fof_simplification,[status(thm)],[c_0_560]) ).

fof(c_0_1168,plain,
    ! [X3,X18] :
      ( ~ class_Ring__and__Field_Oidom(X18)
      | ~ class_Int_Onumber__ring(X18)
      | c_HOL_Ominus__class_Ominus(X3,X3,X18) = c_HOL_Ozero__class_Ozero(X18) ),
    inference(fof_simplification,[status(thm)],[c_0_561]) ).

fof(c_0_1169,plain,
    ! [X17,X18] :
      ( ~ class_Divides_Osemiring__div(X18)
      | c_Divides_Odiv__class_Omod(c_HOL_Ozero__class_Ozero(X18),X17,X18) = c_HOL_Ozero__class_Ozero(X18) ),
    inference(fof_simplification,[status(thm)],[c_0_562]) ).

fof(c_0_1170,plain,
    ! [X17,X18] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X18)
      | c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X18),X17,X18) = c_HOL_Ozero__class_Ozero(X18) ),
    inference(fof_simplification,[status(thm)],[c_0_563]) ).

fof(c_0_1171,plain,
    ! [X17,X18] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X18)
      | c_HOL_Otimes__class_Otimes(X17,c_HOL_Ozero__class_Ozero(X18),X18) = c_HOL_Ozero__class_Ozero(X18) ),
    inference(fof_simplification,[status(thm)],[c_0_564]) ).

fof(c_0_1172,plain,
    ! [X17,X18] :
      ( ~ class_Ring__and__Field_Oring__no__zero__divisors(X18)
      | c_HOL_Otimes__class_Otimes(X17,c_HOL_Ozero__class_Ozero(X18),X18) = c_HOL_Ozero__class_Ozero(X18) ),
    inference(fof_simplification,[status(thm)],[c_0_565]) ).

fof(c_0_1173,plain,
    ! [X16,X18] :
      ( ~ class_Ring__and__Field_Oring__no__zero__divisors(X18)
      | c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X18),X16,X18) = c_HOL_Ozero__class_Ozero(X18) ),
    inference(fof_simplification,[status(thm)],[c_0_566]) ).

fof(c_0_1174,plain,
    ! [X17,X18] :
      ( ~ class_Ring__and__Field_Omult__zero(X18)
      | c_HOL_Otimes__class_Otimes(X17,c_HOL_Ozero__class_Ozero(X18),X18) = c_HOL_Ozero__class_Ozero(X18) ),
    inference(fof_simplification,[status(thm)],[c_0_567]) ).

fof(c_0_1175,plain,
    ! [X17,X18] :
      ( ~ class_Ring__and__Field_Omult__zero(X18)
      | c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X18),X17,X18) = c_HOL_Ozero__class_Ozero(X18) ),
    inference(fof_simplification,[status(thm)],[c_0_568]) ).

fof(c_0_1176,plain,
    ! [X3,X18] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X18)
      | c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X18),X3,X18) = c_HOL_Ozero__class_Ozero(X18) ),
    inference(fof_simplification,[status(thm)],[c_0_569]) ).

fof(c_0_1177,plain,
    ! [X17,X18] :
      ( ~ class_Divides_Osemiring__div(X18)
      | c_Divides_Odiv__class_Omod(X17,c_HOL_Oone__class_Oone(X18),X18) = c_HOL_Ozero__class_Ozero(X18) ),
    inference(fof_simplification,[status(thm)],[c_0_570]) ).

fof(c_0_1178,plain,
    ! [X17,X18] :
      ( ~ class_Divides_Osemiring__div(X18)
      | c_Divides_Odiv__class_Omod(X17,c_HOL_Ozero__class_Ozero(X18),X18) = X17 ),
    inference(fof_simplification,[status(thm)],[c_0_571]) ).

fof(c_0_1179,plain,
    ! [X17,X18] :
      ( ~ class_OrderedGroup_Ogroup__add(X18)
      | c_HOL_Ominus__class_Ominus(X17,c_HOL_Ozero__class_Ozero(X18),X18) = X17 ),
    inference(fof_simplification,[status(thm)],[c_0_572]) ).

fof(c_0_1180,plain,
    ! [X3,X18] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X18)
      | c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(X18),X3,X18) = X3 ),
    inference(fof_simplification,[status(thm)],[c_0_573]) ).

fof(c_0_1181,plain,
    ! [X17,X18] :
      ( ~ class_OrderedGroup_Ocomm__monoid__mult(X18)
      | c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(X18),X17,X18) = X17 ),
    inference(fof_simplification,[status(thm)],[c_0_574]) ).

fof(c_0_1182,plain,
    ! [X17,X18] :
      ( ~ class_OrderedGroup_Omonoid__mult(X18)
      | c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(X18),X17,X18) = X17 ),
    inference(fof_simplification,[status(thm)],[c_0_575]) ).

fof(c_0_1183,plain,
    ! [X17,X18] :
      ( ~ class_OrderedGroup_Omonoid__mult(X18)
      | c_HOL_Otimes__class_Otimes(X17,c_HOL_Oone__class_Oone(X18),X18) = X17 ),
    inference(fof_simplification,[status(thm)],[c_0_576]) ).

fof(c_0_1184,plain,
    ! [X17,X18] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X18)
      | c_HOL_Otimes__class_Otimes(X17,c_HOL_Oone__class_Oone(X18),X18) = X17 ),
    inference(fof_simplification,[status(thm)],[c_0_577]) ).

fof(c_0_1185,plain,
    ! [X17,X18] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X18)
      | c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(X18),X17,X18) = X17 ),
    inference(fof_simplification,[status(thm)],[c_0_578]) ).

fof(c_0_1186,plain,
    ! [X3,X18] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X18)
      | c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X18),X3,X18) = X3 ),
    inference(fof_simplification,[status(thm)],[c_0_579]) ).

fof(c_0_1187,plain,
    ! [X17,X18] :
      ( ~ class_OrderedGroup_Ocomm__monoid__add(X18)
      | c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X18),X17,X18) = X17 ),
    inference(fof_simplification,[status(thm)],[c_0_580]) ).

fof(c_0_1188,plain,
    ! [X17,X18] :
      ( ~ class_OrderedGroup_Ocomm__monoid__add(X18)
      | c_HOL_Oplus__class_Oplus(X17,c_HOL_Ozero__class_Ozero(X18),X18) = X17 ),
    inference(fof_simplification,[status(thm)],[c_0_581]) ).

fof(c_0_1189,plain,
    ! [X17,X18] :
      ( ~ class_OrderedGroup_Omonoid__add(X18)
      | c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X18),X17,X18) = X17 ),
    inference(fof_simplification,[status(thm)],[c_0_582]) ).

fof(c_0_1190,plain,
    ! [X17,X18] :
      ( ~ class_OrderedGroup_Omonoid__add(X18)
      | c_HOL_Oplus__class_Oplus(X17,c_HOL_Ozero__class_Ozero(X18),X18) = X17 ),
    inference(fof_simplification,[status(thm)],[c_0_583]) ).

fof(c_0_1191,plain,
    ! [X17,X18] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X18)
      | c_HOL_Oplus__class_Oplus(X17,c_HOL_Ozero__class_Ozero(X18),X18) = X17 ),
    inference(fof_simplification,[status(thm)],[c_0_584]) ).

fof(c_0_1192,plain,
    ! [X17,X18] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X18)
      | c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X18),X17,X18) = X17 ),
    inference(fof_simplification,[status(thm)],[c_0_585]) ).

fof(c_0_1193,plain,
    ! [X17,X18] :
      ( ~ class_Divides_Osemiring__div(X18)
      | c_Divides_Odiv__class_Omod(X17,X17,X18) = c_HOL_Ozero__class_Ozero(X18) ),
    inference(fof_simplification,[status(thm)],[c_0_586]) ).

fof(c_0_1194,plain,
    ! [X3,X18] :
      ( ~ class_OrderedGroup_Oab__group__add(X18)
      | c_HOL_Ominus__class_Ominus(X3,X3,X18) = c_HOL_Ozero__class_Ozero(X18) ),
    inference(fof_simplification,[status(thm)],[c_0_587]) ).

fof(c_0_1195,plain,
    ! [X3,X18] :
      ( ~ class_OrderedGroup_Ogroup__add(X18)
      | c_HOL_Ominus__class_Ominus(X3,X3,X18) = c_HOL_Ozero__class_Ozero(X18) ),
    inference(fof_simplification,[status(thm)],[c_0_588]) ).

fof(c_0_1196,plain,
    ! [X17,X18] :
      ( ~ class_OrderedGroup_Ogroup__add(X18)
      | c_HOL_Ominus__class_Ominus(X17,X17,X18) = c_HOL_Ozero__class_Ozero(X18) ),
    inference(fof_simplification,[status(thm)],[c_0_589]) ).

fof(c_0_1197,plain,
    ! [X3,X18] :
      ( ~ class_Orderings_Olinorder(X18)
      | c_Orderings_Oord__class_Omin(X3,X3,X18) = X3 ),
    inference(fof_simplification,[status(thm)],[c_0_590]) ).

fof(c_0_1198,plain,
    ! [X3,X18] :
      ( ~ class_Orderings_Olinorder(X18)
      | c_Orderings_Oord__class_Omax(X3,X3,X18) = X3 ),
    inference(fof_simplification,[status(thm)],[c_0_591]) ).

fof(c_0_1199,plain,
    ! [X3,X18] :
      ( ~ class_OrderedGroup_Oab__semigroup__idem__mult(X18)
      | c_HOL_Otimes__class_Otimes(X3,X3,X18) = X3 ),
    inference(fof_simplification,[status(thm)],[c_0_592]) ).

fof(c_0_1200,plain,
    ! [X3,X18] :
      ( ~ class_Orderings_Oorder(X18)
      | c_lessequals(X3,X3,X18) ),
    inference(fof_simplification,[status(thm)],[c_0_593]) ).

fof(c_0_1201,plain,
    ! [X3,X18] :
      ( ~ class_Orderings_Opreorder(X18)
      | c_lessequals(X3,X3,X18) ),
    inference(fof_simplification,[status(thm)],[c_0_594]) ).

fof(c_0_1202,axiom,
    ! [X1] :
      ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
      | X1 = c_HOL_Ozero__class_Ozero(tc_nat) ),
    c_0_595 ).

fof(c_0_1203,plain,
    ! [X4,X5] :
      ( c_Lambda_Obeta(c_Lambda_OdB_OAbs(X5),c_Lambda_OdB_OAbs(X4))
      | ~ c_Lambda_Obeta(X5,X4) ),
    inference(fof_simplification,[status(thm)],[c_0_596]) ).

fof(c_0_1204,axiom,
    ! [X33,X34,X35,X36] :
      ( c_Lambda_OdB_OApp(X36,X34) != c_Lambda_OdB_OApp(X35,X33)
      | X34 = X33 ),
    c_0_597 ).

fof(c_0_1205,axiom,
    ! [X33,X34,X35,X36] :
      ( c_Lambda_OdB_OApp(X36,X34) != c_Lambda_OdB_OApp(X35,X33)
      | X36 = X35 ),
    c_0_598 ).

fof(c_0_1206,plain,
    ! [X4,X8] :
      ( c_InductTermi_OIT(c_Lambda_Olift(X4,X8))
      | ~ c_InductTermi_OIT(X4) ),
    inference(fof_simplification,[status(thm)],[c_0_599]) ).

fof(c_0_1207,plain,
    ! [X18] :
      ( ~ class_Ring__and__Field_Ozero__neq__one(X18)
      | c_HOL_Oone__class_Oone(X18) != c_HOL_Ozero__class_Ozero(X18) ),
    inference(fof_simplification,[status(thm)],[c_0_600]) ).

fof(c_0_1208,plain,
    ! [X18] :
      ( ~ class_Ring__and__Field_Ozero__neq__one(X18)
      | c_HOL_Ozero__class_Ozero(X18) != c_HOL_Oone__class_Oone(X18) ),
    inference(fof_simplification,[status(thm)],[c_0_601]) ).

fof(c_0_1209,plain,
    ! [X6] :
      ( c_InductTermi_OIT(c_Lambda_OdB_OAbs(X6))
      | ~ c_InductTermi_OIT(X6) ),
    inference(fof_simplification,[status(thm)],[c_0_602]) ).

fof(c_0_1210,axiom,
    ! [X10,X11] :
      ( c_Lambda_OdB_OVar(X11) != c_Lambda_OdB_OVar(X10)
      | X11 = X10 ),
    c_0_603 ).

fof(c_0_1211,axiom,
    ! [X12,X13] :
      ( c_Lambda_OdB_OAbs(X13) != c_Lambda_OdB_OAbs(X12)
      | X13 = X12 ),
    c_0_604 ).

fof(c_0_1212,axiom,
    ! [X10,X11] :
      ( c_Suc(X11) != c_Suc(X10)
      | X11 = X10 ),
    c_0_605 ).

fof(c_0_1213,axiom,
    ! [X9,X3] :
      ( c_Suc(X3) != c_Suc(X9)
      | X3 = X9 ),
    c_0_606 ).

fof(c_0_1214,plain,
    ! [X16,X17,X18,X19,X20] :
      ( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X20,X16,tc_nat),X18,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X19,X16,tc_nat),X17,tc_nat),tc_nat)
      | ~ c_HOL_Oord__class_Oless(X18,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X19,X20,tc_nat),X16,tc_nat),X17,tc_nat),tc_nat)
      | ~ c_lessequals(X20,X19,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_607]) ).

fof(c_0_1215,plain,
    ! [X16,X17,X18,X19,X20] :
      ( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X20,X16,tc_nat),X18,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X19,X16,tc_nat),X17,tc_nat),tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X20,X19,tc_nat),X16,tc_nat),X18,tc_nat),X17,tc_nat)
      | ~ c_lessequals(X19,X20,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_608]) ).

fof(c_0_1216,plain,
    ! [X16,X17,X18,X19,X20] :
      ( c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X20,X16,tc_nat),X18,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X19,X16,tc_nat),X17,tc_nat),tc_nat)
      | ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X20,X19,tc_nat),X16,tc_nat),X18,tc_nat),X17,tc_nat)
      | ~ c_lessequals(X19,X20,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_609]) ).

fof(c_0_1217,plain,
    ! [X16,X17,X18,X19,X20] :
      ( c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X20,X16,tc_nat),X18,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X19,X16,tc_nat),X17,tc_nat),tc_nat)
      | ~ c_lessequals(X18,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X19,X20,tc_nat),X16,tc_nat),X17,tc_nat),tc_nat)
      | ~ c_lessequals(X20,X19,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_610]) ).

fof(c_0_1218,plain,
    ! [X40,X41,X42,X43,X44,X45] :
      ( ~ class_Ring__and__Field_Opordered__ring(X45)
      | c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X44,X40,X45),X42,X45),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X43,X40,X45),X41,X45),X45)
      | ~ c_lessequals(X42,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X43,X44,X45),X40,X45),X41,X45),X45) ),
    inference(variable_rename,[status(thm)],[c_0_611]) ).

fof(c_0_1219,plain,
    ! [X40,X41,X42,X43,X44,X45] :
      ( ~ class_Ring__and__Field_Opordered__ring(X45)
      | c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X44,X40,X45),X42,X45),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X43,X40,X45),X41,X45),X45)
      | ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X44,X43,X45),X40,X45),X42,X45),X41,X45) ),
    inference(variable_rename,[status(thm)],[c_0_612]) ).

fof(c_0_1220,plain,
    ! [X40,X41,X42,X43,X44,X45] :
      ( ~ class_Ring__and__Field_Opordered__ring(X45)
      | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X44,X40,X45),X42,X45),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X43,X40,X45),X41,X45),X45)
      | ~ c_HOL_Oord__class_Oless(X42,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X43,X44,X45),X40,X45),X41,X45),X45) ),
    inference(variable_rename,[status(thm)],[c_0_613]) ).

fof(c_0_1221,plain,
    ! [X40,X41,X42,X43,X44,X45] :
      ( ~ class_Ring__and__Field_Opordered__ring(X45)
      | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X44,X40,X45),X42,X45),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X43,X40,X45),X41,X45),X45)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X44,X43,X45),X40,X45),X42,X45),X41,X45) ),
    inference(variable_rename,[status(thm)],[c_0_614]) ).

fof(c_0_1222,plain,
    ! [X16,X17,X18,X19,X20] :
      ( c_HOL_Oord__class_Oless(X18,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X19,X20,tc_nat),X16,tc_nat),X17,tc_nat),tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X20,X16,tc_nat),X18,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X19,X16,tc_nat),X17,tc_nat),tc_nat)
      | ~ c_lessequals(X20,X19,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_615]) ).

fof(c_0_1223,plain,
    ! [X16,X17,X18,X19,X20] :
      ( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X20,X19,tc_nat),X16,tc_nat),X18,tc_nat),X17,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X20,X16,tc_nat),X18,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X19,X16,tc_nat),X17,tc_nat),tc_nat)
      | ~ c_lessequals(X19,X20,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_616]) ).

fof(c_0_1224,plain,
    ! [X16,X17,X18,X19,X20] :
      ( c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X20,X19,tc_nat),X16,tc_nat),X18,tc_nat),X17,tc_nat)
      | ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X20,X16,tc_nat),X18,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X19,X16,tc_nat),X17,tc_nat),tc_nat)
      | ~ c_lessequals(X19,X20,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_617]) ).

fof(c_0_1225,plain,
    ! [X16,X17,X18,X19,X20] :
      ( c_lessequals(X18,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X19,X20,tc_nat),X16,tc_nat),X17,tc_nat),tc_nat)
      | ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X20,X16,tc_nat),X18,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X19,X16,tc_nat),X17,tc_nat),tc_nat)
      | ~ c_lessequals(X20,X19,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_618]) ).

fof(c_0_1226,plain,
    ! [X40,X41,X42,X43,X44,X45] :
      ( ~ class_Ring__and__Field_Opordered__ring(X45)
      | c_lessequals(X42,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X43,X44,X45),X40,X45),X41,X45),X45)
      | ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X44,X40,X45),X42,X45),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X43,X40,X45),X41,X45),X45) ),
    inference(variable_rename,[status(thm)],[c_0_619]) ).

fof(c_0_1227,plain,
    ! [X40,X41,X42,X43,X44,X45] :
      ( ~ class_Ring__and__Field_Opordered__ring(X45)
      | c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X44,X43,X45),X40,X45),X42,X45),X41,X45)
      | ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X44,X40,X45),X42,X45),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X43,X40,X45),X41,X45),X45) ),
    inference(variable_rename,[status(thm)],[c_0_620]) ).

fof(c_0_1228,plain,
    ! [X40,X41,X42,X43,X44,X45] :
      ( ~ class_Ring__and__Field_Opordered__ring(X45)
      | c_HOL_Oord__class_Oless(X42,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X43,X44,X45),X40,X45),X41,X45),X45)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X44,X40,X45),X42,X45),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X43,X40,X45),X41,X45),X45) ),
    inference(variable_rename,[status(thm)],[c_0_621]) ).

fof(c_0_1229,plain,
    ! [X40,X41,X42,X43,X44,X45] :
      ( ~ class_Ring__and__Field_Opordered__ring(X45)
      | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X44,X43,X45),X40,X45),X42,X45),X41,X45)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X44,X40,X45),X42,X45),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X43,X40,X45),X41,X45),X45) ),
    inference(variable_rename,[status(thm)],[c_0_622]) ).

fof(c_0_1230,plain,
    ! [X16,X17,X18,X19,X20] :
      ( c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X20,X16,tc_nat),X18,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X19,X16,tc_nat),X17,tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(X18,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X19,X20,tc_nat),X16,tc_nat),X17,tc_nat),tc_nat)
      | ~ c_lessequals(X20,X19,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_623]) ).

fof(c_0_1231,plain,
    ! [X16,X17,X18,X19,X20] :
      ( c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X20,X16,tc_nat),X18,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X19,X16,tc_nat),X17,tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X20,X19,tc_nat),X16,tc_nat),X18,tc_nat),X17,tc_nat)
      | ~ c_lessequals(X19,X20,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_624]) ).

fof(c_0_1232,plain,
    ! [X16,X17,X18,X19] :
      ( ~ c_lessequals(X18,X19,tc_nat)
      | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X19,X16,tc_nat),X17,tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X18,X16,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X19,X18,tc_nat),X16,tc_nat),X17,tc_nat),tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_625]) ).

fof(c_0_1233,plain,
    ! [X16,X17,X18,X19] :
      ( ~ c_lessequals(X19,X18,tc_nat)
      | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X19,X16,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X18,X19,tc_nat),X16,tc_nat),X17,tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X18,X16,tc_nat),X17,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_626]) ).

fof(c_0_1234,plain,
    ! [X19] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X19)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X19),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X19),c_HOL_Ozero__class_Ozero(X19),X19),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X19),c_HOL_Ozero__class_Ozero(X19),X19),X19),X19) ),
    inference(variable_rename,[status(thm)],[c_0_627]) ).

fof(c_0_1235,plain,
    ! [X40,X41,X42,X43,X44] :
      ( ~ class_Ring__and__Field_Oring(X44)
      | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X43,X40,X44),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X42,X43,X44),X40,X44),X41,X44),X44) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X42,X40,X44),X41,X44) ),
    inference(variable_rename,[status(thm)],[c_0_628]) ).

fof(c_0_1236,plain,
    ! [X40,X41,X42,X43,X44] :
      ( ~ class_Ring__and__Field_Oring(X44)
      | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X43,X40,X44),X41,X44) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X42,X40,X44),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X43,X42,X44),X40,X44),X41,X44),X44) ),
    inference(variable_rename,[status(thm)],[c_0_629]) ).

fof(c_0_1237,plain,
    ! [X31,X32,X33,X34] :
      ( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X34,c_Divides_Odiv__class_Omod(X32,X33,tc_nat),tc_nat),X31,tc_nat),c_HOL_Otimes__class_Otimes(X34,X33,tc_nat),tc_nat)
      | ~ c_HOL_Oord__class_Oless(X31,X34,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X33,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_630]) ).

fof(c_0_1238,plain,
    ! [X19,X20,X21] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X21)
      | X20 = c_HOL_Ozero__class_Ozero(X21)
      | ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X20,X20,X21),c_HOL_Otimes__class_Otimes(X19,X19,X21),X21),c_HOL_Ozero__class_Ozero(X21),X21) ),
    inference(variable_rename,[status(thm)],[c_0_631]) ).

fof(c_0_1239,plain,
    ! [X19,X20,X21] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X21)
      | X19 = c_HOL_Ozero__class_Ozero(X21)
      | ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X20,X20,X21),c_HOL_Otimes__class_Otimes(X19,X19,X21),X21),c_HOL_Ozero__class_Ozero(X21),X21) ),
    inference(variable_rename,[status(thm)],[c_0_632]) ).

fof(c_0_1240,plain,
    ! [X19,X20,X21] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X21)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X20,X20,X21),c_HOL_Otimes__class_Otimes(X19,X19,X21),X21),c_HOL_Ozero__class_Ozero(X21),X21) ),
    inference(variable_rename,[status(thm)],[c_0_633]) ).

fof(c_0_1241,plain,
    ! [X16,X17,X18,X19,X20] :
      ( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X20,X16,tc_nat),X18,tc_nat) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X19,X16,tc_nat),X17,tc_nat)
      | ~ c_lessequals(X19,X20,tc_nat)
      | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X20,X19,tc_nat),X16,tc_nat),X18,tc_nat) = X17 ),
    inference(variable_rename,[status(thm)],[c_0_634]) ).

fof(c_0_1242,plain,
    ! [X16,X17,X18,X19,X20] :
      ( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X20,X16,tc_nat),X18,tc_nat) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X19,X16,tc_nat),X17,tc_nat)
      | ~ c_lessequals(X20,X19,tc_nat)
      | X18 = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X19,X20,tc_nat),X16,tc_nat),X17,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_635]) ).

fof(c_0_1243,plain,
    ! [X20,X21,X22,X23] :
      ( ~ class_Orderings_Olinorder(X23)
      | c_lessequals(c_Orderings_Oord__class_Omax(c_Orderings_Oord__class_Omin(X22,X21,X23),c_Orderings_Oord__class_Omin(X22,X20,X23),X23),c_Orderings_Oord__class_Omin(X22,c_Orderings_Oord__class_Omax(X21,X20,X23),X23),X23) ),
    inference(variable_rename,[status(thm)],[c_0_636]) ).

fof(c_0_1244,plain,
    ! [X20,X21,X22,X23] :
      ( ~ class_Orderings_Olinorder(X23)
      | c_lessequals(c_Orderings_Oord__class_Omax(X22,c_Orderings_Oord__class_Omin(X21,X20,X23),X23),c_Orderings_Oord__class_Omin(c_Orderings_Oord__class_Omax(X22,X21,X23),c_Orderings_Oord__class_Omax(X22,X20,X23),X23),X23) ),
    inference(variable_rename,[status(thm)],[c_0_637]) ).

fof(c_0_1245,plain,
    ! [X40,X41,X42,X43,X44,X45] :
      ( ~ class_Ring__and__Field_Oring(X45)
      | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X44,X40,X45),X42,X45) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X43,X40,X45),X41,X45)
      | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X44,X43,X45),X40,X45),X42,X45) = X41 ),
    inference(variable_rename,[status(thm)],[c_0_638]) ).

fof(c_0_1246,plain,
    ! [X40,X41,X42,X43,X44,X45] :
      ( ~ class_Ring__and__Field_Oring(X45)
      | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X44,X40,X45),X42,X45) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X43,X40,X45),X41,X45)
      | X42 = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X43,X44,X45),X40,X45),X41,X45) ),
    inference(variable_rename,[status(thm)],[c_0_639]) ).

fof(c_0_1247,plain,
    ! [X40,X41,X42,X43,X44] :
      ( ~ class_Ring__and__Field_Osemiring(X44)
      | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X43,X40,X44),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X42,X40,X44),X41,X44),X44) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X43,X42,X44),X40,X44),X41,X44) ),
    inference(variable_rename,[status(thm)],[c_0_640]) ).

fof(c_0_1248,plain,
    ! [X41,X42,X43,X44,X45] :
      ( ~ class_Ring__and__Field_Oidom(X45)
      | ~ class_Int_Onumber__ring(X45)
      | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X44,X42,X45),c_HOL_Otimes__class_Otimes(X43,X41,X45),X45) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X44,X41,X45),c_HOL_Otimes__class_Otimes(X43,X42,X45),X45)
      | X42 = X41
      | X44 = X43 ),
    inference(variable_rename,[status(thm)],[c_0_641]) ).

fof(c_0_1249,plain,
    ! [X28,X29,X30,X31,X32] :
      ( ~ class_Ring__and__Field_Oidom(X32)
      | ~ class_Int_Onumber__ring(X32)
      | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X31,X29,X32),c_HOL_Otimes__class_Otimes(X30,X28,X32),X32) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X31,X28,X32),c_HOL_Otimes__class_Otimes(X30,X29,X32),X32)
      | X29 = X28
      | X31 = X30 ),
    inference(variable_rename,[status(thm)],[c_0_642]) ).

fof(c_0_1250,plain,
    ! [X28,X29,X30,X31] :
      ( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X31,X29,tc_nat),c_HOL_Otimes__class_Otimes(X30,X28,tc_nat),tc_nat) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X31,X28,tc_nat),c_HOL_Otimes__class_Otimes(X30,X29,tc_nat),tc_nat)
      | X29 = X28
      | X31 = X30 ),
    inference(variable_rename,[status(thm)],[c_0_643]) ).

fof(c_0_1251,plain,
    ! [X41,X42,X43,X44] :
      ( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X44,X42,tc_nat),c_HOL_Otimes__class_Otimes(X43,X41,tc_nat),tc_nat) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X44,X41,tc_nat),c_HOL_Otimes__class_Otimes(X43,X42,tc_nat),tc_nat)
      | X42 = X41
      | X44 = X43 ),
    inference(variable_rename,[status(thm)],[c_0_644]) ).

fof(c_0_1252,plain,
    ! [X21,X22,X23,X24] :
      ( ~ class_Divides_Osemiring__div(X24)
      | c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X23,X22,X24),X21,X24) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(X23,X21,X24),c_Divides_Odiv__class_Omod(X22,X21,X24),X24),X21,X24) ),
    inference(variable_rename,[status(thm)],[c_0_645]) ).

fof(c_0_1253,plain,
    ! [X21,X22,X23,X24] :
      ( ~ class_Divides_Osemiring__div(X24)
      | c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X23,X22,X24),X21,X24) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(X23,X21,X24),c_Divides_Odiv__class_Omod(X22,X21,X24),X24),X21,X24) ),
    inference(variable_rename,[status(thm)],[c_0_646]) ).

fof(c_0_1254,plain,
    ! [X21,X22,X23,X24] :
      ( ~ class_Divides_Oring__div(X24)
      | c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X23,X22,X24),X21,X24) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(c_Divides_Odiv__class_Omod(X23,X21,X24),c_Divides_Odiv__class_Omod(X22,X21,X24),X24),X21,X24) ),
    inference(variable_rename,[status(thm)],[c_0_647]) ).

fof(c_0_1255,plain,
    ! [X30,X31,X32,X33,X34] :
      ( c_Lambda_Osubst(c_Lambda_Osubst(X32,c_Lambda_Olift(X30,X34),c_Suc(X33)),c_Lambda_Osubst(X31,X30,X33),X34) = c_Lambda_Osubst(c_Lambda_Osubst(X32,X31,X34),X30,X33)
      | ~ c_HOL_Oord__class_Oless(X34,c_HOL_Oplus__class_Oplus(X33,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_648]) ).

fof(c_0_1256,plain,
    ! [X15,X16,X17,X18] :
      ( c_Lambda_Olift(c_Lambda_Osubst(X15,X16,X17),X18) = c_Lambda_Osubst(c_Lambda_Olift(X15,c_HOL_Oplus__class_Oplus(X18,c_HOL_Oone__class_Oone(tc_nat),tc_nat)),c_Lambda_Olift(X16,X18),X17)
      | ~ c_HOL_Oord__class_Oless(X17,c_HOL_Oplus__class_Oplus(X18,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_649]) ).

fof(c_0_1257,plain,
    ! [X19] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X19)
      | c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X19),c_HOL_Ozero__class_Ozero(X19),X19),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X19),c_HOL_Ozero__class_Ozero(X19),X19),X19),c_HOL_Ozero__class_Ozero(X19),X19) ),
    inference(variable_rename,[status(thm)],[c_0_650]) ).

fof(c_0_1258,plain,
    ! [X39,X40,X41,X42,X43,X44] :
      ( ~ class_Divides_Osemiring__div(X44)
      | c_Divides_Odiv__class_Omod(X41,X39,X44) != c_Divides_Odiv__class_Omod(X40,X39,X44)
      | c_Divides_Odiv__class_Omod(X43,X39,X44) != c_Divides_Odiv__class_Omod(X42,X39,X44)
      | c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X43,X41,X44),X39,X44) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X42,X40,X44),X39,X44) ),
    inference(variable_rename,[status(thm)],[c_0_651]) ).

fof(c_0_1259,plain,
    ! [X39,X40,X41,X42,X43,X44] :
      ( ~ class_Divides_Osemiring__div(X44)
      | c_Divides_Odiv__class_Omod(X41,X39,X44) != c_Divides_Odiv__class_Omod(X40,X39,X44)
      | c_Divides_Odiv__class_Omod(X43,X39,X44) != c_Divides_Odiv__class_Omod(X42,X39,X44)
      | c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X43,X41,X44),X39,X44) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X42,X40,X44),X39,X44) ),
    inference(variable_rename,[status(thm)],[c_0_652]) ).

fof(c_0_1260,plain,
    ! [X39,X40,X41,X42,X43,X44] :
      ( ~ class_Divides_Oring__div(X44)
      | c_Divides_Odiv__class_Omod(X41,X39,X44) != c_Divides_Odiv__class_Omod(X40,X39,X44)
      | c_Divides_Odiv__class_Omod(X43,X39,X44) != c_Divides_Odiv__class_Omod(X42,X39,X44)
      | c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X43,X41,X44),X39,X44) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X42,X40,X44),X39,X44) ),
    inference(variable_rename,[status(thm)],[c_0_653]) ).

fof(c_0_1261,plain,
    ! [X25,X26,X27,X28,X29] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X29)
      | c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X28,X27,X29),c_HOL_Otimes__class_Otimes(X26,X25,X29),X29) = c_HOL_Otimes__class_Otimes(X28,c_HOL_Otimes__class_Otimes(X27,c_HOL_Otimes__class_Otimes(X26,X25,X29),X29),X29) ),
    inference(variable_rename,[status(thm)],[c_0_654]) ).

fof(c_0_1262,plain,
    ! [X25,X26,X27,X28,X29] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X29)
      | c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X28,X27,X29),c_HOL_Otimes__class_Otimes(X26,X25,X29),X29) = c_HOL_Otimes__class_Otimes(X26,c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X28,X27,X29),X25,X29),X29) ),
    inference(variable_rename,[status(thm)],[c_0_655]) ).

fof(c_0_1263,plain,
    ! [X28,X29,X30,X31,X32] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X32)
      | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X31,X29,X32),c_HOL_Otimes__class_Otimes(X30,X28,X32),X32)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X32),X29,X32)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X32),X30,X32)
      | ~ c_HOL_Oord__class_Oless(X29,X28,X32)
      | ~ c_HOL_Oord__class_Oless(X31,X30,X32) ),
    inference(variable_rename,[status(thm)],[c_0_656]) ).

fof(c_0_1264,plain,
    ! [X28,X29,X30,X31,X32] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X32)
      | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X31,X29,X32),c_HOL_Otimes__class_Otimes(X30,X28,X32),X32)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X32),X29,X32)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X32),X31,X32)
      | ~ c_lessequals(X29,X28,X32)
      | ~ c_HOL_Oord__class_Oless(X31,X30,X32) ),
    inference(variable_rename,[status(thm)],[c_0_657]) ).

fof(c_0_1265,plain,
    ! [X28,X29,X30,X31,X32] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X32)
      | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X31,X29,X32),c_HOL_Otimes__class_Otimes(X30,X28,X32),X32)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X32),X29,X32)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X32),X31,X32)
      | ~ c_HOL_Oord__class_Oless(X29,X28,X32)
      | ~ c_lessequals(X31,X30,X32) ),
    inference(variable_rename,[status(thm)],[c_0_658]) ).

fof(c_0_1266,plain,
    ! [X28,X29,X30,X31,X32] :
      ( ~ class_Ring__and__Field_Opordered__semiring(X32)
      | c_lessequals(c_HOL_Otimes__class_Otimes(X31,X29,X32),c_HOL_Otimes__class_Otimes(X30,X28,X32),X32)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X32),X29,X32)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X32),X30,X32)
      | ~ c_lessequals(X29,X28,X32)
      | ~ c_lessequals(X31,X30,X32) ),
    inference(variable_rename,[status(thm)],[c_0_659]) ).

fof(c_0_1267,plain,
    ! [X28,X29,X30,X31,X32] :
      ( ~ class_Ring__and__Field_Opordered__semiring(X32)
      | c_lessequals(c_HOL_Otimes__class_Otimes(X31,X29,X32),c_HOL_Otimes__class_Otimes(X30,X28,X32),X32)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X32),X29,X32)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X32),X31,X32)
      | ~ c_lessequals(X29,X28,X32)
      | ~ c_lessequals(X31,X30,X32) ),
    inference(variable_rename,[status(thm)],[c_0_660]) ).

fof(c_0_1268,plain,
    ! [X28,X29,X30,X31,X32] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X32)
      | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X31,X29,X32),c_HOL_Otimes__class_Otimes(X30,X28,X32),X32)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X32),X29,X32)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X32),X31,X32)
      | ~ c_HOL_Oord__class_Oless(X29,X28,X32)
      | ~ c_HOL_Oord__class_Oless(X31,X30,X32) ),
    inference(variable_rename,[status(thm)],[c_0_661]) ).

fof(c_0_1269,plain,
    ! [X8,X9,X10] :
      ( c_lessequals(X9,X8,tc_nat)
      | ~ c_lessequals(c_HOL_Ominus__class_Ominus(X9,X10,tc_nat),c_HOL_Ominus__class_Ominus(X8,X10,tc_nat),tc_nat)
      | ~ c_lessequals(X10,X8,tc_nat)
      | ~ c_lessequals(X10,X9,tc_nat) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_662])])]) ).

fof(c_0_1270,plain,
    ! [X8,X9,X10] :
      ( c_HOL_Oord__class_Oless(X9,X8,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X9,X10,tc_nat),c_HOL_Ominus__class_Ominus(X8,X10,tc_nat),tc_nat)
      | ~ c_lessequals(X10,X8,tc_nat)
      | ~ c_lessequals(X10,X9,tc_nat) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_663])])]) ).

fof(c_0_1271,plain,
    ! [X19,X20,X21] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X21)
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X21),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X20,X20,X21),c_HOL_Otimes__class_Otimes(X19,X19,X21),X21),X21)
      | X20 = c_HOL_Ozero__class_Ozero(X21) ),
    inference(variable_rename,[status(thm)],[c_0_664]) ).

fof(c_0_1272,plain,
    ! [X19,X20,X21] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X21)
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X21),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X20,X20,X21),c_HOL_Otimes__class_Otimes(X19,X19,X21),X21),X21)
      | X19 = c_HOL_Ozero__class_Ozero(X21) ),
    inference(variable_rename,[status(thm)],[c_0_665]) ).

fof(c_0_1273,plain,
    ! [X19,X20,X21] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X21)
      | c_lessequals(c_HOL_Ozero__class_Ozero(X21),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X20,X20,X21),c_HOL_Otimes__class_Otimes(X19,X19,X21),X21),X21) ),
    inference(variable_rename,[status(thm)],[c_0_666]) ).

fof(c_0_1274,plain,
    ! [X33,X34,X35,X36,X37] :
      ( c_HOL_Oplus__class_Oplus(X36,c_HOL_Otimes__class_Otimes(X37,X35,tc_nat),tc_nat) != c_HOL_Oplus__class_Oplus(X33,c_HOL_Otimes__class_Otimes(X37,X34,tc_nat),tc_nat)
      | c_Divides_Odiv__class_Omod(X36,X37,tc_nat) = c_Divides_Odiv__class_Omod(X33,X37,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_667]) ).

fof(c_0_1275,plain,
    ! [X15,X16,X17,X18] :
      ( c_Lambda_Olift(c_Lambda_Osubst(X15,X16,X17),X18) = c_Lambda_Osubst(c_Lambda_Olift(X15,X18),c_Lambda_Olift(X16,X18),c_HOL_Oplus__class_Oplus(X17,c_HOL_Oone__class_Oone(tc_nat),tc_nat))
      | ~ c_HOL_Oord__class_Oless(X18,c_HOL_Oplus__class_Oplus(X17,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_668]) ).

fof(c_0_1276,plain,
    ! [X21,X22,X23,X24] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X24)
      | c_HOL_Oord__class_Oless(X23,X22,X24)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X24),X21,X24)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X23,X21,X24),c_HOL_Otimes__class_Otimes(X22,X21,X24),X24) ),
    inference(variable_rename,[status(thm)],[c_0_669]) ).

fof(c_0_1277,plain,
    ! [X21,X22,X23,X24] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X24)
      | c_HOL_Oord__class_Oless(X23,X22,X24)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X24),X21,X24)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X21,X23,X24),c_HOL_Otimes__class_Otimes(X21,X22,X24),X24) ),
    inference(variable_rename,[status(thm)],[c_0_670]) ).

fof(c_0_1278,plain,
    ! [X21,X22,X23,X24] :
      ( ~ class_Ring__and__Field_Oordered__semiring(X24)
      | c_HOL_Oord__class_Oless(X23,X22,X24)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X24),X21,X24)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X23,X21,X24),c_HOL_Otimes__class_Otimes(X22,X21,X24),X24) ),
    inference(variable_rename,[status(thm)],[c_0_671]) ).

fof(c_0_1279,plain,
    ! [X21,X22,X23,X24] :
      ( ~ class_Ring__and__Field_Oordered__semiring(X24)
      | c_HOL_Oord__class_Oless(X23,X22,X24)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X24),X21,X24)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X21,X23,X24),c_HOL_Otimes__class_Otimes(X21,X22,X24),X24) ),
    inference(variable_rename,[status(thm)],[c_0_672]) ).

fof(c_0_1280,plain,
    ! [X21,X22,X23,X24] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X24)
      | c_lessequals(X22,X23,X24)
      | ~ c_lessequals(c_HOL_Otimes__class_Otimes(X21,X23,X24),c_HOL_Otimes__class_Otimes(X21,X22,X24),X24)
      | ~ c_HOL_Oord__class_Oless(X21,c_HOL_Ozero__class_Ozero(X24),X24) ),
    inference(variable_rename,[status(thm)],[c_0_673]) ).

fof(c_0_1281,plain,
    ! [X21,X22,X23,X24] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X24)
      | c_lessequals(X23,X22,X24)
      | ~ c_lessequals(c_HOL_Otimes__class_Otimes(X21,X23,X24),c_HOL_Otimes__class_Otimes(X21,X22,X24),X24)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X24),X21,X24) ),
    inference(variable_rename,[status(thm)],[c_0_674]) ).

fof(c_0_1282,plain,
    ! [X21,X22,X23,X24] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X24)
      | c_lessequals(X23,X22,X24)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X24),X21,X24)
      | ~ c_lessequals(c_HOL_Otimes__class_Otimes(X21,X23,X24),c_HOL_Otimes__class_Otimes(X21,X22,X24),X24) ),
    inference(variable_rename,[status(thm)],[c_0_675]) ).

fof(c_0_1283,plain,
    ! [X21,X22,X23,X24] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X24)
      | c_lessequals(X23,X22,X24)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X24),X21,X24)
      | ~ c_lessequals(c_HOL_Otimes__class_Otimes(X23,X21,X24),c_HOL_Otimes__class_Otimes(X22,X21,X24),X24) ),
    inference(variable_rename,[status(thm)],[c_0_676]) ).

fof(c_0_1284,plain,
    ! [X21,X22,X23,X24] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X24)
      | c_HOL_Oord__class_Oless(X22,X23,X24)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X21,X23,X24),c_HOL_Otimes__class_Otimes(X21,X22,X24),X24)
      | ~ c_HOL_Oord__class_Oless(X21,c_HOL_Ozero__class_Ozero(X24),X24) ),
    inference(variable_rename,[status(thm)],[c_0_677]) ).

fof(c_0_1285,plain,
    ! [X21,X22,X23,X24] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X24)
      | c_HOL_Oord__class_Oless(X23,X22,X24)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X21,X23,X24),c_HOL_Otimes__class_Otimes(X21,X22,X24),X24)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X24),X21,X24) ),
    inference(variable_rename,[status(thm)],[c_0_678]) ).

fof(c_0_1286,plain,
    ! [X8,X9,X10] :
      ( c_lessequals(X9,X8,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X10,tc_nat)
      | ~ c_lessequals(c_HOL_Otimes__class_Otimes(X9,X10,tc_nat),c_HOL_Otimes__class_Otimes(X8,X10,tc_nat),tc_nat) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_679])])]) ).

fof(c_0_1287,plain,
    ! [X8,X9,X10] :
      ( c_lessequals(X9,X8,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X10,tc_nat)
      | ~ c_lessequals(c_HOL_Otimes__class_Otimes(X10,X9,tc_nat),c_HOL_Otimes__class_Otimes(X10,X8,tc_nat),tc_nat) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_680])])]) ).

fof(c_0_1288,plain,
    ! [X8,X9,X10] :
      ( c_lessequals(X9,X8,tc_nat)
      | ~ c_lessequals(c_HOL_Otimes__class_Otimes(X10,X9,tc_nat),c_HOL_Otimes__class_Otimes(X10,X8,tc_nat),tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X10,tc_nat) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_681])])]) ).

fof(c_0_1289,plain,
    ! [X8,X9,X10] :
      ( c_HOL_Oord__class_Oless(X9,X8,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X10,X9,tc_nat),c_HOL_Otimes__class_Otimes(X10,X8,tc_nat),tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X10,tc_nat) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_682])])]) ).

fof(c_0_1290,plain,
    ! [X21,X22,X23,X24] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X24)
      | c_HOL_Oord__class_Oless(X21,c_HOL_Ozero__class_Ozero(X24),X24)
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X24),X21,X24)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X21,X23,X24),c_HOL_Otimes__class_Otimes(X21,X22,X24),X24) ),
    inference(variable_rename,[status(thm)],[c_0_683]) ).

fof(c_0_1291,plain,
    ! [X21,X22,X23,X24] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X24)
      | c_HOL_Oord__class_Oless(X21,c_HOL_Ozero__class_Ozero(X24),X24)
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X24),X21,X24)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X23,X21,X24),c_HOL_Otimes__class_Otimes(X22,X21,X24),X24) ),
    inference(variable_rename,[status(thm)],[c_0_684]) ).

fof(c_0_1292,plain,
    ! [X28,X29,X30,X31] :
      ( ~ class_Ring__and__Field_Oidom(X31)
      | ~ class_Int_Onumber__ring(X31)
      | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X28,X30,X31),c_HOL_Otimes__class_Otimes(X28,X29,X31),X31) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X28,X29,X31),c_HOL_Otimes__class_Otimes(X28,X30,X31),X31) ),
    inference(variable_rename,[status(thm)],[c_0_685]) ).

fof(c_0_1293,plain,
    ! [X20,X21,X22,X23] :
      ( ~ class_Ring__and__Field_Oidom(X23)
      | ~ class_Int_Onumber__ring(X23)
      | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X22,X21,X23),c_HOL_Otimes__class_Otimes(X22,X20,X23),X23) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X22,X20,X23),c_HOL_Otimes__class_Otimes(X22,X21,X23),X23) ),
    inference(variable_rename,[status(thm)],[c_0_686]) ).

fof(c_0_1294,plain,
    ! [X21,X22,X23,X24] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X24)
      | c_HOL_Oord__class_Oless(X21,c_HOL_Ozero__class_Ozero(X24),X24)
      | c_HOL_Oord__class_Oless(X23,X22,X24)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X23,X21,X24),c_HOL_Otimes__class_Otimes(X22,X21,X24),X24) ),
    inference(variable_rename,[status(thm)],[c_0_687]) ).

fof(c_0_1295,plain,
    ! [X21,X22,X23,X24] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X24)
      | c_HOL_Oord__class_Oless(X22,X23,X24)
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X24),X21,X24)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X23,X21,X24),c_HOL_Otimes__class_Otimes(X22,X21,X24),X24) ),
    inference(variable_rename,[status(thm)],[c_0_688]) ).

fof(c_0_1296,plain,
    ! [X21,X22,X23,X24] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X24)
      | c_HOL_Oord__class_Oless(X21,c_HOL_Ozero__class_Ozero(X24),X24)
      | c_HOL_Oord__class_Oless(X23,X22,X24)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X21,X23,X24),c_HOL_Otimes__class_Otimes(X21,X22,X24),X24) ),
    inference(variable_rename,[status(thm)],[c_0_689]) ).

fof(c_0_1297,plain,
    ! [X21,X22,X23,X24] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X24)
      | c_HOL_Oord__class_Oless(X22,X23,X24)
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X24),X21,X24)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X21,X23,X24),c_HOL_Otimes__class_Otimes(X21,X22,X24),X24) ),
    inference(variable_rename,[status(thm)],[c_0_690]) ).

fof(c_0_1298,plain,
    ! [X21,X22,X23,X24] :
      ( ~ class_Divides_Osemiring__div(X24)
      | c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(X23,X21,X24),X22,X24),X21,X24) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X23,X22,X24),X21,X24) ),
    inference(variable_rename,[status(thm)],[c_0_691]) ).

fof(c_0_1299,plain,
    ! [X21,X22,X23,X24] :
      ( ~ class_Divides_Oring__div(X24)
      | c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X23,X22,X24),X21,X24) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(c_Divides_Odiv__class_Omod(X23,X21,X24),X22,X24),X21,X24) ),
    inference(variable_rename,[status(thm)],[c_0_692]) ).

fof(c_0_1300,plain,
    ! [X21,X22,X23,X24] :
      ( ~ class_Divides_Oring__div(X24)
      | c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X23,X22,X24),X21,X24) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X23,c_Divides_Odiv__class_Omod(X22,X21,X24),X24),X21,X24) ),
    inference(variable_rename,[status(thm)],[c_0_693]) ).

fof(c_0_1301,plain,
    ! [X25,X26,X27,X28,X29] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X29)
      | c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X28,X27,X29),c_HOL_Otimes__class_Otimes(X26,X25,X29),X29) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X28,X26,X29),c_HOL_Otimes__class_Otimes(X27,X25,X29),X29) ),
    inference(variable_rename,[status(thm)],[c_0_694]) ).

fof(c_0_1302,plain,
    ! [X21,X22,X23,X24] :
      ( ~ class_Divides_Osemiring__div(X24)
      | c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X23,X22,X24),X21,X24) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(X23,X21,X24),X22,X24),X21,X24) ),
    inference(variable_rename,[status(thm)],[c_0_695]) ).

fof(c_0_1303,plain,
    ! [X21,X22,X23,X24] :
      ( ~ class_Divides_Osemiring__div(X24)
      | c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X23,X22,X24),X21,X24) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X23,c_Divides_Odiv__class_Omod(X22,X21,X24),X24),X21,X24) ),
    inference(variable_rename,[status(thm)],[c_0_696]) ).

fof(c_0_1304,plain,
    ! [X21,X22,X23,X24] :
      ( ~ class_Divides_Osemiring__div(X24)
      | c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X23,X22,X24),X21,X24) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(X23,X21,X24),X22,X24),X21,X24) ),
    inference(variable_rename,[status(thm)],[c_0_697]) ).

fof(c_0_1305,plain,
    ! [X21,X22,X23,X24] :
      ( ~ class_Divides_Osemiring__div(X24)
      | c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X23,X22,X24),X21,X24) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X23,c_Divides_Odiv__class_Omod(X22,X21,X24),X24),X21,X24) ),
    inference(variable_rename,[status(thm)],[c_0_698]) ).

fof(c_0_1306,plain,
    ! [X28,X29,X30,X31,X32] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X32)
      | c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X31,X30,X32),c_HOL_Oplus__class_Oplus(X29,X28,X32),X32) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X31,X29,X32),c_HOL_Oplus__class_Oplus(X30,X28,X32),X32) ),
    inference(variable_rename,[status(thm)],[c_0_699]) ).

fof(c_0_1307,plain,
    ! [X21,X22,X23,X24] :
      ( ~ class_Divides_Osemiring__div(X24)
      | c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(X23,X21,X24),X22,X24),X21,X24) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X23,X22,X24),X21,X24) ),
    inference(variable_rename,[status(thm)],[c_0_700]) ).

fof(c_0_1308,plain,
    ! [X21,X22,X23,X24] :
      ( ~ class_Divides_Osemiring__div(X24)
      | c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X23,c_Divides_Odiv__class_Omod(X22,X21,X24),X24),X21,X24) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X23,X22,X24),X21,X24) ),
    inference(variable_rename,[status(thm)],[c_0_701]) ).

fof(c_0_1309,plain,
    ! [X21,X22,X23,X24] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X24)
      | c_HOL_Oord__class_Oless(X22,X23,X24)
      | c_HOL_Oord__class_Oless(X23,X22,X24)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X21,X23,X24),c_HOL_Otimes__class_Otimes(X21,X22,X24),X24) ),
    inference(variable_rename,[status(thm)],[c_0_702]) ).

fof(c_0_1310,plain,
    ! [X21,X22,X23,X24] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X24)
      | c_HOL_Oord__class_Oless(X22,X23,X24)
      | c_HOL_Oord__class_Oless(X23,X22,X24)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X23,X21,X24),c_HOL_Otimes__class_Otimes(X22,X21,X24),X24) ),
    inference(variable_rename,[status(thm)],[c_0_703]) ).

fof(c_0_1311,plain,
    ! [X28,X29,X30,X31,X32] :
      ( ~ class_Ring__and__Field_Oidom(X32)
      | ~ class_Int_Onumber__ring(X32)
      | c_HOL_Oplus__class_Oplus(X28,c_HOL_Otimes__class_Otimes(X29,X31,X32),X32) != c_HOL_Oplus__class_Oplus(X28,c_HOL_Otimes__class_Otimes(X29,X30,X32),X32)
      | X31 = X30
      | X29 = c_HOL_Ozero__class_Ozero(X32) ),
    inference(variable_rename,[status(thm)],[c_0_704]) ).

fof(c_0_1312,plain,
    ! [X15,X16,X17] :
      ( c_HOL_Ominus__class_Ominus(c_Suc(c_HOL_Ominus__class_Ominus(X17,X16,tc_nat)),X15,tc_nat) = c_HOL_Ominus__class_Ominus(c_Suc(X17),c_HOL_Oplus__class_Oplus(X16,X15,tc_nat),tc_nat)
      | ~ c_lessequals(X16,X17,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_705]) ).

fof(c_0_1313,plain,
    ! [X15,X16,X17] :
      ( c_HOL_Ominus__class_Ominus(X15,c_Suc(c_HOL_Ominus__class_Ominus(X17,X16,tc_nat)),tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X15,X16,tc_nat),c_Suc(X17),tc_nat)
      | ~ c_lessequals(X16,X17,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_706]) ).

fof(c_0_1314,plain,
    ! [X8,X9,X10] :
      ( c_lessequals(c_HOL_Ominus__class_Ominus(X9,X10,tc_nat),c_HOL_Ominus__class_Ominus(X8,X10,tc_nat),tc_nat)
      | ~ c_lessequals(X9,X8,tc_nat)
      | ~ c_lessequals(X10,X8,tc_nat)
      | ~ c_lessequals(X10,X9,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_707]) ).

fof(c_0_1315,plain,
    ! [X8,X9,X10] :
      ( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X9,X10,tc_nat),c_HOL_Ominus__class_Ominus(X8,X10,tc_nat),tc_nat)
      | ~ c_HOL_Oord__class_Oless(X9,X8,tc_nat)
      | ~ c_lessequals(X10,X8,tc_nat)
      | ~ c_lessequals(X10,X9,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_708]) ).

fof(c_0_1316,plain,
    ! [X28,X29,X30,X31,X32] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add(X32)
      | c_lessequals(X31,c_HOL_Oplus__class_Oplus(X30,X28,X32),X32)
      | ~ c_lessequals(X29,X28,X32)
      | ~ c_lessequals(X31,c_HOL_Oplus__class_Oplus(X30,X29,X32),X32) ),
    inference(variable_rename,[status(thm)],[c_0_709]) ).

fof(c_0_1317,plain,
    ! [X8,X9,X10] :
      ( c_HOL_Oord__class_Oless(X9,X8,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Suc(X10),X9,tc_nat),c_HOL_Otimes__class_Otimes(c_Suc(X10),X8,tc_nat),tc_nat) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_710])])]) ).

fof(c_0_1318,plain,
    ! [X8,X9,X10] :
      ( c_lessequals(X9,X8,tc_nat)
      | ~ c_lessequals(c_HOL_Otimes__class_Otimes(c_Suc(X10),X9,tc_nat),c_HOL_Otimes__class_Otimes(c_Suc(X10),X8,tc_nat),tc_nat) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_711])])]) ).

fof(c_0_1319,plain,
    ! [X28,X29,X30,X31] :
      ( c_HOL_Oplus__class_Oplus(X28,c_HOL_Otimes__class_Otimes(X29,X31,tc_nat),tc_nat) != c_HOL_Oplus__class_Oplus(X28,c_HOL_Otimes__class_Otimes(X29,X30,tc_nat),tc_nat)
      | X31 = X30
      | X29 = c_HOL_Ozero__class_Ozero(tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_712]) ).

fof(c_0_1320,plain,
    ! [X15,X16,X17] :
      ( c_lessequals(X17,c_HOL_Ominus__class_Ominus(X16,X15,tc_nat),tc_nat)
      | ~ c_lessequals(c_HOL_Oplus__class_Oplus(X17,X15,tc_nat),X16,tc_nat)
      | ~ c_lessequals(X15,X16,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_713]) ).

fof(c_0_1321,plain,
    ! [X15,X16,X17] :
      ( c_lessequals(c_HOL_Oplus__class_Oplus(X17,X15,tc_nat),X16,tc_nat)
      | ~ c_lessequals(X17,c_HOL_Ominus__class_Ominus(X16,X15,tc_nat),tc_nat)
      | ~ c_lessequals(X15,X16,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_714]) ).

fof(c_0_1322,plain,
    ! [X21,X22,X23,X24] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X24)
      | c_lessequals(X23,X22,X24)
      | ~ c_lessequals(c_HOL_Oplus__class_Oplus(X23,X21,X24),c_HOL_Oplus__class_Oplus(X22,X21,X24),X24) ),
    inference(variable_rename,[status(thm)],[c_0_715]) ).

fof(c_0_1323,plain,
    ! [X21,X22,X23,X24] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X24)
      | c_lessequals(X23,X22,X24)
      | ~ c_lessequals(c_HOL_Oplus__class_Oplus(X21,X23,X24),c_HOL_Oplus__class_Oplus(X21,X22,X24),X24) ),
    inference(variable_rename,[status(thm)],[c_0_716]) ).

fof(c_0_1324,plain,
    ! [X21,X22,X23,X24] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X24)
      | c_HOL_Oord__class_Oless(X23,X22,X24)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X23,X21,X24),c_HOL_Oplus__class_Oplus(X22,X21,X24),X24) ),
    inference(variable_rename,[status(thm)],[c_0_717]) ).

fof(c_0_1325,plain,
    ! [X21,X22,X23,X24] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X24)
      | c_HOL_Oord__class_Oless(X23,X22,X24)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X21,X23,X24),c_HOL_Oplus__class_Oplus(X21,X22,X24),X24) ),
    inference(variable_rename,[status(thm)],[c_0_718]) ).

fof(c_0_1326,plain,
    ! [X8,X9,X10] :
      ( c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X9,X10,tc_nat),c_HOL_Ominus__class_Ominus(X8,X10,tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(X9,X8,tc_nat)
      | ~ c_lessequals(X10,X8,tc_nat)
      | ~ c_lessequals(X10,X9,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_719]) ).

fof(c_0_1327,plain,
    ! [X8,X9,X10] :
      ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X10,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X9,X10,tc_nat),c_HOL_Otimes__class_Otimes(X8,X10,tc_nat),tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_720]) ).

fof(c_0_1328,plain,
    ! [X8,X9,X10] :
      ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X10,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X10,X9,tc_nat),c_HOL_Otimes__class_Otimes(X10,X8,tc_nat),tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_721]) ).

fof(c_0_1329,plain,
    ! [X8,X9,X10] :
      ( c_lessequals(X9,X8,tc_nat)
      | ~ c_lessequals(c_HOL_Oplus__class_Oplus(X10,X9,tc_nat),c_HOL_Oplus__class_Oplus(X10,X8,tc_nat),tc_nat) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_722])])]) ).

fof(c_0_1330,plain,
    ! [X8,X9,X10] :
      ( c_HOL_Oord__class_Oless(X9,X8,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X10,X9,tc_nat),c_HOL_Otimes__class_Otimes(X10,X8,tc_nat),tc_nat) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_723])])]) ).

fof(c_0_1331,plain,
    ! [X8,X9,X10] :
      ( c_HOL_Oord__class_Oless(X9,X8,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X9,X10,tc_nat),c_HOL_Otimes__class_Otimes(X8,X10,tc_nat),tc_nat) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_724])])]) ).

fof(c_0_1332,plain,
    ! [X8,X9,X10] :
      ( c_HOL_Oord__class_Oless(X9,X8,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X10,X9,tc_nat),c_HOL_Oplus__class_Oplus(X10,X8,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_1333,plain,
    ! [X21,X22,X23,X24] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X24)
      | c_lessequals(c_HOL_Otimes__class_Otimes(X21,X23,X24),c_HOL_Otimes__class_Otimes(X21,X22,X24),X24)
      | ~ c_lessequals(X22,X23,X24)
      | ~ c_HOL_Oord__class_Oless(X21,c_HOL_Ozero__class_Ozero(X24),X24) ),
    inference(variable_rename,[status(thm)],[c_0_726]) ).

fof(c_0_1334,plain,
    ! [X21,X22,X23,X24] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X24)
      | c_lessequals(c_HOL_Otimes__class_Otimes(X21,X23,X24),c_HOL_Otimes__class_Otimes(X21,X22,X24),X24)
      | ~ c_lessequals(X23,X22,X24)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X24),X21,X24) ),
    inference(variable_rename,[status(thm)],[c_0_727]) ).

fof(c_0_1335,plain,
    ! [X21,X22,X23,X24] :
      ( ~ class_Ring__and__Field_Opordered__ring(X24)
      | c_lessequals(c_HOL_Otimes__class_Otimes(X23,X21,X24),c_HOL_Otimes__class_Otimes(X22,X21,X24),X24)
      | ~ c_lessequals(X21,c_HOL_Ozero__class_Ozero(X24),X24)
      | ~ c_lessequals(X22,X23,X24) ),
    inference(variable_rename,[status(thm)],[c_0_728]) ).

fof(c_0_1336,plain,
    ! [X21,X22,X23,X24] :
      ( ~ class_Ring__and__Field_Opordered__ring(X24)
      | c_lessequals(c_HOL_Otimes__class_Otimes(X21,X23,X24),c_HOL_Otimes__class_Otimes(X21,X22,X24),X24)
      | ~ c_lessequals(X21,c_HOL_Ozero__class_Ozero(X24),X24)
      | ~ c_lessequals(X22,X23,X24) ),
    inference(variable_rename,[status(thm)],[c_0_729]) ).

fof(c_0_1337,plain,
    ! [X21,X22,X23,X24] :
      ( ~ class_Ring__and__Field_Omult__mono(X24)
      | c_lessequals(c_HOL_Otimes__class_Otimes(X23,X21,X24),c_HOL_Otimes__class_Otimes(X22,X21,X24),X24)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X24),X21,X24)
      | ~ c_lessequals(X23,X22,X24) ),
    inference(variable_rename,[status(thm)],[c_0_730]) ).

fof(c_0_1338,plain,
    ! [X21,X22,X23,X24] :
      ( ~ class_Ring__and__Field_Omult__mono(X24)
      | c_lessequals(c_HOL_Otimes__class_Otimes(X21,X23,X24),c_HOL_Otimes__class_Otimes(X21,X22,X24),X24)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X24),X21,X24)
      | ~ c_lessequals(X23,X22,X24) ),
    inference(variable_rename,[status(thm)],[c_0_731]) ).

fof(c_0_1339,plain,
    ! [X21,X22,X23,X24] :
      ( ~ class_Ring__and__Field_Omult__mono1(X24)
      | c_lessequals(c_HOL_Otimes__class_Otimes(X21,X23,X24),c_HOL_Otimes__class_Otimes(X21,X22,X24),X24)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X24),X21,X24)
      | ~ c_lessequals(X23,X22,X24) ),
    inference(variable_rename,[status(thm)],[c_0_732]) ).

fof(c_0_1340,plain,
    ! [X21,X22,X23,X24] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X24)
      | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X21,X23,X24),c_HOL_Otimes__class_Otimes(X21,X22,X24),X24)
      | ~ c_HOL_Oord__class_Oless(X22,X23,X24)
      | ~ c_HOL_Oord__class_Oless(X21,c_HOL_Ozero__class_Ozero(X24),X24) ),
    inference(variable_rename,[status(thm)],[c_0_733]) ).

fof(c_0_1341,plain,
    ! [X21,X22,X23,X24] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X24)
      | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X21,X23,X24),c_HOL_Otimes__class_Otimes(X21,X22,X24),X24)
      | ~ c_HOL_Oord__class_Oless(X23,X22,X24)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X24),X21,X24) ),
    inference(variable_rename,[status(thm)],[c_0_734]) ).

fof(c_0_1342,plain,
    ! [X21,X22,X23,X24] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X24)
      | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X21,X23,X24),c_HOL_Otimes__class_Otimes(X21,X22,X24),X24)
      | ~ c_HOL_Oord__class_Oless(X21,c_HOL_Ozero__class_Ozero(X24),X24)
      | ~ c_HOL_Oord__class_Oless(X22,X23,X24) ),
    inference(variable_rename,[status(thm)],[c_0_735]) ).

fof(c_0_1343,plain,
    ! [X21,X22,X23,X24] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X24)
      | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X21,X23,X24),c_HOL_Otimes__class_Otimes(X21,X22,X24),X24)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X24),X21,X24)
      | ~ c_HOL_Oord__class_Oless(X23,X22,X24) ),
    inference(variable_rename,[status(thm)],[c_0_736]) ).

fof(c_0_1344,plain,
    ! [X21,X22,X23,X24] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X24)
      | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X21,X23,X24),c_HOL_Otimes__class_Otimes(X21,X22,X24),X24)
      | ~ c_HOL_Oord__class_Oless(X23,X22,X24)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X24),X21,X24) ),
    inference(variable_rename,[status(thm)],[c_0_737]) ).

fof(c_0_1345,plain,
    ! [X21,X22,X23,X24] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X24)
      | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X21,X23,X24),c_HOL_Otimes__class_Otimes(X21,X22,X24),X24)
      | ~ c_HOL_Oord__class_Oless(X22,X23,X24)
      | ~ c_HOL_Oord__class_Oless(X21,c_HOL_Ozero__class_Ozero(X24),X24) ),
    inference(variable_rename,[status(thm)],[c_0_738]) ).

fof(c_0_1346,plain,
    ! [X21,X22,X23,X24] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X24)
      | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X23,X21,X24),c_HOL_Otimes__class_Otimes(X22,X21,X24),X24)
      | ~ c_HOL_Oord__class_Oless(X21,c_HOL_Ozero__class_Ozero(X24),X24)
      | ~ c_HOL_Oord__class_Oless(X22,X23,X24) ),
    inference(variable_rename,[status(thm)],[c_0_739]) ).

fof(c_0_1347,plain,
    ! [X21,X22,X23,X24] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X24)
      | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X23,X21,X24),c_HOL_Otimes__class_Otimes(X22,X21,X24),X24)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X24),X21,X24)
      | ~ c_HOL_Oord__class_Oless(X23,X22,X24) ),
    inference(variable_rename,[status(thm)],[c_0_740]) ).

fof(c_0_1348,plain,
    ! [X21,X22,X23,X24] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X24)
      | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X23,X21,X24),c_HOL_Otimes__class_Otimes(X22,X21,X24),X24)
      | ~ c_HOL_Oord__class_Oless(X23,X22,X24)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X24),X21,X24) ),
    inference(variable_rename,[status(thm)],[c_0_741]) ).

fof(c_0_1349,plain,
    ! [X21,X22,X23,X24] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X24)
      | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X23,X21,X24),c_HOL_Otimes__class_Otimes(X22,X21,X24),X24)
      | ~ c_HOL_Oord__class_Oless(X22,X23,X24)
      | ~ c_HOL_Oord__class_Oless(X21,c_HOL_Ozero__class_Ozero(X24),X24) ),
    inference(variable_rename,[status(thm)],[c_0_742]) ).

fof(c_0_1350,plain,
    ! [X21,X22,X23,X24] :
      ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X24)
      | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X21,X23,X24),c_HOL_Otimes__class_Otimes(X21,X22,X24),X24)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X24),X21,X24)
      | ~ c_HOL_Oord__class_Oless(X23,X22,X24) ),
    inference(variable_rename,[status(thm)],[c_0_743]) ).

fof(c_0_1351,plain,
    ! [X19,X20,X21] :
      ( ~ class_Ring__and__Field_Oordered__idom(X21)
      | c_lessequals(c_HOL_Otimes__class_Otimes(X20,X19,X21),X20,X21)
      | ~ c_lessequals(X19,c_HOL_Oone__class_Oone(X21),X21)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X21),X19,X21)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X21),X20,X21) ),
    inference(variable_rename,[status(thm)],[c_0_744]) ).

fof(c_0_1352,plain,
    ! [X19,X20,X21] :
      ( ~ class_Ring__and__Field_Oordered__idom(X21)
      | c_lessequals(c_HOL_Otimes__class_Otimes(X19,X20,X21),X20,X21)
      | ~ c_lessequals(X19,c_HOL_Oone__class_Oone(X21),X21)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X21),X19,X21)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X21),X20,X21) ),
    inference(variable_rename,[status(thm)],[c_0_745]) ).

fof(c_0_1353,plain,
    ! [X8,X9,X10] :
      ( c_lessequals(X9,c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X8,X9,tc_nat),X10,tc_nat),tc_nat)
      | ~ c_lessequals(X10,X8,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_746]) ).

fof(c_0_1354,plain,
    ! [X28,X29,X30,X31,X32] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X32)
      | c_lessequals(c_HOL_Oplus__class_Oplus(X31,X29,X32),c_HOL_Oplus__class_Oplus(X30,X28,X32),X32)
      | ~ c_lessequals(X29,X28,X32)
      | ~ c_lessequals(X31,X30,X32) ),
    inference(variable_rename,[status(thm)],[c_0_747]) ).

fof(c_0_1355,plain,
    ! [X28,X29,X30,X31,X32] :
      ( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X32)
      | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X31,X29,X32),c_HOL_Oplus__class_Oplus(X30,X28,X32),X32)
      | ~ c_HOL_Oord__class_Oless(X29,X28,X32)
      | ~ c_HOL_Oord__class_Oless(X31,X30,X32) ),
    inference(variable_rename,[status(thm)],[c_0_748]) ).

fof(c_0_1356,plain,
    ! [X28,X29,X30,X31,X32] :
      ( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X32)
      | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X31,X29,X32),c_HOL_Oplus__class_Oplus(X30,X28,X32),X32)
      | ~ c_HOL_Oord__class_Oless(X29,X28,X32)
      | ~ c_lessequals(X31,X30,X32) ),
    inference(variable_rename,[status(thm)],[c_0_749]) ).

fof(c_0_1357,plain,
    ! [X28,X29,X30,X31,X32] :
      ( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X32)
      | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X31,X29,X32),c_HOL_Oplus__class_Oplus(X30,X28,X32),X32)
      | ~ c_lessequals(X29,X28,X32)
      | ~ c_HOL_Oord__class_Oless(X31,X30,X32) ),
    inference(variable_rename,[status(thm)],[c_0_750]) ).

fof(c_0_1358,plain,
    ! [X19,X20,X21] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X21)
      | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X20,X20,X21),c_HOL_Otimes__class_Otimes(X19,X19,X21),X21) != c_HOL_Ozero__class_Ozero(X21)
      | X19 = c_HOL_Ozero__class_Ozero(X21) ),
    inference(variable_rename,[status(thm)],[c_0_751]) ).

fof(c_0_1359,plain,
    ! [X19,X20,X21] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X21)
      | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X20,X20,X21),c_HOL_Otimes__class_Otimes(X19,X19,X21),X21) != c_HOL_Ozero__class_Ozero(X21)
      | X20 = c_HOL_Ozero__class_Ozero(X21) ),
    inference(variable_rename,[status(thm)],[c_0_752]) ).

fof(c_0_1360,plain,
    ! [X20,X21,X22,X23] :
      ( ~ class_Orderings_Olinorder(X23)
      | c_Orderings_Oord__class_Omin(c_Orderings_Oord__class_Omax(X21,X20,X23),X22,X23) = c_Orderings_Oord__class_Omax(c_Orderings_Oord__class_Omin(X21,X22,X23),c_Orderings_Oord__class_Omin(X20,X22,X23),X23) ),
    inference(variable_rename,[status(thm)],[c_0_753]) ).

fof(c_0_1361,plain,
    ! [X20,X21,X22,X23] :
      ( ~ class_Orderings_Olinorder(X23)
      | c_Orderings_Oord__class_Omin(X22,c_Orderings_Oord__class_Omax(X21,X20,X23),X23) = c_Orderings_Oord__class_Omax(c_Orderings_Oord__class_Omin(X22,X21,X23),c_Orderings_Oord__class_Omin(X22,X20,X23),X23) ),
    inference(variable_rename,[status(thm)],[c_0_754]) ).

fof(c_0_1362,plain,
    ! [X20,X21,X22,X23] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add(X23)
      | c_HOL_Ominus__class_Ominus(c_Orderings_Oord__class_Omin(X22,X21,X23),X20,X23) = c_Orderings_Oord__class_Omin(c_HOL_Ominus__class_Ominus(X22,X20,X23),c_HOL_Ominus__class_Ominus(X21,X20,X23),X23) ),
    inference(variable_rename,[status(thm)],[c_0_755]) ).

fof(c_0_1363,plain,
    ! [X20,X21,X22,X23] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add(X23)
      | c_HOL_Ominus__class_Ominus(c_Orderings_Oord__class_Omax(X22,X21,X23),X20,X23) = c_Orderings_Oord__class_Omax(c_HOL_Ominus__class_Ominus(X22,X20,X23),c_HOL_Ominus__class_Ominus(X21,X20,X23),X23) ),
    inference(variable_rename,[status(thm)],[c_0_756]) ).

fof(c_0_1364,plain,
    ! [X20,X21,X22,X23] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X23)
      | c_HOL_Oplus__class_Oplus(c_Orderings_Oord__class_Omin(X22,X21,X23),X20,X23) = c_Orderings_Oord__class_Omin(c_HOL_Oplus__class_Oplus(X22,X20,X23),c_HOL_Oplus__class_Oplus(X21,X20,X23),X23) ),
    inference(variable_rename,[status(thm)],[c_0_757]) ).

fof(c_0_1365,plain,
    ! [X20,X21,X22,X23] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X23)
      | c_HOL_Oplus__class_Oplus(c_Orderings_Oord__class_Omax(X22,X21,X23),X20,X23) = c_Orderings_Oord__class_Omax(c_HOL_Oplus__class_Oplus(X22,X20,X23),c_HOL_Oplus__class_Oplus(X21,X20,X23),X23) ),
    inference(variable_rename,[status(thm)],[c_0_758]) ).

fof(c_0_1366,plain,
    ! [X21,X22,X23,X24] :
      ( ~ class_Divides_Osemiring__div(X24)
      | c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X23,c_HOL_Otimes__class_Otimes(X21,X22,X24),X24),X22,X24) = c_Divides_Odiv__class_Omod(X23,X22,X24) ),
    inference(variable_rename,[status(thm)],[c_0_759]) ).

fof(c_0_1367,plain,
    ! [X21,X22,X23,X24] :
      ( ~ class_Divides_Osemiring__div(X24)
      | c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X23,c_HOL_Otimes__class_Otimes(X22,X21,X24),X24),X22,X24) = c_Divides_Odiv__class_Omod(X23,X22,X24) ),
    inference(variable_rename,[status(thm)],[c_0_760]) ).

fof(c_0_1368,plain,
    ! [X19,X20,X21,X22] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X22)
      | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X21,X19,X22),c_HOL_Otimes__class_Otimes(X20,X19,X22),X22) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X21,X20,X22),X19,X22) ),
    inference(variable_rename,[status(thm)],[c_0_761]) ).

fof(c_0_1369,plain,
    ! [X20,X21,X22,X23] :
      ( ~ class_Orderings_Olinorder(X23)
      | c_Orderings_Oord__class_Omax(c_Orderings_Oord__class_Omin(X21,X20,X23),X22,X23) = c_Orderings_Oord__class_Omin(c_Orderings_Oord__class_Omax(X21,X22,X23),c_Orderings_Oord__class_Omax(X20,X22,X23),X23) ),
    inference(variable_rename,[status(thm)],[c_0_762]) ).

fof(c_0_1370,plain,
    ! [X20,X21,X22,X23] :
      ( ~ class_Orderings_Olinorder(X23)
      | c_Orderings_Oord__class_Omax(X22,c_Orderings_Oord__class_Omin(X21,X20,X23),X23) = c_Orderings_Oord__class_Omin(c_Orderings_Oord__class_Omax(X22,X21,X23),c_Orderings_Oord__class_Omax(X22,X20,X23),X23) ),
    inference(variable_rename,[status(thm)],[c_0_763]) ).

fof(c_0_1371,plain,
    ! [X21,X22,X23,X24] :
      ( ~ class_Divides_Osemiring__div(X24)
      | c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X23,X21,X24),c_HOL_Otimes__class_Otimes(X22,X21,X24),X24) = c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(X23,X22,X24),X21,X24) ),
    inference(variable_rename,[status(thm)],[c_0_764]) ).

fof(c_0_1372,plain,
    ! [X21,X22,X23,X24] :
      ( ~ class_Divides_Osemiring__div(X24)
      | c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X21,X23,X24),c_HOL_Otimes__class_Otimes(X21,X22,X24),X24) = c_HOL_Otimes__class_Otimes(X21,c_Divides_Odiv__class_Omod(X23,X22,X24),X24) ),
    inference(variable_rename,[status(thm)],[c_0_765]) ).

fof(c_0_1373,plain,
    ! [X21,X22,X23,X24] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X24)
      | c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X23,X22,X24),X21,X24) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X23,X21,X24),c_HOL_Otimes__class_Otimes(X22,X21,X24),X24) ),
    inference(variable_rename,[status(thm)],[c_0_766]) ).

fof(c_0_1374,plain,
    ! [X21,X22,X23,X24] :
      ( ~ class_Ring__and__Field_Ocomm__semiring(X24)
      | c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X23,X22,X24),X21,X24) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X23,X21,X24),c_HOL_Otimes__class_Otimes(X22,X21,X24),X24) ),
    inference(variable_rename,[status(thm)],[c_0_767]) ).

fof(c_0_1375,plain,
    ! [X20,X21,X22,X23] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X23)
      | c_HOL_Otimes__class_Otimes(X22,c_HOL_Oplus__class_Oplus(X21,X20,X23),X23) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X22,X21,X23),c_HOL_Otimes__class_Otimes(X22,X20,X23),X23) ),
    inference(variable_rename,[status(thm)],[c_0_768]) ).

fof(c_0_1376,plain,
    ! [X8,X9,X10] :
      ( c_lessequals(c_HOL_Otimes__class_Otimes(X10,X9,tc_nat),c_HOL_Otimes__class_Otimes(X10,X8,tc_nat),tc_nat)
      | ~ c_lessequals(X9,X8,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X10,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_769]) ).

fof(c_0_1377,plain,
    ! [X8,X9,X10] :
      ( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X9,X10,tc_nat),c_HOL_Otimes__class_Otimes(X8,X10,tc_nat),tc_nat)
      | ~ c_HOL_Oord__class_Oless(X9,X8,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X10,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_770]) ).

fof(c_0_1378,plain,
    ! [X8,X9,X10] :
      ( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X10,X9,tc_nat),c_HOL_Otimes__class_Otimes(X10,X8,tc_nat),tc_nat)
      | ~ c_HOL_Oord__class_Oless(X9,X8,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X10,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_771]) ).

fof(c_0_1379,plain,
    ! [X15,X16,X17] :
      ( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X15,X17,tc_nat),c_HOL_Otimes__class_Otimes(X15,X16,tc_nat),tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X15,tc_nat)
      | ~ c_HOL_Oord__class_Oless(X17,X16,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_772]) ).

fof(c_0_1380,plain,
    ! [X15,X16,X17] :
      ( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X17,X15,tc_nat),c_HOL_Otimes__class_Otimes(X16,X15,tc_nat),tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X15,tc_nat)
      | ~ c_HOL_Oord__class_Oless(X17,X16,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_773]) ).

fof(c_0_1381,plain,
    ! [X8,X9,X10] :
      ( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X10,X9,tc_nat),c_HOL_Otimes__class_Otimes(X10,X8,tc_nat),tc_nat)
      | ~ c_HOL_Oord__class_Oless(X9,X8,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X10,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_774]) ).

fof(c_0_1382,plain,
    ! [X3,X4] :
      ( c_HOL_Otimes__class_Otimes(X4,X3,tc_nat) = c_HOL_Oplus__class_Oplus(X3,c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X4,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X3,tc_nat),tc_nat)
      | X4 = c_HOL_Ozero__class_Ozero(tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_775]) ).

fof(c_0_1383,plain,
    ! [X29,X30,X31] :
      ( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X31,X29,tc_nat),c_HOL_Ominus__class_Ominus(X31,X30,tc_nat),tc_nat)
      | ~ c_HOL_Oord__class_Oless(X30,X31,tc_nat)
      | ~ c_HOL_Oord__class_Oless(X30,X29,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_776]) ).

fof(c_0_1384,plain,
    ! [X29,X30,X31,X32] :
      ( c_lessequals(c_HOL_Oplus__class_Oplus(X32,X30,tc_nat),c_HOL_Oplus__class_Oplus(X31,X29,tc_nat),tc_nat)
      | ~ c_lessequals(X30,X29,tc_nat)
      | ~ c_lessequals(X32,X31,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_777]) ).

fof(c_0_1385,plain,
    ! [X21,X22,X23] :
      ( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X23,X21,tc_nat),c_HOL_Ominus__class_Ominus(X22,X21,tc_nat),tc_nat)
      | ~ c_lessequals(X21,X23,tc_nat)
      | ~ c_HOL_Oord__class_Oless(X23,X22,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_778]) ).

fof(c_0_1386,plain,
    ! [X29,X30,X31,X32] :
      ( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X32,X30,tc_nat),c_HOL_Oplus__class_Oplus(X31,X29,tc_nat),tc_nat)
      | ~ c_HOL_Oord__class_Oless(X30,X29,tc_nat)
      | ~ c_HOL_Oord__class_Oless(X32,X31,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_779]) ).

fof(c_0_1387,plain,
    ! [X29,X30,X31,X32] :
      ( c_lessequals(c_HOL_Otimes__class_Otimes(X32,X30,tc_nat),c_HOL_Otimes__class_Otimes(X31,X29,tc_nat),tc_nat)
      | ~ c_lessequals(X30,X29,tc_nat)
      | ~ c_lessequals(X32,X31,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_780]) ).

fof(c_0_1388,plain,
    ! [X19,X20,X21] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X21)
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X21),X19,X21)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X21),X20,X21)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X21),c_HOL_Otimes__class_Otimes(X19,X20,X21),X21) ),
    inference(variable_rename,[status(thm)],[c_0_781]) ).

fof(c_0_1389,plain,
    ! [X19,X20,X21] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X21)
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X21),X19,X21)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X21),X20,X21)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X21),c_HOL_Otimes__class_Otimes(X20,X19,X21),X21) ),
    inference(variable_rename,[status(thm)],[c_0_782]) ).

fof(c_0_1390,plain,
    ! [X9,X10] :
      ( ~ c_lessequals(X10,c_HOL_Oplus__class_Oplus(X9,X10,tc_nat),tc_nat)
      | c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X9,X10,tc_nat),X10,tc_nat) = X9 ),
    inference(variable_rename,[status(thm)],[c_0_783]) ).

fof(c_0_1391,plain,
    ! [X15,X16,X17] :
      ( c_lessequals(X16,c_HOL_Oplus__class_Oplus(X17,X15,tc_nat),tc_nat)
      | ~ c_lessequals(c_HOL_Ominus__class_Ominus(X16,X15,tc_nat),X17,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_784]) ).

fof(c_0_1392,plain,
    ! [X15,X16,X17] :
      ( c_lessequals(c_HOL_Ominus__class_Ominus(X16,X15,tc_nat),X17,tc_nat)
      | ~ c_lessequals(X16,c_HOL_Oplus__class_Oplus(X17,X15,tc_nat),tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_785]) ).

fof(c_0_1393,plain,
    ! [X15,X16,X17] :
      ( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X17,X15,tc_nat),X16,tc_nat)
      | ~ c_HOL_Oord__class_Oless(X17,c_HOL_Ominus__class_Ominus(X16,X15,tc_nat),tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_786]) ).

fof(c_0_1394,plain,
    ! [X15,X16,X17] :
      ( c_HOL_Oord__class_Oless(X17,c_HOL_Ominus__class_Ominus(X16,X15,tc_nat),tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X17,X15,tc_nat),X16,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_787]) ).

fof(c_0_1395,plain,
    ! [X20,X21,X22,X23,X24] :
      ( ~ class_OrderedGroup_Oab__group__add(X24)
      | c_HOL_Oplus__class_Oplus(X22,c_HOL_Oplus__class_Oplus(X21,X20,X24),X24) != c_HOL_Oplus__class_Oplus(X21,X23,X24)
      | c_HOL_Oplus__class_Oplus(X22,X20,X24) = X23 ),
    inference(variable_rename,[status(thm)],[c_0_788]) ).

fof(c_0_1396,plain,
    ! [X15,X16,X17] :
      ( c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X17,X16,tc_nat),X15,tc_nat) = c_HOL_Oplus__class_Oplus(X17,c_HOL_Ominus__class_Ominus(X16,X15,tc_nat),tc_nat)
      | ~ c_lessequals(X15,X16,tc_nat) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_789])])]) ).

fof(c_0_1397,plain,
    ! [X15,X16,X17] :
      ( c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X16,X17,tc_nat),X15,tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X16,X15,tc_nat),X17,tc_nat)
      | ~ c_lessequals(X15,X16,tc_nat) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_790])])]) ).

fof(c_0_1398,plain,
    ! [X15,X16,X17] :
      ( c_HOL_Ominus__class_Ominus(X17,c_HOL_Ominus__class_Ominus(X16,X15,tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X17,X15,tc_nat),X16,tc_nat)
      | ~ c_lessequals(X15,X16,tc_nat) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_791])])]) ).

fof(c_0_1399,plain,
    ! [X15,X16,X17] :
      ( c_HOL_Oplus__class_Oplus(X17,c_HOL_Ominus__class_Ominus(X16,X15,tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X17,X16,tc_nat),X15,tc_nat)
      | ~ c_lessequals(X15,X16,tc_nat) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_792])])]) ).

fof(c_0_1400,plain,
    ! [X15,X16,X17] :
      ( c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X16,X15,tc_nat),X17,tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X16,X17,tc_nat),X15,tc_nat)
      | ~ c_lessequals(X15,X16,tc_nat) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_793])])]) ).

fof(c_0_1401,plain,
    ! [X19,X20,X21] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X21)
      | c_lessequals(c_HOL_Ozero__class_Ozero(X21),X19,X21)
      | c_lessequals(X19,c_HOL_Ozero__class_Ozero(X21),X21)
      | ~ c_lessequals(c_HOL_Otimes__class_Otimes(X20,X19,X21),c_HOL_Ozero__class_Ozero(X21),X21) ),
    inference(variable_rename,[status(thm)],[c_0_794]) ).

fof(c_0_1402,plain,
    ! [X19,X20,X21] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X21)
      | c_lessequals(X20,c_HOL_Ozero__class_Ozero(X21),X21)
      | c_lessequals(X19,c_HOL_Ozero__class_Ozero(X21),X21)
      | ~ c_lessequals(c_HOL_Otimes__class_Otimes(X20,X19,X21),c_HOL_Ozero__class_Ozero(X21),X21) ),
    inference(variable_rename,[status(thm)],[c_0_795]) ).

fof(c_0_1403,plain,
    ! [X19,X20,X21] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X21)
      | c_lessequals(c_HOL_Ozero__class_Ozero(X21),X19,X21)
      | c_lessequals(c_HOL_Ozero__class_Ozero(X21),X20,X21)
      | ~ c_lessequals(c_HOL_Otimes__class_Otimes(X20,X19,X21),c_HOL_Ozero__class_Ozero(X21),X21) ),
    inference(variable_rename,[status(thm)],[c_0_796]) ).

fof(c_0_1404,plain,
    ! [X19,X20,X21] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X21)
      | c_lessequals(X20,c_HOL_Ozero__class_Ozero(X21),X21)
      | c_lessequals(c_HOL_Ozero__class_Ozero(X21),X20,X21)
      | ~ c_lessequals(c_HOL_Otimes__class_Otimes(X20,X19,X21),c_HOL_Ozero__class_Ozero(X21),X21) ),
    inference(variable_rename,[status(thm)],[c_0_797]) ).

fof(c_0_1405,plain,
    ! [X19,X20,X21] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X21)
      | c_lessequals(X20,c_HOL_Ozero__class_Ozero(X21),X21)
      | c_lessequals(c_HOL_Ozero__class_Ozero(X21),X20,X21)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X21),c_HOL_Otimes__class_Otimes(X20,X19,X21),X21) ),
    inference(variable_rename,[status(thm)],[c_0_798]) ).

fof(c_0_1406,plain,
    ! [X19,X20,X21] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X21)
      | c_lessequals(X19,c_HOL_Ozero__class_Ozero(X21),X21)
      | c_lessequals(c_HOL_Ozero__class_Ozero(X21),X20,X21)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X21),c_HOL_Otimes__class_Otimes(X20,X19,X21),X21) ),
    inference(variable_rename,[status(thm)],[c_0_799]) ).

fof(c_0_1407,plain,
    ! [X19,X20,X21] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X21)
      | c_lessequals(X20,c_HOL_Ozero__class_Ozero(X21),X21)
      | c_lessequals(c_HOL_Ozero__class_Ozero(X21),X19,X21)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X21),c_HOL_Otimes__class_Otimes(X20,X19,X21),X21) ),
    inference(variable_rename,[status(thm)],[c_0_800]) ).

fof(c_0_1408,plain,
    ! [X19,X20,X21] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X21)
      | c_lessequals(X19,c_HOL_Ozero__class_Ozero(X21),X21)
      | c_lessequals(c_HOL_Ozero__class_Ozero(X21),X19,X21)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X21),c_HOL_Otimes__class_Otimes(X20,X19,X21),X21) ),
    inference(variable_rename,[status(thm)],[c_0_801]) ).

fof(c_0_1409,plain,
    ! [X3,X4] :
      ( c_HOL_Oplus__class_Oplus(X4,X3,tc_nat) = c_Suc(c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X4,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X3,tc_nat))
      | X4 = c_HOL_Ozero__class_Ozero(tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_802]) ).

fof(c_0_1410,plain,
    ! [X3,X4] :
      ( c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Otimes__class_Otimes(X4,X3,tc_nat),tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X4,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X3,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_803]) ).

fof(c_0_1411,plain,
    ! [X3,X4] :
      ( c_lessequals(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Otimes__class_Otimes(X4,X3,tc_nat),tc_nat)
      | ~ c_lessequals(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X3,tc_nat)
      | ~ c_lessequals(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X4,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_804]) ).

fof(c_0_1412,plain,
    ! [X20,X21,X22,X23] :
      ( ~ class_Orderings_Olinorder(X23)
      | c_lessequals(X20,X21,X23)
      | c_lessequals(X20,X22,X23)
      | ~ c_lessequals(X20,c_Orderings_Oord__class_Omax(X22,X21,X23),X23) ),
    inference(variable_rename,[status(thm)],[c_0_805]) ).

fof(c_0_1413,plain,
    ! [X20,X21,X22,X23] :
      ( ~ class_Orderings_Olinorder(X23)
      | c_lessequals(X21,X20,X23)
      | c_lessequals(X22,X20,X23)
      | ~ c_lessequals(c_Orderings_Oord__class_Omin(X22,X21,X23),X20,X23) ),
    inference(variable_rename,[status(thm)],[c_0_806]) ).

fof(c_0_1414,plain,
    ! [X20,X21,X22,X23] :
      ( ~ class_Orderings_Olinorder(X23)
      | c_HOL_Oord__class_Oless(X20,X21,X23)
      | c_HOL_Oord__class_Oless(X20,X22,X23)
      | ~ c_HOL_Oord__class_Oless(X20,c_Orderings_Oord__class_Omax(X22,X21,X23),X23) ),
    inference(variable_rename,[status(thm)],[c_0_807]) ).

fof(c_0_1415,plain,
    ! [X20,X21,X22,X23] :
      ( ~ class_Orderings_Olinorder(X23)
      | c_HOL_Oord__class_Oless(X21,X20,X23)
      | c_HOL_Oord__class_Oless(X22,X20,X23)
      | ~ c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omin(X22,X21,X23),X20,X23) ),
    inference(variable_rename,[status(thm)],[c_0_808]) ).

fof(c_0_1416,plain,
    ! [X8,X9,X10] :
      ( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Suc(X10),X9,tc_nat),c_HOL_Otimes__class_Otimes(c_Suc(X10),X8,tc_nat),tc_nat)
      | ~ c_HOL_Oord__class_Oless(X9,X8,tc_nat) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_809])])]) ).

fof(c_0_1417,plain,
    ! [X8,X9,X10] :
      ( c_lessequals(c_HOL_Otimes__class_Otimes(c_Suc(X10),X9,tc_nat),c_HOL_Otimes__class_Otimes(c_Suc(X10),X8,tc_nat),tc_nat)
      | ~ c_lessequals(X9,X8,tc_nat) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_810])])]) ).

fof(c_0_1418,plain,
    ! [X19,X20,X21] :
      ( ~ class_OrderedGroup_Opordered__comm__monoid__add(X21)
      | c_lessequals(c_HOL_Ozero__class_Ozero(X21),c_HOL_Oplus__class_Oplus(X20,X19,X21),X21)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X21),X19,X21)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X21),X20,X21) ),
    inference(variable_rename,[status(thm)],[c_0_811]) ).

fof(c_0_1419,plain,
    ! [X19,X20,X21] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X21)
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X21),c_HOL_Otimes__class_Otimes(X20,X19,X21),X21)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X21),X19,X21)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X21),X20,X21) ),
    inference(variable_rename,[status(thm)],[c_0_812]) ).

fof(c_0_1420,plain,
    ! [X19,X20,X21] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X21)
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X21),c_HOL_Otimes__class_Otimes(X20,X19,X21),X21)
      | ~ c_HOL_Oord__class_Oless(X19,c_HOL_Ozero__class_Ozero(X21),X21)
      | ~ c_HOL_Oord__class_Oless(X20,c_HOL_Ozero__class_Ozero(X21),X21) ),
    inference(variable_rename,[status(thm)],[c_0_813]) ).

fof(c_0_1421,plain,
    ! [X19,X20,X21] :
      ( ~ class_OrderedGroup_Opordered__comm__monoid__add(X21)
      | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X20,X19,X21),c_HOL_Ozero__class_Ozero(X21),X21)
      | ~ c_HOL_Oord__class_Oless(X19,c_HOL_Ozero__class_Ozero(X21),X21)
      | ~ c_lessequals(X20,c_HOL_Ozero__class_Ozero(X21),X21) ),
    inference(variable_rename,[status(thm)],[c_0_814]) ).

fof(c_0_1422,plain,
    ! [X19,X20,X21] :
      ( ~ class_OrderedGroup_Opordered__comm__monoid__add(X21)
      | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X20,X19,X21),c_HOL_Ozero__class_Ozero(X21),X21)
      | ~ c_lessequals(X19,c_HOL_Ozero__class_Ozero(X21),X21)
      | ~ c_HOL_Oord__class_Oless(X20,c_HOL_Ozero__class_Ozero(X21),X21) ),
    inference(variable_rename,[status(thm)],[c_0_815]) ).

fof(c_0_1423,plain,
    ! [X19,X20,X21] :
      ( ~ class_OrderedGroup_Opordered__comm__monoid__add(X21)
      | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X20,X19,X21),c_HOL_Ozero__class_Ozero(X21),X21)
      | ~ c_HOL_Oord__class_Oless(X19,c_HOL_Ozero__class_Ozero(X21),X21)
      | ~ c_HOL_Oord__class_Oless(X20,c_HOL_Ozero__class_Ozero(X21),X21) ),
    inference(variable_rename,[status(thm)],[c_0_816]) ).

fof(c_0_1424,plain,
    ! [X19,X20,X21] :
      ( ~ class_OrderedGroup_Opordered__comm__monoid__add(X21)
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X21),c_HOL_Oplus__class_Oplus(X20,X19,X21),X21)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X21),X19,X21)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X21),X20,X21) ),
    inference(variable_rename,[status(thm)],[c_0_817]) ).

fof(c_0_1425,plain,
    ! [X19,X20,X21] :
      ( ~ class_OrderedGroup_Opordered__comm__monoid__add(X21)
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X21),c_HOL_Oplus__class_Oplus(X20,X19,X21),X21)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X21),X19,X21)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X21),X20,X21) ),
    inference(variable_rename,[status(thm)],[c_0_818]) ).

fof(c_0_1426,plain,
    ! [X19,X20,X21] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X21)
      | c_lessequals(c_HOL_Otimes__class_Otimes(X20,X19,X21),c_HOL_Ozero__class_Ozero(X21),X21)
      | ~ c_lessequals(X19,c_HOL_Ozero__class_Ozero(X21),X21)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X21),X20,X21) ),
    inference(variable_rename,[status(thm)],[c_0_819]) ).

fof(c_0_1427,plain,
    ! [X19,X20,X21] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X21)
      | c_lessequals(c_HOL_Otimes__class_Otimes(X20,X19,X21),c_HOL_Ozero__class_Ozero(X21),X21)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X21),X19,X21)
      | ~ c_lessequals(X20,c_HOL_Ozero__class_Ozero(X21),X21) ),
    inference(variable_rename,[status(thm)],[c_0_820]) ).

fof(c_0_1428,plain,
    ! [X19,X20,X21] :
      ( ~ class_Ring__and__Field_Opordered__cancel__semiring(X21)
      | c_lessequals(c_HOL_Otimes__class_Otimes(X20,X19,X21),c_HOL_Ozero__class_Ozero(X21),X21)
      | ~ c_lessequals(X19,c_HOL_Ozero__class_Ozero(X21),X21)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X21),X20,X21) ),
    inference(variable_rename,[status(thm)],[c_0_821]) ).

fof(c_0_1429,plain,
    ! [X19,X20,X21] :
      ( ~ class_Ring__and__Field_Opordered__cancel__semiring(X21)
      | c_lessequals(c_HOL_Otimes__class_Otimes(X20,X19,X21),c_HOL_Ozero__class_Ozero(X21),X21)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X21),X19,X21)
      | ~ c_lessequals(X20,c_HOL_Ozero__class_Ozero(X21),X21) ),
    inference(variable_rename,[status(thm)],[c_0_822]) ).

fof(c_0_1430,plain,
    ! [X19,X20,X21] :
      ( ~ class_Ring__and__Field_Opordered__cancel__semiring(X21)
      | c_lessequals(c_HOL_Otimes__class_Otimes(X20,X19,X21),c_HOL_Ozero__class_Ozero(X21),X21)
      | ~ c_lessequals(X19,c_HOL_Ozero__class_Ozero(X21),X21)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X21),X20,X21) ),
    inference(variable_rename,[status(thm)],[c_0_823]) ).

fof(c_0_1431,plain,
    ! [X19,X20,X21] :
      ( ~ class_Ring__and__Field_Opordered__cancel__semiring(X21)
      | c_lessequals(c_HOL_Otimes__class_Otimes(X20,X19,X21),c_HOL_Ozero__class_Ozero(X21),X21)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X21),X19,X21)
      | ~ c_lessequals(X20,c_HOL_Ozero__class_Ozero(X21),X21) ),
    inference(variable_rename,[status(thm)],[c_0_824]) ).

fof(c_0_1432,plain,
    ! [X19,X20,X21] :
      ( ~ class_Ring__and__Field_Opordered__cancel__semiring(X21)
      | c_lessequals(c_HOL_Otimes__class_Otimes(X19,X20,X21),c_HOL_Ozero__class_Ozero(X21),X21)
      | ~ c_lessequals(X19,c_HOL_Ozero__class_Ozero(X21),X21)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X21),X20,X21) ),
    inference(variable_rename,[status(thm)],[c_0_825]) ).

fof(c_0_1433,plain,
    ! [X19,X20,X21] :
      ( ~ class_OrderedGroup_Opordered__comm__monoid__add(X21)
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X21),c_HOL_Oplus__class_Oplus(X20,X19,X21),X21)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X21),X19,X21)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X21),X20,X21) ),
    inference(variable_rename,[status(thm)],[c_0_826]) ).

fof(c_0_1434,plain,
    ! [X19,X20,X21] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X21)
      | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X19,X20,X21),c_HOL_Ozero__class_Ozero(X21),X21)
      | ~ c_HOL_Oord__class_Oless(X19,c_HOL_Ozero__class_Ozero(X21),X21)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X21),X20,X21) ),
    inference(variable_rename,[status(thm)],[c_0_827]) ).

fof(c_0_1435,plain,
    ! [X19,X20,X21] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X21)
      | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X20,X19,X21),c_HOL_Ozero__class_Ozero(X21),X21)
      | ~ c_HOL_Oord__class_Oless(X19,c_HOL_Ozero__class_Ozero(X21),X21)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X21),X20,X21) ),
    inference(variable_rename,[status(thm)],[c_0_828]) ).

fof(c_0_1436,plain,
    ! [X19,X20,X21] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X21)
      | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X20,X19,X21),c_HOL_Ozero__class_Ozero(X21),X21)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X21),X19,X21)
      | ~ c_HOL_Oord__class_Oless(X20,c_HOL_Ozero__class_Ozero(X21),X21) ),
    inference(variable_rename,[status(thm)],[c_0_829]) ).

fof(c_0_1437,plain,
    ! [X19,X20,X21] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X21)
      | c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X21),c_HOL_Otimes__class_Otimes(X20,X19,X21),X21)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X21),X19,X21)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X21),X20,X21) ),
    inference(variable_rename,[status(thm)],[c_0_830]) ).

fof(c_0_1438,plain,
    ! [X19,X20,X21] :
      ( ~ class_OrderedGroup_Opordered__comm__monoid__add(X21)
      | c_lessequals(c_HOL_Oplus__class_Oplus(X20,X19,X21),c_HOL_Ozero__class_Ozero(X21),X21)
      | ~ c_lessequals(X19,c_HOL_Ozero__class_Ozero(X21),X21)
      | ~ c_lessequals(X20,c_HOL_Ozero__class_Ozero(X21),X21) ),
    inference(variable_rename,[status(thm)],[c_0_831]) ).

fof(c_0_1439,plain,
    ! [X19,X20,X21] :
      ( ~ class_Ring__and__Field_Opordered__cancel__semiring(X21)
      | c_lessequals(c_HOL_Ozero__class_Ozero(X21),c_HOL_Otimes__class_Otimes(X20,X19,X21),X21)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X21),X19,X21)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X21),X20,X21) ),
    inference(variable_rename,[status(thm)],[c_0_832]) ).

fof(c_0_1440,plain,
    ! [X19,X20,X21] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X21)
      | c_lessequals(c_HOL_Ozero__class_Ozero(X21),c_HOL_Otimes__class_Otimes(X20,X19,X21),X21)
      | ~ c_lessequals(X19,c_HOL_Ozero__class_Ozero(X21),X21)
      | ~ c_lessequals(X20,c_HOL_Ozero__class_Ozero(X21),X21) ),
    inference(variable_rename,[status(thm)],[c_0_833]) ).

fof(c_0_1441,plain,
    ! [X19,X20,X21] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X21)
      | c_lessequals(c_HOL_Ozero__class_Ozero(X21),c_HOL_Otimes__class_Otimes(X20,X19,X21),X21)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X21),X19,X21)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X21),X20,X21) ),
    inference(variable_rename,[status(thm)],[c_0_834]) ).

fof(c_0_1442,plain,
    ! [X19,X20,X21] :
      ( ~ class_Ring__and__Field_Opordered__ring(X21)
      | c_lessequals(c_HOL_Ozero__class_Ozero(X21),c_HOL_Otimes__class_Otimes(X20,X19,X21),X21)
      | ~ c_lessequals(X19,c_HOL_Ozero__class_Ozero(X21),X21)
      | ~ c_lessequals(X20,c_HOL_Ozero__class_Ozero(X21),X21) ),
    inference(variable_rename,[status(thm)],[c_0_835]) ).

fof(c_0_1443,plain,
    ! [X19,X20,X21] :
      ( ~ class_Ring__and__Field_Opordered__ring(X21)
      | c_lessequals(c_HOL_Ozero__class_Ozero(X21),c_HOL_Otimes__class_Otimes(X20,X19,X21),X21)
      | ~ c_lessequals(X19,c_HOL_Ozero__class_Ozero(X21),X21)
      | ~ c_lessequals(X20,c_HOL_Ozero__class_Ozero(X21),X21) ),
    inference(variable_rename,[status(thm)],[c_0_836]) ).

fof(c_0_1444,plain,
    ! [X19,X20,X21] :
      ( ~ class_Ring__and__Field_Opordered__ring(X21)
      | c_lessequals(c_HOL_Ozero__class_Ozero(X21),c_HOL_Otimes__class_Otimes(X20,X19,X21),X21)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X21),X19,X21)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X21),X20,X21) ),
    inference(variable_rename,[status(thm)],[c_0_837]) ).

fof(c_0_1445,plain,
    ! [X3,X4] :
      ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X3,tc_nat)
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oplus__class_Oplus(X4,X3,tc_nat),tc_nat) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_838])])]) ).

fof(c_0_1446,plain,
    ! [X3,X4] :
      ( c_HOL_Oord__class_Oless(X3,c_HOL_Otimes__class_Otimes(X4,X3,tc_nat),tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X4,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X3,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_839]) ).

fof(c_0_1447,plain,
    ! [X3,X4] :
      ( c_HOL_Oord__class_Oless(X3,c_HOL_Otimes__class_Otimes(X3,X4,tc_nat),tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X4,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X3,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_840]) ).

fof(c_0_1448,plain,
    ! [X21,X22,X23,X24] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X24)
      | c_lessequals(c_HOL_Oplus__class_Oplus(X23,X21,X24),c_HOL_Oplus__class_Oplus(X22,X21,X24),X24)
      | ~ c_lessequals(X23,X22,X24) ),
    inference(variable_rename,[status(thm)],[c_0_841]) ).

fof(c_0_1449,plain,
    ! [X21,X22,X23,X24] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X24)
      | c_lessequals(c_HOL_Oplus__class_Oplus(X21,X23,X24),c_HOL_Oplus__class_Oplus(X21,X22,X24),X24)
      | ~ c_lessequals(X23,X22,X24) ),
    inference(variable_rename,[status(thm)],[c_0_842]) ).

fof(c_0_1450,plain,
    ! [X21,X22,X23,X24] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X24)
      | c_lessequals(c_HOL_Oplus__class_Oplus(X23,X21,X24),c_HOL_Oplus__class_Oplus(X22,X21,X24),X24)
      | ~ c_lessequals(X23,X22,X24) ),
    inference(variable_rename,[status(thm)],[c_0_843]) ).

fof(c_0_1451,plain,
    ! [X21,X22,X23,X24] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X24)
      | c_lessequals(c_HOL_Oplus__class_Oplus(X21,X23,X24),c_HOL_Oplus__class_Oplus(X21,X22,X24),X24)
      | ~ c_lessequals(X23,X22,X24) ),
    inference(variable_rename,[status(thm)],[c_0_844]) ).

fof(c_0_1452,plain,
    ! [X21,X22,X23,X24] :
      ( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X24)
      | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X23,X21,X24),c_HOL_Oplus__class_Oplus(X22,X21,X24),X24)
      | ~ c_HOL_Oord__class_Oless(X23,X22,X24) ),
    inference(variable_rename,[status(thm)],[c_0_845]) ).

fof(c_0_1453,plain,
    ! [X21,X22,X23,X24] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X24)
      | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X23,X21,X24),c_HOL_Oplus__class_Oplus(X22,X21,X24),X24)
      | ~ c_HOL_Oord__class_Oless(X23,X22,X24) ),
    inference(variable_rename,[status(thm)],[c_0_846]) ).

fof(c_0_1454,plain,
    ! [X21,X22,X23,X24] :
      ( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X24)
      | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X21,X23,X24),c_HOL_Oplus__class_Oplus(X21,X22,X24),X24)
      | ~ c_HOL_Oord__class_Oless(X23,X22,X24) ),
    inference(variable_rename,[status(thm)],[c_0_847]) ).

fof(c_0_1455,plain,
    ! [X21,X22,X23,X24] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X24)
      | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X21,X23,X24),c_HOL_Oplus__class_Oplus(X21,X22,X24),X24)
      | ~ c_HOL_Oord__class_Oless(X23,X22,X24) ),
    inference(variable_rename,[status(thm)],[c_0_848]) ).

fof(c_0_1456,plain,
    ! [X21,X22,X23,X24] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X24)
      | ~ class_OrderedGroup_Ocomm__monoid__add(X24)
      | c_lessequals(X22,c_HOL_Oplus__class_Oplus(X23,X21,X24),X24)
      | ~ c_lessequals(X22,X21,X24)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X24),X23,X24) ),
    inference(variable_rename,[status(thm)],[c_0_849]) ).

fof(c_0_1457,plain,
    ! [X21,X22,X23,X24] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X24)
      | ~ class_OrderedGroup_Ocomm__monoid__add(X24)
      | c_lessequals(X22,c_HOL_Oplus__class_Oplus(X23,X21,X24),X24)
      | ~ c_lessequals(X22,X23,X24)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X24),X21,X24) ),
    inference(variable_rename,[status(thm)],[c_0_850]) ).

fof(c_0_1458,plain,
    ! [X21,X22,X23,X24] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X24)
      | ~ class_OrderedGroup_Ocomm__monoid__add(X24)
      | c_HOL_Oord__class_Oless(X22,c_HOL_Oplus__class_Oplus(X23,X21,X24),X24)
      | ~ c_lessequals(X22,X21,X24)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X24),X23,X24) ),
    inference(variable_rename,[status(thm)],[c_0_851]) ).

fof(c_0_1459,plain,
    ! [X21,X22,X23,X24] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X24)
      | ~ class_OrderedGroup_Ocomm__monoid__add(X24)
      | c_HOL_Oord__class_Oless(X22,c_HOL_Oplus__class_Oplus(X23,X21,X24),X24)
      | ~ c_HOL_Oord__class_Oless(X22,X21,X24)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X24),X23,X24) ),
    inference(variable_rename,[status(thm)],[c_0_852]) ).

fof(c_0_1460,plain,
    ! [X8,X9] :
      ( c_Divides_Odiv__class_Omod(c_Suc(c_HOL_Otimes__class_Otimes(X9,X8,tc_nat)),X9,tc_nat) = c_HOL_Oone__class_Oone(tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),X9,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_853]) ).

fof(c_0_1461,plain,
    ! [X21,X22,X23,X24] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X24)
      | c_HOL_Oord__class_Oless(X22,c_HOL_Oplus__class_Oplus(X23,X21,X24),X24)
      | ~ c_HOL_Oord__class_Oless(X22,X21,X24)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X24),X23,X24) ),
    inference(variable_rename,[status(thm)],[c_0_854]) ).

fof(c_0_1462,plain,
    ! [X29,X30,X31] :
      ( c_lessequals(c_HOL_Ominus__class_Ominus(X31,X29,tc_nat),c_HOL_Ominus__class_Ominus(X31,X30,tc_nat),tc_nat)
      | ~ c_lessequals(X30,X29,tc_nat) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_855])])]) ).

fof(c_0_1463,plain,
    ! [X29,X30,X31] :
      ( c_lessequals(c_HOL_Ominus__class_Ominus(X30,X31,tc_nat),c_HOL_Ominus__class_Ominus(X29,X31,tc_nat),tc_nat)
      | ~ c_lessequals(X30,X29,tc_nat) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_856])])]) ).

fof(c_0_1464,plain,
    ! [X15,X16,X17] :
      ( c_lessequals(c_HOL_Oplus__class_Oplus(X17,X15,tc_nat),c_HOL_Oplus__class_Oplus(X16,X15,tc_nat),tc_nat)
      | ~ c_lessequals(X17,X16,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_857]) ).

fof(c_0_1465,plain,
    ! [X8,X9,X10] :
      ( c_lessequals(c_HOL_Oplus__class_Oplus(X10,X9,tc_nat),c_HOL_Oplus__class_Oplus(X10,X8,tc_nat),tc_nat)
      | ~ c_lessequals(X9,X8,tc_nat) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_858])])]) ).

fof(c_0_1466,plain,
    ! [X15,X16,X17] :
      ( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X17,X15,tc_nat),c_HOL_Oplus__class_Oplus(X16,X15,tc_nat),tc_nat)
      | ~ c_HOL_Oord__class_Oless(X17,X16,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_859]) ).

fof(c_0_1467,plain,
    ! [X8,X9,X10] :
      ( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X10,X9,tc_nat),c_HOL_Oplus__class_Oplus(X10,X8,tc_nat),tc_nat)
      | ~ c_HOL_Oord__class_Oless(X9,X8,tc_nat) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_860])])]) ).

fof(c_0_1468,plain,
    ! [X15,X16,X17] :
      ( c_lessequals(c_HOL_Otimes__class_Otimes(X17,X15,tc_nat),c_HOL_Otimes__class_Otimes(X16,X15,tc_nat),tc_nat)
      | ~ c_lessequals(X17,X16,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_861]) ).

fof(c_0_1469,plain,
    ! [X15,X16,X17] :
      ( c_lessequals(c_HOL_Otimes__class_Otimes(X15,X17,tc_nat),c_HOL_Otimes__class_Otimes(X15,X16,tc_nat),tc_nat)
      | ~ c_lessequals(X17,X16,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_862]) ).

fof(c_0_1470,plain,
    ! [X8,X9,X10] :
      ( c_lessequals(c_HOL_Otimes__class_Otimes(X10,X9,tc_nat),c_HOL_Otimes__class_Otimes(X10,X8,tc_nat),tc_nat)
      | ~ c_lessequals(X9,X8,tc_nat) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_863])])]) ).

fof(c_0_1471,plain,
    ! [X8,X9,X10] :
      ( c_lessequals(c_HOL_Otimes__class_Otimes(X9,X10,tc_nat),c_HOL_Otimes__class_Otimes(X8,X10,tc_nat),tc_nat)
      | ~ c_lessequals(X9,X8,tc_nat) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_864])])]) ).

fof(c_0_1472,plain,
    ! [X9,X10,X11] :
      ( c_Lambda_Olift(c_Lambda_Olift(X9,X11),c_Suc(X10)) = c_Lambda_Olift(c_Lambda_Olift(X9,X10),X11)
      | ~ c_HOL_Oord__class_Oless(X11,c_HOL_Oplus__class_Oplus(X10,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_865]) ).

fof(c_0_1473,plain,
    ! [X19,X20,X21] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X21)
      | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X20,X19,X21),X19,X21) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X20,c_HOL_Oone__class_Oone(X21),X21),X19,X21) ),
    inference(variable_rename,[status(thm)],[c_0_866]) ).

fof(c_0_1474,plain,
    ! [X19,X20,X21] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X21)
      | c_HOL_Oplus__class_Oplus(X19,c_HOL_Otimes__class_Otimes(X20,X19,X21),X21) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X20,c_HOL_Oone__class_Oone(X21),X21),X19,X21) ),
    inference(variable_rename,[status(thm)],[c_0_867]) ).

fof(c_0_1475,plain,
    ! [X20,X21,X22,X23] :
      ( ~ class_Orderings_Olinorder(X23)
      | c_lessequals(c_Orderings_Oord__class_Omax(X22,X21,X23),X20,X23)
      | ~ c_lessequals(X21,X20,X23)
      | ~ c_lessequals(X22,X20,X23) ),
    inference(variable_rename,[status(thm)],[c_0_868]) ).

fof(c_0_1476,plain,
    ! [X20,X21,X22,X23] :
      ( ~ class_Orderings_Olinorder(X23)
      | c_lessequals(c_Orderings_Oord__class_Omax(X21,X20,X23),X22,X23)
      | ~ c_lessequals(X20,X22,X23)
      | ~ c_lessequals(X21,X22,X23) ),
    inference(variable_rename,[status(thm)],[c_0_869]) ).

fof(c_0_1477,plain,
    ! [X19,X20,X21,X22] :
      ( ~ class_Orderings_Olinorder(X22)
      | c_lessequals(c_Orderings_Oord__class_Omax(X21,X20,X22),X19,X22)
      | ~ c_lessequals(X20,X19,X22)
      | ~ c_lessequals(X21,X19,X22) ),
    inference(variable_rename,[status(thm)],[c_0_870]) ).

fof(c_0_1478,plain,
    ! [X19,X20,X21,X22] :
      ( ~ class_Orderings_Olinorder(X22)
      | c_lessequals(X19,c_Orderings_Oord__class_Omin(X21,X20,X22),X22)
      | ~ c_lessequals(X19,X20,X22)
      | ~ c_lessequals(X19,X21,X22) ),
    inference(variable_rename,[status(thm)],[c_0_871]) ).

fof(c_0_1479,plain,
    ! [X20,X21,X22,X23] :
      ( ~ class_Orderings_Olinorder(X23)
      | c_lessequals(X22,c_Orderings_Oord__class_Omin(X21,X20,X23),X23)
      | ~ c_lessequals(X22,X20,X23)
      | ~ c_lessequals(X22,X21,X23) ),
    inference(variable_rename,[status(thm)],[c_0_872]) ).

fof(c_0_1480,plain,
    ! [X20,X21,X22,X23] :
      ( ~ class_Orderings_Olinorder(X23)
      | c_lessequals(X22,c_Orderings_Oord__class_Omin(X21,X20,X23),X23)
      | ~ c_lessequals(X22,X20,X23)
      | ~ c_lessequals(X22,X21,X23) ),
    inference(variable_rename,[status(thm)],[c_0_873]) ).

fof(c_0_1481,plain,
    ! [X20,X21,X22,X23] :
      ( ~ class_Orderings_Olinorder(X23)
      | c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omax(X22,X21,X23),X20,X23)
      | ~ c_HOL_Oord__class_Oless(X21,X20,X23)
      | ~ c_HOL_Oord__class_Oless(X22,X20,X23) ),
    inference(variable_rename,[status(thm)],[c_0_874]) ).

fof(c_0_1482,plain,
    ! [X20,X21,X22,X23] :
      ( ~ class_Orderings_Olinorder(X23)
      | c_HOL_Oord__class_Oless(X20,c_Orderings_Oord__class_Omin(X22,X21,X23),X23)
      | ~ c_HOL_Oord__class_Oless(X20,X21,X23)
      | ~ c_HOL_Oord__class_Oless(X20,X22,X23) ),
    inference(variable_rename,[status(thm)],[c_0_875]) ).

fof(c_0_1483,plain,
    ! [X3,X4] :
      ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Otimes__class_Otimes(X4,X3,tc_nat),tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X3,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_876]) ).

fof(c_0_1484,plain,
    ! [X8,X9,X10] :
      ( c_HOL_Ominus__class_Ominus(X9,X10,tc_nat) != c_HOL_Ominus__class_Ominus(X8,X10,tc_nat)
      | ~ c_lessequals(X10,X8,tc_nat)
      | ~ c_lessequals(X10,X9,tc_nat)
      | X9 = X8 ),
    inference(variable_rename,[status(thm)],[c_0_877]) ).

fof(c_0_1485,plain,
    ! [X3,X4] :
      ( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X4,X3,tc_nat),X4,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X3,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_878]) ).

fof(c_0_1486,plain,
    ! [X19,X20] :
      ( ~ class_OrderedGroup_Olordered__ab__group__add(X20)
      | c_lessequals(c_HOL_Ozero__class_Ozero(X20),X19,X20)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X20),c_HOL_Oplus__class_Oplus(X19,X19,X20),X20) ),
    inference(variable_rename,[status(thm)],[c_0_879]) ).

fof(c_0_1487,plain,
    ! [X19,X20] :
      ( ~ class_OrderedGroup_Olordered__ab__group__add(X20)
      | c_HOL_Oord__class_Oless(X19,c_HOL_Ozero__class_Ozero(X20),X20)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X19,X19,X20),c_HOL_Ozero__class_Ozero(X20),X20) ),
    inference(variable_rename,[status(thm)],[c_0_880]) ).

fof(c_0_1488,plain,
    ! [X19,X20] :
      ( ~ class_Ring__and__Field_Oordered__idom(X20)
      | c_HOL_Oord__class_Oless(X19,c_HOL_Ozero__class_Ozero(X20),X20)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X19,X19,X20),c_HOL_Ozero__class_Ozero(X20),X20) ),
    inference(variable_rename,[status(thm)],[c_0_881]) ).

fof(c_0_1489,plain,
    ! [X19,X20] :
      ( ~ class_OrderedGroup_Olordered__ab__group__add(X20)
      | c_lessequals(X19,c_HOL_Ozero__class_Ozero(X20),X20)
      | ~ c_lessequals(c_HOL_Oplus__class_Oplus(X19,X19,X20),c_HOL_Ozero__class_Ozero(X20),X20) ),
    inference(variable_rename,[status(thm)],[c_0_882]) ).

fof(c_0_1490,plain,
    ! [X19,X20] :
      ( ~ class_OrderedGroup_Olordered__ab__group__add(X20)
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X20),X19,X20)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X20),c_HOL_Oplus__class_Oplus(X19,X19,X20),X20) ),
    inference(variable_rename,[status(thm)],[c_0_883]) ).

fof(c_0_1491,plain,
    ! [X3,X4] :
      ( c_lessequals(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X3,tc_nat)
      | ~ c_lessequals(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Otimes__class_Otimes(X4,X3,tc_nat),tc_nat) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_884])])]) ).

fof(c_0_1492,plain,
    ! [X3,X4] :
      ( c_lessequals(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X4,tc_nat)
      | ~ c_lessequals(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Otimes__class_Otimes(X4,X3,tc_nat),tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_885]) ).

fof(c_0_1493,plain,
    ! [X20,X21,X22,X23] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X23)
      | c_HOL_Oplus__class_Oplus(X22,c_HOL_Oplus__class_Oplus(X21,X20,X23),X23) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X22,X21,X23),X20,X23) ),
    inference(variable_rename,[status(thm)],[c_0_886]) ).

fof(c_0_1494,plain,
    ! [X20,X21,X22,X23] :
      ( ~ class_OrderedGroup_Oab__group__add(X23)
      | c_HOL_Oplus__class_Oplus(X22,c_HOL_Oplus__class_Oplus(X21,X20,X23),X23) = c_HOL_Oplus__class_Oplus(X21,c_HOL_Oplus__class_Oplus(X22,X20,X23),X23) ),
    inference(variable_rename,[status(thm)],[c_0_887]) ).

fof(c_0_1495,plain,
    ! [X21,X22,X23,X24] :
      ( ~ class_OrderedGroup_Ocomm__monoid__add(X24)
      | c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X23,X22,X24),X21,X24) = c_HOL_Oplus__class_Oplus(X23,c_HOL_Oplus__class_Oplus(X22,X21,X24),X24) ),
    inference(variable_rename,[status(thm)],[c_0_888]) ).

fof(c_0_1496,plain,
    ! [X21,X22,X23,X24] :
      ( ~ class_OrderedGroup_Ocomm__monoid__add(X24)
      | c_HOL_Oplus__class_Oplus(X23,c_HOL_Oplus__class_Oplus(X22,X21,X24),X24) = c_HOL_Oplus__class_Oplus(X22,c_HOL_Oplus__class_Oplus(X23,X21,X24),X24) ),
    inference(variable_rename,[status(thm)],[c_0_889]) ).

fof(c_0_1497,plain,
    ! [X21,X22,X23,X24] :
      ( ~ class_OrderedGroup_Oab__semigroup__add(X24)
      | c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X23,X22,X24),X21,X24) = c_HOL_Oplus__class_Oplus(X23,c_HOL_Oplus__class_Oplus(X22,X21,X24),X24) ),
    inference(variable_rename,[status(thm)],[c_0_890]) ).

fof(c_0_1498,plain,
    ! [X28,X29,X30,X31] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X31)
      | c_HOL_Oplus__class_Oplus(X30,c_HOL_Oplus__class_Oplus(X29,X28,X31),X31) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X30,X29,X31),X28,X31) ),
    inference(variable_rename,[status(thm)],[c_0_891]) ).

fof(c_0_1499,plain,
    ! [X21,X22,X23,X24] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X24)
      | c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X23,X22,X24),X21,X24) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X23,X21,X24),X22,X24) ),
    inference(variable_rename,[status(thm)],[c_0_892]) ).

fof(c_0_1500,plain,
    ! [X28,X29,X30,X31] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X31)
      | c_HOL_Oplus__class_Oplus(X30,c_HOL_Oplus__class_Oplus(X29,X28,X31),X31) = c_HOL_Oplus__class_Oplus(X29,c_HOL_Oplus__class_Oplus(X30,X28,X31),X31) ),
    inference(variable_rename,[status(thm)],[c_0_893]) ).

fof(c_0_1501,plain,
    ! [X21,X22,X23,X24] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X24)
      | c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X23,X22,X24),X21,X24) = c_HOL_Oplus__class_Oplus(X23,c_HOL_Oplus__class_Oplus(X22,X21,X24),X24) ),
    inference(variable_rename,[status(thm)],[c_0_894]) ).

fof(c_0_1502,plain,
    ! [X20,X21,X22,X23] :
      ( ~ class_Orderings_Olinorder(X23)
      | c_Orderings_Oord__class_Omin(c_Orderings_Oord__class_Omin(X22,X21,X23),X20,X23) = c_Orderings_Oord__class_Omin(X22,c_Orderings_Oord__class_Omin(X21,X20,X23),X23) ),
    inference(variable_rename,[status(thm)],[c_0_895]) ).

fof(c_0_1503,plain,
    ! [X20,X21,X22,X23] :
      ( ~ class_Orderings_Olinorder(X23)
      | c_Orderings_Oord__class_Omin(X22,c_Orderings_Oord__class_Omin(X21,X20,X23),X23) = c_Orderings_Oord__class_Omin(X21,c_Orderings_Oord__class_Omin(X22,X20,X23),X23) ),
    inference(variable_rename,[status(thm)],[c_0_896]) ).

fof(c_0_1504,plain,
    ! [X20,X21,X22,X23] :
      ( ~ class_Orderings_Olinorder(X23)
      | c_Orderings_Oord__class_Omax(c_Orderings_Oord__class_Omax(X22,X21,X23),X20,X23) = c_Orderings_Oord__class_Omax(X22,c_Orderings_Oord__class_Omax(X21,X20,X23),X23) ),
    inference(variable_rename,[status(thm)],[c_0_897]) ).

fof(c_0_1505,plain,
    ! [X20,X21,X22,X23] :
      ( ~ class_Orderings_Olinorder(X23)
      | c_Orderings_Oord__class_Omax(X22,c_Orderings_Oord__class_Omax(X21,X20,X23),X23) = c_Orderings_Oord__class_Omax(X21,c_Orderings_Oord__class_Omax(X22,X20,X23),X23) ),
    inference(variable_rename,[status(thm)],[c_0_898]) ).

fof(c_0_1506,plain,
    ! [X21,X22,X23,X24] :
      ( ~ class_OrderedGroup_Oab__semigroup__mult(X24)
      | c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X23,X22,X24),X21,X24) = c_HOL_Otimes__class_Otimes(X23,c_HOL_Otimes__class_Otimes(X22,X21,X24),X24) ),
    inference(variable_rename,[status(thm)],[c_0_899]) ).

fof(c_0_1507,plain,
    ! [X25,X26,X27,X28] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X28)
      | c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X27,X26,X28),X25,X28) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X27,X25,X28),X26,X28) ),
    inference(variable_rename,[status(thm)],[c_0_900]) ).

fof(c_0_1508,plain,
    ! [X25,X26,X27,X28] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X28)
      | c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X27,X26,X28),X25,X28) = c_HOL_Otimes__class_Otimes(X27,c_HOL_Otimes__class_Otimes(X26,X25,X28),X28) ),
    inference(variable_rename,[status(thm)],[c_0_901]) ).

fof(c_0_1509,plain,
    ! [X24,X25,X26,X27] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X27)
      | c_HOL_Otimes__class_Otimes(X26,c_HOL_Otimes__class_Otimes(X25,X24,X27),X27) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X26,X25,X27),X24,X27) ),
    inference(variable_rename,[status(thm)],[c_0_902]) ).

fof(c_0_1510,plain,
    ! [X24,X25,X26,X27] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X27)
      | c_HOL_Otimes__class_Otimes(X26,c_HOL_Otimes__class_Otimes(X25,X24,X27),X27) = c_HOL_Otimes__class_Otimes(X25,c_HOL_Otimes__class_Otimes(X26,X24,X27),X27) ),
    inference(variable_rename,[status(thm)],[c_0_903]) ).

fof(c_0_1511,plain,
    ! [X20,X21,X22,X23] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X23)
      | c_HOL_Otimes__class_Otimes(X22,c_HOL_Otimes__class_Otimes(X21,X20,X23),X23) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X22,X21,X23),X20,X23) ),
    inference(variable_rename,[status(thm)],[c_0_904]) ).

fof(c_0_1512,plain,
    ! [X8,X9,X10] :
      ( c_HOL_Oord__class_Oless(X9,c_HOL_Oplus__class_Oplus(X8,X10,tc_nat),tc_nat)
      | ~ c_lessequals(X9,X8,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X10,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_905]) ).

fof(c_0_1513,plain,
    ! [X19] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X19)
      | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X19),c_HOL_Ozero__class_Ozero(X19),X19),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X19),c_HOL_Ozero__class_Ozero(X19),X19),X19) = c_HOL_Ozero__class_Ozero(X19) ),
    inference(variable_rename,[status(thm)],[c_0_906]) ).

fof(c_0_1514,plain,
    ! [X19,X20,X21] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add(X21)
      | c_lessequals(X20,X19,X21)
      | ~ c_lessequals(c_HOL_Ominus__class_Ominus(X20,X19,X21),c_HOL_Ozero__class_Ozero(X21),X21) ),
    inference(variable_rename,[status(thm)],[c_0_907]) ).

fof(c_0_1515,plain,
    ! [X19,X20,X21] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add(X21)
      | c_HOL_Oord__class_Oless(X20,X19,X21)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X20,X19,X21),c_HOL_Ozero__class_Ozero(X21),X21) ),
    inference(variable_rename,[status(thm)],[c_0_908]) ).

fof(c_0_1516,plain,
    ! [X27,X28,X29,X30,X31] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add(X31)
      | c_HOL_Ominus__class_Ominus(X30,X28,X31) != c_HOL_Ominus__class_Ominus(X29,X27,X31)
      | c_lessequals(X27,X29,X31)
      | ~ c_lessequals(X28,X30,X31) ),
    inference(variable_rename,[status(thm)],[c_0_909]) ).

fof(c_0_1517,plain,
    ! [X27,X28,X29,X30,X31] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add(X31)
      | c_HOL_Ominus__class_Ominus(X30,X28,X31) != c_HOL_Ominus__class_Ominus(X29,X27,X31)
      | c_lessequals(X28,X30,X31)
      | ~ c_lessequals(X27,X29,X31) ),
    inference(variable_rename,[status(thm)],[c_0_910]) ).

fof(c_0_1518,plain,
    ! [X27,X28,X29,X30,X31] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add(X31)
      | c_HOL_Ominus__class_Ominus(X30,X28,X31) != c_HOL_Ominus__class_Ominus(X29,X27,X31)
      | c_HOL_Oord__class_Oless(X29,X27,X31)
      | ~ c_HOL_Oord__class_Oless(X30,X28,X31) ),
    inference(variable_rename,[status(thm)],[c_0_911]) ).

fof(c_0_1519,plain,
    ! [X27,X28,X29,X30,X31] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add(X31)
      | c_HOL_Ominus__class_Ominus(X30,X28,X31) != c_HOL_Ominus__class_Ominus(X29,X27,X31)
      | c_HOL_Oord__class_Oless(X30,X28,X31)
      | ~ c_HOL_Oord__class_Oless(X29,X27,X31) ),
    inference(variable_rename,[status(thm)],[c_0_912]) ).

fof(c_0_1520,plain,
    ! [X8,X9,X10] :
      ( c_lessequals(c_HOL_Otimes__class_Otimes(X9,X10,tc_nat),c_HOL_Otimes__class_Otimes(X8,X10,tc_nat),tc_nat)
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X10,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_913]) ).

fof(c_0_1521,plain,
    ! [X8,X9,X10] :
      ( c_lessequals(c_HOL_Otimes__class_Otimes(X10,X9,tc_nat),c_HOL_Otimes__class_Otimes(X10,X8,tc_nat),tc_nat)
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X10,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_914]) ).

fof(c_0_1522,plain,
    ! [X20,X21,X22,X23] :
      ( ~ class_Orderings_Olinorder(X23)
      | c_lessequals(X22,X20,X23)
      | ~ c_lessequals(X22,c_Orderings_Oord__class_Omin(X21,X20,X23),X23) ),
    inference(variable_rename,[status(thm)],[c_0_915]) ).

fof(c_0_1523,plain,
    ! [X20,X21,X22,X23] :
      ( ~ class_Orderings_Olinorder(X23)
      | c_lessequals(X22,X21,X23)
      | ~ c_lessequals(X22,c_Orderings_Oord__class_Omin(X21,X20,X23),X23) ),
    inference(variable_rename,[status(thm)],[c_0_916]) ).

fof(c_0_1524,plain,
    ! [X19,X20,X21,X22] :
      ( ~ class_Orderings_Olinorder(X22)
      | c_lessequals(X19,X20,X22)
      | ~ c_lessequals(X19,c_Orderings_Oord__class_Omin(X21,X20,X22),X22) ),
    inference(variable_rename,[status(thm)],[c_0_917]) ).

fof(c_0_1525,plain,
    ! [X19,X20,X21,X22] :
      ( ~ class_Orderings_Olinorder(X22)
      | c_lessequals(X19,X21,X22)
      | ~ c_lessequals(X19,c_Orderings_Oord__class_Omin(X21,X20,X22),X22) ),
    inference(variable_rename,[status(thm)],[c_0_918]) ).

fof(c_0_1526,plain,
    ! [X20,X21,X22,X23] :
      ( ~ class_Orderings_Olinorder(X23)
      | c_lessequals(X21,X20,X23)
      | ~ c_lessequals(c_Orderings_Oord__class_Omax(X22,X21,X23),X20,X23) ),
    inference(variable_rename,[status(thm)],[c_0_919]) ).

fof(c_0_1527,plain,
    ! [X20,X21,X22,X23] :
      ( ~ class_Orderings_Olinorder(X23)
      | c_lessequals(X22,X20,X23)
      | ~ c_lessequals(c_Orderings_Oord__class_Omax(X22,X21,X23),X20,X23) ),
    inference(variable_rename,[status(thm)],[c_0_920]) ).

fof(c_0_1528,plain,
    ! [X19,X20,X21,X22] :
      ( ~ class_Orderings_Olinorder(X22)
      | c_lessequals(X20,X19,X22)
      | ~ c_lessequals(c_Orderings_Oord__class_Omax(X21,X20,X22),X19,X22) ),
    inference(variable_rename,[status(thm)],[c_0_921]) ).

fof(c_0_1529,plain,
    ! [X19,X20,X21,X22] :
      ( ~ class_Orderings_Olinorder(X22)
      | c_lessequals(X21,X19,X22)
      | ~ c_lessequals(c_Orderings_Oord__class_Omax(X21,X20,X22),X19,X22) ),
    inference(variable_rename,[status(thm)],[c_0_922]) ).

fof(c_0_1530,plain,
    ! [X20,X21,X22,X23] :
      ( ~ class_Orderings_Olinorder(X23)
      | c_HOL_Oord__class_Oless(X22,X20,X23)
      | ~ c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omax(X22,X21,X23),X20,X23) ),
    inference(variable_rename,[status(thm)],[c_0_923]) ).

fof(c_0_1531,plain,
    ! [X20,X21,X22,X23] :
      ( ~ class_Orderings_Olinorder(X23)
      | c_HOL_Oord__class_Oless(X21,X20,X23)
      | ~ c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omax(X22,X21,X23),X20,X23) ),
    inference(variable_rename,[status(thm)],[c_0_924]) ).

fof(c_0_1532,plain,
    ! [X20,X21,X22,X23] :
      ( ~ class_Orderings_Olinorder(X23)
      | c_HOL_Oord__class_Oless(X20,X22,X23)
      | ~ c_HOL_Oord__class_Oless(X20,c_Orderings_Oord__class_Omin(X22,X21,X23),X23) ),
    inference(variable_rename,[status(thm)],[c_0_925]) ).

fof(c_0_1533,plain,
    ! [X20,X21,X22,X23] :
      ( ~ class_Orderings_Olinorder(X23)
      | c_HOL_Oord__class_Oless(X20,X21,X23)
      | ~ c_HOL_Oord__class_Oless(X20,c_Orderings_Oord__class_Omin(X22,X21,X23),X23) ),
    inference(variable_rename,[status(thm)],[c_0_926]) ).

fof(c_0_1534,plain,
    ! [X3,X4] :
      ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X3,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Otimes__class_Otimes(X4,X3,tc_nat),tc_nat) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_927])])]) ).

fof(c_0_1535,plain,
    ! [X3,X4] :
      ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Otimes__class_Otimes(X4,X3,tc_nat),tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_928]) ).

fof(c_0_1536,plain,
    ! [X3,X4] :
      ( c_HOL_Oord__class_Oless(X4,X3,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ominus__class_Ominus(X3,X4,tc_nat),tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_929]) ).

fof(c_0_1537,plain,
    ! [X29,X30,X31,X32] :
      ( c_HOL_Oplus__class_Oplus(X30,X31,tc_nat) != c_HOL_Oplus__class_Oplus(X32,X29,tc_nat)
      | ~ c_HOL_Oord__class_Oless(X32,X31,tc_nat)
      | c_HOL_Oord__class_Oless(X30,X29,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_930]) ).

fof(c_0_1538,plain,
    ! [X15,X16,X17] :
      ( c_HOL_Oord__class_Oless(X17,X15,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X17,X16,tc_nat),X15,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_931]) ).

fof(c_0_1539,plain,
    ! [X8,X9,X10] :
      ( c_lessequals(X10,X8,tc_nat)
      | ~ c_lessequals(c_HOL_Oplus__class_Oplus(X9,X10,tc_nat),X8,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_932]) ).

fof(c_0_1540,plain,
    ! [X8,X9,X10] :
      ( c_lessequals(X9,X8,tc_nat)
      | ~ c_lessequals(c_HOL_Oplus__class_Oplus(X9,X10,tc_nat),X8,tc_nat) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_933])])]) ).

fof(c_0_1541,plain,
    ! [X19,X20,X21] :
      ( ~ class_OrderedGroup_Opordered__comm__monoid__add(X21)
      | c_HOL_Oplus__class_Oplus(X20,X19,X21) != c_HOL_Ozero__class_Ozero(X21)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X21),X19,X21)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X21),X20,X21)
      | X19 = c_HOL_Ozero__class_Ozero(X21) ),
    inference(variable_rename,[status(thm)],[c_0_934]) ).

fof(c_0_1542,plain,
    ! [X19,X20,X21] :
      ( ~ class_OrderedGroup_Opordered__comm__monoid__add(X21)
      | c_HOL_Oplus__class_Oplus(X20,X19,X21) != c_HOL_Ozero__class_Ozero(X21)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X21),X19,X21)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X21),X20,X21)
      | X20 = c_HOL_Ozero__class_Ozero(X21) ),
    inference(variable_rename,[status(thm)],[c_0_935]) ).

fof(c_0_1543,plain,
    ! [X3,X4] :
      ( c_Divides_Odiv__class_Omod(X4,X3,tc_nat) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X4,X3,tc_nat),X3,tc_nat)
      | ~ c_lessequals(X3,X4,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_936]) ).

fof(c_0_1544,plain,
    ! [X19] :
      ( ~ class_OrderedGroup_Opordered__comm__monoid__add(X19)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X19),c_HOL_Ozero__class_Ozero(X19),X19)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X19),c_HOL_Ozero__class_Ozero(X19),X19)
      | c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X19),c_HOL_Ozero__class_Ozero(X19),X19) = c_HOL_Ozero__class_Ozero(X19) ),
    inference(variable_rename,[status(thm)],[c_0_937]) ).

fof(c_0_1545,plain,
    ! [X3,X4] :
      ( c_Divides_Odiv__class_Omod(c_Suc(X4),X3,tc_nat) = c_Suc(c_Divides_Odiv__class_Omod(X4,X3,tc_nat))
      | c_Suc(c_Divides_Odiv__class_Omod(X4,X3,tc_nat)) = X3 ),
    inference(variable_rename,[status(thm)],[c_0_938]) ).

fof(c_0_1546,plain,
    ! [X19,X20] :
      ( ~ class_OrderedGroup_Olordered__ab__group__add(X20)
      | c_lessequals(c_HOL_Ozero__class_Ozero(X20),c_HOL_Oplus__class_Oplus(X19,X19,X20),X20)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X20),X19,X20) ),
    inference(variable_rename,[status(thm)],[c_0_939]) ).

fof(c_0_1547,plain,
    ! [X19,X20] :
      ( ~ class_OrderedGroup_Olordered__ab__group__add(X20)
      | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X19,X19,X20),c_HOL_Ozero__class_Ozero(X20),X20)
      | ~ c_HOL_Oord__class_Oless(X19,c_HOL_Ozero__class_Ozero(X20),X20) ),
    inference(variable_rename,[status(thm)],[c_0_940]) ).

fof(c_0_1548,plain,
    ! [X19,X20] :
      ( ~ class_Ring__and__Field_Oordered__idom(X20)
      | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X19,X19,X20),c_HOL_Ozero__class_Ozero(X20),X20)
      | ~ c_HOL_Oord__class_Oless(X19,c_HOL_Ozero__class_Ozero(X20),X20) ),
    inference(variable_rename,[status(thm)],[c_0_941]) ).

fof(c_0_1549,plain,
    ! [X19,X20] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X20)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X19,X19,X20),c_HOL_Ozero__class_Ozero(X20),X20) ),
    inference(variable_rename,[status(thm)],[c_0_942]) ).

fof(c_0_1550,plain,
    ! [X19,X20] :
      ( ~ class_OrderedGroup_Olordered__ab__group__add(X20)
      | c_lessequals(c_HOL_Oplus__class_Oplus(X19,X19,X20),c_HOL_Ozero__class_Ozero(X20),X20)
      | ~ c_lessequals(X19,c_HOL_Ozero__class_Ozero(X20),X20) ),
    inference(variable_rename,[status(thm)],[c_0_943]) ).

fof(c_0_1551,plain,
    ! [X19,X20] :
      ( ~ class_OrderedGroup_Olordered__ab__group__add(X20)
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X20),c_HOL_Oplus__class_Oplus(X19,X19,X20),X20)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X20),X19,X20) ),
    inference(variable_rename,[status(thm)],[c_0_944]) ).

fof(c_0_1552,plain,
    ! [X3,X4] :
      ( c_Divides_Odiv__class_Omod(X4,X3,tc_nat) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X4,X3,tc_nat),X3,tc_nat)
      | c_HOL_Oord__class_Oless(X4,X3,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_945]) ).

fof(c_0_1553,plain,
    ! [X19,X20,X21] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add(X21)
      | c_lessequals(c_HOL_Ominus__class_Ominus(X20,X19,X21),c_HOL_Ozero__class_Ozero(X21),X21)
      | ~ c_lessequals(X20,X19,X21) ),
    inference(variable_rename,[status(thm)],[c_0_946]) ).

fof(c_0_1554,plain,
    ! [X19,X20,X21] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add(X21)
      | c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X20,X19,X21),c_HOL_Ozero__class_Ozero(X21),X21)
      | ~ c_HOL_Oord__class_Oless(X20,X19,X21) ),
    inference(variable_rename,[status(thm)],[c_0_947]) ).

fof(c_0_1555,plain,
    ! [X9,X10,X11] :
      ( c_Lambda_Osubst(c_Lambda_OdB_OVar(X11),X9,X10) = c_Lambda_OdB_OVar(c_HOL_Ominus__class_Ominus(X11,c_HOL_Oone__class_Oone(tc_nat),tc_nat))
      | ~ c_HOL_Oord__class_Oless(X10,X11,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_948]) ).

fof(c_0_1556,plain,
    ! [X16,X17,X18] :
      ( c_Lambda_Osubst(c_Lambda_OdB_OVar(X17),X16,X18) = c_Lambda_OdB_OVar(c_HOL_Ominus__class_Ominus(X17,c_HOL_Oone__class_Oone(tc_nat),tc_nat))
      | ~ c_HOL_Oord__class_Oless(X18,X17,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_949]) ).

fof(c_0_1557,plain,
    ! [X9,X10] :
      ( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X9,c_Suc(X10),tc_nat),X9,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X9,tc_nat) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_950])])]) ).

fof(c_0_1558,plain,
    ! [X8,X9,X10] :
      ( c_HOL_Otimes__class_Otimes(X10,X9,tc_nat) != c_HOL_Otimes__class_Otimes(X10,X8,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X10,tc_nat)
      | X9 = X8 ),
    inference(variable_rename,[status(thm)],[c_0_951]) ).

fof(c_0_1559,plain,
    ! [X20,X21,X22,X23] :
      ( ~ class_Orderings_Olinorder(X23)
      | c_lessequals(c_Orderings_Oord__class_Omin(X22,X21,X23),X20,X23)
      | ~ c_lessequals(X21,X20,X23) ),
    inference(variable_rename,[status(thm)],[c_0_952]) ).

fof(c_0_1560,plain,
    ! [X20,X21,X22,X23] :
      ( ~ class_Orderings_Olinorder(X23)
      | c_lessequals(c_Orderings_Oord__class_Omin(X22,X21,X23),X20,X23)
      | ~ c_lessequals(X22,X20,X23) ),
    inference(variable_rename,[status(thm)],[c_0_953]) ).

fof(c_0_1561,plain,
    ! [X19,X20,X21,X22] :
      ( ~ class_Orderings_Olinorder(X22)
      | c_lessequals(c_Orderings_Oord__class_Omin(X21,X20,X22),X19,X22)
      | ~ c_lessequals(X20,X19,X22) ),
    inference(variable_rename,[status(thm)],[c_0_954]) ).

fof(c_0_1562,plain,
    ! [X19,X20,X21,X22] :
      ( ~ class_Orderings_Olinorder(X22)
      | c_lessequals(c_Orderings_Oord__class_Omin(X21,X20,X22),X19,X22)
      | ~ c_lessequals(X21,X19,X22) ),
    inference(variable_rename,[status(thm)],[c_0_955]) ).

fof(c_0_1563,plain,
    ! [X20,X21,X22,X23] :
      ( ~ class_Orderings_Olinorder(X23)
      | c_lessequals(X20,c_Orderings_Oord__class_Omax(X22,X21,X23),X23)
      | ~ c_lessequals(X20,X21,X23) ),
    inference(variable_rename,[status(thm)],[c_0_956]) ).

fof(c_0_1564,plain,
    ! [X20,X21,X22,X23] :
      ( ~ class_Orderings_Olinorder(X23)
      | c_lessequals(X20,c_Orderings_Oord__class_Omax(X22,X21,X23),X23)
      | ~ c_lessequals(X20,X22,X23) ),
    inference(variable_rename,[status(thm)],[c_0_957]) ).

fof(c_0_1565,plain,
    ! [X19,X20,X21,X22] :
      ( ~ class_Orderings_Olinorder(X22)
      | c_lessequals(X19,c_Orderings_Oord__class_Omax(X21,X20,X22),X22)
      | ~ c_lessequals(X19,X20,X22) ),
    inference(variable_rename,[status(thm)],[c_0_958]) ).

fof(c_0_1566,plain,
    ! [X19,X20,X21,X22] :
      ( ~ class_Orderings_Olinorder(X22)
      | c_lessequals(X19,c_Orderings_Oord__class_Omax(X21,X20,X22),X22)
      | ~ c_lessequals(X19,X21,X22) ),
    inference(variable_rename,[status(thm)],[c_0_959]) ).

fof(c_0_1567,plain,
    ! [X19,X20,X21,X22] :
      ( ~ class_Orderings_Olinorder(X22)
      | c_HOL_Oord__class_Oless(X19,c_Orderings_Oord__class_Omax(X21,X20,X22),X22)
      | ~ c_HOL_Oord__class_Oless(X19,X21,X22) ),
    inference(variable_rename,[status(thm)],[c_0_960]) ).

fof(c_0_1568,plain,
    ! [X19,X20,X21,X22] :
      ( ~ class_Orderings_Olinorder(X22)
      | c_HOL_Oord__class_Oless(X19,c_Orderings_Oord__class_Omax(X21,X20,X22),X22)
      | ~ c_HOL_Oord__class_Oless(X19,X20,X22) ),
    inference(variable_rename,[status(thm)],[c_0_961]) ).

fof(c_0_1569,plain,
    ! [X20,X21,X22,X23] :
      ( ~ class_Orderings_Olinorder(X23)
      | c_HOL_Oord__class_Oless(X20,c_Orderings_Oord__class_Omax(X22,X21,X23),X23)
      | ~ c_HOL_Oord__class_Oless(X20,X22,X23) ),
    inference(variable_rename,[status(thm)],[c_0_962]) ).

fof(c_0_1570,plain,
    ! [X20,X21,X22,X23] :
      ( ~ class_Orderings_Olinorder(X23)
      | c_HOL_Oord__class_Oless(X20,c_Orderings_Oord__class_Omax(X22,X21,X23),X23)
      | ~ c_HOL_Oord__class_Oless(X20,X21,X23) ),
    inference(variable_rename,[status(thm)],[c_0_963]) ).

fof(c_0_1571,plain,
    ! [X19,X20,X21,X22] :
      ( ~ class_Orderings_Olinorder(X22)
      | c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omin(X21,X20,X22),X19,X22)
      | ~ c_HOL_Oord__class_Oless(X21,X19,X22) ),
    inference(variable_rename,[status(thm)],[c_0_964]) ).

fof(c_0_1572,plain,
    ! [X19,X20,X21,X22] :
      ( ~ class_Orderings_Olinorder(X22)
      | c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omin(X21,X20,X22),X19,X22)
      | ~ c_HOL_Oord__class_Oless(X20,X19,X22) ),
    inference(variable_rename,[status(thm)],[c_0_965]) ).

fof(c_0_1573,plain,
    ! [X20,X21,X22,X23] :
      ( ~ class_Orderings_Olinorder(X23)
      | c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omin(X22,X21,X23),X20,X23)
      | ~ c_HOL_Oord__class_Oless(X22,X20,X23) ),
    inference(variable_rename,[status(thm)],[c_0_966]) ).

fof(c_0_1574,plain,
    ! [X20,X21,X22,X23] :
      ( ~ class_Orderings_Olinorder(X23)
      | c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omin(X22,X21,X23),X20,X23)
      | ~ c_HOL_Oord__class_Oless(X21,X20,X23) ),
    inference(variable_rename,[status(thm)],[c_0_967]) ).

fof(c_0_1575,plain,
    ! [X3,X4] :
      ( c_HOL_Ominus__class_Ominus(c_Suc(X4),X3,tc_nat) = c_Suc(c_HOL_Ominus__class_Ominus(X4,X3,tc_nat))
      | ~ c_lessequals(X3,X4,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_968]) ).

fof(c_0_1576,plain,
    ! [X9,X10,X11,X12] :
      ( c_Lambda_Obeta(c_Lambda_Osubst(X11,X9,X12),c_Lambda_Osubst(X10,X9,X12))
      | ~ c_Lambda_Obeta(X11,X10) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_969])])]) ).

fof(c_0_1577,plain,
    ! [X3,X4] :
      ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oplus__class_Oplus(X4,X3,tc_nat),tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X3,tc_nat) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_970])])]) ).

fof(c_0_1578,plain,
    ! [X3,X4] :
      ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oplus__class_Oplus(X4,X3,tc_nat),tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_971]) ).

fof(c_0_1579,plain,
    ! [X19,X20] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X20)
      | c_HOL_Oplus__class_Oplus(X19,X19,X20) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(X20),c_HOL_Oone__class_Oone(X20),X20),X19,X20) ),
    inference(variable_rename,[status(thm)],[c_0_972]) ).

fof(c_0_1580,plain,
    ! [X3,X4] :
      ( c_lessequals(c_Divides_Odiv__class_Omod(X4,X3,tc_nat),X3,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X3,tc_nat) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_973])])]) ).

fof(c_0_1581,plain,
    ! [X3,X4] :
      ( c_HOL_Oord__class_Oless(c_Divides_Odiv__class_Omod(X4,X3,tc_nat),X3,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X3,tc_nat) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_974])])]) ).

fof(c_0_1582,plain,
    ! [X3,X4] :
      ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ominus__class_Ominus(X3,X4,tc_nat),tc_nat)
      | ~ c_HOL_Oord__class_Oless(X4,X3,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_975]) ).

fof(c_0_1583,plain,
    ! [X15,X16] :
      ( ~ c_lessequals(X16,X15,tc_nat)
      | X15 = c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X15,X16,tc_nat),X16,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_976]) ).

fof(c_0_1584,plain,
    ! [X3,X4] :
      ( c_HOL_Oplus__class_Oplus(X3,c_HOL_Ominus__class_Ominus(X4,X3,tc_nat),tc_nat) = X4
      | ~ c_lessequals(X3,X4,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_977]) ).

fof(c_0_1585,plain,
    ! [X3,X4] :
      ( c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X4,X3,tc_nat),X3,tc_nat) = X4
      | ~ c_lessequals(X3,X4,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_978]) ).

fof(c_0_1586,plain,
    ! [X9,X10] :
      ( c_HOL_Ominus__class_Ominus(X9,c_HOL_Ominus__class_Ominus(X9,X10,tc_nat),tc_nat) = X10
      | ~ c_lessequals(X10,X9,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_979]) ).

fof(c_0_1587,plain,
    ! [X20,X21,X22] :
      ( c_HOL_Oord__class_Oless(X22,c_HOL_Oplus__class_Oplus(X21,X20,tc_nat),tc_nat)
      | ~ c_HOL_Oord__class_Oless(X22,X21,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_980]) ).

fof(c_0_1588,plain,
    ! [X20,X21,X22] :
      ( c_HOL_Oord__class_Oless(X22,c_HOL_Oplus__class_Oplus(X21,X20,tc_nat),tc_nat)
      | ~ c_HOL_Oord__class_Oless(X22,X20,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_981]) ).

fof(c_0_1589,plain,
    ! [X15,X16,X17] :
      ( c_HOL_Oord__class_Oless(X17,c_HOL_Oplus__class_Oplus(X16,X15,tc_nat),tc_nat)
      | ~ c_HOL_Oord__class_Oless(X17,X16,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_982]) ).

fof(c_0_1590,plain,
    ! [X15,X16,X17] :
      ( c_HOL_Oord__class_Oless(X17,c_HOL_Oplus__class_Oplus(X15,X16,tc_nat),tc_nat)
      | ~ c_HOL_Oord__class_Oless(X17,X16,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_983]) ).

fof(c_0_1591,plain,
    ! [X15,X16,X17] :
      ( c_lessequals(X17,c_HOL_Oplus__class_Oplus(X15,X16,tc_nat),tc_nat)
      | ~ c_lessequals(X17,X16,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_984]) ).

fof(c_0_1592,plain,
    ! [X15,X16,X17] :
      ( c_lessequals(X17,c_HOL_Oplus__class_Oplus(X16,X15,tc_nat),tc_nat)
      | ~ c_lessequals(X17,X16,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_985]) ).

fof(c_0_1593,plain,
    ! [X20,X21,X22] :
      ( c_lessequals(X22,c_HOL_Oplus__class_Oplus(X21,X20,tc_nat),tc_nat)
      | ~ c_lessequals(X22,X20,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_986]) ).

fof(c_0_1594,plain,
    ! [X20,X21,X22] :
      ( c_lessequals(X22,c_HOL_Oplus__class_Oplus(X21,X20,tc_nat),tc_nat)
      | ~ c_lessequals(X22,X21,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_987]) ).

fof(c_0_1595,plain,
    ! [X15,X16,X17] :
      ( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X17,X15,tc_nat),X16,tc_nat)
      | ~ c_HOL_Oord__class_Oless(X17,X16,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_988]) ).

fof(c_0_1596,plain,
    ! [X20,X21,X22,X23] :
      ( ~ class_Orderings_Opreorder(X23)
      | c_HOL_Oord__class_Oless(X22,X20,X23)
      | ~ c_HOL_Oord__class_Oless(X21,X20,X23)
      | ~ c_HOL_Oord__class_Oless(X22,X21,X23) ),
    inference(variable_rename,[status(thm)],[c_0_989]) ).

fof(c_0_1597,plain,
    ! [X20,X21,X22,X23] :
      ( ~ class_Orderings_Oorder(X23)
      | c_HOL_Oord__class_Oless(X20,X22,X23)
      | ~ c_HOL_Oord__class_Oless(X20,X21,X23)
      | ~ c_HOL_Oord__class_Oless(X21,X22,X23) ),
    inference(variable_rename,[status(thm)],[c_0_990]) ).

fof(c_0_1598,plain,
    ! [X20,X21,X22,X23] :
      ( ~ class_Orderings_Oorder(X23)
      | c_lessequals(X20,X22,X23)
      | ~ c_lessequals(X20,X21,X23)
      | ~ c_lessequals(X21,X22,X23) ),
    inference(variable_rename,[status(thm)],[c_0_991]) ).

fof(c_0_1599,plain,
    ! [X20,X21,X22,X23] :
      ( ~ class_Orderings_Oorder(X23)
      | c_HOL_Oord__class_Oless(X20,X22,X23)
      | ~ c_lessequals(X20,X21,X23)
      | ~ c_HOL_Oord__class_Oless(X21,X22,X23) ),
    inference(variable_rename,[status(thm)],[c_0_992]) ).

fof(c_0_1600,plain,
    ! [X20,X21,X22,X23] :
      ( ~ class_Orderings_Oorder(X23)
      | c_HOL_Oord__class_Oless(X20,X22,X23)
      | ~ c_HOL_Oord__class_Oless(X20,X21,X23)
      | ~ c_lessequals(X21,X22,X23) ),
    inference(variable_rename,[status(thm)],[c_0_993]) ).

fof(c_0_1601,plain,
    ! [X20,X21,X22,X23] :
      ( ~ class_Orderings_Opreorder(X23)
      | c_lessequals(X22,X20,X23)
      | ~ c_lessequals(X21,X20,X23)
      | ~ c_lessequals(X22,X21,X23) ),
    inference(variable_rename,[status(thm)],[c_0_994]) ).

fof(c_0_1602,plain,
    ! [X20,X21,X22,X23] :
      ( ~ class_Orderings_Opreorder(X23)
      | c_HOL_Oord__class_Oless(X22,X20,X23)
      | ~ c_HOL_Oord__class_Oless(X21,X20,X23)
      | ~ c_lessequals(X22,X21,X23) ),
    inference(variable_rename,[status(thm)],[c_0_995]) ).

fof(c_0_1603,plain,
    ! [X20,X21,X22,X23] :
      ( ~ class_Orderings_Opreorder(X23)
      | c_HOL_Oord__class_Oless(X22,X20,X23)
      | ~ c_lessequals(X21,X20,X23)
      | ~ c_HOL_Oord__class_Oless(X22,X21,X23) ),
    inference(variable_rename,[status(thm)],[c_0_996]) ).

fof(c_0_1604,plain,
    ! [X3,X4] :
      ( c_Suc(c_Divides_Odiv__class_Omod(X4,X3,tc_nat)) != X3
      | c_Divides_Odiv__class_Omod(c_Suc(X4),X3,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_997]) ).

fof(c_0_1605,plain,
    ! [X15,X16,X17] :
      ( c_HOL_Oord__class_Oless(c_Suc(X17),X15,tc_nat)
      | ~ c_HOL_Oord__class_Oless(X16,X15,tc_nat)
      | ~ c_HOL_Oord__class_Oless(X17,X16,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_998]) ).

fof(c_0_1606,plain,
    ! [X19,X20,X21] :
      ( ~ class_Divides_Osemiring__div(X21)
      | c_Divides_Odiv__class_Omod(c_Divides_Odiv__class_Omod(X20,X19,X21),X19,X21) = c_Divides_Odiv__class_Omod(X20,X19,X21) ),
    inference(variable_rename,[status(thm)],[c_0_999]) ).

fof(c_0_1607,plain,
    ! [X19,X20,X21] :
      ( ~ class_Orderings_Olinorder(X21)
      | c_Orderings_Oord__class_Omin(X20,c_Orderings_Oord__class_Omin(X20,X19,X21),X21) = c_Orderings_Oord__class_Omin(X20,X19,X21) ),
    inference(variable_rename,[status(thm)],[c_0_1000]) ).

fof(c_0_1608,plain,
    ! [X19,X20,X21] :
      ( ~ class_OrderedGroup_Oab__semigroup__idem__mult(X21)
      | c_HOL_Otimes__class_Otimes(X20,c_HOL_Otimes__class_Otimes(X20,X19,X21),X21) = c_HOL_Otimes__class_Otimes(X20,X19,X21) ),
    inference(variable_rename,[status(thm)],[c_0_1001]) ).

fof(c_0_1609,plain,
    ! [X19,X20,X21] :
      ( ~ class_Divides_Osemiring__div(X21)
      | c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X20,X19,X21),X19,X21) = c_Divides_Odiv__class_Omod(X20,X19,X21) ),
    inference(variable_rename,[status(thm)],[c_0_1002]) ).

fof(c_0_1610,plain,
    ! [X19,X20,X21] :
      ( ~ class_Divides_Osemiring__div(X21)
      | c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X19,X20,X21),X19,X21) = c_Divides_Odiv__class_Omod(X20,X19,X21) ),
    inference(variable_rename,[status(thm)],[c_0_1003]) ).

fof(c_0_1611,plain,
    ! [X19,X20,X21] :
      ( ~ class_Orderings_Olinorder(X21)
      | c_Orderings_Oord__class_Omax(X20,c_Orderings_Oord__class_Omax(X20,X19,X21),X21) = c_Orderings_Oord__class_Omax(X20,X19,X21) ),
    inference(variable_rename,[status(thm)],[c_0_1004]) ).

fof(c_0_1612,plain,
    ! [X2] :
      ( c_Suc(c_HOL_Ominus__class_Ominus(X2,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat)) = X2
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_1005]) ).

fof(c_0_1613,plain,
    ! [X15,X16,X17] :
      ( c_lessequals(X17,X15,tc_nat)
      | ~ c_lessequals(X16,X15,tc_nat)
      | ~ c_lessequals(X17,X16,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_1006]) ).

fof(c_0_1614,plain,
    ! [X3,X4] :
      ( c_HOL_Oplus__class_Oplus(X3,c_HOL_Ominus__class_Ominus(X4,X3,tc_nat),tc_nat) = X4
      | c_HOL_Oord__class_Oless(X4,X3,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_1007]) ).

fof(c_0_1615,plain,
    ! [X2] :
      ( c_Suc(c_HOL_Ominus__class_Ominus(X2,c_HOL_Oone__class_Oone(tc_nat),tc_nat)) = X2
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_1008]) ).

fof(c_0_1616,plain,
    ! [X2] :
      ( X2 = c_Suc(c_HOL_Ominus__class_Ominus(X2,c_HOL_Oone__class_Oone(tc_nat),tc_nat))
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_1009]) ).

fof(c_0_1617,plain,
    ! [X19,X20,X21] :
      ( ~ class_Orderings_Opreorder(X21)
      | c_HOL_Oord__class_Oless(X20,X19,X21)
      | c_lessequals(X19,X20,X21)
      | ~ c_lessequals(X20,X19,X21) ),
    inference(variable_rename,[status(thm)],[c_0_1010]) ).

fof(c_0_1618,plain,
    ! [X19] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X19)
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X19),c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(X19),c_HOL_Oone__class_Oone(X19),X19),X19) ),
    inference(variable_rename,[status(thm)],[c_0_1011]) ).

fof(c_0_1619,plain,
    ! [X20,X21,X22,X23] :
      ( ~ class_Ring__and__Field_Oidom(X23)
      | ~ class_Int_Onumber__ring(X23)
      | c_HOL_Oplus__class_Oplus(X22,X21,X23) != c_HOL_Oplus__class_Oplus(X22,X20,X23)
      | X21 = X20 ),
    inference(variable_rename,[status(thm)],[c_0_1012]) ).

fof(c_0_1620,plain,
    ! [X8,X9,X10] :
      ( c_HOL_Otimes__class_Otimes(c_Suc(X10),X9,tc_nat) != c_HOL_Otimes__class_Otimes(c_Suc(X10),X8,tc_nat)
      | X9 = X8 ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1013])])]) ).

fof(c_0_1621,plain,
    ! [X9,X10] :
      ( c_Lambda_Olift(c_Lambda_OdB_OVar(X10),X9) = c_Lambda_OdB_OVar(c_HOL_Oplus__class_Oplus(X10,c_HOL_Oone__class_Oone(tc_nat),tc_nat))
      | c_HOL_Oord__class_Oless(X10,X9,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_1014]) ).

fof(c_0_1622,plain,
    ! [X19,X20,X21] :
      ( ~ class_Orderings_Oorder(X21)
      | X20 = X19
      | ~ c_lessequals(X19,X20,X21)
      | ~ c_lessequals(X20,X19,X21) ),
    inference(variable_rename,[status(thm)],[c_0_1015]) ).

fof(c_0_1623,plain,
    ! [X19,X20,X21] :
      ( ~ class_Orderings_Oorder(X21)
      | X20 = X19
      | ~ c_lessequals(X19,X20,X21)
      | ~ c_lessequals(X20,X19,X21) ),
    inference(variable_rename,[status(thm)],[c_0_1016]) ).

fof(c_0_1624,plain,
    ! [X19,X20,X21] :
      ( ~ class_Orderings_Oorder(X21)
      | X20 = X19
      | ~ c_lessequals(X20,X19,X21)
      | ~ c_lessequals(X19,X20,X21) ),
    inference(variable_rename,[status(thm)],[c_0_1017]) ).

fof(c_0_1625,plain,
    ! [X19,X20] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X20)
      | c_HOL_Oord__class_Oless(X19,c_HOL_Oplus__class_Oplus(X19,c_HOL_Oone__class_Oone(X20),X20),X20) ),
    inference(variable_rename,[status(thm)],[c_0_1018]) ).

fof(c_0_1626,plain,
    ! [X33,X34,X35,X36] :
      ( ~ class_OrderedGroup_Oab__group__add(X36)
      | c_HOL_Ominus__class_Ominus(X34,X33,X36) != c_HOL_Ominus__class_Ominus(X35,X35,X36)
      | X34 = X33 ),
    inference(variable_rename,[status(thm)],[c_0_1019]) ).

fof(c_0_1627,plain,
    ! [X27,X28,X29,X30] :
      ( ~ class_OrderedGroup_Oab__group__add(X30)
      | c_HOL_Ominus__class_Ominus(X29,X29,X30) != c_HOL_Ominus__class_Ominus(X28,X27,X30)
      | X28 = X27 ),
    inference(variable_rename,[status(thm)],[c_0_1020]) ).

fof(c_0_1628,plain,
    ! [X21,X22,X23,X24] :
      ( ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X24)
      | c_HOL_Oplus__class_Oplus(X23,X22,X24) != c_HOL_Oplus__class_Oplus(X23,X21,X24)
      | X22 = X21 ),
    inference(variable_rename,[status(thm)],[c_0_1021]) ).

fof(c_0_1629,plain,
    ! [X21,X22,X23,X24] :
      ( ~ class_OrderedGroup_Ocancel__semigroup__add(X24)
      | c_HOL_Oplus__class_Oplus(X23,X22,X24) != c_HOL_Oplus__class_Oplus(X23,X21,X24)
      | X22 = X21 ),
    inference(variable_rename,[status(thm)],[c_0_1022]) ).

fof(c_0_1630,plain,
    ! [X21,X22,X23,X24] :
      ( ~ class_OrderedGroup_Ocancel__semigroup__add(X24)
      | c_HOL_Oplus__class_Oplus(X22,X23,X24) != c_HOL_Oplus__class_Oplus(X21,X23,X24)
      | X22 = X21 ),
    inference(variable_rename,[status(thm)],[c_0_1023]) ).

fof(c_0_1631,plain,
    ! [X19,X20] :
      ( ~ class_Orderings_Olinorder(X20)
      | ~ c_lessequals(X19,X19,X20)
      | ~ c_HOL_Oord__class_Oless(X19,X19,X20) ),
    inference(variable_rename,[status(thm)],[c_0_1024]) ).

fof(c_0_1632,plain,
    ! [X19,X20,X21] :
      ( ~ class_Orderings_Olinorder(X21)
      | ~ c_HOL_Oord__class_Oless(X20,X19,X21)
      | ~ c_lessequals(X19,X20,X21) ),
    inference(variable_rename,[status(thm)],[c_0_1025]) ).

fof(c_0_1633,plain,
    ! [X19,X20,X21] :
      ( ~ class_Orderings_Olinorder(X21)
      | ~ c_lessequals(X20,X19,X21)
      | ~ c_HOL_Oord__class_Oless(X19,X20,X21) ),
    inference(variable_rename,[status(thm)],[c_0_1026]) ).

fof(c_0_1634,plain,
    ! [X19,X20,X21] :
      ( ~ class_Orderings_Opreorder(X21)
      | ~ c_lessequals(X19,X20,X21)
      | ~ c_HOL_Oord__class_Oless(X20,X19,X21) ),
    inference(variable_rename,[status(thm)],[c_0_1027]) ).

fof(c_0_1635,plain,
    ! [X19,X20,X21] :
      ( ~ class_Orderings_Oorder(X21)
      | ~ c_HOL_Oord__class_Oless(X20,X19,X21)
      | ~ c_HOL_Oord__class_Oless(X19,X20,X21) ),
    inference(variable_rename,[status(thm)],[c_0_1028]) ).

fof(c_0_1636,plain,
    ! [X19,X20,X21] :
      ( ~ class_Orderings_Olinorder(X21)
      | ~ c_HOL_Oord__class_Oless(X20,X19,X21)
      | ~ c_HOL_Oord__class_Oless(X19,X20,X21) ),
    inference(variable_rename,[status(thm)],[c_0_1029]) ).

fof(c_0_1637,plain,
    ! [X19,X20,X21] :
      ( ~ class_Orderings_Opreorder(X21)
      | ~ c_HOL_Oord__class_Oless(X19,X20,X21)
      | ~ c_HOL_Oord__class_Oless(X20,X19,X21) ),
    inference(variable_rename,[status(thm)],[c_0_1030]) ).

fof(c_0_1638,plain,
    ! [X19,X20,X21] :
      ( ~ class_Orderings_Opreorder(X21)
      | ~ c_HOL_Oord__class_Oless(X19,X20,X21)
      | ~ c_HOL_Oord__class_Oless(X20,X19,X21) ),
    inference(variable_rename,[status(thm)],[c_0_1031]) ).

fof(c_0_1639,plain,
    ! [X3,X4] :
      ( X3 = X4
      | ~ c_HOL_Oord__class_Oless(X3,c_Suc(X4),tc_nat)
      | ~ c_lessequals(X4,X3,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_1032]) ).

fof(c_0_1640,plain,
    ! [X3,X4] :
      ( ~ c_lessequals(X4,X3,tc_nat)
      | ~ c_lessequals(c_Suc(X3),X4,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_1033]) ).

fof(c_0_1641,plain,
    ! [X3,X4] :
      ( ~ c_HOL_Oord__class_Oless(X4,X3,tc_nat)
      | ~ c_HOL_Oord__class_Oless(X3,c_Suc(X4),tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_1034]) ).

fof(c_0_1642,plain,
    ! [X3,X4] :
      ( c_HOL_Ominus__class_Ominus(X3,X4,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)
      | c_HOL_Ominus__class_Ominus(X4,X3,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)
      | X4 = X3 ),
    inference(variable_rename,[status(thm)],[c_0_1035]) ).

fof(c_0_1643,plain,
    ! [X19,X20] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X20)
      | c_lessequals(c_HOL_Ozero__class_Ozero(X20),c_HOL_Otimes__class_Otimes(X19,X19,X20),X20) ),
    inference(variable_rename,[status(thm)],[c_0_1036]) ).

fof(c_0_1644,plain,
    ! [X8,X9,X10] :
      ( c_HOL_Otimes__class_Otimes(X10,X9,tc_nat) != c_HOL_Otimes__class_Otimes(X10,X8,tc_nat)
      | X9 = X8
      | X10 = c_HOL_Ozero__class_Ozero(tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_1037]) ).

fof(c_0_1645,plain,
    ! [X8,X9,X10] :
      ( c_HOL_Otimes__class_Otimes(X10,X9,tc_nat) != c_HOL_Otimes__class_Otimes(X10,X8,tc_nat)
      | X10 = c_HOL_Ozero__class_Ozero(tc_nat)
      | X9 = X8 ),
    inference(variable_rename,[status(thm)],[c_0_1038]) ).

fof(c_0_1646,plain,
    ! [X8,X9,X10] :
      ( c_HOL_Otimes__class_Otimes(X9,X10,tc_nat) != c_HOL_Otimes__class_Otimes(X8,X10,tc_nat)
      | X10 = c_HOL_Ozero__class_Ozero(tc_nat)
      | X9 = X8 ),
    inference(variable_rename,[status(thm)],[c_0_1039]) ).

fof(c_0_1647,plain,
    ! [X19,X20,X21] :
      ( ~ class_Divides_Osemiring__div(X21)
      | c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X20,X19,X21),X19,X21) = c_HOL_Ozero__class_Ozero(X21) ),
    inference(variable_rename,[status(thm)],[c_0_1040]) ).

fof(c_0_1648,plain,
    ! [X19,X20,X21] :
      ( ~ class_Divides_Osemiring__div(X21)
      | c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X19,X20,X21),X19,X21) = c_HOL_Ozero__class_Ozero(X21) ),
    inference(variable_rename,[status(thm)],[c_0_1041]) ).

fof(c_0_1649,plain,
    ! [X3,X4] :
      ( X4 = X3
      | ~ c_lessequals(X3,X4,tc_nat)
      | ~ c_lessequals(X4,X3,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_1042]) ).

fof(c_0_1650,plain,
    ! [X19,X20,X21] :
      ( ~ class_OrderedGroup_Ogroup__add(X21)
      | c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X20,X19,X21),X19,X21) = X20 ),
    inference(variable_rename,[status(thm)],[c_0_1043]) ).

fof(c_0_1651,plain,
    ! [X19,X20,X21] :
      ( ~ class_Orderings_Olinorder(X21)
      | c_Orderings_Oord__class_Omin(X20,c_Orderings_Oord__class_Omax(X20,X19,X21),X21) = X20 ),
    inference(variable_rename,[status(thm)],[c_0_1044]) ).

fof(c_0_1652,plain,
    ! [X19,X20,X21] :
      ( ~ class_Orderings_Olinorder(X21)
      | c_Orderings_Oord__class_Omax(X20,c_Orderings_Oord__class_Omin(X20,X19,X21),X21) = X20 ),
    inference(variable_rename,[status(thm)],[c_0_1045]) ).

fof(c_0_1653,plain,
    ! [X19,X20,X21] :
      ( ~ class_OrderedGroup_Ogroup__add(X21)
      | c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X20,X19,X21),X19,X21) = X20 ),
    inference(variable_rename,[status(thm)],[c_0_1046]) ).

fof(c_0_1654,plain,
    ! [X19,X20,X21] :
      ( ~ class_Orderings_Olinorder(X21)
      | c_lessequals(X20,c_Orderings_Oord__class_Omax(X20,X19,X21),X21) ),
    inference(variable_rename,[status(thm)],[c_0_1047]) ).

fof(c_0_1655,plain,
    ! [X19,X20,X21] :
      ( ~ class_Orderings_Olinorder(X21)
      | c_lessequals(X19,c_Orderings_Oord__class_Omax(X20,X19,X21),X21) ),
    inference(variable_rename,[status(thm)],[c_0_1048]) ).

fof(c_0_1656,plain,
    ! [X19,X20,X21] :
      ( ~ class_Orderings_Olinorder(X21)
      | c_lessequals(c_Orderings_Oord__class_Omin(X20,X19,X21),X20,X21) ),
    inference(variable_rename,[status(thm)],[c_0_1049]) ).

fof(c_0_1657,plain,
    ! [X19,X20,X21] :
      ( ~ class_Orderings_Olinorder(X21)
      | c_lessequals(c_Orderings_Oord__class_Omin(X20,X19,X21),X19,X21) ),
    inference(variable_rename,[status(thm)],[c_0_1050]) ).

fof(c_0_1658,plain,
    ! [X20,X21,X22] :
      ( c_HOL_Oplus__class_Oplus(X22,X21,tc_nat) != c_HOL_Oplus__class_Oplus(X22,X20,tc_nat)
      | X21 = X20 ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1051])])]) ).

fof(c_0_1659,plain,
    ! [X8,X9,X10] :
      ( c_HOL_Oplus__class_Oplus(X9,X10,tc_nat) != c_HOL_Oplus__class_Oplus(X8,X10,tc_nat)
      | X9 = X8 ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1052])])]) ).

fof(c_0_1660,plain,
    ! [X8,X9,X10] :
      ( c_HOL_Oplus__class_Oplus(X10,X9,tc_nat) != c_HOL_Oplus__class_Oplus(X10,X8,tc_nat)
      | X9 = X8 ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1053])])]) ).

fof(c_0_1661,plain,
    ! [X3,X4] :
      ( c_lessequals(X3,X4,tc_nat)
      | ~ c_lessequals(c_Suc(X3),c_Suc(X4),tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_1054]) ).

fof(c_0_1662,plain,
    ! [X3,X4] :
      ( c_HOL_Oord__class_Oless(X4,X3,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_Suc(X4),c_Suc(X3),tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_1055]) ).

fof(c_0_1663,plain,
    ! [X3,X4] :
      ( X4 = c_Suc(X3)
      | c_lessequals(X4,X3,tc_nat)
      | ~ c_lessequals(X4,c_Suc(X3),tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_1056]) ).

fof(c_0_1664,plain,
    ! [X19,X20,X21] :
      ( ~ class_Orderings_Oorder(X21)
      | c_HOL_Oord__class_Oless(X19,X20,X21)
      | X20 = X19
      | ~ c_lessequals(X19,X20,X21) ),
    inference(variable_rename,[status(thm)],[c_0_1057]) ).

fof(c_0_1665,plain,
    ! [X19,X20,X21] :
      ( ~ class_Orderings_Oorder(X21)
      | c_HOL_Oord__class_Oless(X19,X20,X21)
      | ~ c_lessequals(X19,X20,X21)
      | X20 = X19 ),
    inference(variable_rename,[status(thm)],[c_0_1058]) ).

fof(c_0_1666,plain,
    ! [X19,X20,X21] :
      ( ~ class_Orderings_Oorder(X21)
      | X20 = X19
      | c_HOL_Oord__class_Oless(X20,X19,X21)
      | ~ c_lessequals(X20,X19,X21) ),
    inference(variable_rename,[status(thm)],[c_0_1059]) ).

fof(c_0_1667,plain,
    ! [X19,X20,X21] :
      ( ~ class_Orderings_Oorder(X21)
      | c_HOL_Oord__class_Oless(X20,X19,X21)
      | X20 = X19
      | ~ c_lessequals(X20,X19,X21) ),
    inference(variable_rename,[status(thm)],[c_0_1060]) ).

fof(c_0_1668,plain,
    ! [X19,X20,X21] :
      ( ~ class_Orderings_Oorder(X21)
      | c_HOL_Oord__class_Oless(X20,X19,X21)
      | X20 = X19
      | ~ c_lessequals(X20,X19,X21) ),
    inference(variable_rename,[status(thm)],[c_0_1061]) ).

fof(c_0_1669,plain,
    ! [X19,X20,X21] :
      ( ~ class_Orderings_Oorder(X21)
      | c_HOL_Oord__class_Oless(X20,X19,X21)
      | ~ c_lessequals(X20,X19,X21)
      | X20 = X19 ),
    inference(variable_rename,[status(thm)],[c_0_1062]) ).

fof(c_0_1670,plain,
    ! [X19,X20,X21] :
      ( ~ class_Orderings_Olinorder(X21)
      | X20 = X19
      | ~ c_lessequals(X20,X19,X21)
      | c_HOL_Oord__class_Oless(X20,X19,X21) ),
    inference(variable_rename,[status(thm)],[c_0_1063]) ).

fof(c_0_1671,plain,
    ! [X19,X20,X21] :
      ( ~ class_Orderings_Olinorder(X21)
      | X20 = X19
      | c_HOL_Oord__class_Oless(X20,X19,X21)
      | ~ c_lessequals(X20,X19,X21) ),
    inference(variable_rename,[status(thm)],[c_0_1064]) ).

fof(c_0_1672,plain,
    ! [X19,X20,X21] :
      ( ~ class_Orderings_Olinorder(X21)
      | c_Orderings_Oord__class_Omax(X20,X19,X21) != X19
      | c_lessequals(X20,X19,X21) ),
    inference(variable_rename,[status(thm)],[c_0_1065]) ).

fof(c_0_1673,plain,
    ! [X19,X20,X21] :
      ( ~ class_Orderings_Olinorder(X21)
      | c_Orderings_Oord__class_Omin(X20,X19,X21) != X20
      | c_lessequals(X20,X19,X21) ),
    inference(variable_rename,[status(thm)],[c_0_1066]) ).

fof(c_0_1674,plain,
    ! [X3,X4] :
      ( c_lessequals(c_Suc(X3),c_Suc(X4),tc_nat)
      | ~ c_lessequals(X3,X4,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_1067]) ).

fof(c_0_1675,plain,
    ! [X4,X5] :
      ( c_HOL_Oord__class_Oless(c_Suc(X4),c_Suc(X5),tc_nat)
      | ~ c_HOL_Oord__class_Oless(X4,X5,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_1068]) ).

fof(c_0_1676,plain,
    ! [X3,X4] :
      ( c_HOL_Oord__class_Oless(c_Suc(X4),c_Suc(X3),tc_nat)
      | ~ c_HOL_Oord__class_Oless(X4,X3,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_1069]) ).

fof(c_0_1677,plain,
    ! [X19,X20,X21] :
      ( ~ class_Orderings_Olinorder(X21)
      | c_Orderings_Oord__class_Omax(X20,X19,X21) = X19
      | ~ c_lessequals(X20,X19,X21) ),
    inference(variable_rename,[status(thm)],[c_0_1070]) ).

fof(c_0_1678,plain,
    ! [X19,X20,X21] :
      ( ~ class_Orderings_Olinorder(X21)
      | c_Orderings_Oord__class_Omax(X20,X19,X21) = X20
      | ~ c_lessequals(X19,X20,X21) ),
    inference(variable_rename,[status(thm)],[c_0_1071]) ).

fof(c_0_1679,plain,
    ! [X19,X20,X21] :
      ( ~ class_Orderings_Olinorder(X21)
      | c_Orderings_Oord__class_Omin(X20,X19,X21) = X20
      | ~ c_lessequals(X20,X19,X21) ),
    inference(variable_rename,[status(thm)],[c_0_1072]) ).

fof(c_0_1680,plain,
    ! [X19,X20,X21] :
      ( ~ class_Orderings_Olinorder(X21)
      | c_Orderings_Oord__class_Omin(X20,X19,X21) = X19
      | ~ c_lessequals(X19,X20,X21) ),
    inference(variable_rename,[status(thm)],[c_0_1073]) ).

fof(c_0_1681,plain,
    ! [X3,X4] :
      ( X3 = X4
      | ~ c_HOL_Oord__class_Oless(X3,c_Suc(X4),tc_nat)
      | c_HOL_Oord__class_Oless(X3,X4,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_1074]) ).

fof(c_0_1682,plain,
    ! [X3,X4] :
      ( X4 = X3
      | ~ c_HOL_Oord__class_Oless(X3,c_Suc(X4),tc_nat)
      | c_HOL_Oord__class_Oless(X3,X4,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_1075]) ).

fof(c_0_1683,plain,
    ! [X3,X4] :
      ( X4 = X3
      | c_HOL_Oord__class_Oless(X4,X3,tc_nat)
      | ~ c_HOL_Oord__class_Oless(X4,c_Suc(X3),tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_1076]) ).

fof(c_0_1684,plain,
    ! [X16,X17,X18] :
      ( c_Lambda_Osubst(c_Lambda_OdB_OVar(X17),X16,X18) = c_Lambda_OdB_OVar(X17)
      | ~ c_HOL_Oord__class_Oless(X17,X18,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_1077]) ).

fof(c_0_1685,plain,
    ! [X3,X4] :
      ( c_HOL_Oord__class_Oless(c_Suc(X4),X3,tc_nat)
      | c_Suc(X4) = X3
      | ~ c_HOL_Oord__class_Oless(X4,X3,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_1078]) ).

fof(c_0_1686,plain,
    ! [X19,X20,X21] :
      ( ~ class_Orderings_Oorder(X21)
      | c_lessequals(X20,X19,X21)
      | ~ c_HOL_Oord__class_Oless(X20,X19,X21) ),
    inference(variable_rename,[status(thm)],[c_0_1079]) ).

fof(c_0_1687,plain,
    ! [X19,X20,X21] :
      ( ~ class_Orderings_Opreorder(X21)
      | c_lessequals(X20,X19,X21)
      | ~ c_HOL_Oord__class_Oless(X20,X19,X21) ),
    inference(variable_rename,[status(thm)],[c_0_1080]) ).

fof(c_0_1688,plain,
    ! [X3,X4] :
      ( c_HOL_Oord__class_Oless(X4,X3,tc_nat)
      | ~ c_lessequals(c_Suc(X4),X3,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_1081]) ).

fof(c_0_1689,plain,
    ! [X3,X4] :
      ( c_HOL_Oord__class_Oless(X3,X4,tc_nat)
      | ~ c_lessequals(c_Suc(X3),X4,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_1082]) ).

fof(c_0_1690,plain,
    ! [X3,X4] :
      ( c_lessequals(X4,X3,tc_nat)
      | ~ c_HOL_Oord__class_Oless(X4,c_Suc(X3),tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_1083]) ).

fof(c_0_1691,plain,
    ! [X3,X4] :
      ( c_HOL_Oord__class_Oless(X4,X3,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_Suc(X4),X3,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_1084]) ).

fof(c_0_1692,plain,
    ! [X3,X4] :
      ( c_lessequals(X4,X3,tc_nat)
      | ~ c_lessequals(c_Suc(X4),X3,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_1085]) ).

fof(c_0_1693,plain,
    ! [X3,X4] :
      ( c_lessequals(c_Suc(X4),X3,tc_nat)
      | ~ c_HOL_Oord__class_Oless(X4,X3,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_1086]) ).

fof(c_0_1694,plain,
    ! [X3,X4] :
      ( c_lessequals(c_Suc(X3),X4,tc_nat)
      | ~ c_HOL_Oord__class_Oless(X3,X4,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_1087]) ).

fof(c_0_1695,plain,
    ! [X3,X4] :
      ( c_HOL_Oord__class_Oless(X4,c_Suc(X3),tc_nat)
      | ~ c_lessequals(X4,X3,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_1088]) ).

fof(c_0_1696,plain,
    ! [X4] :
      ( ~ c_lessequals(X4,X4,tc_nat)
      | c_HOL_Oord__class_Oless(X4,c_Suc(X4),tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_1089]) ).

fof(c_0_1697,plain,
    ! [X3,X4] :
      ( c_HOL_Oord__class_Oless(X4,c_Suc(X3),tc_nat)
      | ~ c_HOL_Oord__class_Oless(X4,X3,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_1090]) ).

fof(c_0_1698,plain,
    ! [X3,X4] :
      ( c_lessequals(X4,c_Suc(X3),tc_nat)
      | ~ c_lessequals(X4,X3,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_1091]) ).

fof(c_0_1699,plain,
    ! [X3,X4] :
      ( c_HOL_Ominus__class_Ominus(X4,X3,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)
      | c_lessequals(X4,X3,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_1092]) ).

fof(c_0_1700,plain,
    ! [X3,X4] :
      ( c_HOL_Ominus__class_Ominus(X4,X3,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat)
      | ~ c_lessequals(X4,X3,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_1093]) ).

fof(c_0_1701,plain,
    ! [X3,X4] :
      ( c_HOL_Oord__class_Oless(X4,X3,tc_nat)
      | X4 = X3
      | ~ c_lessequals(X4,X3,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_1094]) ).

fof(c_0_1702,plain,
    ! [X3,X4] :
      ( X4 = X3
      | c_HOL_Oord__class_Oless(X4,X3,tc_nat)
      | ~ c_lessequals(X4,X3,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_1095]) ).

fof(c_0_1703,plain,
    ! [X3,X4] :
      ( c_HOL_Oord__class_Oless(X4,X3,tc_nat)
      | X4 = X3
      | ~ c_lessequals(X4,X3,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_1096]) ).

fof(c_0_1704,plain,
    ! [X3,X4] :
      ( c_Divides_Odiv__class_Omod(X4,X3,tc_nat) = X4
      | ~ c_HOL_Oord__class_Oless(X4,X3,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_1097]) ).

fof(c_0_1705,plain,
    ! [X10,X11] :
      ( c_lessequals(X11,X10,tc_nat)
      | ~ c_HOL_Oord__class_Oless(X11,X10,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_1098]) ).

fof(c_0_1706,plain,
    ! [X3,X4] :
      ( c_lessequals(X4,X3,tc_nat)
      | ~ c_HOL_Oord__class_Oless(X4,X3,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_1099]) ).

fof(c_0_1707,plain,
    ! [X9,X10,X11] :
      ( c_Lambda_Osubst(c_Lambda_OdB_OVar(X11),X9,X10) = c_Lambda_OdB_OVar(X11)
      | X11 = X10
      | c_HOL_Oord__class_Oless(X10,X11,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_1100]) ).

fof(c_0_1708,plain,
    ! [X19,X20,X21] :
      ( ~ class_Ring__and__Field_Oordered__idom(X21)
      | c_HOL_Oord__class_Oless(X19,X20,X21)
      | c_HOL_Oord__class_Oless(X20,X19,X21)
      | X20 = X19 ),
    inference(variable_rename,[status(thm)],[c_0_1101]) ).

fof(c_0_1709,plain,
    ! [X19,X20,X21] :
      ( ~ class_Orderings_Olinorder(X21)
      | X20 = X19
      | c_HOL_Oord__class_Oless(X19,X20,X21)
      | c_HOL_Oord__class_Oless(X20,X19,X21) ),
    inference(variable_rename,[status(thm)],[c_0_1102]) ).

fof(c_0_1710,plain,
    ! [X19,X20,X21] :
      ( ~ class_Orderings_Olinorder(X21)
      | c_HOL_Oord__class_Oless(X19,X20,X21)
      | c_HOL_Oord__class_Oless(X20,X19,X21)
      | X20 = X19 ),
    inference(variable_rename,[status(thm)],[c_0_1103]) ).

fof(c_0_1711,plain,
    ! [X19,X20,X21] :
      ( ~ class_Orderings_Olinorder(X21)
      | c_HOL_Oord__class_Oless(X19,X20,X21)
      | X20 = X19
      | c_HOL_Oord__class_Oless(X20,X19,X21) ),
    inference(variable_rename,[status(thm)],[c_0_1104]) ).

fof(c_0_1712,plain,
    ! [X19,X20,X21] :
      ( ~ class_Orderings_Olinorder(X21)
      | X20 = X19
      | c_HOL_Oord__class_Oless(X20,X19,X21)
      | c_HOL_Oord__class_Oless(X19,X20,X21) ),
    inference(variable_rename,[status(thm)],[c_0_1105]) ).

fof(c_0_1713,plain,
    ! [X19,X20,X21] :
      ( ~ class_Orderings_Olinorder(X21)
      | c_HOL_Oord__class_Oless(X20,X19,X21)
      | c_lessequals(X19,X20,X21) ),
    inference(variable_rename,[status(thm)],[c_0_1106]) ).

fof(c_0_1714,plain,
    ! [X19,X20] :
      ( ~ class_Orderings_Olinorder(X20)
      | c_HOL_Oord__class_Oless(X19,X19,X20)
      | c_lessequals(X19,X19,X20) ),
    inference(variable_rename,[status(thm)],[c_0_1107]) ).

fof(c_0_1715,plain,
    ! [X19,X20,X21] :
      ( ~ class_Orderings_Olinorder(X21)
      | c_lessequals(X19,X20,X21)
      | c_HOL_Oord__class_Oless(X20,X19,X21) ),
    inference(variable_rename,[status(thm)],[c_0_1108]) ).

fof(c_0_1716,plain,
    ! [X19,X20,X21] :
      ( ~ class_Orderings_Olinorder(X21)
      | c_HOL_Oord__class_Oless(X19,X20,X21)
      | c_lessequals(X20,X19,X21) ),
    inference(variable_rename,[status(thm)],[c_0_1109]) ).

fof(c_0_1717,plain,
    ! [X19,X20,X21] :
      ( ~ class_Orderings_Olinorder(X21)
      | c_lessequals(X19,X20,X21)
      | c_lessequals(X20,X19,X21) ),
    inference(variable_rename,[status(thm)],[c_0_1110]) ).

fof(c_0_1718,plain,
    ! [X21,X22,X23] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X23)
      | c_HOL_Oplus__class_Oplus(X22,X21,X23) = c_HOL_Oplus__class_Oplus(X21,X22,X23) ),
    inference(variable_rename,[status(thm)],[c_0_1111]) ).

fof(c_0_1719,plain,
    ! [X19,X20,X21] :
      ( ~ class_OrderedGroup_Ocomm__monoid__add(X21)
      | c_HOL_Oplus__class_Oplus(X20,X19,X21) = c_HOL_Oplus__class_Oplus(X19,X20,X21) ),
    inference(variable_rename,[status(thm)],[c_0_1112]) ).

fof(c_0_1720,plain,
    ! [X19,X20,X21] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X21)
      | c_HOL_Oplus__class_Oplus(X20,X19,X21) = c_HOL_Oplus__class_Oplus(X19,X20,X21) ),
    inference(variable_rename,[status(thm)],[c_0_1113]) ).

fof(c_0_1721,plain,
    ! [X19,X20,X21] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X21)
      | c_HOL_Otimes__class_Otimes(X20,X19,X21) = c_HOL_Otimes__class_Otimes(X19,X20,X21) ),
    inference(variable_rename,[status(thm)],[c_0_1114]) ).

fof(c_0_1722,plain,
    ! [X19,X20,X21] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X21)
      | c_HOL_Otimes__class_Otimes(X20,X19,X21) = c_HOL_Otimes__class_Otimes(X19,X20,X21) ),
    inference(variable_rename,[status(thm)],[c_0_1115]) ).

fof(c_0_1723,plain,
    ! [X19,X20,X21] :
      ( ~ class_Orderings_Olinorder(X21)
      | c_Orderings_Oord__class_Omin(X20,X19,X21) = c_Orderings_Oord__class_Omin(X19,X20,X21) ),
    inference(variable_rename,[status(thm)],[c_0_1116]) ).

fof(c_0_1724,plain,
    ! [X19,X20,X21] :
      ( ~ class_Orderings_Olinorder(X21)
      | c_Orderings_Oord__class_Omax(X20,X19,X21) = c_Orderings_Oord__class_Omax(X19,X20,X21) ),
    inference(variable_rename,[status(thm)],[c_0_1117]) ).

fof(c_0_1725,plain,
    ! [X6,X7] :
      ( c_HOL_Oord__class_Oless(X6,X6,tc_nat)
      | c_Lambda_Osubst(c_Lambda_OdB_OVar(X6),X7,X6) = X7 ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1118])])]) ).

fof(c_0_1726,plain,
    ! [X3,X4] :
      ( c_lessequals(c_Suc(X3),X4,tc_nat)
      | c_lessequals(X4,X3,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_1119]) ).

fof(c_0_1727,plain,
    ! [X4] :
      ( c_HOL_Oord__class_Oless(X4,X4,tc_nat)
      | c_HOL_Oord__class_Oless(X4,c_Suc(X4),tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_1120]) ).

fof(c_0_1728,plain,
    ! [X3,X4] :
      ( c_HOL_Oord__class_Oless(X3,c_Suc(X4),tc_nat)
      | c_HOL_Oord__class_Oless(X4,X3,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_1121]) ).

fof(c_0_1729,plain,
    ! [X19] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X19)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X19),c_HOL_Ozero__class_Ozero(X19),X19) ),
    inference(variable_rename,[status(thm)],[c_0_1122]) ).

fof(c_0_1730,plain,
    ! [X19] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X19)
      | ~ c_lessequals(c_HOL_Oone__class_Oone(X19),c_HOL_Ozero__class_Ozero(X19),X19) ),
    inference(variable_rename,[status(thm)],[c_0_1123]) ).

fof(c_0_1731,plain,
    ! [X3,X4] :
      ( c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != c_HOL_Oplus__class_Oplus(X4,X3,tc_nat)
      | X3 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
      | X4 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
    inference(variable_rename,[status(thm)],[c_0_1124]) ).

fof(c_0_1732,plain,
    ! [X3,X4] :
      ( c_HOL_Oplus__class_Oplus(X4,X3,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
      | X3 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
      | X4 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
    inference(variable_rename,[status(thm)],[c_0_1125]) ).

fof(c_0_1733,plain,
    ! [X19,X20,X21] :
      ( ~ class_Ring__and__Field_Oring__no__zero__divisors(X21)
      | c_HOL_Otimes__class_Otimes(X20,X19,X21) != c_HOL_Ozero__class_Ozero(X21)
      | X19 = c_HOL_Ozero__class_Ozero(X21)
      | X20 = c_HOL_Ozero__class_Ozero(X21) ),
    inference(variable_rename,[status(thm)],[c_0_1126]) ).

fof(c_0_1734,plain,
    ! [X19,X20,X21] :
      ( ~ class_Ring__and__Field_Ono__zero__divisors(X21)
      | c_HOL_Otimes__class_Otimes(X20,X19,X21) != c_HOL_Ozero__class_Ozero(X21)
      | X19 = c_HOL_Ozero__class_Ozero(X21)
      | X20 = c_HOL_Ozero__class_Ozero(X21) ),
    inference(variable_rename,[status(thm)],[c_0_1127]) ).

fof(c_0_1735,plain,
    ! [X19,X20,X21] :
      ( ~ class_Ring__and__Field_Ono__zero__divisors(X21)
      | c_HOL_Otimes__class_Otimes(X20,X19,X21) != c_HOL_Ozero__class_Ozero(X21)
      | X20 = c_HOL_Ozero__class_Ozero(X21)
      | X19 = c_HOL_Ozero__class_Ozero(X21) ),
    inference(variable_rename,[status(thm)],[c_0_1128]) ).

fof(c_0_1736,plain,
    ! [X3,X4] :
      ( c_HOL_Oord__class_Oless(X3,X4,tc_nat)
      | c_HOL_Oord__class_Oless(X4,X3,tc_nat)
      | X4 = X3 ),
    inference(variable_rename,[status(thm)],[c_0_1129]) ).

fof(c_0_1737,plain,
    ! [X10,X11] :
      ( c_HOL_Oord__class_Oless(X10,X11,tc_nat)
      | c_HOL_Oord__class_Oless(X11,X10,tc_nat)
      | X11 = X10 ),
    inference(variable_rename,[status(thm)],[c_0_1130]) ).

fof(c_0_1738,plain,
    ! [X19,X20,X21] :
      ( ~ class_Ring__and__Field_Oidom(X21)
      | ~ class_Int_Onumber__ring(X21)
      | c_HOL_Ominus__class_Ominus(X20,X19,X21) != c_HOL_Ozero__class_Ozero(X21)
      | X20 = X19 ),
    inference(variable_rename,[status(thm)],[c_0_1131]) ).

fof(c_0_1739,plain,
    ! [X9,X10] :
      ( c_Lambda_Olift(c_Lambda_OdB_OVar(X10),X9) = c_Lambda_OdB_OVar(X10)
      | ~ c_HOL_Oord__class_Oless(X10,X9,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_1132]) ).

fof(c_0_1740,plain,
    ! [X19,X20,X21] :
      ( ~ class_Ring__and__Field_Oidom(X21)
      | ~ class_Int_Onumber__ring(X21)
      | X19 != c_HOL_Oplus__class_Oplus(X19,X20,X21)
      | X20 = c_HOL_Ozero__class_Ozero(X21) ),
    inference(variable_rename,[status(thm)],[c_0_1133]) ).

fof(c_0_1741,plain,
    ! [X2] :
      ( X2 = c_HOL_Ozero__class_Ozero(tc_nat)
      | ~ c_HOL_Oord__class_Oless(X2,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_1134]) ).

fof(c_0_1742,plain,
    ! [X3,X4] :
      ( c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != c_HOL_Oplus__class_Oplus(X4,X3,tc_nat)
      | X3 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
      | X3 = c_HOL_Ozero__class_Ozero(tc_nat) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1135])])]) ).

fof(c_0_1743,plain,
    ! [X3,X4] :
      ( c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != c_HOL_Oplus__class_Oplus(X4,X3,tc_nat)
      | X4 = c_HOL_Ozero__class_Ozero(tc_nat)
      | X4 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
    inference(variable_rename,[status(thm)],[c_0_1136]) ).

fof(c_0_1744,plain,
    ! [X3,X4] :
      ( c_HOL_Oplus__class_Oplus(X4,X3,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
      | X3 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
      | X3 = c_HOL_Ozero__class_Ozero(tc_nat) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1137])])]) ).

fof(c_0_1745,plain,
    ! [X3,X4] :
      ( c_HOL_Oplus__class_Oplus(X4,X3,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
      | X4 = c_HOL_Ozero__class_Ozero(tc_nat)
      | X4 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
    inference(variable_rename,[status(thm)],[c_0_1138]) ).

fof(c_0_1746,plain,
    ! [X3,X4] :
      ( c_lessequals(X3,X4,tc_nat)
      | c_lessequals(X4,X3,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_1139]) ).

fof(c_0_1747,plain,
    ! [X19,X20] :
      ( ~ class_OrderedGroup_Olordered__ab__group__add(X20)
      | c_HOL_Oplus__class_Oplus(X19,X19,X20) != c_HOL_Ozero__class_Ozero(X20)
      | X19 = c_HOL_Ozero__class_Ozero(X20) ),
    inference(variable_rename,[status(thm)],[c_0_1140]) ).

fof(c_0_1748,plain,
    ! [X3,X4] :
      ( c_HOL_Otimes__class_Otimes(X4,X3,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
      | X4 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
    inference(variable_rename,[status(thm)],[c_0_1141]) ).

fof(c_0_1749,plain,
    ! [X3,X4] :
      ( c_HOL_Otimes__class_Otimes(X4,X3,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
      | X3 = 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_1142])])]) ).

fof(c_0_1750,plain,
    ! [X3,X4] :
      ( c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != c_HOL_Oplus__class_Oplus(X4,X3,tc_nat)
      | X4 = c_HOL_Ozero__class_Ozero(tc_nat)
      | X3 = c_HOL_Ozero__class_Ozero(tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_1143]) ).

fof(c_0_1751,plain,
    ! [X3,X4] :
      ( c_HOL_Oplus__class_Oplus(X4,X3,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
      | X4 = c_HOL_Ozero__class_Ozero(tc_nat)
      | X3 = c_HOL_Ozero__class_Ozero(tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_1144]) ).

fof(c_0_1752,plain,
    ! [X19,X20,X21] :
      ( ~ class_OrderedGroup_Ogroup__add(X21)
      | c_HOL_Ominus__class_Ominus(X20,X19,X21) != c_HOL_Ozero__class_Ozero(X21)
      | X20 = X19 ),
    inference(variable_rename,[status(thm)],[c_0_1145]) ).

fof(c_0_1753,plain,
    ! [X19,X20,X21] :
      ( ~ class_OrderedGroup_Oab__group__add(X21)
      | c_HOL_Ominus__class_Ominus(X20,X19,X21) != c_HOL_Ozero__class_Ozero(X21)
      | X20 = X19 ),
    inference(variable_rename,[status(thm)],[c_0_1146]) ).

fof(c_0_1754,plain,
    ! [X3,X4] :
      ( c_HOL_Otimes__class_Otimes(X4,X3,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)
      | X3 = c_HOL_Ozero__class_Ozero(tc_nat)
      | X4 = c_HOL_Ozero__class_Ozero(tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_1147]) ).

fof(c_0_1755,plain,
    ! [X19,X20] :
      ( ~ class_Orderings_Oorder(X20)
      | ~ c_HOL_Oord__class_Oless(X19,X19,X20) ),
    inference(variable_rename,[status(thm)],[c_0_1148]) ).

fof(c_0_1756,plain,
    ! [X19,X20] :
      ( ~ class_Orderings_Olinorder(X20)
      | ~ c_HOL_Oord__class_Oless(X19,X19,X20) ),
    inference(variable_rename,[status(thm)],[c_0_1149]) ).

fof(c_0_1757,plain,
    ! [X19,X20] :
      ( ~ class_Orderings_Opreorder(X20)
      | ~ c_HOL_Oord__class_Oless(X19,X19,X20) ),
    inference(variable_rename,[status(thm)],[c_0_1150]) ).

fof(c_0_1758,plain,
    ! [X3,X4] :
      ( X4 != c_HOL_Otimes__class_Otimes(X4,X3,tc_nat)
      | X4 = c_HOL_Ozero__class_Ozero(tc_nat)
      | X3 = c_HOL_Oone__class_Oone(tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_1151]) ).

fof(c_0_1759,plain,
    ! [X2] :
      ( X2 = c_HOL_Ozero__class_Ozero(tc_nat)
      | ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_1152]) ).

fof(c_0_1760,plain,
    ! [X3,X4] :
      ( c_HOL_Oplus__class_Oplus(X4,X3,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)
      | X4 = c_HOL_Ozero__class_Ozero(tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_1153]) ).

fof(c_0_1761,plain,
    ! [X3,X4] :
      ( c_HOL_Oplus__class_Oplus(X4,X3,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)
      | X3 = c_HOL_Ozero__class_Ozero(tc_nat) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1154])])]) ).

fof(c_0_1762,plain,
    ! [X3,X4] :
      ( c_HOL_Otimes__class_Otimes(X4,X3,tc_nat) != c_HOL_Oone__class_Oone(tc_nat)
      | X3 = c_HOL_Oone__class_Oone(tc_nat) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1155])])]) ).

fof(c_0_1763,plain,
    ! [X3,X4] :
      ( c_HOL_Otimes__class_Otimes(X4,X3,tc_nat) != c_HOL_Oone__class_Oone(tc_nat)
      | X4 = c_HOL_Oone__class_Oone(tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_1156]) ).

fof(c_0_1764,plain,
    ! [X3,X4] :
      ( c_HOL_Oone__class_Oone(tc_nat) != c_HOL_Otimes__class_Otimes(X4,X3,tc_nat)
      | X4 = c_HOL_Oone__class_Oone(tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_1157]) ).

fof(c_0_1765,plain,
    ! [X3,X4] :
      ( c_HOL_Oone__class_Oone(tc_nat) != c_HOL_Otimes__class_Otimes(X4,X3,tc_nat)
      | X3 = c_HOL_Oone__class_Oone(tc_nat) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1158])])]) ).

fof(c_0_1766,plain,
    ! [X16,X17,X18] :
      ( c_Lambda_Obeta(c_Lambda_OdB_OApp(X16,X18),c_Lambda_OdB_OApp(X16,X17))
      | ~ c_Lambda_Obeta(X18,X17) ),
    inference(variable_rename,[status(thm)],[c_0_1159]) ).

fof(c_0_1767,plain,
    ! [X16,X17,X18] :
      ( c_Lambda_Obeta(c_Lambda_OdB_OApp(X18,X16),c_Lambda_OdB_OApp(X17,X16))
      | ~ c_Lambda_Obeta(X18,X17) ),
    inference(variable_rename,[status(thm)],[c_0_1160]) ).

fof(c_0_1768,plain,
    ! [X9,X10,X11] :
      ( c_Lambda_Obeta(c_Lambda_Olift(X10,X11),c_Lambda_Olift(X9,X11))
      | ~ c_Lambda_Obeta(X10,X9) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1161])])]) ).

fof(c_0_1769,plain,
    ! [X3,X4] :
      ( c_HOL_Oplus__class_Oplus(X4,X3,tc_nat) != X4
      | X3 = c_HOL_Ozero__class_Ozero(tc_nat) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1162])])]) ).

fof(c_0_1770,plain,
    ! [X18,X19] :
      ( X18 != c_HOL_Oplus__class_Oplus(X18,X19,tc_nat)
      | X19 = c_HOL_Ozero__class_Ozero(tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_1163]) ).

fof(c_0_1771,plain,
    ! [X19] :
      ( ~ class_OrderedGroup_Olordered__ab__group__add(X19)
      | c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X19),c_HOL_Ozero__class_Ozero(X19),X19) = c_HOL_Ozero__class_Ozero(X19) ),
    inference(variable_rename,[status(thm)],[c_0_1164]) ).

fof(c_0_1772,plain,
    ! [X19,X20] :
      ( ~ class_Ring__and__Field_Oidom(X20)
      | ~ class_Int_Onumber__ring(X20)
      | X19 = c_HOL_Oplus__class_Oplus(X19,c_HOL_Ozero__class_Ozero(X20),X20) ),
    inference(variable_rename,[status(thm)],[c_0_1165]) ).

fof(c_0_1773,plain,
    ! [X19] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X19)
      | c_lessequals(c_HOL_Ozero__class_Ozero(X19),c_HOL_Oone__class_Oone(X19),X19) ),
    inference(variable_rename,[status(thm)],[c_0_1166]) ).

fof(c_0_1774,plain,
    ! [X19] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X19)
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X19),c_HOL_Oone__class_Oone(X19),X19) ),
    inference(variable_rename,[status(thm)],[c_0_1167]) ).

fof(c_0_1775,plain,
    ! [X19,X20] :
      ( ~ class_Ring__and__Field_Oidom(X20)
      | ~ class_Int_Onumber__ring(X20)
      | c_HOL_Ominus__class_Ominus(X19,X19,X20) = c_HOL_Ozero__class_Ozero(X20) ),
    inference(variable_rename,[status(thm)],[c_0_1168]) ).

fof(c_0_1776,plain,
    ! [X19,X20] :
      ( ~ class_Divides_Osemiring__div(X20)
      | c_Divides_Odiv__class_Omod(c_HOL_Ozero__class_Ozero(X20),X19,X20) = c_HOL_Ozero__class_Ozero(X20) ),
    inference(variable_rename,[status(thm)],[c_0_1169]) ).

fof(c_0_1777,plain,
    ! [X19,X20] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X20)
      | c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X20),X19,X20) = c_HOL_Ozero__class_Ozero(X20) ),
    inference(variable_rename,[status(thm)],[c_0_1170]) ).

fof(c_0_1778,plain,
    ! [X19,X20] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X20)
      | c_HOL_Otimes__class_Otimes(X19,c_HOL_Ozero__class_Ozero(X20),X20) = c_HOL_Ozero__class_Ozero(X20) ),
    inference(variable_rename,[status(thm)],[c_0_1171]) ).

fof(c_0_1779,plain,
    ! [X19,X20] :
      ( ~ class_Ring__and__Field_Oring__no__zero__divisors(X20)
      | c_HOL_Otimes__class_Otimes(X19,c_HOL_Ozero__class_Ozero(X20),X20) = c_HOL_Ozero__class_Ozero(X20) ),
    inference(variable_rename,[status(thm)],[c_0_1172]) ).

fof(c_0_1780,plain,
    ! [X19,X20] :
      ( ~ class_Ring__and__Field_Oring__no__zero__divisors(X20)
      | c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X20),X19,X20) = c_HOL_Ozero__class_Ozero(X20) ),
    inference(variable_rename,[status(thm)],[c_0_1173]) ).

fof(c_0_1781,plain,
    ! [X19,X20] :
      ( ~ class_Ring__and__Field_Omult__zero(X20)
      | c_HOL_Otimes__class_Otimes(X19,c_HOL_Ozero__class_Ozero(X20),X20) = c_HOL_Ozero__class_Ozero(X20) ),
    inference(variable_rename,[status(thm)],[c_0_1174]) ).

fof(c_0_1782,plain,
    ! [X19,X20] :
      ( ~ class_Ring__and__Field_Omult__zero(X20)
      | c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X20),X19,X20) = c_HOL_Ozero__class_Ozero(X20) ),
    inference(variable_rename,[status(thm)],[c_0_1175]) ).

fof(c_0_1783,plain,
    ! [X19,X20] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X20)
      | c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X20),X19,X20) = c_HOL_Ozero__class_Ozero(X20) ),
    inference(variable_rename,[status(thm)],[c_0_1176]) ).

fof(c_0_1784,plain,
    ! [X19,X20] :
      ( ~ class_Divides_Osemiring__div(X20)
      | c_Divides_Odiv__class_Omod(X19,c_HOL_Oone__class_Oone(X20),X20) = c_HOL_Ozero__class_Ozero(X20) ),
    inference(variable_rename,[status(thm)],[c_0_1177]) ).

fof(c_0_1785,plain,
    ! [X19,X20] :
      ( ~ class_Divides_Osemiring__div(X20)
      | c_Divides_Odiv__class_Omod(X19,c_HOL_Ozero__class_Ozero(X20),X20) = X19 ),
    inference(variable_rename,[status(thm)],[c_0_1178]) ).

fof(c_0_1786,plain,
    ! [X19,X20] :
      ( ~ class_OrderedGroup_Ogroup__add(X20)
      | c_HOL_Ominus__class_Ominus(X19,c_HOL_Ozero__class_Ozero(X20),X20) = X19 ),
    inference(variable_rename,[status(thm)],[c_0_1179]) ).

fof(c_0_1787,plain,
    ! [X19,X20] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X20)
      | c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(X20),X19,X20) = X19 ),
    inference(variable_rename,[status(thm)],[c_0_1180]) ).

fof(c_0_1788,plain,
    ! [X19,X20] :
      ( ~ class_OrderedGroup_Ocomm__monoid__mult(X20)
      | c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(X20),X19,X20) = X19 ),
    inference(variable_rename,[status(thm)],[c_0_1181]) ).

fof(c_0_1789,plain,
    ! [X19,X20] :
      ( ~ class_OrderedGroup_Omonoid__mult(X20)
      | c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(X20),X19,X20) = X19 ),
    inference(variable_rename,[status(thm)],[c_0_1182]) ).

fof(c_0_1790,plain,
    ! [X19,X20] :
      ( ~ class_OrderedGroup_Omonoid__mult(X20)
      | c_HOL_Otimes__class_Otimes(X19,c_HOL_Oone__class_Oone(X20),X20) = X19 ),
    inference(variable_rename,[status(thm)],[c_0_1183]) ).

fof(c_0_1791,plain,
    ! [X19,X20] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X20)
      | c_HOL_Otimes__class_Otimes(X19,c_HOL_Oone__class_Oone(X20),X20) = X19 ),
    inference(variable_rename,[status(thm)],[c_0_1184]) ).

fof(c_0_1792,plain,
    ! [X19,X20] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X20)
      | c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(X20),X19,X20) = X19 ),
    inference(variable_rename,[status(thm)],[c_0_1185]) ).

fof(c_0_1793,plain,
    ! [X19,X20] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X20)
      | c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X20),X19,X20) = X19 ),
    inference(variable_rename,[status(thm)],[c_0_1186]) ).

fof(c_0_1794,plain,
    ! [X19,X20] :
      ( ~ class_OrderedGroup_Ocomm__monoid__add(X20)
      | c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X20),X19,X20) = X19 ),
    inference(variable_rename,[status(thm)],[c_0_1187]) ).

fof(c_0_1795,plain,
    ! [X19,X20] :
      ( ~ class_OrderedGroup_Ocomm__monoid__add(X20)
      | c_HOL_Oplus__class_Oplus(X19,c_HOL_Ozero__class_Ozero(X20),X20) = X19 ),
    inference(variable_rename,[status(thm)],[c_0_1188]) ).

fof(c_0_1796,plain,
    ! [X19,X20] :
      ( ~ class_OrderedGroup_Omonoid__add(X20)
      | c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X20),X19,X20) = X19 ),
    inference(variable_rename,[status(thm)],[c_0_1189]) ).

fof(c_0_1797,plain,
    ! [X19,X20] :
      ( ~ class_OrderedGroup_Omonoid__add(X20)
      | c_HOL_Oplus__class_Oplus(X19,c_HOL_Ozero__class_Ozero(X20),X20) = X19 ),
    inference(variable_rename,[status(thm)],[c_0_1190]) ).

fof(c_0_1798,plain,
    ! [X19,X20] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X20)
      | c_HOL_Oplus__class_Oplus(X19,c_HOL_Ozero__class_Ozero(X20),X20) = X19 ),
    inference(variable_rename,[status(thm)],[c_0_1191]) ).

fof(c_0_1799,plain,
    ! [X19,X20] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X20)
      | c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X20),X19,X20) = X19 ),
    inference(variable_rename,[status(thm)],[c_0_1192]) ).

fof(c_0_1800,plain,
    ! [X19,X20] :
      ( ~ class_Divides_Osemiring__div(X20)
      | c_Divides_Odiv__class_Omod(X19,X19,X20) = c_HOL_Ozero__class_Ozero(X20) ),
    inference(variable_rename,[status(thm)],[c_0_1193]) ).

fof(c_0_1801,plain,
    ! [X19,X20] :
      ( ~ class_OrderedGroup_Oab__group__add(X20)
      | c_HOL_Ominus__class_Ominus(X19,X19,X20) = c_HOL_Ozero__class_Ozero(X20) ),
    inference(variable_rename,[status(thm)],[c_0_1194]) ).

fof(c_0_1802,plain,
    ! [X19,X20] :
      ( ~ class_OrderedGroup_Ogroup__add(X20)
      | c_HOL_Ominus__class_Ominus(X19,X19,X20) = c_HOL_Ozero__class_Ozero(X20) ),
    inference(variable_rename,[status(thm)],[c_0_1195]) ).

fof(c_0_1803,plain,
    ! [X19,X20] :
      ( ~ class_OrderedGroup_Ogroup__add(X20)
      | c_HOL_Ominus__class_Ominus(X19,X19,X20) = c_HOL_Ozero__class_Ozero(X20) ),
    inference(variable_rename,[status(thm)],[c_0_1196]) ).

fof(c_0_1804,plain,
    ! [X19,X20] :
      ( ~ class_Orderings_Olinorder(X20)
      | c_Orderings_Oord__class_Omin(X19,X19,X20) = X19 ),
    inference(variable_rename,[status(thm)],[c_0_1197]) ).

fof(c_0_1805,plain,
    ! [X19,X20] :
      ( ~ class_Orderings_Olinorder(X20)
      | c_Orderings_Oord__class_Omax(X19,X19,X20) = X19 ),
    inference(variable_rename,[status(thm)],[c_0_1198]) ).

fof(c_0_1806,plain,
    ! [X19,X20] :
      ( ~ class_OrderedGroup_Oab__semigroup__idem__mult(X20)
      | c_HOL_Otimes__class_Otimes(X19,X19,X20) = X19 ),
    inference(variable_rename,[status(thm)],[c_0_1199]) ).

fof(c_0_1807,plain,
    ! [X19,X20] :
      ( ~ class_Orderings_Oorder(X20)
      | c_lessequals(X19,X19,X20) ),
    inference(variable_rename,[status(thm)],[c_0_1200]) ).

fof(c_0_1808,plain,
    ! [X19,X20] :
      ( ~ class_Orderings_Opreorder(X20)
      | c_lessequals(X19,X19,X20) ),
    inference(variable_rename,[status(thm)],[c_0_1201]) ).

fof(c_0_1809,plain,
    ! [X2] :
      ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat)
      | X2 = c_HOL_Ozero__class_Ozero(tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_1202]) ).

fof(c_0_1810,plain,
    ! [X6,X7] :
      ( c_Lambda_Obeta(c_Lambda_OdB_OAbs(X7),c_Lambda_OdB_OAbs(X6))
      | ~ c_Lambda_Obeta(X7,X6) ),
    inference(variable_rename,[status(thm)],[c_0_1203]) ).

fof(c_0_1811,plain,
    ! [X37,X38,X39,X40] :
      ( c_Lambda_OdB_OApp(X40,X38) != c_Lambda_OdB_OApp(X39,X37)
      | X38 = X37 ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1204])])]) ).

fof(c_0_1812,plain,
    ! [X37,X38,X39,X40] :
      ( c_Lambda_OdB_OApp(X40,X38) != c_Lambda_OdB_OApp(X39,X37)
      | X40 = X39 ),
    inference(variable_rename,[status(thm)],[c_0_1205]) ).

fof(c_0_1813,plain,
    ! [X9,X10] :
      ( c_InductTermi_OIT(c_Lambda_Olift(X9,X10))
      | ~ c_InductTermi_OIT(X9) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1206])])]) ).

fof(c_0_1814,plain,
    ! [X19] :
      ( ~ class_Ring__and__Field_Ozero__neq__one(X19)
      | c_HOL_Oone__class_Oone(X19) != c_HOL_Ozero__class_Ozero(X19) ),
    inference(variable_rename,[status(thm)],[c_0_1207]) ).

fof(c_0_1815,plain,
    ! [X19] :
      ( ~ class_Ring__and__Field_Ozero__neq__one(X19)
      | c_HOL_Ozero__class_Ozero(X19) != c_HOL_Oone__class_Oone(X19) ),
    inference(variable_rename,[status(thm)],[c_0_1208]) ).

fof(c_0_1816,plain,
    ! [X7] :
      ( c_InductTermi_OIT(c_Lambda_OdB_OAbs(X7))
      | ~ c_InductTermi_OIT(X7) ),
    inference(variable_rename,[status(thm)],[c_0_1209]) ).

fof(c_0_1817,plain,
    ! [X12,X13] :
      ( c_Lambda_OdB_OVar(X13) != c_Lambda_OdB_OVar(X12)
      | X13 = X12 ),
    inference(variable_rename,[status(thm)],[c_0_1210]) ).

fof(c_0_1818,plain,
    ! [X14,X15] :
      ( c_Lambda_OdB_OAbs(X15) != c_Lambda_OdB_OAbs(X14)
      | X15 = X14 ),
    inference(variable_rename,[status(thm)],[c_0_1211]) ).

fof(c_0_1819,plain,
    ! [X12,X13] :
      ( c_Suc(X13) != c_Suc(X12)
      | X13 = X12 ),
    inference(variable_rename,[status(thm)],[c_0_1212]) ).

fof(c_0_1820,plain,
    ! [X10,X11] :
      ( c_Suc(X11) != c_Suc(X10)
      | X11 = X10 ),
    inference(variable_rename,[status(thm)],[c_0_1213]) ).

cnf(c_0_1821,plain,
    ( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X4,tc_nat),X3,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X4,tc_nat),X5,tc_nat),tc_nat)
    | ~ c_lessequals(X1,X2,tc_nat)
    | ~ c_HOL_Oord__class_Oless(X3,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),X4,tc_nat),X5,tc_nat),tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_1214]) ).

cnf(c_0_1822,plain,
    ( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X3,tc_nat),X4,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),X5,tc_nat),tc_nat)
    | ~ c_lessequals(X1,X2,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),X3,tc_nat),X4,tc_nat),X5,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_1215]) ).

cnf(c_0_1823,plain,
    ( c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X3,tc_nat),X4,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),X5,tc_nat),tc_nat)
    | ~ c_lessequals(X1,X2,tc_nat)
    | ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),X3,tc_nat),X4,tc_nat),X5,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_1216]) ).

cnf(c_0_1824,plain,
    ( c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X4,tc_nat),X3,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X4,tc_nat),X5,tc_nat),tc_nat)
    | ~ c_lessequals(X1,X2,tc_nat)
    | ~ c_lessequals(X3,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),X4,tc_nat),X5,tc_nat),tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_1217]) ).

cnf(c_0_1825,plain,
    ( c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X5,X4),X1,X4),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X5,X4),X6,X4),X4)
    | ~ c_lessequals(X1,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X3,X4),X5,X4),X6,X4),X4)
    | ~ class_Ring__and__Field_Opordered__ring(X4) ),
    inference(split_conjunct,[status(thm)],[c_0_1218]) ).

cnf(c_0_1826,plain,
    ( c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X4,X3),X5,X3),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X4,X3),X6,X3),X3)
    | ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,X2,X3),X4,X3),X5,X3),X6,X3)
    | ~ class_Ring__and__Field_Opordered__ring(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1219]) ).

cnf(c_0_1827,plain,
    ( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X5,X4),X1,X4),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X5,X4),X6,X4),X4)
    | ~ c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X3,X4),X5,X4),X6,X4),X4)
    | ~ class_Ring__and__Field_Opordered__ring(X4) ),
    inference(split_conjunct,[status(thm)],[c_0_1220]) ).

cnf(c_0_1828,plain,
    ( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X4,X3),X5,X3),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X4,X3),X6,X3),X3)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,X2,X3),X4,X3),X5,X3),X6,X3)
    | ~ class_Ring__and__Field_Opordered__ring(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1221]) ).

cnf(c_0_1829,plain,
    ( c_HOL_Oord__class_Oless(X4,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),X3,tc_nat),X5,tc_nat),tc_nat)
    | ~ c_lessequals(X1,X2,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),X4,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X3,tc_nat),X5,tc_nat),tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_1222]) ).

cnf(c_0_1830,plain,
    ( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),X3,tc_nat),X4,tc_nat),X5,tc_nat)
    | ~ c_lessequals(X1,X2,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X3,tc_nat),X4,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),X5,tc_nat),tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_1223]) ).

cnf(c_0_1831,plain,
    ( c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),X3,tc_nat),X4,tc_nat),X5,tc_nat)
    | ~ c_lessequals(X1,X2,tc_nat)
    | ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X3,tc_nat),X4,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),X5,tc_nat),tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_1224]) ).

cnf(c_0_1832,plain,
    ( c_lessequals(X4,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),X3,tc_nat),X5,tc_nat),tc_nat)
    | ~ c_lessequals(X1,X2,tc_nat)
    | ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),X4,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X3,tc_nat),X5,tc_nat),tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_1225]) ).

cnf(c_0_1833,plain,
    ( c_lessequals(X4,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X5,X1,X3),X2,X3),X6,X3),X3)
    | ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X5,X2,X3),X6,X3),X3)
    | ~ class_Ring__and__Field_Opordered__ring(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1226]) ).

cnf(c_0_1834,plain,
    ( c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,X5,X3),X2,X3),X4,X3),X6,X3)
    | ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X5,X2,X3),X6,X3),X3)
    | ~ class_Ring__and__Field_Opordered__ring(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1227]) ).

cnf(c_0_1835,plain,
    ( c_HOL_Oord__class_Oless(X4,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X5,X1,X3),X2,X3),X6,X3),X3)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X5,X2,X3),X6,X3),X3)
    | ~ class_Ring__and__Field_Opordered__ring(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1228]) ).

cnf(c_0_1836,plain,
    ( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,X5,X3),X2,X3),X4,X3),X6,X3)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X5,X2,X3),X6,X3),X3)
    | ~ class_Ring__and__Field_Opordered__ring(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1229]) ).

cnf(c_0_1837,plain,
    ( c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),X4,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X3,tc_nat),X5,tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(X4,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),X3,tc_nat),X5,tc_nat),tc_nat)
    | ~ c_lessequals(X1,X2,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_1230]) ).

cnf(c_0_1838,plain,
    ( c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X3,tc_nat),X4,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),X5,tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),X3,tc_nat),X4,tc_nat),X5,tc_nat)
    | ~ c_lessequals(X1,X2,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_1231]) ).

cnf(c_0_1839,plain,
    ( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),X3,tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X4,X2,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,X4,tc_nat),X2,tc_nat),X3,tc_nat),tc_nat)
    | ~ c_lessequals(X4,X1,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_1232]) ).

cnf(c_0_1840,plain,
    ( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X3,X1,tc_nat),X2,tc_nat),X4,tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X2,tc_nat),X4,tc_nat)
    | ~ c_lessequals(X1,X3,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_1233]) ).

cnf(c_0_1841,plain,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(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),X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1234]) ).

cnf(c_0_1842,plain,
    ( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X4,X1,X3),X2,X3),X5,X3),X3) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X4,X2,X3),X5,X3)
    | ~ class_Ring__and__Field_Oring(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1235]) ).

cnf(c_0_1843,plain,
    ( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X5,X2,X3),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,X5,X3),X2,X3),X4,X3),X3)
    | ~ class_Ring__and__Field_Oring(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1236]) ).

cnf(c_0_1844,plain,
    ( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,c_Divides_Odiv__class_Omod(X4,X1,tc_nat),tc_nat),X2,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_1237]) ).

cnf(c_0_1845,plain,
    ( X1 = c_HOL_Ozero__class_Ozero(X2)
    | ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X1,X2),c_HOL_Otimes__class_Otimes(X3,X3,X2),X2),c_HOL_Ozero__class_Ozero(X2),X2)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_1238]) ).

cnf(c_0_1846,plain,
    ( X3 = c_HOL_Ozero__class_Ozero(X2)
    | ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X1,X2),c_HOL_Otimes__class_Otimes(X3,X3,X2),X2),c_HOL_Ozero__class_Ozero(X2),X2)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_1239]) ).

cnf(c_0_1847,plain,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X1,X2),c_HOL_Otimes__class_Otimes(X3,X3,X2),X2),c_HOL_Ozero__class_Ozero(X2),X2)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_1240]) ).

cnf(c_0_1848,plain,
    ( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),X3,tc_nat),X4,tc_nat) = X5
    | ~ c_lessequals(X2,X1,tc_nat)
    | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),X4,tc_nat) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X3,tc_nat),X5,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_1241]) ).

cnf(c_0_1849,plain,
    ( X1 = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X3,tc_nat),X4,tc_nat),X5,tc_nat)
    | ~ c_lessequals(X3,X2,tc_nat)
    | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X4,tc_nat),X1,tc_nat) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X4,tc_nat),X5,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_1242]) ).

cnf(c_0_1850,plain,
    ( c_lessequals(c_Orderings_Oord__class_Omax(c_Orderings_Oord__class_Omin(X1,X2,X3),c_Orderings_Oord__class_Omin(X1,X4,X3),X3),c_Orderings_Oord__class_Omin(X1,c_Orderings_Oord__class_Omax(X2,X4,X3),X3),X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1243]) ).

cnf(c_0_1851,plain,
    ( c_lessequals(c_Orderings_Oord__class_Omax(X1,c_Orderings_Oord__class_Omin(X2,X3,X4),X4),c_Orderings_Oord__class_Omin(c_Orderings_Oord__class_Omax(X1,X2,X4),c_Orderings_Oord__class_Omax(X1,X3,X4),X4),X4)
    | ~ class_Orderings_Olinorder(X4) ),
    inference(split_conjunct,[status(thm)],[c_0_1244]) ).

cnf(c_0_1852,plain,
    ( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,X2,X3),X4,X3),X5,X3) = X6
    | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X4,X3),X5,X3) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X4,X3),X6,X3)
    | ~ class_Ring__and__Field_Oring(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1245]) ).

cnf(c_0_1853,plain,
    ( X1 = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X3,X4),X5,X4),X6,X4)
    | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X5,X4),X1,X4) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X5,X4),X6,X4)
    | ~ class_Ring__and__Field_Oring(X4) ),
    inference(split_conjunct,[status(thm)],[c_0_1246]) ).

cnf(c_0_1854,plain,
    ( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X4,X2,X3),X5,X3),X3) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X1,X4,X3),X2,X3),X5,X3)
    | ~ class_Ring__and__Field_Osemiring(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1247]) ).

cnf(c_0_1855,plain,
    ( X1 = X2
    | X3 = X4
    | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X3,X5),c_HOL_Otimes__class_Otimes(X2,X4,X5),X5) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X4,X5),c_HOL_Otimes__class_Otimes(X2,X3,X5),X5)
    | ~ class_Int_Onumber__ring(X5)
    | ~ class_Ring__and__Field_Oidom(X5) ),
    inference(split_conjunct,[status(thm)],[c_0_1248]) ).

cnf(c_0_1856,plain,
    ( X1 = X2
    | X3 = X4
    | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X3,X5),c_HOL_Otimes__class_Otimes(X2,X4,X5),X5) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X4,X5),c_HOL_Otimes__class_Otimes(X2,X3,X5),X5)
    | ~ class_Int_Onumber__ring(X5)
    | ~ class_Ring__and__Field_Oidom(X5) ),
    inference(split_conjunct,[status(thm)],[c_0_1249]) ).

cnf(c_0_1857,plain,
    ( X1 = X2
    | X3 = X4
    | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),c_HOL_Otimes__class_Otimes(X2,X4,tc_nat),tc_nat) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X4,tc_nat),c_HOL_Otimes__class_Otimes(X2,X3,tc_nat),tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_1250]) ).

cnf(c_0_1858,plain,
    ( X1 = X2
    | X3 = X4
    | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),c_HOL_Otimes__class_Otimes(X2,X4,tc_nat),tc_nat) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X4,tc_nat),c_HOL_Otimes__class_Otimes(X2,X3,tc_nat),tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_1251]) ).

cnf(c_0_1859,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_1252]) ).

cnf(c_0_1860,plain,
    ( c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X1,X2,X3),X4,X3) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(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_1253]) ).

cnf(c_0_1861,plain,
    ( c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X1,X2,X3),X4,X3) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(c_Divides_Odiv__class_Omod(X1,X4,X3),c_Divides_Odiv__class_Omod(X2,X4,X3),X3),X4,X3)
    | ~ class_Divides_Oring__div(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1254]) ).

cnf(c_0_1862,plain,
    ( c_Lambda_Osubst(c_Lambda_Osubst(X3,c_Lambda_Olift(X4,X1),c_Suc(X2)),c_Lambda_Osubst(X5,X4,X2),X1) = c_Lambda_Osubst(c_Lambda_Osubst(X3,X5,X1),X4,X2)
    | ~ c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(X2,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_1255]) ).

cnf(c_0_1863,plain,
    ( c_Lambda_Olift(c_Lambda_Osubst(X3,X4,X1),X2) = c_Lambda_Osubst(c_Lambda_Olift(X3,c_HOL_Oplus__class_Oplus(X2,c_HOL_Oone__class_Oone(tc_nat),tc_nat)),c_Lambda_Olift(X4,X2),X1)
    | ~ c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(X2,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_1256]) ).

cnf(c_0_1864,plain,
    ( c_lessequals(c_HOL_Oplus__class_Oplus(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),c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1257]) ).

cnf(c_0_1865,plain,
    ( c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X1,X2,X3),X4,X3) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(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_1258]) ).

cnf(c_0_1866,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_1259]) ).

cnf(c_0_1867,plain,
    ( c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X1,X2,X3),X4,X3) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(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_Oring__div(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1260]) ).

cnf(c_0_1868,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_1261]) ).

cnf(c_0_1869,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_1262]) ).

cnf(c_0_1870,plain,
    ( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X2,X5,X3),X3)
    | ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | ~ c_HOL_Oord__class_Oless(X4,X5,X3)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
    | ~ class_Ring__and__Field_Oordered__semiring__strict(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1263]) ).

cnf(c_0_1871,plain,
    ( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X2,X5,X3),X3)
    | ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | ~ c_lessequals(X4,X5,X3)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X1,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_1264]) ).

cnf(c_0_1872,plain,
    ( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X2,X5,X3),X3)
    | ~ c_lessequals(X1,X2,X3)
    | ~ c_HOL_Oord__class_Oless(X4,X5,X3)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X1,X3)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
    | ~ class_Ring__and__Field_Oordered__semiring__strict(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1265]) ).

cnf(c_0_1873,plain,
    ( c_lessequals(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X2,X5,X3),X3)
    | ~ c_lessequals(X1,X2,X3)
    | ~ c_lessequals(X4,X5,X3)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X2,X3)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
    | ~ class_Ring__and__Field_Opordered__semiring(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1266]) ).

cnf(c_0_1874,plain,
    ( c_lessequals(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X2,X5,X3),X3)
    | ~ c_lessequals(X1,X2,X3)
    | ~ c_lessequals(X4,X5,X3)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X1,X3)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
    | ~ class_Ring__and__Field_Opordered__semiring(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1267]) ).

cnf(c_0_1875,plain,
    ( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X2,X5,X3),X3)
    | ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | ~ c_HOL_Oord__class_Oless(X4,X5,X3)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X1,X3)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
    | ~ class_Ring__and__Field_Oordered__semiring__strict(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1268]) ).

cnf(c_0_1876,plain,
    ( c_lessequals(X2,X3,tc_nat)
    | ~ c_lessequals(X1,X2,tc_nat)
    | ~ c_lessequals(X1,X3,tc_nat)
    | ~ c_lessequals(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),c_HOL_Ominus__class_Ominus(X3,X1,tc_nat),tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_1269]) ).

cnf(c_0_1877,plain,
    ( c_HOL_Oord__class_Oless(X2,X3,tc_nat)
    | ~ c_lessequals(X1,X2,tc_nat)
    | ~ c_lessequals(X1,X3,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),c_HOL_Ominus__class_Ominus(X3,X1,tc_nat),tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_1270]) ).

cnf(c_0_1878,plain,
    ( X1 = c_HOL_Ozero__class_Ozero(X2)
    | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X1,X2),c_HOL_Otimes__class_Otimes(X3,X3,X2),X2),X2)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_1271]) ).

cnf(c_0_1879,plain,
    ( X1 = c_HOL_Ozero__class_Ozero(X2)
    | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X3,X2),c_HOL_Otimes__class_Otimes(X1,X1,X2),X2),X2)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_1272]) ).

cnf(c_0_1880,plain,
    ( c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X2,X1),c_HOL_Otimes__class_Otimes(X3,X3,X1),X1),X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1273]) ).

cnf(c_0_1881,plain,
    ( c_Divides_Odiv__class_Omod(X1,X2,tc_nat) = c_Divides_Odiv__class_Omod(X3,X2,tc_nat)
    | c_HOL_Oplus__class_Oplus(X1,c_HOL_Otimes__class_Otimes(X2,X4,tc_nat),tc_nat) != c_HOL_Oplus__class_Oplus(X3,c_HOL_Otimes__class_Otimes(X2,X5,tc_nat),tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_1274]) ).

cnf(c_0_1882,plain,
    ( c_Lambda_Olift(c_Lambda_Osubst(X3,X4,X2),X1) = c_Lambda_Osubst(c_Lambda_Olift(X3,X1),c_Lambda_Olift(X4,X1),c_HOL_Oplus__class_Oplus(X2,c_HOL_Oone__class_Oone(tc_nat),tc_nat))
    | ~ c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(X2,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_1275]) ).

cnf(c_0_1883,plain,
    ( 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)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X2,X3)
    | ~ class_Ring__and__Field_Oordered__semiring__strict(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1276]) ).

cnf(c_0_1884,plain,
    ( 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)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X1,X3)
    | ~ class_Ring__and__Field_Oordered__semiring__strict(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1277]) ).

cnf(c_0_1885,plain,
    ( 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)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X2,X3)
    | ~ class_Ring__and__Field_Oordered__semiring(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1278]) ).

cnf(c_0_1886,plain,
    ( 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)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X1,X3)
    | ~ class_Ring__and__Field_Oordered__semiring(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1279]) ).

cnf(c_0_1887,plain,
    ( c_lessequals(X4,X3,X2)
    | ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
    | ~ c_lessequals(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_1280]) ).

cnf(c_0_1888,plain,
    ( c_lessequals(X3,X4,X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | ~ c_lessequals(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_1281]) ).

cnf(c_0_1889,plain,
    ( c_lessequals(X2,X4,X3)
    | ~ c_lessequals(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X1,X4,X3),X3)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X1,X3)
    | ~ class_Ring__and__Field_Oordered__semiring__strict(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1282]) ).

cnf(c_0_1890,plain,
    ( c_lessequals(X1,X4,X3)
    | ~ c_lessequals(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X4,X2,X3),X3)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3)
    | ~ class_Ring__and__Field_Oordered__semiring__strict(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1283]) ).

cnf(c_0_1891,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_1284]) ).

cnf(c_0_1892,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_1285]) ).

cnf(c_0_1893,plain,
    ( c_lessequals(X1,X3,tc_nat)
    | ~ c_lessequals(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(split_conjunct,[status(thm)],[c_0_1286]) ).

cnf(c_0_1894,plain,
    ( c_lessequals(X2,X3,tc_nat)
    | ~ c_lessequals(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_1287]) ).

cnf(c_0_1895,plain,
    ( c_lessequals(X2,X3,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
    | ~ c_lessequals(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_1288]) ).

cnf(c_0_1896,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_1289]) ).

cnf(c_0_1897,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_1290]) ).

cnf(c_0_1898,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_1291]) ).

cnf(c_0_1899,plain,
    ( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X1,X4,X3),X3) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X1,X2,X3),X3)
    | ~ class_Int_Onumber__ring(X3)
    | ~ class_Ring__and__Field_Oidom(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1292]) ).

cnf(c_0_1900,plain,
    ( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X1,X4,X3),X3) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X1,X2,X3),X3)
    | ~ class_Int_Onumber__ring(X3)
    | ~ class_Ring__and__Field_Oidom(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1293]) ).

cnf(c_0_1901,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_1294]) ).

cnf(c_0_1902,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_1295]) ).

cnf(c_0_1903,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_1296]) ).

cnf(c_0_1904,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_1297]) ).

cnf(c_0_1905,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_1298]) ).

cnf(c_0_1906,plain,
    ( c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X1,X2,X3),X4,X3) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(c_Divides_Odiv__class_Omod(X1,X4,X3),X2,X3),X4,X3)
    | ~ class_Divides_Oring__div(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1299]) ).

cnf(c_0_1907,plain,
    ( c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X1,X2,X3),X4,X3) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X1,c_Divides_Odiv__class_Omod(X2,X4,X3),X3),X4,X3)
    | ~ class_Divides_Oring__div(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1300]) ).

cnf(c_0_1908,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_1301]) ).

cnf(c_0_1909,plain,
    ( c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X1,X2,X3),X4,X3) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(X1,X4,X3),X2,X3),X4,X3)
    | ~ class_Divides_Osemiring__div(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1302]) ).

cnf(c_0_1910,plain,
    ( c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X1,X2,X3),X4,X3) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X1,c_Divides_Odiv__class_Omod(X2,X4,X3),X3),X4,X3)
    | ~ class_Divides_Osemiring__div(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1303]) ).

cnf(c_0_1911,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_1304]) ).

cnf(c_0_1912,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_1305]) ).

cnf(c_0_1913,plain,
    ( c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X2,X3),c_HOL_Oplus__class_Oplus(X4,X5,X3),X3) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X4,X3),c_HOL_Oplus__class_Oplus(X2,X5,X3),X3)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1306]) ).

cnf(c_0_1914,plain,
    ( c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(X1,X2,X3),X4,X3),X2,X3) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X1,X4,X3),X2,X3)
    | ~ class_Divides_Osemiring__div(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1307]) ).

cnf(c_0_1915,plain,
    ( c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X1,c_Divides_Odiv__class_Omod(X2,X3,X4),X4),X3,X4) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X1,X2,X4),X3,X4)
    | ~ class_Divides_Osemiring__div(X4) ),
    inference(split_conjunct,[status(thm)],[c_0_1308]) ).

cnf(c_0_1916,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_1309]) ).

cnf(c_0_1917,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_1310]) ).

cnf(c_0_1918,plain,
    ( X1 = c_HOL_Ozero__class_Ozero(X2)
    | X3 = X4
    | c_HOL_Oplus__class_Oplus(X5,c_HOL_Otimes__class_Otimes(X1,X3,X2),X2) != c_HOL_Oplus__class_Oplus(X5,c_HOL_Otimes__class_Otimes(X1,X4,X2),X2)
    | ~ class_Int_Onumber__ring(X2)
    | ~ class_Ring__and__Field_Oidom(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_1311]) ).

cnf(c_0_1919,plain,
    ( c_HOL_Ominus__class_Ominus(c_Suc(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat)),X3,tc_nat) = c_HOL_Ominus__class_Ominus(c_Suc(X2),c_HOL_Oplus__class_Oplus(X1,X3,tc_nat),tc_nat)
    | ~ c_lessequals(X1,X2,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_1312]) ).

cnf(c_0_1920,plain,
    ( c_HOL_Ominus__class_Ominus(X3,c_Suc(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat)),tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X3,X1,tc_nat),c_Suc(X2),tc_nat)
    | ~ c_lessequals(X1,X2,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_1313]) ).

cnf(c_0_1921,plain,
    ( c_lessequals(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),c_HOL_Ominus__class_Ominus(X3,X1,tc_nat),tc_nat)
    | ~ c_lessequals(X1,X2,tc_nat)
    | ~ c_lessequals(X1,X3,tc_nat)
    | ~ c_lessequals(X2,X3,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_1314]) ).

cnf(c_0_1922,plain,
    ( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),c_HOL_Ominus__class_Ominus(X3,X1,tc_nat),tc_nat)
    | ~ c_lessequals(X1,X2,tc_nat)
    | ~ c_lessequals(X1,X3,tc_nat)
    | ~ c_HOL_Oord__class_Oless(X2,X3,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_1315]) ).

cnf(c_0_1923,plain,
    ( c_lessequals(X1,c_HOL_Oplus__class_Oplus(X2,X5,X4),X4)
    | ~ c_lessequals(X1,c_HOL_Oplus__class_Oplus(X2,X3,X4),X4)
    | ~ c_lessequals(X3,X5,X4)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X4) ),
    inference(split_conjunct,[status(thm)],[c_0_1316]) ).

cnf(c_0_1924,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_1317]) ).

cnf(c_0_1925,plain,
    ( c_lessequals(X2,X3,tc_nat)
    | ~ c_lessequals(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_1318]) ).

cnf(c_0_1926,plain,
    ( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
    | X2 = X3
    | c_HOL_Oplus__class_Oplus(X4,c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),tc_nat) != c_HOL_Oplus__class_Oplus(X4,c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_1319]) ).

cnf(c_0_1927,plain,
    ( c_lessequals(X3,c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),tc_nat)
    | ~ c_lessequals(X1,X2,tc_nat)
    | ~ c_lessequals(c_HOL_Oplus__class_Oplus(X3,X1,tc_nat),X2,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_1320]) ).

cnf(c_0_1928,plain,
    ( c_lessequals(c_HOL_Oplus__class_Oplus(X3,X1,tc_nat),X2,tc_nat)
    | ~ c_lessequals(X1,X2,tc_nat)
    | ~ c_lessequals(X3,c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_1321]) ).

cnf(c_0_1929,plain,
    ( c_lessequals(X1,X4,X3)
    | ~ c_lessequals(c_HOL_Oplus__class_Oplus(X1,X2,X3),c_HOL_Oplus__class_Oplus(X4,X2,X3),X3)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1322]) ).

cnf(c_0_1930,plain,
    ( c_lessequals(X2,X4,X3)
    | ~ c_lessequals(c_HOL_Oplus__class_Oplus(X1,X2,X3),c_HOL_Oplus__class_Oplus(X1,X4,X3),X3)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1323]) ).

cnf(c_0_1931,plain,
    ( c_HOL_Oord__class_Oless(X1,X4,X3)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X2,X3),c_HOL_Oplus__class_Oplus(X4,X2,X3),X3)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1324]) ).

cnf(c_0_1932,plain,
    ( c_HOL_Oord__class_Oless(X2,X4,X3)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X2,X3),c_HOL_Oplus__class_Oplus(X1,X4,X3),X3)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1325]) ).

cnf(c_0_1933,plain,
    ( c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),c_HOL_Ominus__class_Ominus(X3,X1,tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(X2,X3,tc_nat)
    | ~ c_lessequals(X1,X2,tc_nat)
    | ~ c_lessequals(X1,X3,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_1326]) ).

cnf(c_0_1934,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_1327]) ).

cnf(c_0_1935,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_1328]) ).

cnf(c_0_1936,plain,
    ( c_lessequals(X2,X3,tc_nat)
    | ~ c_lessequals(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),c_HOL_Oplus__class_Oplus(X1,X3,tc_nat),tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_1329]) ).

cnf(c_0_1937,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_1330]) ).

cnf(c_0_1938,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_1331]) ).

cnf(c_0_1939,plain,
    ( c_HOL_Oord__class_Oless(X2,X3,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),c_HOL_Oplus__class_Oplus(X1,X3,tc_nat),tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_1332]) ).

cnf(c_0_1940,plain,
    ( c_lessequals(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_lessequals(X3,X4,X2)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_1333]) ).

cnf(c_0_1941,plain,
    ( c_lessequals(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_lessequals(X3,X4,X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1334]) ).

cnf(c_0_1942,plain,
    ( c_lessequals(c_HOL_Otimes__class_Otimes(X2,X4,X3),c_HOL_Otimes__class_Otimes(X1,X4,X3),X3)
    | ~ c_lessequals(X1,X2,X3)
    | ~ c_lessequals(X4,c_HOL_Ozero__class_Ozero(X3),X3)
    | ~ class_Ring__and__Field_Opordered__ring(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1335]) ).

cnf(c_0_1943,plain,
    ( c_lessequals(c_HOL_Otimes__class_Otimes(X4,X2,X3),c_HOL_Otimes__class_Otimes(X4,X1,X3),X3)
    | ~ c_lessequals(X1,X2,X3)
    | ~ c_lessequals(X4,c_HOL_Ozero__class_Ozero(X3),X3)
    | ~ class_Ring__and__Field_Opordered__ring(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1336]) ).

cnf(c_0_1944,plain,
    ( c_lessequals(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X2,X4,X3),X3)
    | ~ c_lessequals(X1,X2,X3)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
    | ~ class_Ring__and__Field_Omult__mono(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1337]) ).

cnf(c_0_1945,plain,
    ( c_lessequals(c_HOL_Otimes__class_Otimes(X4,X1,X3),c_HOL_Otimes__class_Otimes(X4,X2,X3),X3)
    | ~ c_lessequals(X1,X2,X3)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
    | ~ class_Ring__and__Field_Omult__mono(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1338]) ).

cnf(c_0_1946,plain,
    ( c_lessequals(c_HOL_Otimes__class_Otimes(X4,X1,X3),c_HOL_Otimes__class_Otimes(X4,X2,X3),X3)
    | ~ c_lessequals(X1,X2,X3)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
    | ~ class_Ring__and__Field_Omult__mono1(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1339]) ).

cnf(c_0_1947,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_1340]) ).

cnf(c_0_1948,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_1341]) ).

cnf(c_0_1949,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_1342]) ).

cnf(c_0_1950,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_1343]) ).

cnf(c_0_1951,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_1344]) ).

cnf(c_0_1952,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_1345]) ).

cnf(c_0_1953,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_1346]) ).

cnf(c_0_1954,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_1347]) ).

cnf(c_0_1955,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_1348]) ).

cnf(c_0_1956,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_1349]) ).

cnf(c_0_1957,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_1350]) ).

cnf(c_0_1958,plain,
    ( c_lessequals(c_HOL_Otimes__class_Otimes(X2,X3,X1),X2,X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
    | ~ c_lessequals(X3,c_HOL_Oone__class_Oone(X1),X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1351]) ).

cnf(c_0_1959,plain,
    ( c_lessequals(c_HOL_Otimes__class_Otimes(X3,X2,X1),X2,X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
    | ~ c_lessequals(X3,c_HOL_Oone__class_Oone(X1),X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1352]) ).

cnf(c_0_1960,plain,
    ( c_lessequals(X3,c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X2,X3,tc_nat),X1,tc_nat),tc_nat)
    | ~ c_lessequals(X1,X2,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_1353]) ).

cnf(c_0_1961,plain,
    ( c_lessequals(c_HOL_Oplus__class_Oplus(X1,X4,X3),c_HOL_Oplus__class_Oplus(X2,X5,X3),X3)
    | ~ c_lessequals(X1,X2,X3)
    | ~ c_lessequals(X4,X5,X3)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1354]) ).

cnf(c_0_1962,plain,
    ( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X4,X3),c_HOL_Oplus__class_Oplus(X2,X5,X3),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_1355]) ).

cnf(c_0_1963,plain,
    ( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X4,X3),c_HOL_Oplus__class_Oplus(X2,X5,X3),X3)
    | ~ c_lessequals(X1,X2,X3)
    | ~ c_HOL_Oord__class_Oless(X4,X5,X3)
    | ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1356]) ).

cnf(c_0_1964,plain,
    ( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X4,X3),c_HOL_Oplus__class_Oplus(X2,X5,X3),X3)
    | ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | ~ c_lessequals(X4,X5,X3)
    | ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1357]) ).

cnf(c_0_1965,plain,
    ( X1 = c_HOL_Ozero__class_Ozero(X2)
    | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X3,X2),c_HOL_Otimes__class_Otimes(X1,X1,X2),X2) != c_HOL_Ozero__class_Ozero(X2)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_1358]) ).

cnf(c_0_1966,plain,
    ( X1 = c_HOL_Ozero__class_Ozero(X2)
    | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X1,X2),c_HOL_Otimes__class_Otimes(X3,X3,X2),X2) != c_HOL_Ozero__class_Ozero(X2)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_1359]) ).

cnf(c_0_1967,plain,
    ( c_Orderings_Oord__class_Omin(c_Orderings_Oord__class_Omax(X1,X2,X3),X4,X3) = c_Orderings_Oord__class_Omax(c_Orderings_Oord__class_Omin(X1,X4,X3),c_Orderings_Oord__class_Omin(X2,X4,X3),X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1360]) ).

cnf(c_0_1968,plain,
    ( c_Orderings_Oord__class_Omin(X1,c_Orderings_Oord__class_Omax(X2,X3,X4),X4) = c_Orderings_Oord__class_Omax(c_Orderings_Oord__class_Omin(X1,X2,X4),c_Orderings_Oord__class_Omin(X1,X3,X4),X4)
    | ~ class_Orderings_Olinorder(X4) ),
    inference(split_conjunct,[status(thm)],[c_0_1361]) ).

cnf(c_0_1969,plain,
    ( c_HOL_Ominus__class_Ominus(c_Orderings_Oord__class_Omin(X1,X2,X3),X4,X3) = c_Orderings_Oord__class_Omin(c_HOL_Ominus__class_Ominus(X1,X4,X3),c_HOL_Ominus__class_Ominus(X2,X4,X3),X3)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1362]) ).

cnf(c_0_1970,plain,
    ( c_HOL_Ominus__class_Ominus(c_Orderings_Oord__class_Omax(X1,X2,X3),X4,X3) = c_Orderings_Oord__class_Omax(c_HOL_Ominus__class_Ominus(X1,X4,X3),c_HOL_Ominus__class_Ominus(X2,X4,X3),X3)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1363]) ).

cnf(c_0_1971,plain,
    ( c_HOL_Oplus__class_Oplus(c_Orderings_Oord__class_Omin(X1,X2,X3),X4,X3) = c_Orderings_Oord__class_Omin(c_HOL_Oplus__class_Oplus(X1,X4,X3),c_HOL_Oplus__class_Oplus(X2,X4,X3),X3)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1364]) ).

cnf(c_0_1972,plain,
    ( c_HOL_Oplus__class_Oplus(c_Orderings_Oord__class_Omax(X1,X2,X3),X4,X3) = c_Orderings_Oord__class_Omax(c_HOL_Oplus__class_Oplus(X1,X4,X3),c_HOL_Oplus__class_Oplus(X2,X4,X3),X3)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1365]) ).

cnf(c_0_1973,plain,
    ( c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X1,c_HOL_Otimes__class_Otimes(X2,X3,X4),X4),X3,X4) = c_Divides_Odiv__class_Omod(X1,X3,X4)
    | ~ class_Divides_Osemiring__div(X4) ),
    inference(split_conjunct,[status(thm)],[c_0_1366]) ).

cnf(c_0_1974,plain,
    ( c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X1,c_HOL_Otimes__class_Otimes(X2,X3,X4),X4),X2,X4) = c_Divides_Odiv__class_Omod(X1,X2,X4)
    | ~ class_Divides_Osemiring__div(X4) ),
    inference(split_conjunct,[status(thm)],[c_0_1367]) ).

cnf(c_0_1975,plain,
    ( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X4,X2,X3),X3) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X1,X4,X3),X2,X3)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1368]) ).

cnf(c_0_1976,plain,
    ( c_Orderings_Oord__class_Omax(c_Orderings_Oord__class_Omin(X1,X2,X3),X4,X3) = c_Orderings_Oord__class_Omin(c_Orderings_Oord__class_Omax(X1,X4,X3),c_Orderings_Oord__class_Omax(X2,X4,X3),X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1369]) ).

cnf(c_0_1977,plain,
    ( c_Orderings_Oord__class_Omax(X1,c_Orderings_Oord__class_Omin(X2,X3,X4),X4) = c_Orderings_Oord__class_Omin(c_Orderings_Oord__class_Omax(X1,X2,X4),c_Orderings_Oord__class_Omax(X1,X3,X4),X4)
    | ~ class_Orderings_Olinorder(X4) ),
    inference(split_conjunct,[status(thm)],[c_0_1370]) ).

cnf(c_0_1978,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_1371]) ).

cnf(c_0_1979,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_1372]) ).

cnf(c_0_1980,plain,
    ( c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X1,X2,X3),X4,X3) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X2,X4,X3),X3)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1373]) ).

cnf(c_0_1981,plain,
    ( c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X1,X2,X3),X4,X3) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X2,X4,X3),X3)
    | ~ class_Ring__and__Field_Ocomm__semiring(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1374]) ).

cnf(c_0_1982,plain,
    ( c_HOL_Otimes__class_Otimes(X1,c_HOL_Oplus__class_Oplus(X2,X3,X4),X4) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,X4),c_HOL_Otimes__class_Otimes(X1,X3,X4),X4)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X4) ),
    inference(split_conjunct,[status(thm)],[c_0_1375]) ).

cnf(c_0_1983,plain,
    ( c_lessequals(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_lessequals(X2,X3,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_1376]) ).

cnf(c_0_1984,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_1377]) ).

cnf(c_0_1985,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_1378]) ).

cnf(c_0_1986,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_1379]) ).

cnf(c_0_1987,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_1380]) ).

cnf(c_0_1988,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_1381]) ).

cnf(c_0_1989,plain,
    ( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
    | c_HOL_Otimes__class_Otimes(X1,X2,tc_nat) = c_HOL_Oplus__class_Oplus(X2,c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X2,tc_nat),tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_1382]) ).

cnf(c_0_1990,plain,
    ( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X3,X2,tc_nat),c_HOL_Ominus__class_Ominus(X3,X1,tc_nat),tc_nat)
    | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | ~ c_HOL_Oord__class_Oless(X1,X3,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_1383]) ).

cnf(c_0_1991,plain,
    ( c_lessequals(c_HOL_Oplus__class_Oplus(X1,X3,tc_nat),c_HOL_Oplus__class_Oplus(X2,X4,tc_nat),tc_nat)
    | ~ c_lessequals(X1,X2,tc_nat)
    | ~ c_lessequals(X3,X4,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_1384]) ).

cnf(c_0_1992,plain,
    ( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,X3,tc_nat),c_HOL_Ominus__class_Ominus(X2,X3,tc_nat),tc_nat)
    | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | ~ c_lessequals(X3,X1,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_1385]) ).

cnf(c_0_1993,plain,
    ( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X3,tc_nat),c_HOL_Oplus__class_Oplus(X2,X4,tc_nat),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_1386]) ).

cnf(c_0_1994,plain,
    ( c_lessequals(c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),c_HOL_Otimes__class_Otimes(X2,X4,tc_nat),tc_nat)
    | ~ c_lessequals(X1,X2,tc_nat)
    | ~ c_lessequals(X3,X4,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_1387]) ).

cnf(c_0_1995,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_1388]) ).

cnf(c_0_1996,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_1389]) ).

cnf(c_0_1997,plain,
    ( c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),X2,tc_nat) = X1
    | ~ c_lessequals(X2,c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_1390]) ).

cnf(c_0_1998,plain,
    ( c_lessequals(X1,c_HOL_Oplus__class_Oplus(X3,X2,tc_nat),tc_nat)
    | ~ c_lessequals(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),X3,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_1391]) ).

cnf(c_0_1999,plain,
    ( c_lessequals(c_HOL_Ominus__class_Ominus(X1,X3,tc_nat),X2,tc_nat)
    | ~ c_lessequals(X1,c_HOL_Oplus__class_Oplus(X2,X3,tc_nat),tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_1392]) ).

cnf(c_0_2000,plain,
    ( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X3,tc_nat),X2,tc_nat)
    | ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ominus__class_Ominus(X2,X3,tc_nat),tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_1393]) ).

cnf(c_0_2001,plain,
    ( c_HOL_Oord__class_Oless(X1,c_HOL_Ominus__class_Ominus(X3,X2,tc_nat),tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),X3,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_1394]) ).

cnf(c_0_2002,plain,
    ( c_HOL_Oplus__class_Oplus(X1,X2,X3) = X4
    | c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X5,X2,X3),X3) != c_HOL_Oplus__class_Oplus(X5,X4,X3)
    | ~ class_OrderedGroup_Oab__group__add(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1395]) ).

cnf(c_0_2003,plain,
    ( c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X3,X2,tc_nat),X1,tc_nat) = c_HOL_Oplus__class_Oplus(X3,c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),tc_nat)
    | ~ c_lessequals(X1,X2,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_1396]) ).

cnf(c_0_2004,plain,
    ( c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X2,X3,tc_nat),X1,tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),X3,tc_nat)
    | ~ c_lessequals(X1,X2,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_1397]) ).

cnf(c_0_2005,plain,
    ( c_HOL_Ominus__class_Ominus(X3,c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X3,X1,tc_nat),X2,tc_nat)
    | ~ c_lessequals(X1,X2,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_1398]) ).

cnf(c_0_2006,plain,
    ( c_HOL_Oplus__class_Oplus(X3,c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X3,X2,tc_nat),X1,tc_nat)
    | ~ c_lessequals(X1,X2,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_1399]) ).

cnf(c_0_2007,plain,
    ( c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),X3,tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X2,X3,tc_nat),X1,tc_nat)
    | ~ c_lessequals(X1,X2,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_1400]) ).

cnf(c_0_2008,plain,
    ( c_lessequals(X2,c_HOL_Ozero__class_Ozero(X3),X3)
    | c_lessequals(c_HOL_Ozero__class_Ozero(X3),X2,X3)
    | ~ c_lessequals(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1401]) ).

cnf(c_0_2009,plain,
    ( c_lessequals(X2,c_HOL_Ozero__class_Ozero(X3),X3)
    | c_lessequals(X1,c_HOL_Ozero__class_Ozero(X3),X3)
    | ~ c_lessequals(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1402]) ).

cnf(c_0_2010,plain,
    ( c_lessequals(c_HOL_Ozero__class_Ozero(X3),X1,X3)
    | c_lessequals(c_HOL_Ozero__class_Ozero(X3),X2,X3)
    | ~ c_lessequals(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1403]) ).

cnf(c_0_2011,plain,
    ( c_lessequals(c_HOL_Ozero__class_Ozero(X3),X1,X3)
    | c_lessequals(X1,c_HOL_Ozero__class_Ozero(X3),X3)
    | ~ c_lessequals(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1404]) ).

cnf(c_0_2012,plain,
    ( c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1405]) ).

cnf(c_0_2013,plain,
    ( c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1406]) ).

cnf(c_0_2014,plain,
    ( c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
    | c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1407]) ).

cnf(c_0_2015,plain,
    ( c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
    | c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1408]) ).

cnf(c_0_2016,plain,
    ( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
    | c_HOL_Oplus__class_Oplus(X1,X2,tc_nat) = c_Suc(c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X2,tc_nat)) ),
    inference(split_conjunct,[status(thm)],[c_0_1409]) ).

cnf(c_0_2017,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_1410]) ).

cnf(c_0_2018,plain,
    ( c_lessequals(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),tc_nat)
    | ~ c_lessequals(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X1,tc_nat)
    | ~ c_lessequals(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X2,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_1411]) ).

cnf(c_0_2019,plain,
    ( c_lessequals(X1,X2,X4)
    | c_lessequals(X1,X3,X4)
    | ~ c_lessequals(X1,c_Orderings_Oord__class_Omax(X2,X3,X4),X4)
    | ~ class_Orderings_Olinorder(X4) ),
    inference(split_conjunct,[status(thm)],[c_0_1412]) ).

cnf(c_0_2020,plain,
    ( c_lessequals(X1,X4,X3)
    | c_lessequals(X2,X4,X3)
    | ~ c_lessequals(c_Orderings_Oord__class_Omin(X1,X2,X3),X4,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1413]) ).

cnf(c_0_2021,plain,
    ( c_HOL_Oord__class_Oless(X1,X2,X4)
    | c_HOL_Oord__class_Oless(X1,X3,X4)
    | ~ c_HOL_Oord__class_Oless(X1,c_Orderings_Oord__class_Omax(X2,X3,X4),X4)
    | ~ class_Orderings_Olinorder(X4) ),
    inference(split_conjunct,[status(thm)],[c_0_1414]) ).

cnf(c_0_2022,plain,
    ( c_HOL_Oord__class_Oless(X1,X4,X3)
    | c_HOL_Oord__class_Oless(X2,X4,X3)
    | ~ c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omin(X1,X2,X3),X4,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1415]) ).

cnf(c_0_2023,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_1416]) ).

cnf(c_0_2024,plain,
    ( c_lessequals(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_lessequals(X1,X2,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_1417]) ).

cnf(c_0_2025,plain,
    ( c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(X2,X3,X1),X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
    | ~ class_OrderedGroup_Opordered__comm__monoid__add(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1418]) ).

cnf(c_0_2026,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_1419]) ).

cnf(c_0_2027,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_1420]) ).

cnf(c_0_2028,plain,
    ( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X3,X2),c_HOL_Ozero__class_Ozero(X2),X2)
    | ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
    | ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X2),X2)
    | ~ class_OrderedGroup_Opordered__comm__monoid__add(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_1421]) ).

cnf(c_0_2029,plain,
    ( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X3,X2),c_HOL_Ozero__class_Ozero(X2),X2)
    | ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
    | ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X2),X2)
    | ~ class_OrderedGroup_Opordered__comm__monoid__add(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_1422]) ).

cnf(c_0_2030,plain,
    ( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(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(X3,c_HOL_Ozero__class_Ozero(X2),X2)
    | ~ class_OrderedGroup_Opordered__comm__monoid__add(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_1423]) ).

cnf(c_0_2031,plain,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(X2,X3,X1),X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
    | ~ class_OrderedGroup_Opordered__comm__monoid__add(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1424]) ).

cnf(c_0_2032,plain,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(X2,X3,X1),X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
    | ~ class_OrderedGroup_Opordered__comm__monoid__add(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1425]) ).

cnf(c_0_2033,plain,
    ( c_lessequals(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1426]) ).

cnf(c_0_2034,plain,
    ( c_lessequals(c_HOL_Otimes__class_Otimes(X1,X3,X2),c_HOL_Ozero__class_Ozero(X2),X2)
    | ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X3,X2)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_1427]) ).

cnf(c_0_2035,plain,
    ( c_lessequals(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ class_Ring__and__Field_Opordered__cancel__semiring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1428]) ).

cnf(c_0_2036,plain,
    ( c_lessequals(c_HOL_Otimes__class_Otimes(X1,X3,X2),c_HOL_Ozero__class_Ozero(X2),X2)
    | ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X3,X2)
    | ~ class_Ring__and__Field_Opordered__cancel__semiring(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_1429]) ).

cnf(c_0_2037,plain,
    ( c_lessequals(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ class_Ring__and__Field_Opordered__cancel__semiring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1430]) ).

cnf(c_0_2038,plain,
    ( c_lessequals(c_HOL_Otimes__class_Otimes(X1,X3,X2),c_HOL_Ozero__class_Ozero(X2),X2)
    | ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X3,X2)
    | ~ class_Ring__and__Field_Opordered__cancel__semiring(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_1431]) ).

cnf(c_0_2039,plain,
    ( c_lessequals(c_HOL_Otimes__class_Otimes(X3,X2,X1),c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ class_Ring__and__Field_Opordered__cancel__semiring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1432]) ).

cnf(c_0_2040,plain,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(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_OrderedGroup_Opordered__comm__monoid__add(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1433]) ).

cnf(c_0_2041,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_1434]) ).

cnf(c_0_2042,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_1435]) ).

cnf(c_0_2043,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_1436]) ).

cnf(c_0_2044,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_1437]) ).

cnf(c_0_2045,plain,
    ( c_lessequals(c_HOL_Oplus__class_Oplus(X1,X3,X2),c_HOL_Ozero__class_Ozero(X2),X2)
    | ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
    | ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X2),X2)
    | ~ class_OrderedGroup_Opordered__comm__monoid__add(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_1438]) ).

cnf(c_0_2046,plain,
    ( c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
    | ~ class_Ring__and__Field_Opordered__cancel__semiring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1439]) ).

cnf(c_0_2047,plain,
    ( c_lessequals(c_HOL_Ozero__class_Ozero(X2),c_HOL_Otimes__class_Otimes(X1,X3,X2),X2)
    | ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
    | ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X2),X2)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_1440]) ).

cnf(c_0_2048,plain,
    ( c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1441]) ).

cnf(c_0_2049,plain,
    ( c_lessequals(c_HOL_Ozero__class_Ozero(X2),c_HOL_Otimes__class_Otimes(X1,X3,X2),X2)
    | ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
    | ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X2),X2)
    | ~ class_Ring__and__Field_Opordered__ring(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_1442]) ).

cnf(c_0_2050,plain,
    ( c_lessequals(c_HOL_Ozero__class_Ozero(X2),c_HOL_Otimes__class_Otimes(X1,X3,X2),X2)
    | ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
    | ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X2),X2)
    | ~ class_Ring__and__Field_Opordered__ring(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_1443]) ).

cnf(c_0_2051,plain,
    ( c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
    | ~ class_Ring__and__Field_Opordered__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1444]) ).

cnf(c_0_2052,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),c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_1445]) ).

cnf(c_0_2053,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_1446]) ).

cnf(c_0_2054,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_1447]) ).

cnf(c_0_2055,plain,
    ( c_lessequals(c_HOL_Oplus__class_Oplus(X1,X4,X3),c_HOL_Oplus__class_Oplus(X2,X4,X3),X3)
    | ~ c_lessequals(X1,X2,X3)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1448]) ).

cnf(c_0_2056,plain,
    ( c_lessequals(c_HOL_Oplus__class_Oplus(X4,X1,X3),c_HOL_Oplus__class_Oplus(X4,X2,X3),X3)
    | ~ c_lessequals(X1,X2,X3)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1449]) ).

cnf(c_0_2057,plain,
    ( c_lessequals(c_HOL_Oplus__class_Oplus(X1,X4,X3),c_HOL_Oplus__class_Oplus(X2,X4,X3),X3)
    | ~ c_lessequals(X1,X2,X3)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1450]) ).

cnf(c_0_2058,plain,
    ( c_lessequals(c_HOL_Oplus__class_Oplus(X4,X1,X3),c_HOL_Oplus__class_Oplus(X4,X2,X3),X3)
    | ~ c_lessequals(X1,X2,X3)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1451]) ).

cnf(c_0_2059,plain,
    ( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X4,X3),c_HOL_Oplus__class_Oplus(X2,X4,X3),X3)
    | ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1452]) ).

cnf(c_0_2060,plain,
    ( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X4,X3),c_HOL_Oplus__class_Oplus(X2,X4,X3),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_1453]) ).

cnf(c_0_2061,plain,
    ( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X4,X1,X3),c_HOL_Oplus__class_Oplus(X4,X2,X3),X3)
    | ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1454]) ).

cnf(c_0_2062,plain,
    ( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X4,X1,X3),c_HOL_Oplus__class_Oplus(X4,X2,X3),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_1455]) ).

cnf(c_0_2063,plain,
    ( c_lessequals(X3,c_HOL_Oplus__class_Oplus(X2,X4,X1),X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | ~ c_lessequals(X3,X4,X1)
    | ~ class_OrderedGroup_Ocomm__monoid__add(X1)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1456]) ).

cnf(c_0_2064,plain,
    ( c_lessequals(X3,c_HOL_Oplus__class_Oplus(X4,X2,X1),X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | ~ c_lessequals(X3,X4,X1)
    | ~ class_OrderedGroup_Ocomm__monoid__add(X1)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1457]) ).

cnf(c_0_2065,plain,
    ( c_HOL_Oord__class_Oless(X3,c_HOL_Oplus__class_Oplus(X2,X4,X1),X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | ~ c_lessequals(X3,X4,X1)
    | ~ class_OrderedGroup_Ocomm__monoid__add(X1)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1458]) ).

cnf(c_0_2066,plain,
    ( c_HOL_Oord__class_Oless(X3,c_HOL_Oplus__class_Oplus(X2,X4,X1),X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | ~ c_HOL_Oord__class_Oless(X3,X4,X1)
    | ~ class_OrderedGroup_Ocomm__monoid__add(X1)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1459]) ).

cnf(c_0_2067,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_1460]) ).

cnf(c_0_2068,plain,
    ( c_HOL_Oord__class_Oless(X3,c_HOL_Oplus__class_Oplus(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__semidom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1461]) ).

cnf(c_0_2069,plain,
    ( c_lessequals(c_HOL_Ominus__class_Ominus(X3,X2,tc_nat),c_HOL_Ominus__class_Ominus(X3,X1,tc_nat),tc_nat)
    | ~ c_lessequals(X1,X2,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_1462]) ).

cnf(c_0_2070,plain,
    ( c_lessequals(c_HOL_Ominus__class_Ominus(X1,X3,tc_nat),c_HOL_Ominus__class_Ominus(X2,X3,tc_nat),tc_nat)
    | ~ c_lessequals(X1,X2,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_1463]) ).

cnf(c_0_2071,plain,
    ( c_lessequals(c_HOL_Oplus__class_Oplus(X1,X3,tc_nat),c_HOL_Oplus__class_Oplus(X2,X3,tc_nat),tc_nat)
    | ~ c_lessequals(X1,X2,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_1464]) ).

cnf(c_0_2072,plain,
    ( c_lessequals(c_HOL_Oplus__class_Oplus(X3,X1,tc_nat),c_HOL_Oplus__class_Oplus(X3,X2,tc_nat),tc_nat)
    | ~ c_lessequals(X1,X2,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_1465]) ).

cnf(c_0_2073,plain,
    ( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X3,tc_nat),c_HOL_Oplus__class_Oplus(X2,X3,tc_nat),tc_nat)
    | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_1466]) ).

cnf(c_0_2074,plain,
    ( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X3,X1,tc_nat),c_HOL_Oplus__class_Oplus(X3,X2,tc_nat),tc_nat)
    | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_1467]) ).

cnf(c_0_2075,plain,
    ( c_lessequals(c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),c_HOL_Otimes__class_Otimes(X2,X3,tc_nat),tc_nat)
    | ~ c_lessequals(X1,X2,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_1468]) ).

cnf(c_0_2076,plain,
    ( c_lessequals(c_HOL_Otimes__class_Otimes(X3,X1,tc_nat),c_HOL_Otimes__class_Otimes(X3,X2,tc_nat),tc_nat)
    | ~ c_lessequals(X1,X2,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_1469]) ).

cnf(c_0_2077,plain,
    ( c_lessequals(c_HOL_Otimes__class_Otimes(X3,X1,tc_nat),c_HOL_Otimes__class_Otimes(X3,X2,tc_nat),tc_nat)
    | ~ c_lessequals(X1,X2,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_1470]) ).

cnf(c_0_2078,plain,
    ( c_lessequals(c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),c_HOL_Otimes__class_Otimes(X2,X3,tc_nat),tc_nat)
    | ~ c_lessequals(X1,X2,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_1471]) ).

cnf(c_0_2079,plain,
    ( c_Lambda_Olift(c_Lambda_Olift(X3,X1),c_Suc(X2)) = c_Lambda_Olift(c_Lambda_Olift(X3,X2),X1)
    | ~ c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(X2,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_1472]) ).

cnf(c_0_2080,plain,
    ( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,X3),X2,X3) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(X3),X3),X2,X3)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1473]) ).

cnf(c_0_2081,plain,
    ( c_HOL_Oplus__class_Oplus(X1,c_HOL_Otimes__class_Otimes(X2,X1,X3),X3) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X2,c_HOL_Oone__class_Oone(X3),X3),X1,X3)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1474]) ).

cnf(c_0_2082,plain,
    ( c_lessequals(c_Orderings_Oord__class_Omax(X1,X4,X3),X2,X3)
    | ~ c_lessequals(X1,X2,X3)
    | ~ c_lessequals(X4,X2,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1475]) ).

cnf(c_0_2083,plain,
    ( c_lessequals(c_Orderings_Oord__class_Omax(X1,X4,X3),X2,X3)
    | ~ c_lessequals(X1,X2,X3)
    | ~ c_lessequals(X4,X2,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1476]) ).

cnf(c_0_2084,plain,
    ( c_lessequals(c_Orderings_Oord__class_Omax(X1,X4,X3),X2,X3)
    | ~ c_lessequals(X1,X2,X3)
    | ~ c_lessequals(X4,X2,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1477]) ).

cnf(c_0_2085,plain,
    ( c_lessequals(X1,c_Orderings_Oord__class_Omin(X2,X4,X3),X3)
    | ~ c_lessequals(X1,X2,X3)
    | ~ c_lessequals(X1,X4,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1478]) ).

cnf(c_0_2086,plain,
    ( c_lessequals(X1,c_Orderings_Oord__class_Omin(X2,X4,X3),X3)
    | ~ c_lessequals(X1,X2,X3)
    | ~ c_lessequals(X1,X4,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1479]) ).

cnf(c_0_2087,plain,
    ( c_lessequals(X1,c_Orderings_Oord__class_Omin(X2,X4,X3),X3)
    | ~ c_lessequals(X1,X2,X3)
    | ~ c_lessequals(X1,X4,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1480]) ).

cnf(c_0_2088,plain,
    ( c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omax(X1,X4,X3),X2,X3)
    | ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | ~ c_HOL_Oord__class_Oless(X4,X2,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1481]) ).

cnf(c_0_2089,plain,
    ( c_HOL_Oord__class_Oless(X1,c_Orderings_Oord__class_Omin(X2,X4,X3),X3)
    | ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | ~ c_HOL_Oord__class_Oless(X1,X4,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1482]) ).

cnf(c_0_2090,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_1483]) ).

cnf(c_0_2091,plain,
    ( X1 = X2
    | ~ c_lessequals(X3,X1,tc_nat)
    | ~ c_lessequals(X3,X2,tc_nat)
    | c_HOL_Ominus__class_Ominus(X1,X3,tc_nat) != c_HOL_Ominus__class_Ominus(X2,X3,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_1484]) ).

cnf(c_0_2092,plain,
    ( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X2,X1,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),X2,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_1485]) ).

cnf(c_0_2093,plain,
    ( c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(X2,X2,X1),X1)
    | ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1486]) ).

cnf(c_0_2094,plain,
    ( c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X1,X2),c_HOL_Ozero__class_Ozero(X2),X2)
    | ~ class_OrderedGroup_Olordered__ab__group__add(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_1487]) ).

cnf(c_0_2095,plain,
    ( c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X1,X2),c_HOL_Ozero__class_Ozero(X2),X2)
    | ~ class_Ring__and__Field_Oordered__idom(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_1488]) ).

cnf(c_0_2096,plain,
    ( c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
    | ~ c_lessequals(c_HOL_Oplus__class_Oplus(X1,X1,X2),c_HOL_Ozero__class_Ozero(X2),X2)
    | ~ class_OrderedGroup_Olordered__ab__group__add(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_1489]) ).

cnf(c_0_2097,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_Oplus__class_Oplus(X2,X2,X1),X1)
    | ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1490]) ).

cnf(c_0_2098,plain,
    ( c_lessequals(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X2,tc_nat)
    | ~ c_lessequals(c_Suc(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_1491]) ).

cnf(c_0_2099,plain,
    ( c_lessequals(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X1,tc_nat)
    | ~ c_lessequals(c_Suc(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_1492]) ).

cnf(c_0_2100,plain,
    ( c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X2,X3,X4),X4) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X2,X4),X3,X4)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X4) ),
    inference(split_conjunct,[status(thm)],[c_0_1493]) ).

cnf(c_0_2101,plain,
    ( c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X2,X3,X4),X4) = c_HOL_Oplus__class_Oplus(X2,c_HOL_Oplus__class_Oplus(X1,X3,X4),X4)
    | ~ class_OrderedGroup_Oab__group__add(X4) ),
    inference(split_conjunct,[status(thm)],[c_0_1494]) ).

cnf(c_0_2102,plain,
    ( c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X2,X3),X4,X3) = c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X2,X4,X3),X3)
    | ~ class_OrderedGroup_Ocomm__monoid__add(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1495]) ).

cnf(c_0_2103,plain,
    ( c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X2,X3,X4),X4) = c_HOL_Oplus__class_Oplus(X2,c_HOL_Oplus__class_Oplus(X1,X3,X4),X4)
    | ~ class_OrderedGroup_Ocomm__monoid__add(X4) ),
    inference(split_conjunct,[status(thm)],[c_0_1496]) ).

cnf(c_0_2104,plain,
    ( c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X2,X3),X4,X3) = c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X2,X4,X3),X3)
    | ~ class_OrderedGroup_Oab__semigroup__add(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1497]) ).

cnf(c_0_2105,plain,
    ( c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X2,X3,X4),X4) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X2,X4),X3,X4)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X4) ),
    inference(split_conjunct,[status(thm)],[c_0_1498]) ).

cnf(c_0_2106,plain,
    ( c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X2,X3),X4,X3) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X4,X3),X2,X3)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1499]) ).

cnf(c_0_2107,plain,
    ( c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X2,X3,X4),X4) = c_HOL_Oplus__class_Oplus(X2,c_HOL_Oplus__class_Oplus(X1,X3,X4),X4)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X4) ),
    inference(split_conjunct,[status(thm)],[c_0_1500]) ).

cnf(c_0_2108,plain,
    ( c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X2,X3),X4,X3) = c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X2,X4,X3),X3)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1501]) ).

cnf(c_0_2109,plain,
    ( c_Orderings_Oord__class_Omin(c_Orderings_Oord__class_Omin(X1,X2,X3),X4,X3) = c_Orderings_Oord__class_Omin(X1,c_Orderings_Oord__class_Omin(X2,X4,X3),X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1502]) ).

cnf(c_0_2110,plain,
    ( c_Orderings_Oord__class_Omin(X1,c_Orderings_Oord__class_Omin(X2,X3,X4),X4) = c_Orderings_Oord__class_Omin(X2,c_Orderings_Oord__class_Omin(X1,X3,X4),X4)
    | ~ class_Orderings_Olinorder(X4) ),
    inference(split_conjunct,[status(thm)],[c_0_1503]) ).

cnf(c_0_2111,plain,
    ( c_Orderings_Oord__class_Omax(c_Orderings_Oord__class_Omax(X1,X2,X3),X4,X3) = c_Orderings_Oord__class_Omax(X1,c_Orderings_Oord__class_Omax(X2,X4,X3),X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1504]) ).

cnf(c_0_2112,plain,
    ( c_Orderings_Oord__class_Omax(X1,c_Orderings_Oord__class_Omax(X2,X3,X4),X4) = c_Orderings_Oord__class_Omax(X2,c_Orderings_Oord__class_Omax(X1,X3,X4),X4)
    | ~ class_Orderings_Olinorder(X4) ),
    inference(split_conjunct,[status(thm)],[c_0_1505]) ).

cnf(c_0_2113,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_1506]) ).

cnf(c_0_2114,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_1507]) ).

cnf(c_0_2115,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_1508]) ).

cnf(c_0_2116,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_1509]) ).

cnf(c_0_2117,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_1510]) ).

cnf(c_0_2118,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_1511]) ).

cnf(c_0_2119,plain,
    ( c_HOL_Oord__class_Oless(X2,c_HOL_Oplus__class_Oplus(X3,X1,tc_nat),tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
    | ~ c_lessequals(X2,X3,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_1512]) ).

cnf(c_0_2120,plain,
    ( c_HOL_Oplus__class_Oplus(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) = c_HOL_Ozero__class_Ozero(X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1513]) ).

cnf(c_0_2121,plain,
    ( c_lessequals(X1,X2,X3)
    | ~ c_lessequals(c_HOL_Ominus__class_Ominus(X1,X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1514]) ).

cnf(c_0_2122,plain,
    ( c_HOL_Oord__class_Oless(X1,X2,X3)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1515]) ).

cnf(c_0_2123,plain,
    ( c_lessequals(X4,X5,X3)
    | ~ c_lessequals(X1,X2,X3)
    | c_HOL_Ominus__class_Ominus(X2,X1,X3) != c_HOL_Ominus__class_Ominus(X5,X4,X3)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1516]) ).

cnf(c_0_2124,plain,
    ( c_lessequals(X4,X5,X3)
    | ~ c_lessequals(X1,X2,X3)
    | c_HOL_Ominus__class_Ominus(X5,X4,X3) != c_HOL_Ominus__class_Ominus(X2,X1,X3)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1517]) ).

cnf(c_0_2125,plain,
    ( c_HOL_Oord__class_Oless(X4,X5,X3)
    | ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | c_HOL_Ominus__class_Ominus(X1,X2,X3) != c_HOL_Ominus__class_Ominus(X4,X5,X3)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1518]) ).

cnf(c_0_2126,plain,
    ( c_HOL_Oord__class_Oless(X4,X5,X3)
    | ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | c_HOL_Ominus__class_Ominus(X4,X5,X3) != c_HOL_Ominus__class_Ominus(X1,X2,X3)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1519]) ).

cnf(c_0_2127,plain,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
    | c_lessequals(c_HOL_Otimes__class_Otimes(X2,X1,tc_nat),c_HOL_Otimes__class_Otimes(X3,X1,tc_nat),tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_1520]) ).

cnf(c_0_2128,plain,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
    | c_lessequals(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_1521]) ).

cnf(c_0_2129,plain,
    ( c_lessequals(X1,X3,X4)
    | ~ c_lessequals(X1,c_Orderings_Oord__class_Omin(X2,X3,X4),X4)
    | ~ class_Orderings_Olinorder(X4) ),
    inference(split_conjunct,[status(thm)],[c_0_1522]) ).

cnf(c_0_2130,plain,
    ( c_lessequals(X1,X2,X4)
    | ~ c_lessequals(X1,c_Orderings_Oord__class_Omin(X2,X3,X4),X4)
    | ~ class_Orderings_Olinorder(X4) ),
    inference(split_conjunct,[status(thm)],[c_0_1523]) ).

cnf(c_0_2131,plain,
    ( c_lessequals(X1,X3,X4)
    | ~ c_lessequals(X1,c_Orderings_Oord__class_Omin(X2,X3,X4),X4)
    | ~ class_Orderings_Olinorder(X4) ),
    inference(split_conjunct,[status(thm)],[c_0_1524]) ).

cnf(c_0_2132,plain,
    ( c_lessequals(X1,X2,X4)
    | ~ c_lessequals(X1,c_Orderings_Oord__class_Omin(X2,X3,X4),X4)
    | ~ class_Orderings_Olinorder(X4) ),
    inference(split_conjunct,[status(thm)],[c_0_1525]) ).

cnf(c_0_2133,plain,
    ( c_lessequals(X2,X4,X3)
    | ~ c_lessequals(c_Orderings_Oord__class_Omax(X1,X2,X3),X4,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1526]) ).

cnf(c_0_2134,plain,
    ( c_lessequals(X1,X4,X3)
    | ~ c_lessequals(c_Orderings_Oord__class_Omax(X1,X2,X3),X4,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1527]) ).

cnf(c_0_2135,plain,
    ( c_lessequals(X2,X4,X3)
    | ~ c_lessequals(c_Orderings_Oord__class_Omax(X1,X2,X3),X4,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1528]) ).

cnf(c_0_2136,plain,
    ( c_lessequals(X1,X4,X3)
    | ~ c_lessequals(c_Orderings_Oord__class_Omax(X1,X2,X3),X4,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1529]) ).

cnf(c_0_2137,plain,
    ( c_HOL_Oord__class_Oless(X1,X4,X3)
    | ~ c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omax(X1,X2,X3),X4,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1530]) ).

cnf(c_0_2138,plain,
    ( c_HOL_Oord__class_Oless(X2,X4,X3)
    | ~ c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omax(X1,X2,X3),X4,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1531]) ).

cnf(c_0_2139,plain,
    ( c_HOL_Oord__class_Oless(X1,X2,X4)
    | ~ c_HOL_Oord__class_Oless(X1,c_Orderings_Oord__class_Omin(X2,X3,X4),X4)
    | ~ class_Orderings_Olinorder(X4) ),
    inference(split_conjunct,[status(thm)],[c_0_1532]) ).

cnf(c_0_2140,plain,
    ( c_HOL_Oord__class_Oless(X1,X3,X4)
    | ~ c_HOL_Oord__class_Oless(X1,c_Orderings_Oord__class_Omin(X2,X3,X4),X4)
    | ~ class_Orderings_Olinorder(X4) ),
    inference(split_conjunct,[status(thm)],[c_0_1533]) ).

cnf(c_0_2141,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_1534]) ).

cnf(c_0_2142,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_1535]) ).

cnf(c_0_2143,plain,
    ( c_HOL_Oord__class_Oless(X2,X1,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_1536]) ).

cnf(c_0_2144,plain,
    ( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | ~ c_HOL_Oord__class_Oless(X3,X4,tc_nat)
    | c_HOL_Oplus__class_Oplus(X1,X4,tc_nat) != c_HOL_Oplus__class_Oplus(X3,X2,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_1537]) ).

cnf(c_0_2145,plain,
    ( c_HOL_Oord__class_Oless(X1,X3,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),X3,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_1538]) ).

cnf(c_0_2146,plain,
    ( c_lessequals(X2,X3,tc_nat)
    | ~ c_lessequals(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),X3,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_1539]) ).

cnf(c_0_2147,plain,
    ( c_lessequals(X1,X3,tc_nat)
    | ~ c_lessequals(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),X3,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_1540]) ).

cnf(c_0_2148,plain,
    ( X1 = c_HOL_Ozero__class_Ozero(X2)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X3,X2)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X1,X2)
    | c_HOL_Oplus__class_Oplus(X3,X1,X2) != c_HOL_Ozero__class_Ozero(X2)
    | ~ class_OrderedGroup_Opordered__comm__monoid__add(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_1541]) ).

cnf(c_0_2149,plain,
    ( X1 = c_HOL_Ozero__class_Ozero(X2)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X1,X2)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X3,X2)
    | c_HOL_Oplus__class_Oplus(X1,X3,X2) != c_HOL_Ozero__class_Ozero(X2)
    | ~ class_OrderedGroup_Opordered__comm__monoid__add(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_1542]) ).

cnf(c_0_2150,plain,
    ( c_Divides_Odiv__class_Omod(X2,X1,tc_nat) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),X1,tc_nat)
    | ~ c_lessequals(X1,X2,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_1543]) ).

cnf(c_0_2151,plain,
    ( c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ozero__class_Ozero(X1),X1) = c_HOL_Ozero__class_Ozero(X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ class_OrderedGroup_Opordered__comm__monoid__add(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1544]) ).

cnf(c_0_2152,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_1545]) ).

cnf(c_0_2153,plain,
    ( c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(X2,X2,X1),X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1546]) ).

cnf(c_0_2154,plain,
    ( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X1,X2),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_1547]) ).

cnf(c_0_2155,plain,
    ( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X1,X2),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_1548]) ).

cnf(c_0_2156,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_1549]) ).

cnf(c_0_2157,plain,
    ( c_lessequals(c_HOL_Oplus__class_Oplus(X1,X1,X2),c_HOL_Ozero__class_Ozero(X2),X2)
    | ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
    | ~ class_OrderedGroup_Olordered__ab__group__add(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_1550]) ).

cnf(c_0_2158,plain,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(X2,X2,X1),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_1551]) ).

cnf(c_0_2159,plain,
    ( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | c_Divides_Odiv__class_Omod(X1,X2,tc_nat) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),X2,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_1552]) ).

cnf(c_0_2160,plain,
    ( c_lessequals(c_HOL_Ominus__class_Ominus(X1,X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
    | ~ c_lessequals(X1,X2,X3)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1553]) ).

cnf(c_0_2161,plain,
    ( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
    | ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1554]) ).

cnf(c_0_2162,plain,
    ( c_Lambda_Osubst(c_Lambda_OdB_OVar(X2),X3,X1) = c_Lambda_OdB_OVar(c_HOL_Ominus__class_Ominus(X2,c_HOL_Oone__class_Oone(tc_nat),tc_nat))
    | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_1555]) ).

cnf(c_0_2163,plain,
    ( c_Lambda_Osubst(c_Lambda_OdB_OVar(X2),X3,X1) = c_Lambda_OdB_OVar(c_HOL_Ominus__class_Ominus(X2,c_HOL_Oone__class_Oone(tc_nat),tc_nat))
    | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_1556]) ).

cnf(c_0_2164,plain,
    ( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,c_Suc(X2),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_1557]) ).

cnf(c_0_2165,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_1558]) ).

cnf(c_0_2166,plain,
    ( c_lessequals(c_Orderings_Oord__class_Omin(X4,X1,X3),X2,X3)
    | ~ c_lessequals(X1,X2,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1559]) ).

cnf(c_0_2167,plain,
    ( c_lessequals(c_Orderings_Oord__class_Omin(X1,X4,X3),X2,X3)
    | ~ c_lessequals(X1,X2,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1560]) ).

cnf(c_0_2168,plain,
    ( c_lessequals(c_Orderings_Oord__class_Omin(X4,X1,X3),X2,X3)
    | ~ c_lessequals(X1,X2,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1561]) ).

cnf(c_0_2169,plain,
    ( c_lessequals(c_Orderings_Oord__class_Omin(X1,X4,X3),X2,X3)
    | ~ c_lessequals(X1,X2,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1562]) ).

cnf(c_0_2170,plain,
    ( c_lessequals(X1,c_Orderings_Oord__class_Omax(X4,X2,X3),X3)
    | ~ c_lessequals(X1,X2,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1563]) ).

cnf(c_0_2171,plain,
    ( c_lessequals(X1,c_Orderings_Oord__class_Omax(X2,X4,X3),X3)
    | ~ c_lessequals(X1,X2,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1564]) ).

cnf(c_0_2172,plain,
    ( c_lessequals(X1,c_Orderings_Oord__class_Omax(X4,X2,X3),X3)
    | ~ c_lessequals(X1,X2,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1565]) ).

cnf(c_0_2173,plain,
    ( c_lessequals(X1,c_Orderings_Oord__class_Omax(X2,X4,X3),X3)
    | ~ c_lessequals(X1,X2,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1566]) ).

cnf(c_0_2174,plain,
    ( c_HOL_Oord__class_Oless(X1,c_Orderings_Oord__class_Omax(X2,X4,X3),X3)
    | ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1567]) ).

cnf(c_0_2175,plain,
    ( c_HOL_Oord__class_Oless(X1,c_Orderings_Oord__class_Omax(X4,X2,X3),X3)
    | ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1568]) ).

cnf(c_0_2176,plain,
    ( c_HOL_Oord__class_Oless(X1,c_Orderings_Oord__class_Omax(X2,X4,X3),X3)
    | ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1569]) ).

cnf(c_0_2177,plain,
    ( c_HOL_Oord__class_Oless(X1,c_Orderings_Oord__class_Omax(X4,X2,X3),X3)
    | ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1570]) ).

cnf(c_0_2178,plain,
    ( c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omin(X1,X4,X3),X2,X3)
    | ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1571]) ).

cnf(c_0_2179,plain,
    ( c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omin(X4,X1,X3),X2,X3)
    | ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1572]) ).

cnf(c_0_2180,plain,
    ( c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omin(X1,X4,X3),X2,X3)
    | ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1573]) ).

cnf(c_0_2181,plain,
    ( c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omin(X4,X1,X3),X2,X3)
    | ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1574]) ).

cnf(c_0_2182,plain,
    ( c_HOL_Ominus__class_Ominus(c_Suc(X2),X1,tc_nat) = c_Suc(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat))
    | ~ c_lessequals(X1,X2,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_1575]) ).

cnf(c_0_2183,plain,
    ( c_Lambda_Obeta(c_Lambda_Osubst(X1,X3,X4),c_Lambda_Osubst(X2,X3,X4))
    | ~ c_Lambda_Obeta(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_1576]) ).

cnf(c_0_2184,plain,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oplus__class_Oplus(X2,X1,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_1577]) ).

cnf(c_0_2185,plain,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oplus__class_Oplus(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_1578]) ).

cnf(c_0_2186,plain,
    ( c_HOL_Oplus__class_Oplus(X1,X1,X2) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(X2),c_HOL_Oone__class_Oone(X2),X2),X1,X2)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_1579]) ).

cnf(c_0_2187,plain,
    ( c_lessequals(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_1580]) ).

cnf(c_0_2188,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_1581]) ).

cnf(c_0_2189,plain,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),tc_nat)
    | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_1582]) ).

cnf(c_0_2190,plain,
    ( X1 = c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),X2,tc_nat)
    | ~ c_lessequals(X2,X1,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_1583]) ).

cnf(c_0_2191,plain,
    ( c_HOL_Oplus__class_Oplus(X1,c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),tc_nat) = X2
    | ~ c_lessequals(X1,X2,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_1584]) ).

cnf(c_0_2192,plain,
    ( c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),X1,tc_nat) = X2
    | ~ c_lessequals(X1,X2,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_1585]) ).

cnf(c_0_2193,plain,
    ( c_HOL_Ominus__class_Ominus(X2,c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),tc_nat) = X1
    | ~ c_lessequals(X1,X2,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_1586]) ).

cnf(c_0_2194,plain,
    ( c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(X2,X3,tc_nat),tc_nat)
    | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_1587]) ).

cnf(c_0_2195,plain,
    ( c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(X3,X2,tc_nat),tc_nat)
    | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_1588]) ).

cnf(c_0_2196,plain,
    ( c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(X2,X3,tc_nat),tc_nat)
    | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_1589]) ).

cnf(c_0_2197,plain,
    ( c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(X3,X2,tc_nat),tc_nat)
    | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_1590]) ).

cnf(c_0_2198,plain,
    ( c_lessequals(X1,c_HOL_Oplus__class_Oplus(X3,X2,tc_nat),tc_nat)
    | ~ c_lessequals(X1,X2,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_1591]) ).

cnf(c_0_2199,plain,
    ( c_lessequals(X1,c_HOL_Oplus__class_Oplus(X2,X3,tc_nat),tc_nat)
    | ~ c_lessequals(X1,X2,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_1592]) ).

cnf(c_0_2200,plain,
    ( c_lessequals(X1,c_HOL_Oplus__class_Oplus(X3,X2,tc_nat),tc_nat)
    | ~ c_lessequals(X1,X2,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_1593]) ).

cnf(c_0_2201,plain,
    ( c_lessequals(X1,c_HOL_Oplus__class_Oplus(X2,X3,tc_nat),tc_nat)
    | ~ c_lessequals(X1,X2,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_1594]) ).

cnf(c_0_2202,plain,
    ( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,X3,tc_nat),X2,tc_nat)
    | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_1595]) ).

cnf(c_0_2203,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_1596]) ).

cnf(c_0_2204,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_1597]) ).

cnf(c_0_2205,plain,
    ( c_lessequals(X4,X2,X3)
    | ~ c_lessequals(X1,X2,X3)
    | ~ c_lessequals(X4,X1,X3)
    | ~ class_Orderings_Oorder(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1598]) ).

cnf(c_0_2206,plain,
    ( c_HOL_Oord__class_Oless(X4,X2,X3)
    | ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | ~ c_lessequals(X4,X1,X3)
    | ~ class_Orderings_Oorder(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1599]) ).

cnf(c_0_2207,plain,
    ( c_HOL_Oord__class_Oless(X4,X2,X3)
    | ~ c_lessequals(X1,X2,X3)
    | ~ c_HOL_Oord__class_Oless(X4,X1,X3)
    | ~ class_Orderings_Oorder(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1600]) ).

cnf(c_0_2208,plain,
    ( c_lessequals(X1,X4,X3)
    | ~ c_lessequals(X1,X2,X3)
    | ~ c_lessequals(X2,X4,X3)
    | ~ class_Orderings_Opreorder(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1601]) ).

cnf(c_0_2209,plain,
    ( c_HOL_Oord__class_Oless(X1,X4,X3)
    | ~ c_lessequals(X1,X2,X3)
    | ~ c_HOL_Oord__class_Oless(X2,X4,X3)
    | ~ class_Orderings_Opreorder(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1602]) ).

cnf(c_0_2210,plain,
    ( c_HOL_Oord__class_Oless(X1,X4,X3)
    | ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | ~ c_lessequals(X2,X4,X3)
    | ~ class_Orderings_Opreorder(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1603]) ).

cnf(c_0_2211,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_1604]) ).

cnf(c_0_2212,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_1605]) ).

cnf(c_0_2213,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_1606]) ).

cnf(c_0_2214,plain,
    ( c_Orderings_Oord__class_Omin(X1,c_Orderings_Oord__class_Omin(X1,X2,X3),X3) = c_Orderings_Oord__class_Omin(X1,X2,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1607]) ).

cnf(c_0_2215,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_1608]) ).

cnf(c_0_2216,plain,
    ( c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(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_1609]) ).

cnf(c_0_2217,plain,
    ( c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X1,X2,X3),X1,X3) = c_Divides_Odiv__class_Omod(X2,X1,X3)
    | ~ class_Divides_Osemiring__div(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1610]) ).

cnf(c_0_2218,plain,
    ( c_Orderings_Oord__class_Omax(X1,c_Orderings_Oord__class_Omax(X1,X2,X3),X3) = c_Orderings_Oord__class_Omax(X1,X2,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1611]) ).

cnf(c_0_2219,plain,
    ( c_Suc(c_HOL_Ominus__class_Ominus(X1,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat)) = X1
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_1612]) ).

cnf(c_0_2220,plain,
    ( c_lessequals(X1,X3,tc_nat)
    | ~ c_lessequals(X1,X2,tc_nat)
    | ~ c_lessequals(X2,X3,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_1613]) ).

cnf(c_0_2221,plain,
    ( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | c_HOL_Oplus__class_Oplus(X2,c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),tc_nat) = X1 ),
    inference(split_conjunct,[status(thm)],[c_0_1614]) ).

cnf(c_0_2222,plain,
    ( c_Suc(c_HOL_Ominus__class_Ominus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat)) = X1
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_1615]) ).

cnf(c_0_2223,plain,
    ( X1 = c_Suc(c_HOL_Ominus__class_Ominus(X1,c_HOL_Oone__class_Oone(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_1616]) ).

cnf(c_0_2224,plain,
    ( c_lessequals(X2,X1,X3)
    | c_HOL_Oord__class_Oless(X1,X2,X3)
    | ~ c_lessequals(X1,X2,X3)
    | ~ class_Orderings_Opreorder(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1617]) ).

cnf(c_0_2225,plain,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(X1),c_HOL_Oone__class_Oone(X1),X1),X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1618]) ).

cnf(c_0_2226,plain,
    ( X1 = X2
    | c_HOL_Oplus__class_Oplus(X3,X1,X4) != c_HOL_Oplus__class_Oplus(X3,X2,X4)
    | ~ class_Int_Onumber__ring(X4)
    | ~ class_Ring__and__Field_Oidom(X4) ),
    inference(split_conjunct,[status(thm)],[c_0_1619]) ).

cnf(c_0_2227,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_1620]) ).

cnf(c_0_2228,plain,
    ( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | c_Lambda_Olift(c_Lambda_OdB_OVar(X1),X2) = c_Lambda_OdB_OVar(c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat)) ),
    inference(split_conjunct,[status(thm)],[c_0_1621]) ).

cnf(c_0_2229,plain,
    ( X1 = X2
    | ~ c_lessequals(X1,X2,X3)
    | ~ c_lessequals(X2,X1,X3)
    | ~ class_Orderings_Oorder(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1622]) ).

cnf(c_0_2230,plain,
    ( X1 = X2
    | ~ c_lessequals(X1,X2,X3)
    | ~ c_lessequals(X2,X1,X3)
    | ~ class_Orderings_Oorder(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1623]) ).

cnf(c_0_2231,plain,
    ( X2 = X1
    | ~ c_lessequals(X1,X2,X3)
    | ~ c_lessequals(X2,X1,X3)
    | ~ class_Orderings_Oorder(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1624]) ).

cnf(c_0_2232,plain,
    ( c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(X2),X2),X2)
    | ~ class_Ring__and__Field_Oordered__semidom(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_1625]) ).

cnf(c_0_2233,plain,
    ( X1 = X2
    | c_HOL_Ominus__class_Ominus(X1,X2,X3) != c_HOL_Ominus__class_Ominus(X4,X4,X3)
    | ~ class_OrderedGroup_Oab__group__add(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1626]) ).

cnf(c_0_2234,plain,
    ( X1 = X2
    | c_HOL_Ominus__class_Ominus(X3,X3,X4) != c_HOL_Ominus__class_Ominus(X1,X2,X4)
    | ~ class_OrderedGroup_Oab__group__add(X4) ),
    inference(split_conjunct,[status(thm)],[c_0_1627]) ).

cnf(c_0_2235,plain,
    ( X1 = X2
    | c_HOL_Oplus__class_Oplus(X3,X1,X4) != c_HOL_Oplus__class_Oplus(X3,X2,X4)
    | ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X4) ),
    inference(split_conjunct,[status(thm)],[c_0_1628]) ).

cnf(c_0_2236,plain,
    ( X1 = X2
    | c_HOL_Oplus__class_Oplus(X3,X1,X4) != c_HOL_Oplus__class_Oplus(X3,X2,X4)
    | ~ class_OrderedGroup_Ocancel__semigroup__add(X4) ),
    inference(split_conjunct,[status(thm)],[c_0_1629]) ).

cnf(c_0_2237,plain,
    ( X1 = X2
    | c_HOL_Oplus__class_Oplus(X1,X3,X4) != c_HOL_Oplus__class_Oplus(X2,X3,X4)
    | ~ class_OrderedGroup_Ocancel__semigroup__add(X4) ),
    inference(split_conjunct,[status(thm)],[c_0_1630]) ).

cnf(c_0_2238,plain,
    ( ~ c_HOL_Oord__class_Oless(X1,X1,X2)
    | ~ c_lessequals(X1,X1,X2)
    | ~ class_Orderings_Olinorder(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_1631]) ).

cnf(c_0_2239,plain,
    ( ~ c_lessequals(X1,X2,X3)
    | ~ c_HOL_Oord__class_Oless(X2,X1,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1632]) ).

cnf(c_0_2240,plain,
    ( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | ~ c_lessequals(X2,X1,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1633]) ).

cnf(c_0_2241,plain,
    ( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | ~ c_lessequals(X2,X1,X3)
    | ~ class_Orderings_Opreorder(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1634]) ).

cnf(c_0_2242,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_1635]) ).

cnf(c_0_2243,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_1636]) ).

cnf(c_0_2244,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_1637]) ).

cnf(c_0_2245,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_1638]) ).

cnf(c_0_2246,plain,
    ( X2 = X1
    | ~ c_lessequals(X1,X2,tc_nat)
    | ~ c_HOL_Oord__class_Oless(X2,c_Suc(X1),tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_1639]) ).

cnf(c_0_2247,plain,
    ( ~ c_lessequals(c_Suc(X1),X2,tc_nat)
    | ~ c_lessequals(X2,X1,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_1640]) ).

cnf(c_0_2248,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_1641]) ).

cnf(c_0_2249,plain,
    ( X1 = X2
    | c_HOL_Ominus__class_Ominus(X1,X2,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)
    | c_HOL_Ominus__class_Ominus(X2,X1,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_1642]) ).

cnf(c_0_2250,plain,
    ( c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X2,X1),X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1643]) ).

cnf(c_0_2251,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_1644]) ).

cnf(c_0_2252,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_1645]) ).

cnf(c_0_2253,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_1646]) ).

cnf(c_0_2254,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_1647]) ).

cnf(c_0_2255,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_1648]) ).

cnf(c_0_2256,plain,
    ( X1 = X2
    | ~ c_lessequals(X1,X2,tc_nat)
    | ~ c_lessequals(X2,X1,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_1649]) ).

cnf(c_0_2257,plain,
    ( c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X1,X2,X3),X2,X3) = X1
    | ~ class_OrderedGroup_Ogroup__add(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1650]) ).

cnf(c_0_2258,plain,
    ( c_Orderings_Oord__class_Omin(X1,c_Orderings_Oord__class_Omax(X1,X2,X3),X3) = X1
    | ~ class_Orderings_Olinorder(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1651]) ).

cnf(c_0_2259,plain,
    ( c_Orderings_Oord__class_Omax(X1,c_Orderings_Oord__class_Omin(X1,X2,X3),X3) = X1
    | ~ class_Orderings_Olinorder(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1652]) ).

cnf(c_0_2260,plain,
    ( c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X1,X2,X3),X2,X3) = X1
    | ~ class_OrderedGroup_Ogroup__add(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1653]) ).

cnf(c_0_2261,plain,
    ( c_lessequals(X1,c_Orderings_Oord__class_Omax(X1,X2,X3),X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1654]) ).

cnf(c_0_2262,plain,
    ( c_lessequals(X1,c_Orderings_Oord__class_Omax(X2,X1,X3),X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1655]) ).

cnf(c_0_2263,plain,
    ( c_lessequals(c_Orderings_Oord__class_Omin(X1,X2,X3),X1,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1656]) ).

cnf(c_0_2264,plain,
    ( c_lessequals(c_Orderings_Oord__class_Omin(X1,X2,X3),X2,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1657]) ).

cnf(c_0_2265,plain,
    ( X1 = X2
    | c_HOL_Oplus__class_Oplus(X3,X1,tc_nat) != c_HOL_Oplus__class_Oplus(X3,X2,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_1658]) ).

cnf(c_0_2266,plain,
    ( X1 = X2
    | c_HOL_Oplus__class_Oplus(X1,X3,tc_nat) != c_HOL_Oplus__class_Oplus(X2,X3,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_1659]) ).

cnf(c_0_2267,plain,
    ( X1 = X2
    | c_HOL_Oplus__class_Oplus(X3,X1,tc_nat) != c_HOL_Oplus__class_Oplus(X3,X2,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_1660]) ).

cnf(c_0_2268,plain,
    ( c_lessequals(X1,X2,tc_nat)
    | ~ c_lessequals(c_Suc(X1),c_Suc(X2),tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_1661]) ).

cnf(c_0_2269,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_1662]) ).

cnf(c_0_2270,plain,
    ( c_lessequals(X1,X2,tc_nat)
    | X1 = c_Suc(X2)
    | ~ c_lessequals(X1,c_Suc(X2),tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_1663]) ).

cnf(c_0_2271,plain,
    ( X2 = X1
    | c_HOL_Oord__class_Oless(X1,X2,X3)
    | ~ c_lessequals(X1,X2,X3)
    | ~ class_Orderings_Oorder(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1664]) ).

cnf(c_0_2272,plain,
    ( X1 = X2
    | c_HOL_Oord__class_Oless(X2,X1,X3)
    | ~ c_lessequals(X2,X1,X3)
    | ~ class_Orderings_Oorder(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1665]) ).

cnf(c_0_2273,plain,
    ( c_HOL_Oord__class_Oless(X1,X2,X3)
    | X1 = X2
    | ~ c_lessequals(X1,X2,X3)
    | ~ class_Orderings_Oorder(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1666]) ).

cnf(c_0_2274,plain,
    ( X1 = X2
    | c_HOL_Oord__class_Oless(X1,X2,X3)
    | ~ c_lessequals(X1,X2,X3)
    | ~ class_Orderings_Oorder(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1667]) ).

cnf(c_0_2275,plain,
    ( X1 = X2
    | c_HOL_Oord__class_Oless(X1,X2,X3)
    | ~ c_lessequals(X1,X2,X3)
    | ~ class_Orderings_Oorder(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1668]) ).

cnf(c_0_2276,plain,
    ( X1 = X2
    | c_HOL_Oord__class_Oless(X1,X2,X3)
    | ~ c_lessequals(X1,X2,X3)
    | ~ class_Orderings_Oorder(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1669]) ).

cnf(c_0_2277,plain,
    ( c_HOL_Oord__class_Oless(X1,X2,X3)
    | X1 = X2
    | ~ c_lessequals(X1,X2,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1670]) ).

cnf(c_0_2278,plain,
    ( c_HOL_Oord__class_Oless(X1,X2,X3)
    | X1 = X2
    | ~ c_lessequals(X1,X2,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1671]) ).

cnf(c_0_2279,plain,
    ( c_lessequals(X1,X2,X3)
    | c_Orderings_Oord__class_Omax(X1,X2,X3) != X2
    | ~ class_Orderings_Olinorder(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1672]) ).

cnf(c_0_2280,plain,
    ( c_lessequals(X1,X2,X3)
    | c_Orderings_Oord__class_Omin(X1,X2,X3) != X1
    | ~ class_Orderings_Olinorder(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1673]) ).

cnf(c_0_2281,plain,
    ( c_lessequals(c_Suc(X1),c_Suc(X2),tc_nat)
    | ~ c_lessequals(X1,X2,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_1674]) ).

cnf(c_0_2282,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_1675]) ).

cnf(c_0_2283,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_1676]) ).

cnf(c_0_2284,plain,
    ( c_Orderings_Oord__class_Omax(X1,X2,X3) = X2
    | ~ c_lessequals(X1,X2,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1677]) ).

cnf(c_0_2285,plain,
    ( c_Orderings_Oord__class_Omax(X2,X1,X3) = X2
    | ~ c_lessequals(X1,X2,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1678]) ).

cnf(c_0_2286,plain,
    ( c_Orderings_Oord__class_Omin(X1,X2,X3) = X1
    | ~ c_lessequals(X1,X2,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1679]) ).

cnf(c_0_2287,plain,
    ( c_Orderings_Oord__class_Omin(X2,X1,X3) = X1
    | ~ c_lessequals(X1,X2,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1680]) ).

cnf(c_0_2288,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_1681]) ).

cnf(c_0_2289,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_1682]) ).

cnf(c_0_2290,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_1683]) ).

cnf(c_0_2291,plain,
    ( 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_1684]) ).

cnf(c_0_2292,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_1685]) ).

cnf(c_0_2293,plain,
    ( c_lessequals(X1,X2,X3)
    | ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | ~ class_Orderings_Oorder(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1686]) ).

cnf(c_0_2294,plain,
    ( c_lessequals(X1,X2,X3)
    | ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | ~ class_Orderings_Opreorder(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1687]) ).

cnf(c_0_2295,plain,
    ( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | ~ c_lessequals(c_Suc(X1),X2,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_1688]) ).

cnf(c_0_2296,plain,
    ( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | ~ c_lessequals(c_Suc(X1),X2,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_1689]) ).

cnf(c_0_2297,plain,
    ( c_lessequals(X1,X2,tc_nat)
    | ~ c_HOL_Oord__class_Oless(X1,c_Suc(X2),tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_1690]) ).

cnf(c_0_2298,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_1691]) ).

cnf(c_0_2299,plain,
    ( c_lessequals(X1,X2,tc_nat)
    | ~ c_lessequals(c_Suc(X1),X2,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_1692]) ).

cnf(c_0_2300,plain,
    ( c_lessequals(c_Suc(X1),X2,tc_nat)
    | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_1693]) ).

cnf(c_0_2301,plain,
    ( c_lessequals(c_Suc(X1),X2,tc_nat)
    | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_1694]) ).

cnf(c_0_2302,plain,
    ( c_HOL_Oord__class_Oless(X1,c_Suc(X2),tc_nat)
    | ~ c_lessequals(X1,X2,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_1695]) ).

cnf(c_0_2303,plain,
    ( c_HOL_Oord__class_Oless(X1,c_Suc(X1),tc_nat)
    | ~ c_lessequals(X1,X1,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_1696]) ).

cnf(c_0_2304,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_1697]) ).

cnf(c_0_2305,plain,
    ( c_lessequals(X1,c_Suc(X2),tc_nat)
    | ~ c_lessequals(X1,X2,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_1698]) ).

cnf(c_0_2306,plain,
    ( c_lessequals(X1,X2,tc_nat)
    | c_HOL_Ominus__class_Ominus(X1,X2,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_1699]) ).

cnf(c_0_2307,plain,
    ( c_HOL_Ominus__class_Ominus(X1,X2,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat)
    | ~ c_lessequals(X1,X2,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_1700]) ).

cnf(c_0_2308,plain,
    ( X1 = X2
    | c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | ~ c_lessequals(X1,X2,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_1701]) ).

cnf(c_0_2309,plain,
    ( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | X1 = X2
    | ~ c_lessequals(X1,X2,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_1702]) ).

cnf(c_0_2310,plain,
    ( X1 = X2
    | c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | ~ c_lessequals(X1,X2,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_1703]) ).

cnf(c_0_2311,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_1704]) ).

cnf(c_0_2312,plain,
    ( c_lessequals(X1,X2,tc_nat)
    | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_1705]) ).

cnf(c_0_2313,plain,
    ( c_lessequals(X1,X2,tc_nat)
    | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_1706]) ).

cnf(c_0_2314,plain,
    ( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | X2 = X1
    | c_Lambda_Osubst(c_Lambda_OdB_OVar(X2),X3,X1) = c_Lambda_OdB_OVar(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_1707]) ).

cnf(c_0_2315,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_1708]) ).

cnf(c_0_2316,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_1709]) ).

cnf(c_0_2317,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_1710]) ).

cnf(c_0_2318,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_1711]) ).

cnf(c_0_2319,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_1712]) ).

cnf(c_0_2320,plain,
    ( c_lessequals(X1,X2,X3)
    | c_HOL_Oord__class_Oless(X2,X1,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1713]) ).

cnf(c_0_2321,plain,
    ( c_lessequals(X1,X1,X2)
    | c_HOL_Oord__class_Oless(X1,X1,X2)
    | ~ class_Orderings_Olinorder(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_1714]) ).

cnf(c_0_2322,plain,
    ( c_HOL_Oord__class_Oless(X1,X2,X3)
    | c_lessequals(X2,X1,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1715]) ).

cnf(c_0_2323,plain,
    ( c_lessequals(X1,X2,X3)
    | c_HOL_Oord__class_Oless(X2,X1,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1716]) ).

cnf(c_0_2324,plain,
    ( c_lessequals(X1,X2,X3)
    | c_lessequals(X2,X1,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1717]) ).

cnf(c_0_2325,plain,
    ( c_HOL_Oplus__class_Oplus(X1,X2,X3) = c_HOL_Oplus__class_Oplus(X2,X1,X3)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1718]) ).

cnf(c_0_2326,plain,
    ( c_HOL_Oplus__class_Oplus(X1,X2,X3) = c_HOL_Oplus__class_Oplus(X2,X1,X3)
    | ~ class_OrderedGroup_Ocomm__monoid__add(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1719]) ).

cnf(c_0_2327,plain,
    ( c_HOL_Oplus__class_Oplus(X1,X2,X3) = c_HOL_Oplus__class_Oplus(X2,X1,X3)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1720]) ).

cnf(c_0_2328,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_1721]) ).

cnf(c_0_2329,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_1722]) ).

cnf(c_0_2330,plain,
    ( c_Orderings_Oord__class_Omin(X1,X2,X3) = c_Orderings_Oord__class_Omin(X2,X1,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1723]) ).

cnf(c_0_2331,plain,
    ( c_Orderings_Oord__class_Omax(X1,X2,X3) = c_Orderings_Oord__class_Omax(X2,X1,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1724]) ).

cnf(c_0_2332,plain,
    ( 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_1725]) ).

cnf(c_0_2333,plain,
    ( c_lessequals(X1,X2,tc_nat)
    | c_lessequals(c_Suc(X2),X1,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_1726]) ).

cnf(c_0_2334,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_1727]) ).

cnf(c_0_2335,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_1728]) ).

cnf(c_0_2336,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_1729]) ).

cnf(c_0_2337,plain,
    ( ~ c_lessequals(c_HOL_Oone__class_Oone(X1),c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1730]) ).

cnf(c_0_2338,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)) != c_HOL_Oplus__class_Oplus(X1,X2,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_1731]) ).

cnf(c_0_2339,plain,
    ( X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
    | X2 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
    | c_HOL_Oplus__class_Oplus(X1,X2,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
    inference(split_conjunct,[status(thm)],[c_0_1732]) ).

cnf(c_0_2340,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_1733]) ).

cnf(c_0_2341,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_1734]) ).

cnf(c_0_2342,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_1735]) ).

cnf(c_0_2343,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_1736]) ).

cnf(c_0_2344,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_1737]) ).

cnf(c_0_2345,plain,
    ( X1 = X2
    | c_HOL_Ominus__class_Ominus(X1,X2,X3) != c_HOL_Ozero__class_Ozero(X3)
    | ~ class_Int_Onumber__ring(X3)
    | ~ class_Ring__and__Field_Oidom(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1738]) ).

cnf(c_0_2346,plain,
    ( 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_1739]) ).

cnf(c_0_2347,plain,
    ( X1 = c_HOL_Ozero__class_Ozero(X2)
    | X3 != c_HOL_Oplus__class_Oplus(X3,X1,X2)
    | ~ class_Int_Onumber__ring(X2)
    | ~ class_Ring__and__Field_Oidom(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_1740]) ).

cnf(c_0_2348,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_1741]) ).

cnf(c_0_2349,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)) != c_HOL_Oplus__class_Oplus(X2,X1,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_1742]) ).

cnf(c_0_2350,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)) != c_HOL_Oplus__class_Oplus(X1,X2,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_1743]) ).

cnf(c_0_2351,plain,
    ( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
    | X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
    | c_HOL_Oplus__class_Oplus(X2,X1,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
    inference(split_conjunct,[status(thm)],[c_0_1744]) ).

cnf(c_0_2352,plain,
    ( X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
    | X1 = c_HOL_Ozero__class_Ozero(tc_nat)
    | c_HOL_Oplus__class_Oplus(X1,X2,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
    inference(split_conjunct,[status(thm)],[c_0_1745]) ).

cnf(c_0_2353,plain,
    ( c_lessequals(X1,X2,tc_nat)
    | c_lessequals(X2,X1,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_1746]) ).

cnf(c_0_2354,plain,
    ( X1 = c_HOL_Ozero__class_Ozero(X2)
    | c_HOL_Oplus__class_Oplus(X1,X1,X2) != c_HOL_Ozero__class_Ozero(X2)
    | ~ class_OrderedGroup_Olordered__ab__group__add(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_1747]) ).

cnf(c_0_2355,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_1748]) ).

cnf(c_0_2356,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_1749]) ).

cnf(c_0_2357,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)) != c_HOL_Oplus__class_Oplus(X2,X1,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_1750]) ).

cnf(c_0_2358,plain,
    ( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
    | X2 = c_HOL_Ozero__class_Ozero(tc_nat)
    | c_HOL_Oplus__class_Oplus(X2,X1,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
    inference(split_conjunct,[status(thm)],[c_0_1751]) ).

cnf(c_0_2359,plain,
    ( X1 = X2
    | c_HOL_Ominus__class_Ominus(X1,X2,X3) != c_HOL_Ozero__class_Ozero(X3)
    | ~ class_OrderedGroup_Ogroup__add(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1752]) ).

cnf(c_0_2360,plain,
    ( X1 = X2
    | c_HOL_Ominus__class_Ominus(X1,X2,X3) != c_HOL_Ozero__class_Ozero(X3)
    | ~ class_OrderedGroup_Oab__group__add(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1753]) ).

cnf(c_0_2361,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_1754]) ).

cnf(c_0_2362,plain,
    ( ~ c_HOL_Oord__class_Oless(X1,X1,X2)
    | ~ class_Orderings_Oorder(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_1755]) ).

cnf(c_0_2363,plain,
    ( ~ c_HOL_Oord__class_Oless(X1,X1,X2)
    | ~ class_Orderings_Olinorder(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_1756]) ).

cnf(c_0_2364,plain,
    ( ~ c_HOL_Oord__class_Oless(X1,X1,X2)
    | ~ class_Orderings_Opreorder(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_1757]) ).

cnf(c_0_2365,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_1758]) ).

cnf(c_0_2366,plain,
    ( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
    | ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_1759]) ).

cnf(c_0_2367,plain,
    ( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
    | c_HOL_Oplus__class_Oplus(X1,X2,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_1760]) ).

cnf(c_0_2368,plain,
    ( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
    | c_HOL_Oplus__class_Oplus(X2,X1,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_1761]) ).

cnf(c_0_2369,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_1762]) ).

cnf(c_0_2370,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_1763]) ).

cnf(c_0_2371,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_1764]) ).

cnf(c_0_2372,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_1765]) ).

cnf(c_0_2373,plain,
    ( c_Lambda_Obeta(c_Lambda_OdB_OApp(X3,X1),c_Lambda_OdB_OApp(X3,X2))
    | ~ c_Lambda_Obeta(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_1766]) ).

cnf(c_0_2374,plain,
    ( c_Lambda_Obeta(c_Lambda_OdB_OApp(X1,X3),c_Lambda_OdB_OApp(X2,X3))
    | ~ c_Lambda_Obeta(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_1767]) ).

cnf(c_0_2375,plain,
    ( c_Lambda_Obeta(c_Lambda_Olift(X1,X3),c_Lambda_Olift(X2,X3))
    | ~ c_Lambda_Obeta(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_1768]) ).

cnf(c_0_2376,plain,
    ( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
    | c_HOL_Oplus__class_Oplus(X2,X1,tc_nat) != X2 ),
    inference(split_conjunct,[status(thm)],[c_0_1769]) ).

cnf(c_0_2377,plain,
    ( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
    | X2 != c_HOL_Oplus__class_Oplus(X2,X1,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_1770]) ).

cnf(c_0_2378,plain,
    ( c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ozero__class_Ozero(X1),X1) = c_HOL_Ozero__class_Ozero(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1771]) ).

cnf(c_0_2379,plain,
    ( X1 = c_HOL_Oplus__class_Oplus(X1,c_HOL_Ozero__class_Ozero(X2),X2)
    | ~ class_Int_Onumber__ring(X2)
    | ~ class_Ring__and__Field_Oidom(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_1772]) ).

cnf(c_0_2380,plain,
    ( c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oone__class_Oone(X1),X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1773]) ).

cnf(c_0_2381,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_1774]) ).

cnf(c_0_2382,plain,
    ( c_HOL_Ominus__class_Ominus(X1,X1,X2) = c_HOL_Ozero__class_Ozero(X2)
    | ~ class_Int_Onumber__ring(X2)
    | ~ class_Ring__and__Field_Oidom(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_1775]) ).

cnf(c_0_2383,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_1776]) ).

cnf(c_0_2384,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_1777]) ).

cnf(c_0_2385,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_1778]) ).

cnf(c_0_2386,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_1779]) ).

cnf(c_0_2387,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_1780]) ).

cnf(c_0_2388,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_1781]) ).

cnf(c_0_2389,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_1782]) ).

cnf(c_0_2390,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_1783]) ).

cnf(c_0_2391,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_1784]) ).

cnf(c_0_2392,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_1785]) ).

cnf(c_0_2393,plain,
    ( c_HOL_Ominus__class_Ominus(X1,c_HOL_Ozero__class_Ozero(X2),X2) = X1
    | ~ class_OrderedGroup_Ogroup__add(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_1786]) ).

cnf(c_0_2394,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_1787]) ).

cnf(c_0_2395,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_1788]) ).

cnf(c_0_2396,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_1789]) ).

cnf(c_0_2397,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_1790]) ).

cnf(c_0_2398,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_1791]) ).

cnf(c_0_2399,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_1792]) ).

cnf(c_0_2400,plain,
    ( c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X1),X2,X1) = X2
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1793]) ).

cnf(c_0_2401,plain,
    ( c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X1),X2,X1) = X2
    | ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1794]) ).

cnf(c_0_2402,plain,
    ( c_HOL_Oplus__class_Oplus(X1,c_HOL_Ozero__class_Ozero(X2),X2) = X1
    | ~ class_OrderedGroup_Ocomm__monoid__add(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_1795]) ).

cnf(c_0_2403,plain,
    ( c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X1),X2,X1) = X2
    | ~ class_OrderedGroup_Omonoid__add(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1796]) ).

cnf(c_0_2404,plain,
    ( c_HOL_Oplus__class_Oplus(X1,c_HOL_Ozero__class_Ozero(X2),X2) = X1
    | ~ class_OrderedGroup_Omonoid__add(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_1797]) ).

cnf(c_0_2405,plain,
    ( c_HOL_Oplus__class_Oplus(X1,c_HOL_Ozero__class_Ozero(X2),X2) = X1
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_1798]) ).

cnf(c_0_2406,plain,
    ( c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X1),X2,X1) = X2
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1799]) ).

cnf(c_0_2407,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_1800]) ).

cnf(c_0_2408,plain,
    ( c_HOL_Ominus__class_Ominus(X1,X1,X2) = c_HOL_Ozero__class_Ozero(X2)
    | ~ class_OrderedGroup_Oab__group__add(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_1801]) ).

cnf(c_0_2409,plain,
    ( c_HOL_Ominus__class_Ominus(X1,X1,X2) = c_HOL_Ozero__class_Ozero(X2)
    | ~ class_OrderedGroup_Ogroup__add(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_1802]) ).

cnf(c_0_2410,plain,
    ( c_HOL_Ominus__class_Ominus(X1,X1,X2) = c_HOL_Ozero__class_Ozero(X2)
    | ~ class_OrderedGroup_Ogroup__add(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_1803]) ).

cnf(c_0_2411,plain,
    ( c_Orderings_Oord__class_Omin(X1,X1,X2) = X1
    | ~ class_Orderings_Olinorder(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_1804]) ).

cnf(c_0_2412,plain,
    ( c_Orderings_Oord__class_Omax(X1,X1,X2) = X1
    | ~ class_Orderings_Olinorder(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_1805]) ).

cnf(c_0_2413,plain,
    ( c_HOL_Otimes__class_Otimes(X1,X1,X2) = X1
    | ~ class_OrderedGroup_Oab__semigroup__idem__mult(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_1806]) ).

cnf(c_0_2414,plain,
    ( c_lessequals(X1,X1,X2)
    | ~ class_Orderings_Oorder(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_1807]) ).

cnf(c_0_2415,plain,
    ( c_lessequals(X1,X1,X2)
    | ~ class_Orderings_Opreorder(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_1808]) ).

cnf(c_0_2416,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_1809]) ).

cnf(c_0_2417,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_1810]) ).

cnf(c_0_2418,plain,
    ( X1 = X2
    | c_Lambda_OdB_OApp(X3,X1) != c_Lambda_OdB_OApp(X4,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_1811]) ).

cnf(c_0_2419,plain,
    ( X1 = X2
    | c_Lambda_OdB_OApp(X1,X3) != c_Lambda_OdB_OApp(X2,X4) ),
    inference(split_conjunct,[status(thm)],[c_0_1812]) ).

cnf(c_0_2420,plain,
    ( c_InductTermi_OIT(c_Lambda_Olift(X1,X2))
    | ~ c_InductTermi_OIT(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1813]) ).

cnf(c_0_2421,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_1814]) ).

cnf(c_0_2422,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_1815]) ).

cnf(c_0_2423,plain,
    ( c_InductTermi_OIT(c_Lambda_OdB_OAbs(X1))
    | ~ c_InductTermi_OIT(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1816]) ).

cnf(c_0_2424,plain,
    ( X1 = X2
    | c_Lambda_OdB_OVar(X1) != c_Lambda_OdB_OVar(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_1817]) ).

cnf(c_0_2425,plain,
    ( X1 = X2
    | c_Lambda_OdB_OAbs(X1) != c_Lambda_OdB_OAbs(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_1818]) ).

cnf(c_0_2426,plain,
    ( X1 = X2
    | c_Suc(X1) != c_Suc(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_1819]) ).

cnf(c_0_2427,plain,
    ( X1 = X2
    | c_Suc(X1) != c_Suc(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_1820]) ).

cnf(c_0_2428,plain,
    ( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X4,tc_nat),X3,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X4,tc_nat),X5,tc_nat),tc_nat)
    | ~ c_lessequals(X1,X2,tc_nat)
    | ~ c_HOL_Oord__class_Oless(X3,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),X4,tc_nat),X5,tc_nat),tc_nat) ),
    c_0_1821,
    [final] ).

cnf(c_0_2429,plain,
    ( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X3,tc_nat),X4,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),X5,tc_nat),tc_nat)
    | ~ c_lessequals(X1,X2,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),X3,tc_nat),X4,tc_nat),X5,tc_nat) ),
    c_0_1822,
    [final] ).

cnf(c_0_2430,plain,
    ( c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X3,tc_nat),X4,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),X5,tc_nat),tc_nat)
    | ~ c_lessequals(X1,X2,tc_nat)
    | ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),X3,tc_nat),X4,tc_nat),X5,tc_nat) ),
    c_0_1823,
    [final] ).

cnf(c_0_2431,plain,
    ( c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X4,tc_nat),X3,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X4,tc_nat),X5,tc_nat),tc_nat)
    | ~ c_lessequals(X1,X2,tc_nat)
    | ~ c_lessequals(X3,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),X4,tc_nat),X5,tc_nat),tc_nat) ),
    c_0_1824,
    [final] ).

cnf(c_0_2432,plain,
    ( c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X5,X4),X1,X4),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X5,X4),X6,X4),X4)
    | ~ c_lessequals(X1,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X3,X4),X5,X4),X6,X4),X4)
    | ~ class_Ring__and__Field_Opordered__ring(X4) ),
    c_0_1825,
    [final] ).

cnf(c_0_2433,plain,
    ( c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X4,X3),X5,X3),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X4,X3),X6,X3),X3)
    | ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,X2,X3),X4,X3),X5,X3),X6,X3)
    | ~ class_Ring__and__Field_Opordered__ring(X3) ),
    c_0_1826,
    [final] ).

cnf(c_0_2434,plain,
    ( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X5,X4),X1,X4),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X5,X4),X6,X4),X4)
    | ~ c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X3,X4),X5,X4),X6,X4),X4)
    | ~ class_Ring__and__Field_Opordered__ring(X4) ),
    c_0_1827,
    [final] ).

cnf(c_0_2435,plain,
    ( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X4,X3),X5,X3),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X4,X3),X6,X3),X3)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,X2,X3),X4,X3),X5,X3),X6,X3)
    | ~ class_Ring__and__Field_Opordered__ring(X3) ),
    c_0_1828,
    [final] ).

cnf(c_0_2436,plain,
    ( c_HOL_Oord__class_Oless(X4,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),X3,tc_nat),X5,tc_nat),tc_nat)
    | ~ c_lessequals(X1,X2,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),X4,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X3,tc_nat),X5,tc_nat),tc_nat) ),
    c_0_1829,
    [final] ).

cnf(c_0_2437,plain,
    ( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),X3,tc_nat),X4,tc_nat),X5,tc_nat)
    | ~ c_lessequals(X1,X2,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X3,tc_nat),X4,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),X5,tc_nat),tc_nat) ),
    c_0_1830,
    [final] ).

cnf(c_0_2438,plain,
    ( c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),X3,tc_nat),X4,tc_nat),X5,tc_nat)
    | ~ c_lessequals(X1,X2,tc_nat)
    | ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X3,tc_nat),X4,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),X5,tc_nat),tc_nat) ),
    c_0_1831,
    [final] ).

cnf(c_0_2439,plain,
    ( c_lessequals(X4,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),X3,tc_nat),X5,tc_nat),tc_nat)
    | ~ c_lessequals(X1,X2,tc_nat)
    | ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),X4,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X3,tc_nat),X5,tc_nat),tc_nat) ),
    c_0_1832,
    [final] ).

cnf(c_0_2440,plain,
    ( c_lessequals(X4,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X5,X1,X3),X2,X3),X6,X3),X3)
    | ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X5,X2,X3),X6,X3),X3)
    | ~ class_Ring__and__Field_Opordered__ring(X3) ),
    c_0_1833,
    [final] ).

cnf(c_0_2441,plain,
    ( c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,X5,X3),X2,X3),X4,X3),X6,X3)
    | ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X5,X2,X3),X6,X3),X3)
    | ~ class_Ring__and__Field_Opordered__ring(X3) ),
    c_0_1834,
    [final] ).

cnf(c_0_2442,plain,
    ( c_HOL_Oord__class_Oless(X4,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X5,X1,X3),X2,X3),X6,X3),X3)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X5,X2,X3),X6,X3),X3)
    | ~ class_Ring__and__Field_Opordered__ring(X3) ),
    c_0_1835,
    [final] ).

cnf(c_0_2443,plain,
    ( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,X5,X3),X2,X3),X4,X3),X6,X3)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X5,X2,X3),X6,X3),X3)
    | ~ class_Ring__and__Field_Opordered__ring(X3) ),
    c_0_1836,
    [final] ).

cnf(c_0_2444,plain,
    ( c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),X4,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X3,tc_nat),X5,tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(X4,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),X3,tc_nat),X5,tc_nat),tc_nat)
    | ~ c_lessequals(X1,X2,tc_nat) ),
    c_0_1837,
    [final] ).

cnf(c_0_2445,plain,
    ( c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X3,tc_nat),X4,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),X5,tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),X3,tc_nat),X4,tc_nat),X5,tc_nat)
    | ~ c_lessequals(X1,X2,tc_nat) ),
    c_0_1838,
    [final] ).

cnf(c_0_2446,plain,
    ( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X4,X2,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,X4,tc_nat),X2,tc_nat),X3,tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),X3,tc_nat)
    | ~ c_lessequals(X4,X1,tc_nat) ),
    c_0_1839,
    [final] ).

cnf(c_0_2447,plain,
    ( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X3,X1,tc_nat),X2,tc_nat),X4,tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X2,tc_nat),X4,tc_nat)
    | ~ c_lessequals(X1,X3,tc_nat) ),
    c_0_1840,
    [final] ).

cnf(c_0_2448,plain,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(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),X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    c_0_1841,
    [final] ).

cnf(c_0_2449,plain,
    ( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X4,X1,X3),X2,X3),X5,X3),X3) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X4,X2,X3),X5,X3)
    | ~ class_Ring__and__Field_Oring(X3) ),
    c_0_1842,
    [final] ).

cnf(c_0_2450,plain,
    ( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X5,X2,X3),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,X5,X3),X2,X3),X4,X3),X3) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3)
    | ~ class_Ring__and__Field_Oring(X3) ),
    c_0_1843,
    [final] ).

cnf(c_0_2451,plain,
    ( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,c_Divides_Odiv__class_Omod(X4,X1,tc_nat),tc_nat),X2,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_1844,
    [final] ).

cnf(c_0_2452,plain,
    ( X1 = c_HOL_Ozero__class_Ozero(X2)
    | ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X1,X2),c_HOL_Otimes__class_Otimes(X3,X3,X2),X2),c_HOL_Ozero__class_Ozero(X2),X2)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
    c_0_1845,
    [final] ).

cnf(c_0_2453,plain,
    ( X3 = c_HOL_Ozero__class_Ozero(X2)
    | ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X1,X2),c_HOL_Otimes__class_Otimes(X3,X3,X2),X2),c_HOL_Ozero__class_Ozero(X2),X2)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
    c_0_1846,
    [final] ).

cnf(c_0_2454,plain,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X1,X2),c_HOL_Otimes__class_Otimes(X3,X3,X2),X2),c_HOL_Ozero__class_Ozero(X2),X2)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
    c_0_1847,
    [final] ).

cnf(c_0_2455,plain,
    ( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),X3,tc_nat),X4,tc_nat) = X5
    | ~ c_lessequals(X2,X1,tc_nat)
    | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),X4,tc_nat) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X3,tc_nat),X5,tc_nat) ),
    c_0_1848,
    [final] ).

cnf(c_0_2456,plain,
    ( X1 = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X3,tc_nat),X4,tc_nat),X5,tc_nat)
    | ~ c_lessequals(X3,X2,tc_nat)
    | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X4,tc_nat),X1,tc_nat) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X4,tc_nat),X5,tc_nat) ),
    c_0_1849,
    [final] ).

cnf(c_0_2457,plain,
    ( c_lessequals(c_Orderings_Oord__class_Omax(c_Orderings_Oord__class_Omin(X1,X2,X3),c_Orderings_Oord__class_Omin(X1,X4,X3),X3),c_Orderings_Oord__class_Omin(X1,c_Orderings_Oord__class_Omax(X2,X4,X3),X3),X3)
    | ~ class_Orderings_Olinorder(X3) ),
    c_0_1850,
    [final] ).

cnf(c_0_2458,plain,
    ( c_lessequals(c_Orderings_Oord__class_Omax(X1,c_Orderings_Oord__class_Omin(X2,X3,X4),X4),c_Orderings_Oord__class_Omin(c_Orderings_Oord__class_Omax(X1,X2,X4),c_Orderings_Oord__class_Omax(X1,X3,X4),X4),X4)
    | ~ class_Orderings_Olinorder(X4) ),
    c_0_1851,
    [final] ).

cnf(c_0_2459,plain,
    ( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,X2,X3),X4,X3),X5,X3) = X6
    | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X4,X3),X5,X3) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X4,X3),X6,X3)
    | ~ class_Ring__and__Field_Oring(X3) ),
    c_0_1852,
    [final] ).

cnf(c_0_2460,plain,
    ( X1 = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X3,X4),X5,X4),X6,X4)
    | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X5,X4),X1,X4) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X5,X4),X6,X4)
    | ~ class_Ring__and__Field_Oring(X4) ),
    c_0_1853,
    [final] ).

cnf(c_0_2461,plain,
    ( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X4,X2,X3),X5,X3),X3) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X1,X4,X3),X2,X3),X5,X3)
    | ~ class_Ring__and__Field_Osemiring(X3) ),
    c_0_1854,
    [final] ).

cnf(c_0_2462,plain,
    ( X1 = X2
    | X3 = X4
    | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X3,X5),c_HOL_Otimes__class_Otimes(X2,X4,X5),X5) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X4,X5),c_HOL_Otimes__class_Otimes(X2,X3,X5),X5)
    | ~ class_Int_Onumber__ring(X5)
    | ~ class_Ring__and__Field_Oidom(X5) ),
    c_0_1855,
    [final] ).

cnf(c_0_2463,plain,
    ( X1 = X2
    | X3 = X4
    | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X3,X5),c_HOL_Otimes__class_Otimes(X2,X4,X5),X5) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X4,X5),c_HOL_Otimes__class_Otimes(X2,X3,X5),X5)
    | ~ class_Int_Onumber__ring(X5)
    | ~ class_Ring__and__Field_Oidom(X5) ),
    c_0_1856,
    [final] ).

cnf(c_0_2464,plain,
    ( X1 = X2
    | X3 = X4
    | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),c_HOL_Otimes__class_Otimes(X2,X4,tc_nat),tc_nat) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X4,tc_nat),c_HOL_Otimes__class_Otimes(X2,X3,tc_nat),tc_nat) ),
    c_0_1857,
    [final] ).

cnf(c_0_2465,plain,
    ( X1 = X2
    | X3 = X4
    | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),c_HOL_Otimes__class_Otimes(X2,X4,tc_nat),tc_nat) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X4,tc_nat),c_HOL_Otimes__class_Otimes(X2,X3,tc_nat),tc_nat) ),
    c_0_1858,
    [final] ).

cnf(c_0_2466,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_1859,
    [final] ).

cnf(c_0_2467,plain,
    ( c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(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_Oplus__class_Oplus(X1,X2,X3),X4,X3)
    | ~ class_Divides_Osemiring__div(X3) ),
    c_0_1860,
    [final] ).

cnf(c_0_2468,plain,
    ( c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(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_Ominus__class_Ominus(X1,X2,X3),X4,X3)
    | ~ class_Divides_Oring__div(X3) ),
    c_0_1861,
    [final] ).

cnf(c_0_2469,plain,
    ( c_Lambda_Osubst(c_Lambda_Osubst(X3,c_Lambda_Olift(X4,X1),c_Suc(X2)),c_Lambda_Osubst(X5,X4,X2),X1) = c_Lambda_Osubst(c_Lambda_Osubst(X3,X5,X1),X4,X2)
    | ~ c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(X2,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat) ),
    c_0_1862,
    [final] ).

cnf(c_0_2470,plain,
    ( c_Lambda_Osubst(c_Lambda_Olift(X3,c_HOL_Oplus__class_Oplus(X2,c_HOL_Oone__class_Oone(tc_nat),tc_nat)),c_Lambda_Olift(X4,X2),X1) = c_Lambda_Olift(c_Lambda_Osubst(X3,X4,X1),X2)
    | ~ c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(X2,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat) ),
    c_0_1863,
    [final] ).

cnf(c_0_2471,plain,
    ( c_lessequals(c_HOL_Oplus__class_Oplus(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),c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    c_0_1864,
    [final] ).

cnf(c_0_2472,plain,
    ( c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X1,X2,X3),X4,X3) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(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_1865,
    [final] ).

cnf(c_0_2473,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_1866,
    [final] ).

cnf(c_0_2474,plain,
    ( c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X1,X2,X3),X4,X3) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(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_Oring__div(X3) ),
    c_0_1867,
    [final] ).

cnf(c_0_2475,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_1868,
    [final] ).

cnf(c_0_2476,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_1869,
    [final] ).

cnf(c_0_2477,plain,
    ( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X2,X5,X3),X3)
    | ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | ~ c_HOL_Oord__class_Oless(X4,X5,X3)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
    | ~ class_Ring__and__Field_Oordered__semiring__strict(X3) ),
    c_0_1870,
    [final] ).

cnf(c_0_2478,plain,
    ( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X2,X5,X3),X3)
    | ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | ~ c_lessequals(X4,X5,X3)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X1,X3)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X4,X3)
    | ~ class_Ring__and__Field_Oordered__semiring__strict(X3) ),
    c_0_1871,
    [final] ).

cnf(c_0_2479,plain,
    ( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X2,X5,X3),X3)
    | ~ c_lessequals(X1,X2,X3)
    | ~ c_HOL_Oord__class_Oless(X4,X5,X3)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X1,X3)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
    | ~ class_Ring__and__Field_Oordered__semiring__strict(X3) ),
    c_0_1872,
    [final] ).

cnf(c_0_2480,plain,
    ( c_lessequals(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X2,X5,X3),X3)
    | ~ c_lessequals(X1,X2,X3)
    | ~ c_lessequals(X4,X5,X3)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X2,X3)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
    | ~ class_Ring__and__Field_Opordered__semiring(X3) ),
    c_0_1873,
    [final] ).

cnf(c_0_2481,plain,
    ( c_lessequals(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X2,X5,X3),X3)
    | ~ c_lessequals(X1,X2,X3)
    | ~ c_lessequals(X4,X5,X3)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X1,X3)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
    | ~ class_Ring__and__Field_Opordered__semiring(X3) ),
    c_0_1874,
    [final] ).

cnf(c_0_2482,plain,
    ( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X2,X5,X3),X3)
    | ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | ~ c_HOL_Oord__class_Oless(X4,X5,X3)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X1,X3)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
    | ~ class_Ring__and__Field_Oordered__semiring__strict(X3) ),
    c_0_1875,
    [final] ).

cnf(c_0_2483,plain,
    ( c_lessequals(X2,X3,tc_nat)
    | ~ c_lessequals(X1,X2,tc_nat)
    | ~ c_lessequals(X1,X3,tc_nat)
    | ~ c_lessequals(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),c_HOL_Ominus__class_Ominus(X3,X1,tc_nat),tc_nat) ),
    c_0_1876,
    [final] ).

cnf(c_0_2484,plain,
    ( c_HOL_Oord__class_Oless(X2,X3,tc_nat)
    | ~ c_lessequals(X1,X2,tc_nat)
    | ~ c_lessequals(X1,X3,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),c_HOL_Ominus__class_Ominus(X3,X1,tc_nat),tc_nat) ),
    c_0_1877,
    [final] ).

cnf(c_0_2485,plain,
    ( X1 = c_HOL_Ozero__class_Ozero(X2)
    | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X1,X2),c_HOL_Otimes__class_Otimes(X3,X3,X2),X2),X2)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
    c_0_1878,
    [final] ).

cnf(c_0_2486,plain,
    ( X1 = c_HOL_Ozero__class_Ozero(X2)
    | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X3,X2),c_HOL_Otimes__class_Otimes(X1,X1,X2),X2),X2)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
    c_0_1879,
    [final] ).

cnf(c_0_2487,plain,
    ( c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X2,X1),c_HOL_Otimes__class_Otimes(X3,X3,X1),X1),X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    c_0_1880,
    [final] ).

cnf(c_0_2488,plain,
    ( c_Divides_Odiv__class_Omod(X1,X2,tc_nat) = c_Divides_Odiv__class_Omod(X3,X2,tc_nat)
    | c_HOL_Oplus__class_Oplus(X1,c_HOL_Otimes__class_Otimes(X2,X4,tc_nat),tc_nat) != c_HOL_Oplus__class_Oplus(X3,c_HOL_Otimes__class_Otimes(X2,X5,tc_nat),tc_nat) ),
    c_0_1881,
    [final] ).

cnf(c_0_2489,plain,
    ( c_Lambda_Osubst(c_Lambda_Olift(X3,X1),c_Lambda_Olift(X4,X1),c_HOL_Oplus__class_Oplus(X2,c_HOL_Oone__class_Oone(tc_nat),tc_nat)) = c_Lambda_Olift(c_Lambda_Osubst(X3,X4,X2),X1)
    | ~ c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(X2,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat) ),
    c_0_1882,
    [final] ).

cnf(c_0_2490,plain,
    ( 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)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X2,X3)
    | ~ class_Ring__and__Field_Oordered__semiring__strict(X3) ),
    c_0_1883,
    [final] ).

cnf(c_0_2491,plain,
    ( 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)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X1,X3)
    | ~ class_Ring__and__Field_Oordered__semiring__strict(X3) ),
    c_0_1884,
    [final] ).

cnf(c_0_2492,plain,
    ( 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)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X2,X3)
    | ~ class_Ring__and__Field_Oordered__semiring(X3) ),
    c_0_1885,
    [final] ).

cnf(c_0_2493,plain,
    ( 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)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X1,X3)
    | ~ class_Ring__and__Field_Oordered__semiring(X3) ),
    c_0_1886,
    [final] ).

cnf(c_0_2494,plain,
    ( c_lessequals(X4,X3,X2)
    | ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
    | ~ c_lessequals(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_1887,
    [final] ).

cnf(c_0_2495,plain,
    ( c_lessequals(X3,X4,X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | ~ c_lessequals(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_1888,
    [final] ).

cnf(c_0_2496,plain,
    ( c_lessequals(X2,X4,X3)
    | ~ c_lessequals(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X1,X4,X3),X3)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X1,X3)
    | ~ class_Ring__and__Field_Oordered__semiring__strict(X3) ),
    c_0_1889,
    [final] ).

cnf(c_0_2497,plain,
    ( c_lessequals(X1,X4,X3)
    | ~ c_lessequals(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X4,X2,X3),X3)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3)
    | ~ class_Ring__and__Field_Oordered__semiring__strict(X3) ),
    c_0_1890,
    [final] ).

cnf(c_0_2498,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_1891,
    [final] ).

cnf(c_0_2499,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_1892,
    [final] ).

cnf(c_0_2500,plain,
    ( c_lessequals(X1,X3,tc_nat)
    | ~ c_lessequals(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) ),
    c_0_1893,
    [final] ).

cnf(c_0_2501,plain,
    ( c_lessequals(X2,X3,tc_nat)
    | ~ c_lessequals(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_1894,
    [final] ).

cnf(c_0_2502,plain,
    ( c_lessequals(X2,X3,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
    | ~ c_lessequals(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat) ),
    c_0_1895,
    [final] ).

cnf(c_0_2503,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_1896,
    [final] ).

cnf(c_0_2504,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_1897,
    [final] ).

cnf(c_0_2505,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_1898,
    [final] ).

cnf(c_0_2506,plain,
    ( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X1,X4,X3),X3) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X1,X2,X3),X3)
    | ~ class_Int_Onumber__ring(X3)
    | ~ class_Ring__and__Field_Oidom(X3) ),
    c_0_1899,
    [final] ).

cnf(c_0_2507,plain,
    ( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X1,X4,X3),X3) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X1,X2,X3),X3)
    | ~ class_Int_Onumber__ring(X3)
    | ~ class_Ring__and__Field_Oidom(X3) ),
    c_0_1900,
    [final] ).

cnf(c_0_2508,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_1901,
    [final] ).

cnf(c_0_2509,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_1902,
    [final] ).

cnf(c_0_2510,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_1903,
    [final] ).

cnf(c_0_2511,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_1904,
    [final] ).

cnf(c_0_2512,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_1905,
    [final] ).

cnf(c_0_2513,plain,
    ( c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(c_Divides_Odiv__class_Omod(X1,X4,X3),X2,X3),X4,X3) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X1,X2,X3),X4,X3)
    | ~ class_Divides_Oring__div(X3) ),
    c_0_1906,
    [final] ).

cnf(c_0_2514,plain,
    ( c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X1,c_Divides_Odiv__class_Omod(X2,X4,X3),X3),X4,X3) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X1,X2,X3),X4,X3)
    | ~ class_Divides_Oring__div(X3) ),
    c_0_1907,
    [final] ).

cnf(c_0_2515,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_1908,
    [final] ).

cnf(c_0_2516,plain,
    ( c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(X1,X4,X3),X2,X3),X4,X3) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X1,X2,X3),X4,X3)
    | ~ class_Divides_Osemiring__div(X3) ),
    c_0_1909,
    [final] ).

cnf(c_0_2517,plain,
    ( c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X1,c_Divides_Odiv__class_Omod(X2,X4,X3),X3),X4,X3) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X1,X2,X3),X4,X3)
    | ~ class_Divides_Osemiring__div(X3) ),
    c_0_1910,
    [final] ).

cnf(c_0_2518,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_1911,
    [final] ).

cnf(c_0_2519,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_1912,
    [final] ).

cnf(c_0_2520,plain,
    ( c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X2,X3),c_HOL_Oplus__class_Oplus(X4,X5,X3),X3) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X4,X3),c_HOL_Oplus__class_Oplus(X2,X5,X3),X3)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
    c_0_1913,
    [final] ).

cnf(c_0_2521,plain,
    ( c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(X1,X2,X3),X4,X3),X2,X3) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X1,X4,X3),X2,X3)
    | ~ class_Divides_Osemiring__div(X3) ),
    c_0_1914,
    [final] ).

cnf(c_0_2522,plain,
    ( c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X1,c_Divides_Odiv__class_Omod(X2,X3,X4),X4),X3,X4) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X1,X2,X4),X3,X4)
    | ~ class_Divides_Osemiring__div(X4) ),
    c_0_1915,
    [final] ).

cnf(c_0_2523,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_1916,
    [final] ).

cnf(c_0_2524,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_1917,
    [final] ).

cnf(c_0_2525,plain,
    ( X1 = c_HOL_Ozero__class_Ozero(X2)
    | X3 = X4
    | c_HOL_Oplus__class_Oplus(X5,c_HOL_Otimes__class_Otimes(X1,X3,X2),X2) != c_HOL_Oplus__class_Oplus(X5,c_HOL_Otimes__class_Otimes(X1,X4,X2),X2)
    | ~ class_Int_Onumber__ring(X2)
    | ~ class_Ring__and__Field_Oidom(X2) ),
    c_0_1918,
    [final] ).

cnf(c_0_2526,plain,
    ( c_HOL_Ominus__class_Ominus(c_Suc(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat)),X3,tc_nat) = c_HOL_Ominus__class_Ominus(c_Suc(X2),c_HOL_Oplus__class_Oplus(X1,X3,tc_nat),tc_nat)
    | ~ c_lessequals(X1,X2,tc_nat) ),
    c_0_1919,
    [final] ).

cnf(c_0_2527,plain,
    ( c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X3,X1,tc_nat),c_Suc(X2),tc_nat) = c_HOL_Ominus__class_Ominus(X3,c_Suc(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat)),tc_nat)
    | ~ c_lessequals(X1,X2,tc_nat) ),
    c_0_1920,
    [final] ).

cnf(c_0_2528,plain,
    ( c_lessequals(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),c_HOL_Ominus__class_Ominus(X3,X1,tc_nat),tc_nat)
    | ~ c_lessequals(X1,X2,tc_nat)
    | ~ c_lessequals(X1,X3,tc_nat)
    | ~ c_lessequals(X2,X3,tc_nat) ),
    c_0_1921,
    [final] ).

cnf(c_0_2529,plain,
    ( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),c_HOL_Ominus__class_Ominus(X3,X1,tc_nat),tc_nat)
    | ~ c_lessequals(X1,X2,tc_nat)
    | ~ c_lessequals(X1,X3,tc_nat)
    | ~ c_HOL_Oord__class_Oless(X2,X3,tc_nat) ),
    c_0_1922,
    [final] ).

cnf(c_0_2530,plain,
    ( c_lessequals(X1,c_HOL_Oplus__class_Oplus(X2,X5,X4),X4)
    | ~ c_lessequals(X1,c_HOL_Oplus__class_Oplus(X2,X3,X4),X4)
    | ~ c_lessequals(X3,X5,X4)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X4) ),
    c_0_1923,
    [final] ).

cnf(c_0_2531,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_1924,
    [final] ).

cnf(c_0_2532,plain,
    ( c_lessequals(X2,X3,tc_nat)
    | ~ c_lessequals(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_1925,
    [final] ).

cnf(c_0_2533,plain,
    ( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
    | X2 = X3
    | c_HOL_Oplus__class_Oplus(X4,c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),tc_nat) != c_HOL_Oplus__class_Oplus(X4,c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat) ),
    c_0_1926,
    [final] ).

cnf(c_0_2534,plain,
    ( c_lessequals(X3,c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),tc_nat)
    | ~ c_lessequals(X1,X2,tc_nat)
    | ~ c_lessequals(c_HOL_Oplus__class_Oplus(X3,X1,tc_nat),X2,tc_nat) ),
    c_0_1927,
    [final] ).

cnf(c_0_2535,plain,
    ( c_lessequals(c_HOL_Oplus__class_Oplus(X3,X1,tc_nat),X2,tc_nat)
    | ~ c_lessequals(X1,X2,tc_nat)
    | ~ c_lessequals(X3,c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),tc_nat) ),
    c_0_1928,
    [final] ).

cnf(c_0_2536,plain,
    ( c_lessequals(X1,X4,X3)
    | ~ c_lessequals(c_HOL_Oplus__class_Oplus(X1,X2,X3),c_HOL_Oplus__class_Oplus(X4,X2,X3),X3)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3) ),
    c_0_1929,
    [final] ).

cnf(c_0_2537,plain,
    ( c_lessequals(X2,X4,X3)
    | ~ c_lessequals(c_HOL_Oplus__class_Oplus(X1,X2,X3),c_HOL_Oplus__class_Oplus(X1,X4,X3),X3)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3) ),
    c_0_1930,
    [final] ).

cnf(c_0_2538,plain,
    ( c_HOL_Oord__class_Oless(X1,X4,X3)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X2,X3),c_HOL_Oplus__class_Oplus(X4,X2,X3),X3)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3) ),
    c_0_1931,
    [final] ).

cnf(c_0_2539,plain,
    ( c_HOL_Oord__class_Oless(X2,X4,X3)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X2,X3),c_HOL_Oplus__class_Oplus(X1,X4,X3),X3)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3) ),
    c_0_1932,
    [final] ).

cnf(c_0_2540,plain,
    ( c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),c_HOL_Ominus__class_Ominus(X3,X1,tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(X2,X3,tc_nat)
    | ~ c_lessequals(X1,X2,tc_nat)
    | ~ c_lessequals(X1,X3,tc_nat) ),
    c_0_1933,
    [final] ).

cnf(c_0_2541,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_1934,
    [final] ).

cnf(c_0_2542,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_1935,
    [final] ).

cnf(c_0_2543,plain,
    ( c_lessequals(X2,X3,tc_nat)
    | ~ c_lessequals(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),c_HOL_Oplus__class_Oplus(X1,X3,tc_nat),tc_nat) ),
    c_0_1936,
    [final] ).

cnf(c_0_2544,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_1937,
    [final] ).

cnf(c_0_2545,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_1938,
    [final] ).

cnf(c_0_2546,plain,
    ( c_HOL_Oord__class_Oless(X2,X3,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),c_HOL_Oplus__class_Oplus(X1,X3,tc_nat),tc_nat) ),
    c_0_1939,
    [final] ).

cnf(c_0_2547,plain,
    ( c_lessequals(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_lessequals(X3,X4,X2)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
    c_0_1940,
    [final] ).

cnf(c_0_2548,plain,
    ( c_lessequals(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_lessequals(X3,X4,X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    c_0_1941,
    [final] ).

cnf(c_0_2549,plain,
    ( c_lessequals(c_HOL_Otimes__class_Otimes(X2,X4,X3),c_HOL_Otimes__class_Otimes(X1,X4,X3),X3)
    | ~ c_lessequals(X1,X2,X3)
    | ~ c_lessequals(X4,c_HOL_Ozero__class_Ozero(X3),X3)
    | ~ class_Ring__and__Field_Opordered__ring(X3) ),
    c_0_1942,
    [final] ).

cnf(c_0_2550,plain,
    ( c_lessequals(c_HOL_Otimes__class_Otimes(X4,X2,X3),c_HOL_Otimes__class_Otimes(X4,X1,X3),X3)
    | ~ c_lessequals(X1,X2,X3)
    | ~ c_lessequals(X4,c_HOL_Ozero__class_Ozero(X3),X3)
    | ~ class_Ring__and__Field_Opordered__ring(X3) ),
    c_0_1943,
    [final] ).

cnf(c_0_2551,plain,
    ( c_lessequals(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X2,X4,X3),X3)
    | ~ c_lessequals(X1,X2,X3)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
    | ~ class_Ring__and__Field_Omult__mono(X3) ),
    c_0_1944,
    [final] ).

cnf(c_0_2552,plain,
    ( c_lessequals(c_HOL_Otimes__class_Otimes(X4,X1,X3),c_HOL_Otimes__class_Otimes(X4,X2,X3),X3)
    | ~ c_lessequals(X1,X2,X3)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
    | ~ class_Ring__and__Field_Omult__mono(X3) ),
    c_0_1945,
    [final] ).

cnf(c_0_2553,plain,
    ( c_lessequals(c_HOL_Otimes__class_Otimes(X4,X1,X3),c_HOL_Otimes__class_Otimes(X4,X2,X3),X3)
    | ~ c_lessequals(X1,X2,X3)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
    | ~ class_Ring__and__Field_Omult__mono1(X3) ),
    c_0_1946,
    [final] ).

cnf(c_0_2554,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_1947,
    [final] ).

cnf(c_0_2555,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_1948,
    [final] ).

cnf(c_0_2556,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_1949,
    [final] ).

cnf(c_0_2557,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_1950,
    [final] ).

cnf(c_0_2558,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_1951,
    [final] ).

cnf(c_0_2559,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_1952,
    [final] ).

cnf(c_0_2560,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_1953,
    [final] ).

cnf(c_0_2561,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_1954,
    [final] ).

cnf(c_0_2562,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_1955,
    [final] ).

cnf(c_0_2563,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_1956,
    [final] ).

cnf(c_0_2564,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_1957,
    [final] ).

cnf(c_0_2565,plain,
    ( c_lessequals(c_HOL_Otimes__class_Otimes(X2,X3,X1),X2,X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
    | ~ c_lessequals(X3,c_HOL_Oone__class_Oone(X1),X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    c_0_1958,
    [final] ).

cnf(c_0_2566,plain,
    ( c_lessequals(c_HOL_Otimes__class_Otimes(X3,X2,X1),X2,X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
    | ~ c_lessequals(X3,c_HOL_Oone__class_Oone(X1),X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    c_0_1959,
    [final] ).

cnf(c_0_2567,plain,
    ( c_lessequals(X3,c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X2,X3,tc_nat),X1,tc_nat),tc_nat)
    | ~ c_lessequals(X1,X2,tc_nat) ),
    c_0_1960,
    [final] ).

cnf(c_0_2568,plain,
    ( c_lessequals(c_HOL_Oplus__class_Oplus(X1,X4,X3),c_HOL_Oplus__class_Oplus(X2,X5,X3),X3)
    | ~ c_lessequals(X1,X2,X3)
    | ~ c_lessequals(X4,X5,X3)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add(X3) ),
    c_0_1961,
    [final] ).

cnf(c_0_2569,plain,
    ( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X4,X3),c_HOL_Oplus__class_Oplus(X2,X5,X3),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_1962,
    [final] ).

cnf(c_0_2570,plain,
    ( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X4,X3),c_HOL_Oplus__class_Oplus(X2,X5,X3),X3)
    | ~ c_lessequals(X1,X2,X3)
    | ~ c_HOL_Oord__class_Oless(X4,X5,X3)
    | ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X3) ),
    c_0_1963,
    [final] ).

cnf(c_0_2571,plain,
    ( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X4,X3),c_HOL_Oplus__class_Oplus(X2,X5,X3),X3)
    | ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | ~ c_lessequals(X4,X5,X3)
    | ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X3) ),
    c_0_1964,
    [final] ).

cnf(c_0_2572,plain,
    ( X1 = c_HOL_Ozero__class_Ozero(X2)
    | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X3,X2),c_HOL_Otimes__class_Otimes(X1,X1,X2),X2) != c_HOL_Ozero__class_Ozero(X2)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
    c_0_1965,
    [final] ).

cnf(c_0_2573,plain,
    ( X1 = c_HOL_Ozero__class_Ozero(X2)
    | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X1,X2),c_HOL_Otimes__class_Otimes(X3,X3,X2),X2) != c_HOL_Ozero__class_Ozero(X2)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
    c_0_1966,
    [final] ).

cnf(c_0_2574,plain,
    ( c_Orderings_Oord__class_Omax(c_Orderings_Oord__class_Omin(X1,X4,X3),c_Orderings_Oord__class_Omin(X2,X4,X3),X3) = c_Orderings_Oord__class_Omin(c_Orderings_Oord__class_Omax(X1,X2,X3),X4,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    c_0_1967,
    [final] ).

cnf(c_0_2575,plain,
    ( c_Orderings_Oord__class_Omax(c_Orderings_Oord__class_Omin(X1,X2,X4),c_Orderings_Oord__class_Omin(X1,X3,X4),X4) = c_Orderings_Oord__class_Omin(X1,c_Orderings_Oord__class_Omax(X2,X3,X4),X4)
    | ~ class_Orderings_Olinorder(X4) ),
    c_0_1968,
    [final] ).

cnf(c_0_2576,plain,
    ( c_Orderings_Oord__class_Omin(c_HOL_Ominus__class_Ominus(X1,X4,X3),c_HOL_Ominus__class_Ominus(X2,X4,X3),X3) = c_HOL_Ominus__class_Ominus(c_Orderings_Oord__class_Omin(X1,X2,X3),X4,X3)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
    c_0_1969,
    [final] ).

cnf(c_0_2577,plain,
    ( c_Orderings_Oord__class_Omax(c_HOL_Ominus__class_Ominus(X1,X4,X3),c_HOL_Ominus__class_Ominus(X2,X4,X3),X3) = c_HOL_Ominus__class_Ominus(c_Orderings_Oord__class_Omax(X1,X2,X3),X4,X3)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
    c_0_1970,
    [final] ).

cnf(c_0_2578,plain,
    ( c_Orderings_Oord__class_Omin(c_HOL_Oplus__class_Oplus(X1,X4,X3),c_HOL_Oplus__class_Oplus(X2,X4,X3),X3) = c_HOL_Oplus__class_Oplus(c_Orderings_Oord__class_Omin(X1,X2,X3),X4,X3)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3) ),
    c_0_1971,
    [final] ).

cnf(c_0_2579,plain,
    ( c_Orderings_Oord__class_Omax(c_HOL_Oplus__class_Oplus(X1,X4,X3),c_HOL_Oplus__class_Oplus(X2,X4,X3),X3) = c_HOL_Oplus__class_Oplus(c_Orderings_Oord__class_Omax(X1,X2,X3),X4,X3)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3) ),
    c_0_1972,
    [final] ).

cnf(c_0_2580,plain,
    ( c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X1,c_HOL_Otimes__class_Otimes(X2,X3,X4),X4),X3,X4) = c_Divides_Odiv__class_Omod(X1,X3,X4)
    | ~ class_Divides_Osemiring__div(X4) ),
    c_0_1973,
    [final] ).

cnf(c_0_2581,plain,
    ( c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X1,c_HOL_Otimes__class_Otimes(X2,X3,X4),X4),X2,X4) = c_Divides_Odiv__class_Omod(X1,X2,X4)
    | ~ class_Divides_Osemiring__div(X4) ),
    c_0_1974,
    [final] ).

cnf(c_0_2582,plain,
    ( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X4,X2,X3),X3) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X1,X4,X3),X2,X3)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
    c_0_1975,
    [final] ).

cnf(c_0_2583,plain,
    ( c_Orderings_Oord__class_Omin(c_Orderings_Oord__class_Omax(X1,X4,X3),c_Orderings_Oord__class_Omax(X2,X4,X3),X3) = c_Orderings_Oord__class_Omax(c_Orderings_Oord__class_Omin(X1,X2,X3),X4,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    c_0_1976,
    [final] ).

cnf(c_0_2584,plain,
    ( c_Orderings_Oord__class_Omin(c_Orderings_Oord__class_Omax(X1,X2,X4),c_Orderings_Oord__class_Omax(X1,X3,X4),X4) = c_Orderings_Oord__class_Omax(X1,c_Orderings_Oord__class_Omin(X2,X3,X4),X4)
    | ~ class_Orderings_Olinorder(X4) ),
    c_0_1977,
    [final] ).

cnf(c_0_2585,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_1978,
    [final] ).

cnf(c_0_2586,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_1979,
    [final] ).

cnf(c_0_2587,plain,
    ( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X2,X4,X3),X3) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X1,X2,X3),X4,X3)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
    c_0_1980,
    [final] ).

cnf(c_0_2588,plain,
    ( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X2,X4,X3),X3) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X1,X2,X3),X4,X3)
    | ~ class_Ring__and__Field_Ocomm__semiring(X3) ),
    c_0_1981,
    [final] ).

cnf(c_0_2589,plain,
    ( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,X4),c_HOL_Otimes__class_Otimes(X1,X3,X4),X4) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Oplus__class_Oplus(X2,X3,X4),X4)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X4) ),
    c_0_1982,
    [final] ).

cnf(c_0_2590,plain,
    ( c_lessequals(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_lessequals(X2,X3,tc_nat) ),
    c_0_1983,
    [final] ).

cnf(c_0_2591,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_1984,
    [final] ).

cnf(c_0_2592,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_1985,
    [final] ).

cnf(c_0_2593,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_1986,
    [final] ).

cnf(c_0_2594,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_1987,
    [final] ).

cnf(c_0_2595,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_1988,
    [final] ).

cnf(c_0_2596,plain,
    ( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
    | c_HOL_Oplus__class_Oplus(X2,c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X2,tc_nat),tc_nat) = c_HOL_Otimes__class_Otimes(X1,X2,tc_nat) ),
    c_0_1989,
    [final] ).

cnf(c_0_2597,plain,
    ( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X3,X2,tc_nat),c_HOL_Ominus__class_Ominus(X3,X1,tc_nat),tc_nat)
    | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | ~ c_HOL_Oord__class_Oless(X1,X3,tc_nat) ),
    c_0_1990,
    [final] ).

cnf(c_0_2598,plain,
    ( c_lessequals(c_HOL_Oplus__class_Oplus(X1,X3,tc_nat),c_HOL_Oplus__class_Oplus(X2,X4,tc_nat),tc_nat)
    | ~ c_lessequals(X1,X2,tc_nat)
    | ~ c_lessequals(X3,X4,tc_nat) ),
    c_0_1991,
    [final] ).

cnf(c_0_2599,plain,
    ( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,X3,tc_nat),c_HOL_Ominus__class_Ominus(X2,X3,tc_nat),tc_nat)
    | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | ~ c_lessequals(X3,X1,tc_nat) ),
    c_0_1992,
    [final] ).

cnf(c_0_2600,plain,
    ( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X3,tc_nat),c_HOL_Oplus__class_Oplus(X2,X4,tc_nat),tc_nat)
    | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | ~ c_HOL_Oord__class_Oless(X3,X4,tc_nat) ),
    c_0_1993,
    [final] ).

cnf(c_0_2601,plain,
    ( c_lessequals(c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),c_HOL_Otimes__class_Otimes(X2,X4,tc_nat),tc_nat)
    | ~ c_lessequals(X1,X2,tc_nat)
    | ~ c_lessequals(X3,X4,tc_nat) ),
    c_0_1994,
    [final] ).

cnf(c_0_2602,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_1995,
    [final] ).

cnf(c_0_2603,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_1996,
    [final] ).

cnf(c_0_2604,plain,
    ( c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),X2,tc_nat) = X1
    | ~ c_lessequals(X2,c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat) ),
    c_0_1997,
    [final] ).

cnf(c_0_2605,plain,
    ( c_lessequals(X1,c_HOL_Oplus__class_Oplus(X3,X2,tc_nat),tc_nat)
    | ~ c_lessequals(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),X3,tc_nat) ),
    c_0_1998,
    [final] ).

cnf(c_0_2606,plain,
    ( c_lessequals(c_HOL_Ominus__class_Ominus(X1,X3,tc_nat),X2,tc_nat)
    | ~ c_lessequals(X1,c_HOL_Oplus__class_Oplus(X2,X3,tc_nat),tc_nat) ),
    c_0_1999,
    [final] ).

cnf(c_0_2607,plain,
    ( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X3,tc_nat),X2,tc_nat)
    | ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ominus__class_Ominus(X2,X3,tc_nat),tc_nat) ),
    c_0_2000,
    [final] ).

cnf(c_0_2608,plain,
    ( c_HOL_Oord__class_Oless(X1,c_HOL_Ominus__class_Ominus(X3,X2,tc_nat),tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),X3,tc_nat) ),
    c_0_2001,
    [final] ).

cnf(c_0_2609,plain,
    ( c_HOL_Oplus__class_Oplus(X1,X2,X3) = X4
    | c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X5,X2,X3),X3) != c_HOL_Oplus__class_Oplus(X5,X4,X3)
    | ~ class_OrderedGroup_Oab__group__add(X3) ),
    c_0_2002,
    [final] ).

cnf(c_0_2610,plain,
    ( c_HOL_Oplus__class_Oplus(X3,c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X3,X2,tc_nat),X1,tc_nat)
    | ~ c_lessequals(X1,X2,tc_nat) ),
    c_0_2003,
    [final] ).

cnf(c_0_2611,plain,
    ( c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),X3,tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X2,X3,tc_nat),X1,tc_nat)
    | ~ c_lessequals(X1,X2,tc_nat) ),
    c_0_2004,
    [final] ).

cnf(c_0_2612,plain,
    ( c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X3,X1,tc_nat),X2,tc_nat) = c_HOL_Ominus__class_Ominus(X3,c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),tc_nat)
    | ~ c_lessequals(X1,X2,tc_nat) ),
    c_0_2005,
    [final] ).

cnf(c_0_2613,plain,
    ( c_HOL_Oplus__class_Oplus(X3,c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X3,X2,tc_nat),X1,tc_nat)
    | ~ c_lessequals(X1,X2,tc_nat) ),
    c_0_2006,
    [final] ).

cnf(c_0_2614,plain,
    ( c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),X3,tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X2,X3,tc_nat),X1,tc_nat)
    | ~ c_lessequals(X1,X2,tc_nat) ),
    c_0_2007,
    [final] ).

cnf(c_0_2615,plain,
    ( c_lessequals(X2,c_HOL_Ozero__class_Ozero(X3),X3)
    | c_lessequals(c_HOL_Ozero__class_Ozero(X3),X2,X3)
    | ~ c_lessequals(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X3) ),
    c_0_2008,
    [final] ).

cnf(c_0_2616,plain,
    ( c_lessequals(X2,c_HOL_Ozero__class_Ozero(X3),X3)
    | c_lessequals(X1,c_HOL_Ozero__class_Ozero(X3),X3)
    | ~ c_lessequals(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X3) ),
    c_0_2009,
    [final] ).

cnf(c_0_2617,plain,
    ( c_lessequals(c_HOL_Ozero__class_Ozero(X3),X1,X3)
    | c_lessequals(c_HOL_Ozero__class_Ozero(X3),X2,X3)
    | ~ c_lessequals(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X3) ),
    c_0_2010,
    [final] ).

cnf(c_0_2618,plain,
    ( c_lessequals(c_HOL_Ozero__class_Ozero(X3),X1,X3)
    | c_lessequals(X1,c_HOL_Ozero__class_Ozero(X3),X3)
    | ~ c_lessequals(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X3) ),
    c_0_2011,
    [final] ).

cnf(c_0_2619,plain,
    ( c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    c_0_2012,
    [final] ).

cnf(c_0_2620,plain,
    ( c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    c_0_2013,
    [final] ).

cnf(c_0_2621,plain,
    ( c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
    | c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    c_0_2014,
    [final] ).

cnf(c_0_2622,plain,
    ( c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
    | c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    c_0_2015,
    [final] ).

cnf(c_0_2623,plain,
    ( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
    | c_Suc(c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X2,tc_nat)) = c_HOL_Oplus__class_Oplus(X1,X2,tc_nat) ),
    c_0_2016,
    [final] ).

cnf(c_0_2624,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_2017,
    [final] ).

cnf(c_0_2625,plain,
    ( c_lessequals(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),tc_nat)
    | ~ c_lessequals(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X1,tc_nat)
    | ~ c_lessequals(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X2,tc_nat) ),
    c_0_2018,
    [final] ).

cnf(c_0_2626,plain,
    ( c_lessequals(X1,X2,X4)
    | c_lessequals(X1,X3,X4)
    | ~ c_lessequals(X1,c_Orderings_Oord__class_Omax(X2,X3,X4),X4)
    | ~ class_Orderings_Olinorder(X4) ),
    c_0_2019,
    [final] ).

cnf(c_0_2627,plain,
    ( c_lessequals(X1,X4,X3)
    | c_lessequals(X2,X4,X3)
    | ~ c_lessequals(c_Orderings_Oord__class_Omin(X1,X2,X3),X4,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    c_0_2020,
    [final] ).

cnf(c_0_2628,plain,
    ( c_HOL_Oord__class_Oless(X1,X2,X4)
    | c_HOL_Oord__class_Oless(X1,X3,X4)
    | ~ c_HOL_Oord__class_Oless(X1,c_Orderings_Oord__class_Omax(X2,X3,X4),X4)
    | ~ class_Orderings_Olinorder(X4) ),
    c_0_2021,
    [final] ).

cnf(c_0_2629,plain,
    ( c_HOL_Oord__class_Oless(X1,X4,X3)
    | c_HOL_Oord__class_Oless(X2,X4,X3)
    | ~ c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omin(X1,X2,X3),X4,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    c_0_2022,
    [final] ).

cnf(c_0_2630,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_2023,
    [final] ).

cnf(c_0_2631,plain,
    ( c_lessequals(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_lessequals(X1,X2,tc_nat) ),
    c_0_2024,
    [final] ).

cnf(c_0_2632,plain,
    ( c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(X2,X3,X1),X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
    | ~ class_OrderedGroup_Opordered__comm__monoid__add(X1) ),
    c_0_2025,
    [final] ).

cnf(c_0_2633,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_2026,
    [final] ).

cnf(c_0_2634,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_2027,
    [final] ).

cnf(c_0_2635,plain,
    ( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X3,X2),c_HOL_Ozero__class_Ozero(X2),X2)
    | ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
    | ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X2),X2)
    | ~ class_OrderedGroup_Opordered__comm__monoid__add(X2) ),
    c_0_2028,
    [final] ).

cnf(c_0_2636,plain,
    ( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X3,X2),c_HOL_Ozero__class_Ozero(X2),X2)
    | ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
    | ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X2),X2)
    | ~ class_OrderedGroup_Opordered__comm__monoid__add(X2) ),
    c_0_2029,
    [final] ).

cnf(c_0_2637,plain,
    ( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(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(X3,c_HOL_Ozero__class_Ozero(X2),X2)
    | ~ class_OrderedGroup_Opordered__comm__monoid__add(X2) ),
    c_0_2030,
    [final] ).

cnf(c_0_2638,plain,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(X2,X3,X1),X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
    | ~ class_OrderedGroup_Opordered__comm__monoid__add(X1) ),
    c_0_2031,
    [final] ).

cnf(c_0_2639,plain,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(X2,X3,X1),X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
    | ~ class_OrderedGroup_Opordered__comm__monoid__add(X1) ),
    c_0_2032,
    [final] ).

cnf(c_0_2640,plain,
    ( c_lessequals(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    c_0_2033,
    [final] ).

cnf(c_0_2641,plain,
    ( c_lessequals(c_HOL_Otimes__class_Otimes(X1,X3,X2),c_HOL_Ozero__class_Ozero(X2),X2)
    | ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X3,X2)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
    c_0_2034,
    [final] ).

cnf(c_0_2642,plain,
    ( c_lessequals(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ class_Ring__and__Field_Opordered__cancel__semiring(X1) ),
    c_0_2035,
    [final] ).

cnf(c_0_2643,plain,
    ( c_lessequals(c_HOL_Otimes__class_Otimes(X1,X3,X2),c_HOL_Ozero__class_Ozero(X2),X2)
    | ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X3,X2)
    | ~ class_Ring__and__Field_Opordered__cancel__semiring(X2) ),
    c_0_2036,
    [final] ).

cnf(c_0_2644,plain,
    ( c_lessequals(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ class_Ring__and__Field_Opordered__cancel__semiring(X1) ),
    c_0_2037,
    [final] ).

cnf(c_0_2645,plain,
    ( c_lessequals(c_HOL_Otimes__class_Otimes(X1,X3,X2),c_HOL_Ozero__class_Ozero(X2),X2)
    | ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X3,X2)
    | ~ class_Ring__and__Field_Opordered__cancel__semiring(X2) ),
    c_0_2038,
    [final] ).

cnf(c_0_2646,plain,
    ( c_lessequals(c_HOL_Otimes__class_Otimes(X3,X2,X1),c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ class_Ring__and__Field_Opordered__cancel__semiring(X1) ),
    c_0_2039,
    [final] ).

cnf(c_0_2647,plain,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(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_OrderedGroup_Opordered__comm__monoid__add(X1) ),
    c_0_2040,
    [final] ).

cnf(c_0_2648,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_2041,
    [final] ).

cnf(c_0_2649,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_2042,
    [final] ).

cnf(c_0_2650,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_2043,
    [final] ).

cnf(c_0_2651,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_2044,
    [final] ).

cnf(c_0_2652,plain,
    ( c_lessequals(c_HOL_Oplus__class_Oplus(X1,X3,X2),c_HOL_Ozero__class_Ozero(X2),X2)
    | ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
    | ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X2),X2)
    | ~ class_OrderedGroup_Opordered__comm__monoid__add(X2) ),
    c_0_2045,
    [final] ).

cnf(c_0_2653,plain,
    ( c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
    | ~ class_Ring__and__Field_Opordered__cancel__semiring(X1) ),
    c_0_2046,
    [final] ).

cnf(c_0_2654,plain,
    ( c_lessequals(c_HOL_Ozero__class_Ozero(X2),c_HOL_Otimes__class_Otimes(X1,X3,X2),X2)
    | ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
    | ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X2),X2)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
    c_0_2047,
    [final] ).

cnf(c_0_2655,plain,
    ( c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    c_0_2048,
    [final] ).

cnf(c_0_2656,plain,
    ( c_lessequals(c_HOL_Ozero__class_Ozero(X2),c_HOL_Otimes__class_Otimes(X1,X3,X2),X2)
    | ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
    | ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X2),X2)
    | ~ class_Ring__and__Field_Opordered__ring(X2) ),
    c_0_2049,
    [final] ).

cnf(c_0_2657,plain,
    ( c_lessequals(c_HOL_Ozero__class_Ozero(X2),c_HOL_Otimes__class_Otimes(X1,X3,X2),X2)
    | ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
    | ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X2),X2)
    | ~ class_Ring__and__Field_Opordered__ring(X2) ),
    c_0_2050,
    [final] ).

cnf(c_0_2658,plain,
    ( c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
    | ~ class_Ring__and__Field_Opordered__ring(X1) ),
    c_0_2051,
    [final] ).

cnf(c_0_2659,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),c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat) ),
    c_0_2052,
    [final] ).

cnf(c_0_2660,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_2053,
    [final] ).

cnf(c_0_2661,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_2054,
    [final] ).

cnf(c_0_2662,plain,
    ( c_lessequals(c_HOL_Oplus__class_Oplus(X1,X4,X3),c_HOL_Oplus__class_Oplus(X2,X4,X3),X3)
    | ~ c_lessequals(X1,X2,X3)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3) ),
    c_0_2055,
    [final] ).

cnf(c_0_2663,plain,
    ( c_lessequals(c_HOL_Oplus__class_Oplus(X4,X1,X3),c_HOL_Oplus__class_Oplus(X4,X2,X3),X3)
    | ~ c_lessequals(X1,X2,X3)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3) ),
    c_0_2056,
    [final] ).

cnf(c_0_2664,plain,
    ( c_lessequals(c_HOL_Oplus__class_Oplus(X1,X4,X3),c_HOL_Oplus__class_Oplus(X2,X4,X3),X3)
    | ~ c_lessequals(X1,X2,X3)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add(X3) ),
    c_0_2057,
    [final] ).

cnf(c_0_2665,plain,
    ( c_lessequals(c_HOL_Oplus__class_Oplus(X4,X1,X3),c_HOL_Oplus__class_Oplus(X4,X2,X3),X3)
    | ~ c_lessequals(X1,X2,X3)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add(X3) ),
    c_0_2058,
    [final] ).

cnf(c_0_2666,plain,
    ( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X4,X3),c_HOL_Oplus__class_Oplus(X2,X4,X3),X3)
    | ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X3) ),
    c_0_2059,
    [final] ).

cnf(c_0_2667,plain,
    ( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X4,X3),c_HOL_Oplus__class_Oplus(X2,X4,X3),X3)
    | ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3) ),
    c_0_2060,
    [final] ).

cnf(c_0_2668,plain,
    ( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X4,X1,X3),c_HOL_Oplus__class_Oplus(X4,X2,X3),X3)
    | ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X3) ),
    c_0_2061,
    [final] ).

cnf(c_0_2669,plain,
    ( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X4,X1,X3),c_HOL_Oplus__class_Oplus(X4,X2,X3),X3)
    | ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3) ),
    c_0_2062,
    [final] ).

cnf(c_0_2670,plain,
    ( c_lessequals(X3,c_HOL_Oplus__class_Oplus(X2,X4,X1),X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | ~ c_lessequals(X3,X4,X1)
    | ~ class_OrderedGroup_Ocomm__monoid__add(X1)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
    c_0_2063,
    [final] ).

cnf(c_0_2671,plain,
    ( c_lessequals(X3,c_HOL_Oplus__class_Oplus(X4,X2,X1),X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | ~ c_lessequals(X3,X4,X1)
    | ~ class_OrderedGroup_Ocomm__monoid__add(X1)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
    c_0_2064,
    [final] ).

cnf(c_0_2672,plain,
    ( c_HOL_Oord__class_Oless(X3,c_HOL_Oplus__class_Oplus(X2,X4,X1),X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | ~ c_lessequals(X3,X4,X1)
    | ~ class_OrderedGroup_Ocomm__monoid__add(X1)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
    c_0_2065,
    [final] ).

cnf(c_0_2673,plain,
    ( c_HOL_Oord__class_Oless(X3,c_HOL_Oplus__class_Oplus(X2,X4,X1),X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | ~ c_HOL_Oord__class_Oless(X3,X4,X1)
    | ~ class_OrderedGroup_Ocomm__monoid__add(X1)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
    c_0_2066,
    [final] ).

cnf(c_0_2674,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_2067,
    [final] ).

cnf(c_0_2675,plain,
    ( c_HOL_Oord__class_Oless(X3,c_HOL_Oplus__class_Oplus(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__semidom(X1) ),
    c_0_2068,
    [final] ).

cnf(c_0_2676,plain,
    ( c_lessequals(c_HOL_Ominus__class_Ominus(X3,X2,tc_nat),c_HOL_Ominus__class_Ominus(X3,X1,tc_nat),tc_nat)
    | ~ c_lessequals(X1,X2,tc_nat) ),
    c_0_2069,
    [final] ).

cnf(c_0_2677,plain,
    ( c_lessequals(c_HOL_Ominus__class_Ominus(X1,X3,tc_nat),c_HOL_Ominus__class_Ominus(X2,X3,tc_nat),tc_nat)
    | ~ c_lessequals(X1,X2,tc_nat) ),
    c_0_2070,
    [final] ).

cnf(c_0_2678,plain,
    ( c_lessequals(c_HOL_Oplus__class_Oplus(X1,X3,tc_nat),c_HOL_Oplus__class_Oplus(X2,X3,tc_nat),tc_nat)
    | ~ c_lessequals(X1,X2,tc_nat) ),
    c_0_2071,
    [final] ).

cnf(c_0_2679,plain,
    ( c_lessequals(c_HOL_Oplus__class_Oplus(X3,X1,tc_nat),c_HOL_Oplus__class_Oplus(X3,X2,tc_nat),tc_nat)
    | ~ c_lessequals(X1,X2,tc_nat) ),
    c_0_2072,
    [final] ).

cnf(c_0_2680,plain,
    ( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X3,tc_nat),c_HOL_Oplus__class_Oplus(X2,X3,tc_nat),tc_nat)
    | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
    c_0_2073,
    [final] ).

cnf(c_0_2681,plain,
    ( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X3,X1,tc_nat),c_HOL_Oplus__class_Oplus(X3,X2,tc_nat),tc_nat)
    | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
    c_0_2074,
    [final] ).

cnf(c_0_2682,plain,
    ( c_lessequals(c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),c_HOL_Otimes__class_Otimes(X2,X3,tc_nat),tc_nat)
    | ~ c_lessequals(X1,X2,tc_nat) ),
    c_0_2075,
    [final] ).

cnf(c_0_2683,plain,
    ( c_lessequals(c_HOL_Otimes__class_Otimes(X3,X1,tc_nat),c_HOL_Otimes__class_Otimes(X3,X2,tc_nat),tc_nat)
    | ~ c_lessequals(X1,X2,tc_nat) ),
    c_0_2076,
    [final] ).

cnf(c_0_2684,plain,
    ( c_lessequals(c_HOL_Otimes__class_Otimes(X3,X1,tc_nat),c_HOL_Otimes__class_Otimes(X3,X2,tc_nat),tc_nat)
    | ~ c_lessequals(X1,X2,tc_nat) ),
    c_0_2077,
    [final] ).

cnf(c_0_2685,plain,
    ( c_lessequals(c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),c_HOL_Otimes__class_Otimes(X2,X3,tc_nat),tc_nat)
    | ~ c_lessequals(X1,X2,tc_nat) ),
    c_0_2078,
    [final] ).

cnf(c_0_2686,plain,
    ( c_Lambda_Olift(c_Lambda_Olift(X3,X1),c_Suc(X2)) = c_Lambda_Olift(c_Lambda_Olift(X3,X2),X1)
    | ~ c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(X2,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat) ),
    c_0_2079,
    [final] ).

cnf(c_0_2687,plain,
    ( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,X3),X2,X3) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(X3),X3),X2,X3)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
    c_0_2080,
    [final] ).

cnf(c_0_2688,plain,
    ( c_HOL_Oplus__class_Oplus(X1,c_HOL_Otimes__class_Otimes(X2,X1,X3),X3) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X2,c_HOL_Oone__class_Oone(X3),X3),X1,X3)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
    c_0_2081,
    [final] ).

cnf(c_0_2689,plain,
    ( c_lessequals(c_Orderings_Oord__class_Omax(X1,X4,X3),X2,X3)
    | ~ c_lessequals(X1,X2,X3)
    | ~ c_lessequals(X4,X2,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    c_0_2082,
    [final] ).

cnf(c_0_2690,plain,
    ( c_lessequals(c_Orderings_Oord__class_Omax(X1,X4,X3),X2,X3)
    | ~ c_lessequals(X1,X2,X3)
    | ~ c_lessequals(X4,X2,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    c_0_2083,
    [final] ).

cnf(c_0_2691,plain,
    ( c_lessequals(c_Orderings_Oord__class_Omax(X1,X4,X3),X2,X3)
    | ~ c_lessequals(X1,X2,X3)
    | ~ c_lessequals(X4,X2,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    c_0_2084,
    [final] ).

cnf(c_0_2692,plain,
    ( c_lessequals(X1,c_Orderings_Oord__class_Omin(X2,X4,X3),X3)
    | ~ c_lessequals(X1,X2,X3)
    | ~ c_lessequals(X1,X4,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    c_0_2085,
    [final] ).

cnf(c_0_2693,plain,
    ( c_lessequals(X1,c_Orderings_Oord__class_Omin(X2,X4,X3),X3)
    | ~ c_lessequals(X1,X2,X3)
    | ~ c_lessequals(X1,X4,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    c_0_2086,
    [final] ).

cnf(c_0_2694,plain,
    ( c_lessequals(X1,c_Orderings_Oord__class_Omin(X2,X4,X3),X3)
    | ~ c_lessequals(X1,X2,X3)
    | ~ c_lessequals(X1,X4,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    c_0_2087,
    [final] ).

cnf(c_0_2695,plain,
    ( c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omax(X1,X4,X3),X2,X3)
    | ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | ~ c_HOL_Oord__class_Oless(X4,X2,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    c_0_2088,
    [final] ).

cnf(c_0_2696,plain,
    ( c_HOL_Oord__class_Oless(X1,c_Orderings_Oord__class_Omin(X2,X4,X3),X3)
    | ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | ~ c_HOL_Oord__class_Oless(X1,X4,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    c_0_2089,
    [final] ).

cnf(c_0_2697,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_2090,
    [final] ).

cnf(c_0_2698,plain,
    ( X1 = X2
    | ~ c_lessequals(X3,X1,tc_nat)
    | ~ c_lessequals(X3,X2,tc_nat)
    | c_HOL_Ominus__class_Ominus(X1,X3,tc_nat) != c_HOL_Ominus__class_Ominus(X2,X3,tc_nat) ),
    c_0_2091,
    [final] ).

cnf(c_0_2699,plain,
    ( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X2,X1,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),X2,tc_nat) ),
    c_0_2092,
    [final] ).

cnf(c_0_2700,plain,
    ( c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(X2,X2,X1),X1)
    | ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
    c_0_2093,
    [final] ).

cnf(c_0_2701,plain,
    ( c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X1,X2),c_HOL_Ozero__class_Ozero(X2),X2)
    | ~ class_OrderedGroup_Olordered__ab__group__add(X2) ),
    c_0_2094,
    [final] ).

cnf(c_0_2702,plain,
    ( c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X1,X2),c_HOL_Ozero__class_Ozero(X2),X2)
    | ~ class_Ring__and__Field_Oordered__idom(X2) ),
    c_0_2095,
    [final] ).

cnf(c_0_2703,plain,
    ( c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
    | ~ c_lessequals(c_HOL_Oplus__class_Oplus(X1,X1,X2),c_HOL_Ozero__class_Ozero(X2),X2)
    | ~ class_OrderedGroup_Olordered__ab__group__add(X2) ),
    c_0_2096,
    [final] ).

cnf(c_0_2704,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_Oplus__class_Oplus(X2,X2,X1),X1)
    | ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
    c_0_2097,
    [final] ).

cnf(c_0_2705,plain,
    ( c_lessequals(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X2,tc_nat)
    | ~ c_lessequals(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),tc_nat) ),
    c_0_2098,
    [final] ).

cnf(c_0_2706,plain,
    ( c_lessequals(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X1,tc_nat)
    | ~ c_lessequals(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),tc_nat) ),
    c_0_2099,
    [final] ).

cnf(c_0_2707,plain,
    ( c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X2,X4),X3,X4) = c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X2,X3,X4),X4)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X4) ),
    c_0_2100,
    [final] ).

cnf(c_0_2708,plain,
    ( c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X2,X3,X4),X4) = c_HOL_Oplus__class_Oplus(X2,c_HOL_Oplus__class_Oplus(X1,X3,X4),X4)
    | ~ class_OrderedGroup_Oab__group__add(X4) ),
    c_0_2101,
    [final] ).

cnf(c_0_2709,plain,
    ( c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X2,X3),X4,X3) = c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X2,X4,X3),X3)
    | ~ class_OrderedGroup_Ocomm__monoid__add(X3) ),
    c_0_2102,
    [final] ).

cnf(c_0_2710,plain,
    ( c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X2,X3,X4),X4) = c_HOL_Oplus__class_Oplus(X2,c_HOL_Oplus__class_Oplus(X1,X3,X4),X4)
    | ~ class_OrderedGroup_Ocomm__monoid__add(X4) ),
    c_0_2103,
    [final] ).

cnf(c_0_2711,plain,
    ( c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X2,X3),X4,X3) = c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X2,X4,X3),X3)
    | ~ class_OrderedGroup_Oab__semigroup__add(X3) ),
    c_0_2104,
    [final] ).

cnf(c_0_2712,plain,
    ( c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X2,X4),X3,X4) = c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X2,X3,X4),X4)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X4) ),
    c_0_2105,
    [final] ).

cnf(c_0_2713,plain,
    ( c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X2,X3),X4,X3) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X4,X3),X2,X3)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
    c_0_2106,
    [final] ).

cnf(c_0_2714,plain,
    ( c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X2,X3,X4),X4) = c_HOL_Oplus__class_Oplus(X2,c_HOL_Oplus__class_Oplus(X1,X3,X4),X4)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X4) ),
    c_0_2107,
    [final] ).

cnf(c_0_2715,plain,
    ( c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X2,X3),X4,X3) = c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X2,X4,X3),X3)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
    c_0_2108,
    [final] ).

cnf(c_0_2716,plain,
    ( c_Orderings_Oord__class_Omin(c_Orderings_Oord__class_Omin(X1,X2,X3),X4,X3) = c_Orderings_Oord__class_Omin(X1,c_Orderings_Oord__class_Omin(X2,X4,X3),X3)
    | ~ class_Orderings_Olinorder(X3) ),
    c_0_2109,
    [final] ).

cnf(c_0_2717,plain,
    ( c_Orderings_Oord__class_Omin(X1,c_Orderings_Oord__class_Omin(X2,X3,X4),X4) = c_Orderings_Oord__class_Omin(X2,c_Orderings_Oord__class_Omin(X1,X3,X4),X4)
    | ~ class_Orderings_Olinorder(X4) ),
    c_0_2110,
    [final] ).

cnf(c_0_2718,plain,
    ( c_Orderings_Oord__class_Omax(c_Orderings_Oord__class_Omax(X1,X2,X3),X4,X3) = c_Orderings_Oord__class_Omax(X1,c_Orderings_Oord__class_Omax(X2,X4,X3),X3)
    | ~ class_Orderings_Olinorder(X3) ),
    c_0_2111,
    [final] ).

cnf(c_0_2719,plain,
    ( c_Orderings_Oord__class_Omax(X1,c_Orderings_Oord__class_Omax(X2,X3,X4),X4) = c_Orderings_Oord__class_Omax(X2,c_Orderings_Oord__class_Omax(X1,X3,X4),X4)
    | ~ class_Orderings_Olinorder(X4) ),
    c_0_2112,
    [final] ).

cnf(c_0_2720,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_2113,
    [final] ).

cnf(c_0_2721,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_2114,
    [final] ).

cnf(c_0_2722,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_2115,
    [final] ).

cnf(c_0_2723,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_2116,
    [final] ).

cnf(c_0_2724,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_2117,
    [final] ).

cnf(c_0_2725,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_2118,
    [final] ).

cnf(c_0_2726,plain,
    ( c_HOL_Oord__class_Oless(X2,c_HOL_Oplus__class_Oplus(X3,X1,tc_nat),tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
    | ~ c_lessequals(X2,X3,tc_nat) ),
    c_0_2119,
    [final] ).

cnf(c_0_2727,plain,
    ( c_HOL_Oplus__class_Oplus(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) = c_HOL_Ozero__class_Ozero(X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    c_0_2120,
    [final] ).

cnf(c_0_2728,plain,
    ( c_lessequals(X1,X2,X3)
    | ~ c_lessequals(c_HOL_Ominus__class_Ominus(X1,X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
    c_0_2121,
    [final] ).

cnf(c_0_2729,plain,
    ( c_HOL_Oord__class_Oless(X1,X2,X3)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
    c_0_2122,
    [final] ).

cnf(c_0_2730,plain,
    ( c_lessequals(X4,X5,X3)
    | ~ c_lessequals(X1,X2,X3)
    | c_HOL_Ominus__class_Ominus(X2,X1,X3) != c_HOL_Ominus__class_Ominus(X5,X4,X3)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
    c_0_2123,
    [final] ).

cnf(c_0_2731,plain,
    ( c_lessequals(X4,X5,X3)
    | ~ c_lessequals(X1,X2,X3)
    | c_HOL_Ominus__class_Ominus(X5,X4,X3) != c_HOL_Ominus__class_Ominus(X2,X1,X3)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
    c_0_2124,
    [final] ).

cnf(c_0_2732,plain,
    ( c_HOL_Oord__class_Oless(X4,X5,X3)
    | ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | c_HOL_Ominus__class_Ominus(X1,X2,X3) != c_HOL_Ominus__class_Ominus(X4,X5,X3)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
    c_0_2125,
    [final] ).

cnf(c_0_2733,plain,
    ( c_HOL_Oord__class_Oless(X4,X5,X3)
    | ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | c_HOL_Ominus__class_Ominus(X4,X5,X3) != c_HOL_Ominus__class_Ominus(X1,X2,X3)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
    c_0_2126,
    [final] ).

cnf(c_0_2734,plain,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
    | c_lessequals(c_HOL_Otimes__class_Otimes(X2,X1,tc_nat),c_HOL_Otimes__class_Otimes(X3,X1,tc_nat),tc_nat) ),
    c_0_2127,
    [final] ).

cnf(c_0_2735,plain,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
    | c_lessequals(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat) ),
    c_0_2128,
    [final] ).

cnf(c_0_2736,plain,
    ( c_lessequals(X1,X3,X4)
    | ~ c_lessequals(X1,c_Orderings_Oord__class_Omin(X2,X3,X4),X4)
    | ~ class_Orderings_Olinorder(X4) ),
    c_0_2129,
    [final] ).

cnf(c_0_2737,plain,
    ( c_lessequals(X1,X2,X4)
    | ~ c_lessequals(X1,c_Orderings_Oord__class_Omin(X2,X3,X4),X4)
    | ~ class_Orderings_Olinorder(X4) ),
    c_0_2130,
    [final] ).

cnf(c_0_2738,plain,
    ( c_lessequals(X1,X3,X4)
    | ~ c_lessequals(X1,c_Orderings_Oord__class_Omin(X2,X3,X4),X4)
    | ~ class_Orderings_Olinorder(X4) ),
    c_0_2131,
    [final] ).

cnf(c_0_2739,plain,
    ( c_lessequals(X1,X2,X4)
    | ~ c_lessequals(X1,c_Orderings_Oord__class_Omin(X2,X3,X4),X4)
    | ~ class_Orderings_Olinorder(X4) ),
    c_0_2132,
    [final] ).

cnf(c_0_2740,plain,
    ( c_lessequals(X2,X4,X3)
    | ~ c_lessequals(c_Orderings_Oord__class_Omax(X1,X2,X3),X4,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    c_0_2133,
    [final] ).

cnf(c_0_2741,plain,
    ( c_lessequals(X1,X4,X3)
    | ~ c_lessequals(c_Orderings_Oord__class_Omax(X1,X2,X3),X4,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    c_0_2134,
    [final] ).

cnf(c_0_2742,plain,
    ( c_lessequals(X2,X4,X3)
    | ~ c_lessequals(c_Orderings_Oord__class_Omax(X1,X2,X3),X4,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    c_0_2135,
    [final] ).

cnf(c_0_2743,plain,
    ( c_lessequals(X1,X4,X3)
    | ~ c_lessequals(c_Orderings_Oord__class_Omax(X1,X2,X3),X4,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    c_0_2136,
    [final] ).

cnf(c_0_2744,plain,
    ( c_HOL_Oord__class_Oless(X1,X4,X3)
    | ~ c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omax(X1,X2,X3),X4,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    c_0_2137,
    [final] ).

cnf(c_0_2745,plain,
    ( c_HOL_Oord__class_Oless(X2,X4,X3)
    | ~ c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omax(X1,X2,X3),X4,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    c_0_2138,
    [final] ).

cnf(c_0_2746,plain,
    ( c_HOL_Oord__class_Oless(X1,X2,X4)
    | ~ c_HOL_Oord__class_Oless(X1,c_Orderings_Oord__class_Omin(X2,X3,X4),X4)
    | ~ class_Orderings_Olinorder(X4) ),
    c_0_2139,
    [final] ).

cnf(c_0_2747,plain,
    ( c_HOL_Oord__class_Oless(X1,X3,X4)
    | ~ c_HOL_Oord__class_Oless(X1,c_Orderings_Oord__class_Omin(X2,X3,X4),X4)
    | ~ class_Orderings_Olinorder(X4) ),
    c_0_2140,
    [final] ).

cnf(c_0_2748,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_2141,
    [final] ).

cnf(c_0_2749,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_2142,
    [final] ).

cnf(c_0_2750,plain,
    ( c_HOL_Oord__class_Oless(X2,X1,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),tc_nat) ),
    c_0_2143,
    [final] ).

cnf(c_0_2751,plain,
    ( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | ~ c_HOL_Oord__class_Oless(X3,X4,tc_nat)
    | c_HOL_Oplus__class_Oplus(X1,X4,tc_nat) != c_HOL_Oplus__class_Oplus(X3,X2,tc_nat) ),
    c_0_2144,
    [final] ).

cnf(c_0_2752,plain,
    ( c_HOL_Oord__class_Oless(X1,X3,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),X3,tc_nat) ),
    c_0_2145,
    [final] ).

cnf(c_0_2753,plain,
    ( c_lessequals(X2,X3,tc_nat)
    | ~ c_lessequals(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),X3,tc_nat) ),
    c_0_2146,
    [final] ).

cnf(c_0_2754,plain,
    ( c_lessequals(X1,X3,tc_nat)
    | ~ c_lessequals(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),X3,tc_nat) ),
    c_0_2147,
    [final] ).

cnf(c_0_2755,plain,
    ( X1 = c_HOL_Ozero__class_Ozero(X2)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X3,X2)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X1,X2)
    | c_HOL_Oplus__class_Oplus(X3,X1,X2) != c_HOL_Ozero__class_Ozero(X2)
    | ~ class_OrderedGroup_Opordered__comm__monoid__add(X2) ),
    c_0_2148,
    [final] ).

cnf(c_0_2756,plain,
    ( X1 = c_HOL_Ozero__class_Ozero(X2)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X1,X2)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X3,X2)
    | c_HOL_Oplus__class_Oplus(X1,X3,X2) != c_HOL_Ozero__class_Ozero(X2)
    | ~ class_OrderedGroup_Opordered__comm__monoid__add(X2) ),
    c_0_2149,
    [final] ).

cnf(c_0_2757,plain,
    ( c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),X1,tc_nat) = c_Divides_Odiv__class_Omod(X2,X1,tc_nat)
    | ~ c_lessequals(X1,X2,tc_nat) ),
    c_0_2150,
    [final] ).

cnf(c_0_2758,plain,
    ( c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ozero__class_Ozero(X1),X1) = c_HOL_Ozero__class_Ozero(X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ class_OrderedGroup_Opordered__comm__monoid__add(X1) ),
    c_0_2151,
    [final] ).

cnf(c_0_2759,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_2152,
    [final] ).

cnf(c_0_2760,plain,
    ( c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(X2,X2,X1),X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
    c_0_2153,
    [final] ).

cnf(c_0_2761,plain,
    ( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X1,X2),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_2154,
    [final] ).

cnf(c_0_2762,plain,
    ( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X1,X2),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_2155,
    [final] ).

cnf(c_0_2763,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_2156,
    [final] ).

cnf(c_0_2764,plain,
    ( c_lessequals(c_HOL_Oplus__class_Oplus(X1,X1,X2),c_HOL_Ozero__class_Ozero(X2),X2)
    | ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
    | ~ class_OrderedGroup_Olordered__ab__group__add(X2) ),
    c_0_2157,
    [final] ).

cnf(c_0_2765,plain,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(X2,X2,X1),X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
    c_0_2158,
    [final] ).

cnf(c_0_2766,plain,
    ( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),X2,tc_nat) = c_Divides_Odiv__class_Omod(X1,X2,tc_nat) ),
    c_0_2159,
    [final] ).

cnf(c_0_2767,plain,
    ( c_lessequals(c_HOL_Ominus__class_Ominus(X1,X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
    | ~ c_lessequals(X1,X2,X3)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
    c_0_2160,
    [final] ).

cnf(c_0_2768,plain,
    ( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
    | ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
    c_0_2161,
    [final] ).

cnf(c_0_2769,plain,
    ( c_Lambda_Osubst(c_Lambda_OdB_OVar(X2),X3,X1) = c_Lambda_OdB_OVar(c_HOL_Ominus__class_Ominus(X2,c_HOL_Oone__class_Oone(tc_nat),tc_nat))
    | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
    c_0_2162,
    [final] ).

cnf(c_0_2770,plain,
    ( c_Lambda_Osubst(c_Lambda_OdB_OVar(X2),X3,X1) = c_Lambda_OdB_OVar(c_HOL_Ominus__class_Ominus(X2,c_HOL_Oone__class_Oone(tc_nat),tc_nat))
    | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
    c_0_2163,
    [final] ).

cnf(c_0_2771,plain,
    ( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,c_Suc(X2),tc_nat),X1,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
    c_0_2164,
    [final] ).

cnf(c_0_2772,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_2165,
    [final] ).

cnf(c_0_2773,plain,
    ( c_lessequals(c_Orderings_Oord__class_Omin(X4,X1,X3),X2,X3)
    | ~ c_lessequals(X1,X2,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    c_0_2166,
    [final] ).

cnf(c_0_2774,plain,
    ( c_lessequals(c_Orderings_Oord__class_Omin(X1,X4,X3),X2,X3)
    | ~ c_lessequals(X1,X2,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    c_0_2167,
    [final] ).

cnf(c_0_2775,plain,
    ( c_lessequals(c_Orderings_Oord__class_Omin(X4,X1,X3),X2,X3)
    | ~ c_lessequals(X1,X2,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    c_0_2168,
    [final] ).

cnf(c_0_2776,plain,
    ( c_lessequals(c_Orderings_Oord__class_Omin(X1,X4,X3),X2,X3)
    | ~ c_lessequals(X1,X2,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    c_0_2169,
    [final] ).

cnf(c_0_2777,plain,
    ( c_lessequals(X1,c_Orderings_Oord__class_Omax(X4,X2,X3),X3)
    | ~ c_lessequals(X1,X2,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    c_0_2170,
    [final] ).

cnf(c_0_2778,plain,
    ( c_lessequals(X1,c_Orderings_Oord__class_Omax(X2,X4,X3),X3)
    | ~ c_lessequals(X1,X2,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    c_0_2171,
    [final] ).

cnf(c_0_2779,plain,
    ( c_lessequals(X1,c_Orderings_Oord__class_Omax(X4,X2,X3),X3)
    | ~ c_lessequals(X1,X2,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    c_0_2172,
    [final] ).

cnf(c_0_2780,plain,
    ( c_lessequals(X1,c_Orderings_Oord__class_Omax(X2,X4,X3),X3)
    | ~ c_lessequals(X1,X2,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    c_0_2173,
    [final] ).

cnf(c_0_2781,plain,
    ( c_HOL_Oord__class_Oless(X1,c_Orderings_Oord__class_Omax(X2,X4,X3),X3)
    | ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    c_0_2174,
    [final] ).

cnf(c_0_2782,plain,
    ( c_HOL_Oord__class_Oless(X1,c_Orderings_Oord__class_Omax(X4,X2,X3),X3)
    | ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    c_0_2175,
    [final] ).

cnf(c_0_2783,plain,
    ( c_HOL_Oord__class_Oless(X1,c_Orderings_Oord__class_Omax(X2,X4,X3),X3)
    | ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    c_0_2176,
    [final] ).

cnf(c_0_2784,plain,
    ( c_HOL_Oord__class_Oless(X1,c_Orderings_Oord__class_Omax(X4,X2,X3),X3)
    | ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    c_0_2177,
    [final] ).

cnf(c_0_2785,plain,
    ( c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omin(X1,X4,X3),X2,X3)
    | ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    c_0_2178,
    [final] ).

cnf(c_0_2786,plain,
    ( c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omin(X4,X1,X3),X2,X3)
    | ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    c_0_2179,
    [final] ).

cnf(c_0_2787,plain,
    ( c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omin(X1,X4,X3),X2,X3)
    | ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    c_0_2180,
    [final] ).

cnf(c_0_2788,plain,
    ( c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omin(X4,X1,X3),X2,X3)
    | ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    c_0_2181,
    [final] ).

cnf(c_0_2789,plain,
    ( c_Suc(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat)) = c_HOL_Ominus__class_Ominus(c_Suc(X2),X1,tc_nat)
    | ~ c_lessequals(X1,X2,tc_nat) ),
    c_0_2182,
    [final] ).

cnf(c_0_2790,plain,
    ( c_Lambda_Obeta(c_Lambda_Osubst(X1,X3,X4),c_Lambda_Osubst(X2,X3,X4))
    | ~ c_Lambda_Obeta(X1,X2) ),
    c_0_2183,
    [final] ).

cnf(c_0_2791,plain,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oplus__class_Oplus(X2,X1,tc_nat),tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
    c_0_2184,
    [final] ).

cnf(c_0_2792,plain,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
    c_0_2185,
    [final] ).

cnf(c_0_2793,plain,
    ( c_HOL_Oplus__class_Oplus(X1,X1,X2) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(X2),c_HOL_Oone__class_Oone(X2),X2),X1,X2)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X2) ),
    c_0_2186,
    [final] ).

cnf(c_0_2794,plain,
    ( c_lessequals(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_2187,
    [final] ).

cnf(c_0_2795,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_2188,
    [final] ).

cnf(c_0_2796,plain,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),tc_nat)
    | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
    c_0_2189,
    [final] ).

cnf(c_0_2797,plain,
    ( c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),X2,tc_nat) = X1
    | ~ c_lessequals(X2,X1,tc_nat) ),
    c_0_2190,
    [final] ).

cnf(c_0_2798,plain,
    ( c_HOL_Oplus__class_Oplus(X1,c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),tc_nat) = X2
    | ~ c_lessequals(X1,X2,tc_nat) ),
    c_0_2191,
    [final] ).

cnf(c_0_2799,plain,
    ( c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),X1,tc_nat) = X2
    | ~ c_lessequals(X1,X2,tc_nat) ),
    c_0_2192,
    [final] ).

cnf(c_0_2800,plain,
    ( c_HOL_Ominus__class_Ominus(X2,c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),tc_nat) = X1
    | ~ c_lessequals(X1,X2,tc_nat) ),
    c_0_2193,
    [final] ).

cnf(c_0_2801,plain,
    ( c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(X2,X3,tc_nat),tc_nat)
    | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
    c_0_2194,
    [final] ).

cnf(c_0_2802,plain,
    ( c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(X3,X2,tc_nat),tc_nat)
    | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
    c_0_2195,
    [final] ).

cnf(c_0_2803,plain,
    ( c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(X2,X3,tc_nat),tc_nat)
    | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
    c_0_2196,
    [final] ).

cnf(c_0_2804,plain,
    ( c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(X3,X2,tc_nat),tc_nat)
    | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
    c_0_2197,
    [final] ).

cnf(c_0_2805,plain,
    ( c_lessequals(X1,c_HOL_Oplus__class_Oplus(X3,X2,tc_nat),tc_nat)
    | ~ c_lessequals(X1,X2,tc_nat) ),
    c_0_2198,
    [final] ).

cnf(c_0_2806,plain,
    ( c_lessequals(X1,c_HOL_Oplus__class_Oplus(X2,X3,tc_nat),tc_nat)
    | ~ c_lessequals(X1,X2,tc_nat) ),
    c_0_2199,
    [final] ).

cnf(c_0_2807,plain,
    ( c_lessequals(X1,c_HOL_Oplus__class_Oplus(X3,X2,tc_nat),tc_nat)
    | ~ c_lessequals(X1,X2,tc_nat) ),
    c_0_2200,
    [final] ).

cnf(c_0_2808,plain,
    ( c_lessequals(X1,c_HOL_Oplus__class_Oplus(X2,X3,tc_nat),tc_nat)
    | ~ c_lessequals(X1,X2,tc_nat) ),
    c_0_2201,
    [final] ).

cnf(c_0_2809,plain,
    ( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,X3,tc_nat),X2,tc_nat)
    | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
    c_0_2202,
    [final] ).

cnf(c_0_2810,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_2203,
    [final] ).

cnf(c_0_2811,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_2204,
    [final] ).

cnf(c_0_2812,plain,
    ( c_lessequals(X4,X2,X3)
    | ~ c_lessequals(X1,X2,X3)
    | ~ c_lessequals(X4,X1,X3)
    | ~ class_Orderings_Oorder(X3) ),
    c_0_2205,
    [final] ).

cnf(c_0_2813,plain,
    ( c_HOL_Oord__class_Oless(X4,X2,X3)
    | ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | ~ c_lessequals(X4,X1,X3)
    | ~ class_Orderings_Oorder(X3) ),
    c_0_2206,
    [final] ).

cnf(c_0_2814,plain,
    ( c_HOL_Oord__class_Oless(X4,X2,X3)
    | ~ c_lessequals(X1,X2,X3)
    | ~ c_HOL_Oord__class_Oless(X4,X1,X3)
    | ~ class_Orderings_Oorder(X3) ),
    c_0_2207,
    [final] ).

cnf(c_0_2815,plain,
    ( c_lessequals(X1,X4,X3)
    | ~ c_lessequals(X1,X2,X3)
    | ~ c_lessequals(X2,X4,X3)
    | ~ class_Orderings_Opreorder(X3) ),
    c_0_2208,
    [final] ).

cnf(c_0_2816,plain,
    ( c_HOL_Oord__class_Oless(X1,X4,X3)
    | ~ c_lessequals(X1,X2,X3)
    | ~ c_HOL_Oord__class_Oless(X2,X4,X3)
    | ~ class_Orderings_Opreorder(X3) ),
    c_0_2209,
    [final] ).

cnf(c_0_2817,plain,
    ( c_HOL_Oord__class_Oless(X1,X4,X3)
    | ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | ~ c_lessequals(X2,X4,X3)
    | ~ class_Orderings_Opreorder(X3) ),
    c_0_2210,
    [final] ).

cnf(c_0_2818,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_2211,
    [final] ).

cnf(c_0_2819,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_2212,
    [final] ).

cnf(c_0_2820,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_2213,
    [final] ).

cnf(c_0_2821,plain,
    ( c_Orderings_Oord__class_Omin(X1,c_Orderings_Oord__class_Omin(X1,X2,X3),X3) = c_Orderings_Oord__class_Omin(X1,X2,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    c_0_2214,
    [final] ).

cnf(c_0_2822,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_2215,
    [final] ).

cnf(c_0_2823,plain,
    ( c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X1,X2,X3),X2,X3) = c_Divides_Odiv__class_Omod(X1,X2,X3)
    | ~ class_Divides_Osemiring__div(X3) ),
    c_0_2216,
    [final] ).

cnf(c_0_2824,plain,
    ( c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X1,X2,X3),X1,X3) = c_Divides_Odiv__class_Omod(X2,X1,X3)
    | ~ class_Divides_Osemiring__div(X3) ),
    c_0_2217,
    [final] ).

cnf(c_0_2825,plain,
    ( c_Orderings_Oord__class_Omax(X1,c_Orderings_Oord__class_Omax(X1,X2,X3),X3) = c_Orderings_Oord__class_Omax(X1,X2,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    c_0_2218,
    [final] ).

cnf(c_0_2826,plain,
    ( c_Suc(c_HOL_Ominus__class_Ominus(X1,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat)) = X1
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
    c_0_2219,
    [final] ).

cnf(c_0_2827,plain,
    ( c_lessequals(X1,X3,tc_nat)
    | ~ c_lessequals(X1,X2,tc_nat)
    | ~ c_lessequals(X2,X3,tc_nat) ),
    c_0_2220,
    [final] ).

cnf(c_0_2828,plain,
    ( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | c_HOL_Oplus__class_Oplus(X2,c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),tc_nat) = X1 ),
    c_0_2221,
    [final] ).

cnf(c_0_2829,plain,
    ( c_Suc(c_HOL_Ominus__class_Ominus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat)) = X1
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
    c_0_2222,
    [final] ).

cnf(c_0_2830,plain,
    ( c_Suc(c_HOL_Ominus__class_Ominus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat)) = X1
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
    c_0_2223,
    [final] ).

cnf(c_0_2831,plain,
    ( c_lessequals(X2,X1,X3)
    | c_HOL_Oord__class_Oless(X1,X2,X3)
    | ~ c_lessequals(X1,X2,X3)
    | ~ class_Orderings_Opreorder(X3) ),
    c_0_2224,
    [final] ).

cnf(c_0_2832,plain,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(X1),c_HOL_Oone__class_Oone(X1),X1),X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    c_0_2225,
    [final] ).

cnf(c_0_2833,plain,
    ( X1 = X2
    | c_HOL_Oplus__class_Oplus(X3,X1,X4) != c_HOL_Oplus__class_Oplus(X3,X2,X4)
    | ~ class_Int_Onumber__ring(X4)
    | ~ class_Ring__and__Field_Oidom(X4) ),
    c_0_2226,
    [final] ).

cnf(c_0_2834,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_2227,
    [final] ).

cnf(c_0_2835,plain,
    ( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | c_Lambda_Olift(c_Lambda_OdB_OVar(X1),X2) = c_Lambda_OdB_OVar(c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat)) ),
    c_0_2228,
    [final] ).

cnf(c_0_2836,plain,
    ( X1 = X2
    | ~ c_lessequals(X1,X2,X3)
    | ~ c_lessequals(X2,X1,X3)
    | ~ class_Orderings_Oorder(X3) ),
    c_0_2229,
    [final] ).

cnf(c_0_2837,plain,
    ( X1 = X2
    | ~ c_lessequals(X1,X2,X3)
    | ~ c_lessequals(X2,X1,X3)
    | ~ class_Orderings_Oorder(X3) ),
    c_0_2230,
    [final] ).

cnf(c_0_2838,plain,
    ( X2 = X1
    | ~ c_lessequals(X1,X2,X3)
    | ~ c_lessequals(X2,X1,X3)
    | ~ class_Orderings_Oorder(X3) ),
    c_0_2231,
    [final] ).

cnf(c_0_2839,plain,
    ( c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(X2),X2),X2)
    | ~ class_Ring__and__Field_Oordered__semidom(X2) ),
    c_0_2232,
    [final] ).

cnf(c_0_2840,plain,
    ( X1 = X2
    | c_HOL_Ominus__class_Ominus(X1,X2,X3) != c_HOL_Ominus__class_Ominus(X4,X4,X3)
    | ~ class_OrderedGroup_Oab__group__add(X3) ),
    c_0_2233,
    [final] ).

cnf(c_0_2841,plain,
    ( X1 = X2
    | c_HOL_Ominus__class_Ominus(X3,X3,X4) != c_HOL_Ominus__class_Ominus(X1,X2,X4)
    | ~ class_OrderedGroup_Oab__group__add(X4) ),
    c_0_2234,
    [final] ).

cnf(c_0_2842,plain,
    ( X1 = X2
    | c_HOL_Oplus__class_Oplus(X3,X1,X4) != c_HOL_Oplus__class_Oplus(X3,X2,X4)
    | ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X4) ),
    c_0_2235,
    [final] ).

cnf(c_0_2843,plain,
    ( X1 = X2
    | c_HOL_Oplus__class_Oplus(X3,X1,X4) != c_HOL_Oplus__class_Oplus(X3,X2,X4)
    | ~ class_OrderedGroup_Ocancel__semigroup__add(X4) ),
    c_0_2236,
    [final] ).

cnf(c_0_2844,plain,
    ( X1 = X2
    | c_HOL_Oplus__class_Oplus(X1,X3,X4) != c_HOL_Oplus__class_Oplus(X2,X3,X4)
    | ~ class_OrderedGroup_Ocancel__semigroup__add(X4) ),
    c_0_2237,
    [final] ).

cnf(c_0_2845,plain,
    ( ~ c_HOL_Oord__class_Oless(X1,X1,X2)
    | ~ c_lessequals(X1,X1,X2)
    | ~ class_Orderings_Olinorder(X2) ),
    c_0_2238,
    [final] ).

cnf(c_0_2846,plain,
    ( ~ c_lessequals(X1,X2,X3)
    | ~ c_HOL_Oord__class_Oless(X2,X1,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    c_0_2239,
    [final] ).

cnf(c_0_2847,plain,
    ( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | ~ c_lessequals(X2,X1,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    c_0_2240,
    [final] ).

cnf(c_0_2848,plain,
    ( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | ~ c_lessequals(X2,X1,X3)
    | ~ class_Orderings_Opreorder(X3) ),
    c_0_2241,
    [final] ).

cnf(c_0_2849,plain,
    ( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | ~ c_HOL_Oord__class_Oless(X2,X1,X3)
    | ~ class_Orderings_Oorder(X3) ),
    c_0_2242,
    [final] ).

cnf(c_0_2850,plain,
    ( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | ~ c_HOL_Oord__class_Oless(X2,X1,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    c_0_2243,
    [final] ).

cnf(c_0_2851,plain,
    ( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | ~ c_HOL_Oord__class_Oless(X2,X1,X3)
    | ~ class_Orderings_Opreorder(X3) ),
    c_0_2244,
    [final] ).

cnf(c_0_2852,plain,
    ( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | ~ c_HOL_Oord__class_Oless(X2,X1,X3)
    | ~ class_Orderings_Opreorder(X3) ),
    c_0_2245,
    [final] ).

cnf(c_0_2853,plain,
    ( X2 = X1
    | ~ c_lessequals(X1,X2,tc_nat)
    | ~ c_HOL_Oord__class_Oless(X2,c_Suc(X1),tc_nat) ),
    c_0_2246,
    [final] ).

cnf(c_0_2854,plain,
    ( ~ c_lessequals(c_Suc(X1),X2,tc_nat)
    | ~ c_lessequals(X2,X1,tc_nat) ),
    c_0_2247,
    [final] ).

cnf(c_0_2855,plain,
    ( ~ c_HOL_Oord__class_Oless(X1,c_Suc(X2),tc_nat)
    | ~ c_HOL_Oord__class_Oless(X2,X1,tc_nat) ),
    c_0_2248,
    [final] ).

cnf(c_0_2856,plain,
    ( X1 = X2
    | c_HOL_Ominus__class_Ominus(X1,X2,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)
    | c_HOL_Ominus__class_Ominus(X2,X1,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) ),
    c_0_2249,
    [final] ).

cnf(c_0_2857,plain,
    ( c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X2,X1),X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    c_0_2250,
    [final] ).

cnf(c_0_2858,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_2251,
    [final] ).

cnf(c_0_2859,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_2252,
    [final] ).

cnf(c_0_2860,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_2253,
    [final] ).

cnf(c_0_2861,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_2254,
    [final] ).

cnf(c_0_2862,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_2255,
    [final] ).

cnf(c_0_2863,plain,
    ( X1 = X2
    | ~ c_lessequals(X1,X2,tc_nat)
    | ~ c_lessequals(X2,X1,tc_nat) ),
    c_0_2256,
    [final] ).

cnf(c_0_2864,plain,
    ( c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X1,X2,X3),X2,X3) = X1
    | ~ class_OrderedGroup_Ogroup__add(X3) ),
    c_0_2257,
    [final] ).

cnf(c_0_2865,plain,
    ( c_Orderings_Oord__class_Omin(X1,c_Orderings_Oord__class_Omax(X1,X2,X3),X3) = X1
    | ~ class_Orderings_Olinorder(X3) ),
    c_0_2258,
    [final] ).

cnf(c_0_2866,plain,
    ( c_Orderings_Oord__class_Omax(X1,c_Orderings_Oord__class_Omin(X1,X2,X3),X3) = X1
    | ~ class_Orderings_Olinorder(X3) ),
    c_0_2259,
    [final] ).

cnf(c_0_2867,plain,
    ( c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X1,X2,X3),X2,X3) = X1
    | ~ class_OrderedGroup_Ogroup__add(X3) ),
    c_0_2260,
    [final] ).

cnf(c_0_2868,plain,
    ( c_lessequals(X1,c_Orderings_Oord__class_Omax(X1,X2,X3),X3)
    | ~ class_Orderings_Olinorder(X3) ),
    c_0_2261,
    [final] ).

cnf(c_0_2869,plain,
    ( c_lessequals(X1,c_Orderings_Oord__class_Omax(X2,X1,X3),X3)
    | ~ class_Orderings_Olinorder(X3) ),
    c_0_2262,
    [final] ).

cnf(c_0_2870,plain,
    ( c_lessequals(c_Orderings_Oord__class_Omin(X1,X2,X3),X1,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    c_0_2263,
    [final] ).

cnf(c_0_2871,plain,
    ( c_lessequals(c_Orderings_Oord__class_Omin(X1,X2,X3),X2,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    c_0_2264,
    [final] ).

cnf(c_0_2872,plain,
    ( X1 = X2
    | c_HOL_Oplus__class_Oplus(X3,X1,tc_nat) != c_HOL_Oplus__class_Oplus(X3,X2,tc_nat) ),
    c_0_2265,
    [final] ).

cnf(c_0_2873,plain,
    ( X1 = X2
    | c_HOL_Oplus__class_Oplus(X1,X3,tc_nat) != c_HOL_Oplus__class_Oplus(X2,X3,tc_nat) ),
    c_0_2266,
    [final] ).

cnf(c_0_2874,plain,
    ( X1 = X2
    | c_HOL_Oplus__class_Oplus(X3,X1,tc_nat) != c_HOL_Oplus__class_Oplus(X3,X2,tc_nat) ),
    c_0_2267,
    [final] ).

cnf(c_0_2875,plain,
    ( c_lessequals(X1,X2,tc_nat)
    | ~ c_lessequals(c_Suc(X1),c_Suc(X2),tc_nat) ),
    c_0_2268,
    [final] ).

cnf(c_0_2876,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_2269,
    [final] ).

cnf(c_0_2877,plain,
    ( c_lessequals(X1,X2,tc_nat)
    | X1 = c_Suc(X2)
    | ~ c_lessequals(X1,c_Suc(X2),tc_nat) ),
    c_0_2270,
    [final] ).

cnf(c_0_2878,plain,
    ( X2 = X1
    | c_HOL_Oord__class_Oless(X1,X2,X3)
    | ~ c_lessequals(X1,X2,X3)
    | ~ class_Orderings_Oorder(X3) ),
    c_0_2271,
    [final] ).

cnf(c_0_2879,plain,
    ( X1 = X2
    | c_HOL_Oord__class_Oless(X2,X1,X3)
    | ~ c_lessequals(X2,X1,X3)
    | ~ class_Orderings_Oorder(X3) ),
    c_0_2272,
    [final] ).

cnf(c_0_2880,plain,
    ( c_HOL_Oord__class_Oless(X1,X2,X3)
    | X1 = X2
    | ~ c_lessequals(X1,X2,X3)
    | ~ class_Orderings_Oorder(X3) ),
    c_0_2273,
    [final] ).

cnf(c_0_2881,plain,
    ( X1 = X2
    | c_HOL_Oord__class_Oless(X1,X2,X3)
    | ~ c_lessequals(X1,X2,X3)
    | ~ class_Orderings_Oorder(X3) ),
    c_0_2274,
    [final] ).

cnf(c_0_2882,plain,
    ( X1 = X2
    | c_HOL_Oord__class_Oless(X1,X2,X3)
    | ~ c_lessequals(X1,X2,X3)
    | ~ class_Orderings_Oorder(X3) ),
    c_0_2275,
    [final] ).

cnf(c_0_2883,plain,
    ( X1 = X2
    | c_HOL_Oord__class_Oless(X1,X2,X3)
    | ~ c_lessequals(X1,X2,X3)
    | ~ class_Orderings_Oorder(X3) ),
    c_0_2276,
    [final] ).

cnf(c_0_2884,plain,
    ( c_HOL_Oord__class_Oless(X1,X2,X3)
    | X1 = X2
    | ~ c_lessequals(X1,X2,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    c_0_2277,
    [final] ).

cnf(c_0_2885,plain,
    ( c_HOL_Oord__class_Oless(X1,X2,X3)
    | X1 = X2
    | ~ c_lessequals(X1,X2,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    c_0_2278,
    [final] ).

cnf(c_0_2886,plain,
    ( c_lessequals(X1,X2,X3)
    | c_Orderings_Oord__class_Omax(X1,X2,X3) != X2
    | ~ class_Orderings_Olinorder(X3) ),
    c_0_2279,
    [final] ).

cnf(c_0_2887,plain,
    ( c_lessequals(X1,X2,X3)
    | c_Orderings_Oord__class_Omin(X1,X2,X3) != X1
    | ~ class_Orderings_Olinorder(X3) ),
    c_0_2280,
    [final] ).

cnf(c_0_2888,plain,
    ( c_lessequals(c_Suc(X1),c_Suc(X2),tc_nat)
    | ~ c_lessequals(X1,X2,tc_nat) ),
    c_0_2281,
    [final] ).

cnf(c_0_2889,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_2282,
    [final] ).

cnf(c_0_2890,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_2283,
    [final] ).

cnf(c_0_2891,plain,
    ( c_Orderings_Oord__class_Omax(X1,X2,X3) = X2
    | ~ c_lessequals(X1,X2,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    c_0_2284,
    [final] ).

cnf(c_0_2892,plain,
    ( c_Orderings_Oord__class_Omax(X2,X1,X3) = X2
    | ~ c_lessequals(X1,X2,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    c_0_2285,
    [final] ).

cnf(c_0_2893,plain,
    ( c_Orderings_Oord__class_Omin(X1,X2,X3) = X1
    | ~ c_lessequals(X1,X2,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    c_0_2286,
    [final] ).

cnf(c_0_2894,plain,
    ( c_Orderings_Oord__class_Omin(X2,X1,X3) = X1
    | ~ c_lessequals(X1,X2,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    c_0_2287,
    [final] ).

cnf(c_0_2895,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_2288,
    [final] ).

cnf(c_0_2896,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_2289,
    [final] ).

cnf(c_0_2897,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_2290,
    [final] ).

cnf(c_0_2898,plain,
    ( 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_2291,
    [final] ).

cnf(c_0_2899,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_2292,
    [final] ).

cnf(c_0_2900,plain,
    ( c_lessequals(X1,X2,X3)
    | ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | ~ class_Orderings_Oorder(X3) ),
    c_0_2293,
    [final] ).

cnf(c_0_2901,plain,
    ( c_lessequals(X1,X2,X3)
    | ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | ~ class_Orderings_Opreorder(X3) ),
    c_0_2294,
    [final] ).

cnf(c_0_2902,plain,
    ( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | ~ c_lessequals(c_Suc(X1),X2,tc_nat) ),
    c_0_2295,
    [final] ).

cnf(c_0_2903,plain,
    ( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | ~ c_lessequals(c_Suc(X1),X2,tc_nat) ),
    c_0_2296,
    [final] ).

cnf(c_0_2904,plain,
    ( c_lessequals(X1,X2,tc_nat)
    | ~ c_HOL_Oord__class_Oless(X1,c_Suc(X2),tc_nat) ),
    c_0_2297,
    [final] ).

cnf(c_0_2905,plain,
    ( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_Suc(X1),X2,tc_nat) ),
    c_0_2298,
    [final] ).

cnf(c_0_2906,plain,
    ( c_lessequals(X1,X2,tc_nat)
    | ~ c_lessequals(c_Suc(X1),X2,tc_nat) ),
    c_0_2299,
    [final] ).

cnf(c_0_2907,plain,
    ( c_lessequals(c_Suc(X1),X2,tc_nat)
    | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
    c_0_2300,
    [final] ).

cnf(c_0_2908,plain,
    ( c_lessequals(c_Suc(X1),X2,tc_nat)
    | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
    c_0_2301,
    [final] ).

cnf(c_0_2909,plain,
    ( c_HOL_Oord__class_Oless(X1,c_Suc(X2),tc_nat)
    | ~ c_lessequals(X1,X2,tc_nat) ),
    c_0_2302,
    [final] ).

cnf(c_0_2910,plain,
    ( c_HOL_Oord__class_Oless(X1,c_Suc(X1),tc_nat)
    | ~ c_lessequals(X1,X1,tc_nat) ),
    c_0_2303,
    [final] ).

cnf(c_0_2911,plain,
    ( c_HOL_Oord__class_Oless(X1,c_Suc(X2),tc_nat)
    | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
    c_0_2304,
    [final] ).

cnf(c_0_2912,plain,
    ( c_lessequals(X1,c_Suc(X2),tc_nat)
    | ~ c_lessequals(X1,X2,tc_nat) ),
    c_0_2305,
    [final] ).

cnf(c_0_2913,plain,
    ( c_lessequals(X1,X2,tc_nat)
    | c_HOL_Ominus__class_Ominus(X1,X2,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) ),
    c_0_2306,
    [final] ).

cnf(c_0_2914,plain,
    ( c_HOL_Ominus__class_Ominus(X1,X2,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat)
    | ~ c_lessequals(X1,X2,tc_nat) ),
    c_0_2307,
    [final] ).

cnf(c_0_2915,plain,
    ( X1 = X2
    | c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | ~ c_lessequals(X1,X2,tc_nat) ),
    c_0_2308,
    [final] ).

cnf(c_0_2916,plain,
    ( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | X1 = X2
    | ~ c_lessequals(X1,X2,tc_nat) ),
    c_0_2309,
    [final] ).

cnf(c_0_2917,plain,
    ( X1 = X2
    | c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | ~ c_lessequals(X1,X2,tc_nat) ),
    c_0_2310,
    [final] ).

cnf(c_0_2918,plain,
    ( c_Divides_Odiv__class_Omod(X1,X2,tc_nat) = X1
    | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
    c_0_2311,
    [final] ).

cnf(c_0_2919,plain,
    ( c_lessequals(X1,X2,tc_nat)
    | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
    c_0_2312,
    [final] ).

cnf(c_0_2920,plain,
    ( c_lessequals(X1,X2,tc_nat)
    | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
    c_0_2313,
    [final] ).

cnf(c_0_2921,plain,
    ( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | X2 = X1
    | c_Lambda_Osubst(c_Lambda_OdB_OVar(X2),X3,X1) = c_Lambda_OdB_OVar(X2) ),
    c_0_2314,
    [final] ).

cnf(c_0_2922,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_2315,
    [final] ).

cnf(c_0_2923,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_2316,
    [final] ).

cnf(c_0_2924,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_2317,
    [final] ).

cnf(c_0_2925,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_2318,
    [final] ).

cnf(c_0_2926,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_2319,
    [final] ).

cnf(c_0_2927,plain,
    ( c_lessequals(X1,X2,X3)
    | c_HOL_Oord__class_Oless(X2,X1,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    c_0_2320,
    [final] ).

cnf(c_0_2928,plain,
    ( c_lessequals(X1,X1,X2)
    | c_HOL_Oord__class_Oless(X1,X1,X2)
    | ~ class_Orderings_Olinorder(X2) ),
    c_0_2321,
    [final] ).

cnf(c_0_2929,plain,
    ( c_HOL_Oord__class_Oless(X1,X2,X3)
    | c_lessequals(X2,X1,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    c_0_2322,
    [final] ).

cnf(c_0_2930,plain,
    ( c_lessequals(X1,X2,X3)
    | c_HOL_Oord__class_Oless(X2,X1,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    c_0_2323,
    [final] ).

cnf(c_0_2931,plain,
    ( c_lessequals(X1,X2,X3)
    | c_lessequals(X2,X1,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    c_0_2324,
    [final] ).

cnf(c_0_2932,plain,
    ( c_HOL_Oplus__class_Oplus(X1,X2,X3) = c_HOL_Oplus__class_Oplus(X2,X1,X3)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
    c_0_2325,
    [final] ).

cnf(c_0_2933,plain,
    ( c_HOL_Oplus__class_Oplus(X1,X2,X3) = c_HOL_Oplus__class_Oplus(X2,X1,X3)
    | ~ class_OrderedGroup_Ocomm__monoid__add(X3) ),
    c_0_2326,
    [final] ).

cnf(c_0_2934,plain,
    ( c_HOL_Oplus__class_Oplus(X1,X2,X3) = c_HOL_Oplus__class_Oplus(X2,X1,X3)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
    c_0_2327,
    [final] ).

cnf(c_0_2935,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_2328,
    [final] ).

cnf(c_0_2936,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_2329,
    [final] ).

cnf(c_0_2937,plain,
    ( c_Orderings_Oord__class_Omin(X1,X2,X3) = c_Orderings_Oord__class_Omin(X2,X1,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    c_0_2330,
    [final] ).

cnf(c_0_2938,plain,
    ( c_Orderings_Oord__class_Omax(X1,X2,X3) = c_Orderings_Oord__class_Omax(X2,X1,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    c_0_2331,
    [final] ).

cnf(c_0_2939,plain,
    ( c_Lambda_Osubst(c_Lambda_OdB_OVar(X1),X2,X1) = X2
    | c_HOL_Oord__class_Oless(X1,X1,tc_nat) ),
    c_0_2332,
    [final] ).

cnf(c_0_2940,plain,
    ( c_lessequals(X1,X2,tc_nat)
    | c_lessequals(c_Suc(X2),X1,tc_nat) ),
    c_0_2333,
    [final] ).

cnf(c_0_2941,plain,
    ( c_HOL_Oord__class_Oless(X1,c_Suc(X1),tc_nat)
    | c_HOL_Oord__class_Oless(X1,X1,tc_nat) ),
    c_0_2334,
    [final] ).

cnf(c_0_2942,plain,
    ( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | c_HOL_Oord__class_Oless(X2,c_Suc(X1),tc_nat) ),
    c_0_2335,
    [final] ).

cnf(c_0_2943,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_2336,
    [final] ).

cnf(c_0_2944,plain,
    ( ~ c_lessequals(c_HOL_Oone__class_Oone(X1),c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    c_0_2337,
    [final] ).

cnf(c_0_2945,plain,
    ( X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
    | X2 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
    | c_HOL_Oplus__class_Oplus(X1,X2,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
    c_0_2338,
    [final] ).

cnf(c_0_2946,plain,
    ( X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
    | X2 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
    | c_HOL_Oplus__class_Oplus(X1,X2,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
    c_0_2339,
    [final] ).

cnf(c_0_2947,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_2340,
    [final] ).

cnf(c_0_2948,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_2341,
    [final] ).

cnf(c_0_2949,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_2342,
    [final] ).

cnf(c_0_2950,plain,
    ( X1 = X2
    | c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | c_HOL_Oord__class_Oless(X2,X1,tc_nat) ),
    c_0_2343,
    [final] ).

cnf(c_0_2951,plain,
    ( X1 = X2
    | c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | c_HOL_Oord__class_Oless(X2,X1,tc_nat) ),
    c_0_2344,
    [final] ).

cnf(c_0_2952,plain,
    ( X1 = X2
    | c_HOL_Ominus__class_Ominus(X1,X2,X3) != c_HOL_Ozero__class_Ozero(X3)
    | ~ class_Int_Onumber__ring(X3)
    | ~ class_Ring__and__Field_Oidom(X3) ),
    c_0_2345,
    [final] ).

cnf(c_0_2953,plain,
    ( 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_2346,
    [final] ).

cnf(c_0_2954,plain,
    ( X1 = c_HOL_Ozero__class_Ozero(X2)
    | c_HOL_Oplus__class_Oplus(X3,X1,X2) != X3
    | ~ class_Int_Onumber__ring(X2)
    | ~ class_Ring__and__Field_Oidom(X2) ),
    c_0_2347,
    [final] ).

cnf(c_0_2955,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_2348,
    [final] ).

cnf(c_0_2956,plain,
    ( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
    | X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
    | c_HOL_Oplus__class_Oplus(X2,X1,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
    c_0_2349,
    [final] ).

cnf(c_0_2957,plain,
    ( X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
    | X1 = c_HOL_Ozero__class_Ozero(tc_nat)
    | c_HOL_Oplus__class_Oplus(X1,X2,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
    c_0_2350,
    [final] ).

cnf(c_0_2958,plain,
    ( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
    | X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
    | c_HOL_Oplus__class_Oplus(X2,X1,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
    c_0_2351,
    [final] ).

cnf(c_0_2959,plain,
    ( X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
    | X1 = c_HOL_Ozero__class_Ozero(tc_nat)
    | c_HOL_Oplus__class_Oplus(X1,X2,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
    c_0_2352,
    [final] ).

cnf(c_0_2960,plain,
    ( c_lessequals(X1,X2,tc_nat)
    | c_lessequals(X2,X1,tc_nat) ),
    c_0_2353,
    [final] ).

cnf(c_0_2961,plain,
    ( X1 = c_HOL_Ozero__class_Ozero(X2)
    | c_HOL_Oplus__class_Oplus(X1,X1,X2) != c_HOL_Ozero__class_Ozero(X2)
    | ~ class_OrderedGroup_Olordered__ab__group__add(X2) ),
    c_0_2354,
    [final] ).

cnf(c_0_2962,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_2355,
    [final] ).

cnf(c_0_2963,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_2356,
    [final] ).

cnf(c_0_2964,plain,
    ( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
    | X2 = c_HOL_Ozero__class_Ozero(tc_nat)
    | c_HOL_Oplus__class_Oplus(X2,X1,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
    c_0_2357,
    [final] ).

cnf(c_0_2965,plain,
    ( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
    | X2 = c_HOL_Ozero__class_Ozero(tc_nat)
    | c_HOL_Oplus__class_Oplus(X2,X1,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
    c_0_2358,
    [final] ).

cnf(c_0_2966,plain,
    ( X1 = X2
    | c_HOL_Ominus__class_Ominus(X1,X2,X3) != c_HOL_Ozero__class_Ozero(X3)
    | ~ class_OrderedGroup_Ogroup__add(X3) ),
    c_0_2359,
    [final] ).

cnf(c_0_2967,plain,
    ( X1 = X2
    | c_HOL_Ominus__class_Ominus(X1,X2,X3) != c_HOL_Ozero__class_Ozero(X3)
    | ~ class_OrderedGroup_Oab__group__add(X3) ),
    c_0_2360,
    [final] ).

cnf(c_0_2968,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_2361,
    [final] ).

cnf(c_0_2969,plain,
    ( ~ c_HOL_Oord__class_Oless(X1,X1,X2)
    | ~ class_Orderings_Oorder(X2) ),
    c_0_2362,
    [final] ).

cnf(c_0_2970,plain,
    ( ~ c_HOL_Oord__class_Oless(X1,X1,X2)
    | ~ class_Orderings_Olinorder(X2) ),
    c_0_2363,
    [final] ).

cnf(c_0_2971,plain,
    ( ~ c_HOL_Oord__class_Oless(X1,X1,X2)
    | ~ class_Orderings_Opreorder(X2) ),
    c_0_2364,
    [final] ).

cnf(c_0_2972,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_2365,
    [final] ).

cnf(c_0_2973,plain,
    ( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
    | ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ),
    c_0_2366,
    [final] ).

cnf(c_0_2974,plain,
    ( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
    | c_HOL_Oplus__class_Oplus(X1,X2,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) ),
    c_0_2367,
    [final] ).

cnf(c_0_2975,plain,
    ( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
    | c_HOL_Oplus__class_Oplus(X2,X1,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) ),
    c_0_2368,
    [final] ).

cnf(c_0_2976,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_2369,
    [final] ).

cnf(c_0_2977,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_2370,
    [final] ).

cnf(c_0_2978,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_2371,
    [final] ).

cnf(c_0_2979,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_2372,
    [final] ).

cnf(c_0_2980,plain,
    ( c_Lambda_Obeta(c_Lambda_OdB_OApp(X3,X1),c_Lambda_OdB_OApp(X3,X2))
    | ~ c_Lambda_Obeta(X1,X2) ),
    c_0_2373,
    [final] ).

cnf(c_0_2981,plain,
    ( c_Lambda_Obeta(c_Lambda_OdB_OApp(X1,X3),c_Lambda_OdB_OApp(X2,X3))
    | ~ c_Lambda_Obeta(X1,X2) ),
    c_0_2374,
    [final] ).

cnf(c_0_2982,plain,
    ( c_Lambda_Obeta(c_Lambda_Olift(X1,X3),c_Lambda_Olift(X2,X3))
    | ~ c_Lambda_Obeta(X1,X2) ),
    c_0_2375,
    [final] ).

cnf(c_0_2983,plain,
    ( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
    | c_HOL_Oplus__class_Oplus(X2,X1,tc_nat) != X2 ),
    c_0_2376,
    [final] ).

cnf(c_0_2984,plain,
    ( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
    | c_HOL_Oplus__class_Oplus(X2,X1,tc_nat) != X2 ),
    c_0_2377,
    [final] ).

cnf(c_0_2985,plain,
    ( c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ozero__class_Ozero(X1),X1) = c_HOL_Ozero__class_Ozero(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
    c_0_2378,
    [final] ).

cnf(c_0_2986,plain,
    ( c_HOL_Oplus__class_Oplus(X1,c_HOL_Ozero__class_Ozero(X2),X2) = X1
    | ~ class_Int_Onumber__ring(X2)
    | ~ class_Ring__and__Field_Oidom(X2) ),
    c_0_2379,
    [final] ).

cnf(c_0_2987,plain,
    ( c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oone__class_Oone(X1),X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    c_0_2380,
    [final] ).

cnf(c_0_2988,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_2381,
    [final] ).

cnf(c_0_2989,plain,
    ( c_HOL_Ominus__class_Ominus(X1,X1,X2) = c_HOL_Ozero__class_Ozero(X2)
    | ~ class_Int_Onumber__ring(X2)
    | ~ class_Ring__and__Field_Oidom(X2) ),
    c_0_2382,
    [final] ).

cnf(c_0_2990,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_2383,
    [final] ).

cnf(c_0_2991,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_2384,
    [final] ).

cnf(c_0_2992,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_2385,
    [final] ).

cnf(c_0_2993,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_2386,
    [final] ).

cnf(c_0_2994,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_2387,
    [final] ).

cnf(c_0_2995,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_2388,
    [final] ).

cnf(c_0_2996,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_2389,
    [final] ).

cnf(c_0_2997,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_2390,
    [final] ).

cnf(c_0_2998,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_2391,
    [final] ).

cnf(c_0_2999,plain,
    ( c_Divides_Odiv__class_Omod(X1,c_HOL_Ozero__class_Ozero(X2),X2) = X1
    | ~ class_Divides_Osemiring__div(X2) ),
    c_0_2392,
    [final] ).

cnf(c_0_3000,plain,
    ( c_HOL_Ominus__class_Ominus(X1,c_HOL_Ozero__class_Ozero(X2),X2) = X1
    | ~ class_OrderedGroup_Ogroup__add(X2) ),
    c_0_2393,
    [final] ).

cnf(c_0_3001,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_2394,
    [final] ).

cnf(c_0_3002,plain,
    ( c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(X1),X2,X1) = X2
    | ~ class_OrderedGroup_Ocomm__monoid__mult(X1) ),
    c_0_2395,
    [final] ).

cnf(c_0_3003,plain,
    ( c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(X1),X2,X1) = X2
    | ~ class_OrderedGroup_Omonoid__mult(X1) ),
    c_0_2396,
    [final] ).

cnf(c_0_3004,plain,
    ( c_HOL_Otimes__class_Otimes(X1,c_HOL_Oone__class_Oone(X2),X2) = X1
    | ~ class_OrderedGroup_Omonoid__mult(X2) ),
    c_0_2397,
    [final] ).

cnf(c_0_3005,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_2398,
    [final] ).

cnf(c_0_3006,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_2399,
    [final] ).

cnf(c_0_3007,plain,
    ( c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X1),X2,X1) = X2
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    c_0_2400,
    [final] ).

cnf(c_0_3008,plain,
    ( c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X1),X2,X1) = X2
    | ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
    c_0_2401,
    [final] ).

cnf(c_0_3009,plain,
    ( c_HOL_Oplus__class_Oplus(X1,c_HOL_Ozero__class_Ozero(X2),X2) = X1
    | ~ class_OrderedGroup_Ocomm__monoid__add(X2) ),
    c_0_2402,
    [final] ).

cnf(c_0_3010,plain,
    ( c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X1),X2,X1) = X2
    | ~ class_OrderedGroup_Omonoid__add(X1) ),
    c_0_2403,
    [final] ).

cnf(c_0_3011,plain,
    ( c_HOL_Oplus__class_Oplus(X1,c_HOL_Ozero__class_Ozero(X2),X2) = X1
    | ~ class_OrderedGroup_Omonoid__add(X2) ),
    c_0_2404,
    [final] ).

cnf(c_0_3012,plain,
    ( c_HOL_Oplus__class_Oplus(X1,c_HOL_Ozero__class_Ozero(X2),X2) = X1
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X2) ),
    c_0_2405,
    [final] ).

cnf(c_0_3013,plain,
    ( c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X1),X2,X1) = X2
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    c_0_2406,
    [final] ).

cnf(c_0_3014,plain,
    ( c_Divides_Odiv__class_Omod(X1,X1,X2) = c_HOL_Ozero__class_Ozero(X2)
    | ~ class_Divides_Osemiring__div(X2) ),
    c_0_2407,
    [final] ).

cnf(c_0_3015,plain,
    ( c_HOL_Ominus__class_Ominus(X1,X1,X2) = c_HOL_Ozero__class_Ozero(X2)
    | ~ class_OrderedGroup_Oab__group__add(X2) ),
    c_0_2408,
    [final] ).

cnf(c_0_3016,plain,
    ( c_HOL_Ominus__class_Ominus(X1,X1,X2) = c_HOL_Ozero__class_Ozero(X2)
    | ~ class_OrderedGroup_Ogroup__add(X2) ),
    c_0_2409,
    [final] ).

cnf(c_0_3017,plain,
    ( c_HOL_Ominus__class_Ominus(X1,X1,X2) = c_HOL_Ozero__class_Ozero(X2)
    | ~ class_OrderedGroup_Ogroup__add(X2) ),
    c_0_2410,
    [final] ).

cnf(c_0_3018,plain,
    ( c_Orderings_Oord__class_Omin(X1,X1,X2) = X1
    | ~ class_Orderings_Olinorder(X2) ),
    c_0_2411,
    [final] ).

cnf(c_0_3019,plain,
    ( c_Orderings_Oord__class_Omax(X1,X1,X2) = X1
    | ~ class_Orderings_Olinorder(X2) ),
    c_0_2412,
    [final] ).

cnf(c_0_3020,plain,
    ( c_HOL_Otimes__class_Otimes(X1,X1,X2) = X1
    | ~ class_OrderedGroup_Oab__semigroup__idem__mult(X2) ),
    c_0_2413,
    [final] ).

cnf(c_0_3021,plain,
    ( c_lessequals(X1,X1,X2)
    | ~ class_Orderings_Oorder(X2) ),
    c_0_2414,
    [final] ).

cnf(c_0_3022,plain,
    ( c_lessequals(X1,X1,X2)
    | ~ class_Orderings_Opreorder(X2) ),
    c_0_2415,
    [final] ).

cnf(c_0_3023,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_2416,
    [final] ).

cnf(c_0_3024,plain,
    ( c_Lambda_Obeta(c_Lambda_OdB_OAbs(X1),c_Lambda_OdB_OAbs(X2))
    | ~ c_Lambda_Obeta(X1,X2) ),
    c_0_2417,
    [final] ).

cnf(c_0_3025,plain,
    ( X1 = X2
    | c_Lambda_OdB_OApp(X3,X1) != c_Lambda_OdB_OApp(X4,X2) ),
    c_0_2418,
    [final] ).

cnf(c_0_3026,plain,
    ( X1 = X2
    | c_Lambda_OdB_OApp(X1,X3) != c_Lambda_OdB_OApp(X2,X4) ),
    c_0_2419,
    [final] ).

cnf(c_0_3027,plain,
    ( c_InductTermi_OIT(c_Lambda_Olift(X1,X2))
    | ~ c_InductTermi_OIT(X1) ),
    c_0_2420,
    [final] ).

cnf(c_0_3028,plain,
    ( c_HOL_Ozero__class_Ozero(X1) != c_HOL_Oone__class_Oone(X1)
    | ~ class_Ring__and__Field_Ozero__neq__one(X1) ),
    c_0_2421,
    [final] ).

cnf(c_0_3029,plain,
    ( c_HOL_Ozero__class_Ozero(X1) != c_HOL_Oone__class_Oone(X1)
    | ~ class_Ring__and__Field_Ozero__neq__one(X1) ),
    c_0_2422,
    [final] ).

cnf(c_0_3030,plain,
    ( c_InductTermi_OIT(c_Lambda_OdB_OAbs(X1))
    | ~ c_InductTermi_OIT(X1) ),
    c_0_2423,
    [final] ).

cnf(c_0_3031,plain,
    ( X1 = X2
    | c_Lambda_OdB_OVar(X1) != c_Lambda_OdB_OVar(X2) ),
    c_0_2424,
    [final] ).

cnf(c_0_3032,plain,
    ( X1 = X2
    | c_Lambda_OdB_OAbs(X1) != c_Lambda_OdB_OAbs(X2) ),
    c_0_2425,
    [final] ).

cnf(c_0_3033,plain,
    ( X1 = X2
    | c_Suc(X1) != c_Suc(X2) ),
    c_0_2426,
    [final] ).

cnf(c_0_3034,plain,
    ( X1 = X2
    | c_Suc(X1) != c_Suc(X2) ),
    c_0_2427,
    [final] ).

% End CNF derivation
% Generating one_way clauses for all literals in the CNF.
cnf(c_0_2428_0,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X4,tc_nat),X3,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X4,tc_nat),X5,tc_nat),tc_nat)
    | ~ c_lessequals(X1,X2,tc_nat)
    | ~ c_HOL_Oord__class_Oless(X3,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),X4,tc_nat),X5,tc_nat),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2428]) ).

cnf(c_0_2428_1,axiom,
    ( ~ c_lessequals(X1,X2,tc_nat)
    | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X4,tc_nat),X3,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X4,tc_nat),X5,tc_nat),tc_nat)
    | ~ c_HOL_Oord__class_Oless(X3,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),X4,tc_nat),X5,tc_nat),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2428]) ).

cnf(c_0_2428_2,axiom,
    ( ~ c_HOL_Oord__class_Oless(X3,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),X4,tc_nat),X5,tc_nat),tc_nat)
    | ~ c_lessequals(X1,X2,tc_nat)
    | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X4,tc_nat),X3,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X4,tc_nat),X5,tc_nat),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2428]) ).

cnf(c_0_2429_0,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X3,tc_nat),X4,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),X5,tc_nat),tc_nat)
    | ~ c_lessequals(X1,X2,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),X3,tc_nat),X4,tc_nat),X5,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2429]) ).

cnf(c_0_2429_1,axiom,
    ( ~ c_lessequals(X1,X2,tc_nat)
    | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X3,tc_nat),X4,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),X5,tc_nat),tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),X3,tc_nat),X4,tc_nat),X5,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2429]) ).

cnf(c_0_2429_2,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),X3,tc_nat),X4,tc_nat),X5,tc_nat)
    | ~ c_lessequals(X1,X2,tc_nat)
    | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X3,tc_nat),X4,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),X5,tc_nat),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2429]) ).

cnf(c_0_2430_0,axiom,
    ( c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X3,tc_nat),X4,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),X5,tc_nat),tc_nat)
    | ~ c_lessequals(X1,X2,tc_nat)
    | ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),X3,tc_nat),X4,tc_nat),X5,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2430]) ).

cnf(c_0_2430_1,axiom,
    ( ~ c_lessequals(X1,X2,tc_nat)
    | c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X3,tc_nat),X4,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),X5,tc_nat),tc_nat)
    | ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),X3,tc_nat),X4,tc_nat),X5,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2430]) ).

cnf(c_0_2430_2,axiom,
    ( ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),X3,tc_nat),X4,tc_nat),X5,tc_nat)
    | ~ c_lessequals(X1,X2,tc_nat)
    | c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X3,tc_nat),X4,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),X5,tc_nat),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2430]) ).

cnf(c_0_2431_0,axiom,
    ( c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X4,tc_nat),X3,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X4,tc_nat),X5,tc_nat),tc_nat)
    | ~ c_lessequals(X1,X2,tc_nat)
    | ~ c_lessequals(X3,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),X4,tc_nat),X5,tc_nat),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2431]) ).

cnf(c_0_2431_1,axiom,
    ( ~ c_lessequals(X1,X2,tc_nat)
    | c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X4,tc_nat),X3,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X4,tc_nat),X5,tc_nat),tc_nat)
    | ~ c_lessequals(X3,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),X4,tc_nat),X5,tc_nat),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2431]) ).

cnf(c_0_2431_2,axiom,
    ( ~ c_lessequals(X3,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),X4,tc_nat),X5,tc_nat),tc_nat)
    | ~ c_lessequals(X1,X2,tc_nat)
    | c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X4,tc_nat),X3,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X4,tc_nat),X5,tc_nat),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2431]) ).

cnf(c_0_2432_0,axiom,
    ( c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X5,X4),X1,X4),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X5,X4),X6,X4),X4)
    | ~ c_lessequals(X1,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X3,X4),X5,X4),X6,X4),X4)
    | ~ class_Ring__and__Field_Opordered__ring(X4) ),
    inference(literals_permutation,[status(thm)],[c_0_2432]) ).

cnf(c_0_2432_1,axiom,
    ( ~ c_lessequals(X1,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X3,X4),X5,X4),X6,X4),X4)
    | c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X5,X4),X1,X4),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X5,X4),X6,X4),X4)
    | ~ class_Ring__and__Field_Opordered__ring(X4) ),
    inference(literals_permutation,[status(thm)],[c_0_2432]) ).

cnf(c_0_2432_2,axiom,
    ( ~ class_Ring__and__Field_Opordered__ring(X4)
    | ~ c_lessequals(X1,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X3,X4),X5,X4),X6,X4),X4)
    | c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X5,X4),X1,X4),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X5,X4),X6,X4),X4) ),
    inference(literals_permutation,[status(thm)],[c_0_2432]) ).

cnf(c_0_2433_0,axiom,
    ( c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X4,X3),X5,X3),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X4,X3),X6,X3),X3)
    | ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,X2,X3),X4,X3),X5,X3),X6,X3)
    | ~ class_Ring__and__Field_Opordered__ring(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2433]) ).

cnf(c_0_2433_1,axiom,
    ( ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,X2,X3),X4,X3),X5,X3),X6,X3)
    | c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X4,X3),X5,X3),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X4,X3),X6,X3),X3)
    | ~ class_Ring__and__Field_Opordered__ring(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2433]) ).

cnf(c_0_2433_2,axiom,
    ( ~ class_Ring__and__Field_Opordered__ring(X3)
    | ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,X2,X3),X4,X3),X5,X3),X6,X3)
    | c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X4,X3),X5,X3),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X4,X3),X6,X3),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2433]) ).

cnf(c_0_2434_0,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X5,X4),X1,X4),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X5,X4),X6,X4),X4)
    | ~ c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X3,X4),X5,X4),X6,X4),X4)
    | ~ class_Ring__and__Field_Opordered__ring(X4) ),
    inference(literals_permutation,[status(thm)],[c_0_2434]) ).

cnf(c_0_2434_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X3,X4),X5,X4),X6,X4),X4)
    | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X5,X4),X1,X4),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X5,X4),X6,X4),X4)
    | ~ class_Ring__and__Field_Opordered__ring(X4) ),
    inference(literals_permutation,[status(thm)],[c_0_2434]) ).

cnf(c_0_2434_2,axiom,
    ( ~ class_Ring__and__Field_Opordered__ring(X4)
    | ~ c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X3,X4),X5,X4),X6,X4),X4)
    | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X5,X4),X1,X4),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X5,X4),X6,X4),X4) ),
    inference(literals_permutation,[status(thm)],[c_0_2434]) ).

cnf(c_0_2435_0,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X4,X3),X5,X3),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X4,X3),X6,X3),X3)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,X2,X3),X4,X3),X5,X3),X6,X3)
    | ~ class_Ring__and__Field_Opordered__ring(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2435]) ).

cnf(c_0_2435_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,X2,X3),X4,X3),X5,X3),X6,X3)
    | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X4,X3),X5,X3),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X4,X3),X6,X3),X3)
    | ~ class_Ring__and__Field_Opordered__ring(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2435]) ).

cnf(c_0_2435_2,axiom,
    ( ~ class_Ring__and__Field_Opordered__ring(X3)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,X2,X3),X4,X3),X5,X3),X6,X3)
    | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X4,X3),X5,X3),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X4,X3),X6,X3),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2435]) ).

cnf(c_0_2436_0,axiom,
    ( c_HOL_Oord__class_Oless(X4,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),X3,tc_nat),X5,tc_nat),tc_nat)
    | ~ c_lessequals(X1,X2,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),X4,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X3,tc_nat),X5,tc_nat),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2436]) ).

cnf(c_0_2436_1,axiom,
    ( ~ c_lessequals(X1,X2,tc_nat)
    | c_HOL_Oord__class_Oless(X4,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),X3,tc_nat),X5,tc_nat),tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),X4,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X3,tc_nat),X5,tc_nat),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2436]) ).

cnf(c_0_2436_2,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),X4,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X3,tc_nat),X5,tc_nat),tc_nat)
    | ~ c_lessequals(X1,X2,tc_nat)
    | c_HOL_Oord__class_Oless(X4,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),X3,tc_nat),X5,tc_nat),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2436]) ).

cnf(c_0_2437_0,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),X3,tc_nat),X4,tc_nat),X5,tc_nat)
    | ~ c_lessequals(X1,X2,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X3,tc_nat),X4,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),X5,tc_nat),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2437]) ).

cnf(c_0_2437_1,axiom,
    ( ~ c_lessequals(X1,X2,tc_nat)
    | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),X3,tc_nat),X4,tc_nat),X5,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X3,tc_nat),X4,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),X5,tc_nat),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2437]) ).

cnf(c_0_2437_2,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X3,tc_nat),X4,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),X5,tc_nat),tc_nat)
    | ~ c_lessequals(X1,X2,tc_nat)
    | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),X3,tc_nat),X4,tc_nat),X5,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2437]) ).

cnf(c_0_2438_0,axiom,
    ( c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),X3,tc_nat),X4,tc_nat),X5,tc_nat)
    | ~ c_lessequals(X1,X2,tc_nat)
    | ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X3,tc_nat),X4,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),X5,tc_nat),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2438]) ).

cnf(c_0_2438_1,axiom,
    ( ~ c_lessequals(X1,X2,tc_nat)
    | c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),X3,tc_nat),X4,tc_nat),X5,tc_nat)
    | ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X3,tc_nat),X4,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),X5,tc_nat),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2438]) ).

cnf(c_0_2438_2,axiom,
    ( ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X3,tc_nat),X4,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),X5,tc_nat),tc_nat)
    | ~ c_lessequals(X1,X2,tc_nat)
    | c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),X3,tc_nat),X4,tc_nat),X5,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2438]) ).

cnf(c_0_2439_0,axiom,
    ( c_lessequals(X4,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),X3,tc_nat),X5,tc_nat),tc_nat)
    | ~ c_lessequals(X1,X2,tc_nat)
    | ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),X4,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X3,tc_nat),X5,tc_nat),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2439]) ).

cnf(c_0_2439_1,axiom,
    ( ~ c_lessequals(X1,X2,tc_nat)
    | c_lessequals(X4,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),X3,tc_nat),X5,tc_nat),tc_nat)
    | ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),X4,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X3,tc_nat),X5,tc_nat),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2439]) ).

cnf(c_0_2439_2,axiom,
    ( ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),X4,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X3,tc_nat),X5,tc_nat),tc_nat)
    | ~ c_lessequals(X1,X2,tc_nat)
    | c_lessequals(X4,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),X3,tc_nat),X5,tc_nat),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2439]) ).

cnf(c_0_2440_0,axiom,
    ( c_lessequals(X4,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X5,X1,X3),X2,X3),X6,X3),X3)
    | ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X5,X2,X3),X6,X3),X3)
    | ~ class_Ring__and__Field_Opordered__ring(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2440]) ).

cnf(c_0_2440_1,axiom,
    ( ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X5,X2,X3),X6,X3),X3)
    | c_lessequals(X4,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X5,X1,X3),X2,X3),X6,X3),X3)
    | ~ class_Ring__and__Field_Opordered__ring(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2440]) ).

cnf(c_0_2440_2,axiom,
    ( ~ class_Ring__and__Field_Opordered__ring(X3)
    | ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X5,X2,X3),X6,X3),X3)
    | c_lessequals(X4,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X5,X1,X3),X2,X3),X6,X3),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2440]) ).

cnf(c_0_2441_0,axiom,
    ( c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,X5,X3),X2,X3),X4,X3),X6,X3)
    | ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X5,X2,X3),X6,X3),X3)
    | ~ class_Ring__and__Field_Opordered__ring(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2441]) ).

cnf(c_0_2441_1,axiom,
    ( ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X5,X2,X3),X6,X3),X3)
    | c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,X5,X3),X2,X3),X4,X3),X6,X3)
    | ~ class_Ring__and__Field_Opordered__ring(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2441]) ).

cnf(c_0_2441_2,axiom,
    ( ~ class_Ring__and__Field_Opordered__ring(X3)
    | ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X5,X2,X3),X6,X3),X3)
    | c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,X5,X3),X2,X3),X4,X3),X6,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2441]) ).

cnf(c_0_2442_0,axiom,
    ( c_HOL_Oord__class_Oless(X4,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X5,X1,X3),X2,X3),X6,X3),X3)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X5,X2,X3),X6,X3),X3)
    | ~ class_Ring__and__Field_Opordered__ring(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2442]) ).

cnf(c_0_2442_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X5,X2,X3),X6,X3),X3)
    | c_HOL_Oord__class_Oless(X4,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X5,X1,X3),X2,X3),X6,X3),X3)
    | ~ class_Ring__and__Field_Opordered__ring(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2442]) ).

cnf(c_0_2442_2,axiom,
    ( ~ class_Ring__and__Field_Opordered__ring(X3)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X5,X2,X3),X6,X3),X3)
    | c_HOL_Oord__class_Oless(X4,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X5,X1,X3),X2,X3),X6,X3),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2442]) ).

cnf(c_0_2443_0,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,X5,X3),X2,X3),X4,X3),X6,X3)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X5,X2,X3),X6,X3),X3)
    | ~ class_Ring__and__Field_Opordered__ring(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2443]) ).

cnf(c_0_2443_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X5,X2,X3),X6,X3),X3)
    | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,X5,X3),X2,X3),X4,X3),X6,X3)
    | ~ class_Ring__and__Field_Opordered__ring(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2443]) ).

cnf(c_0_2443_2,axiom,
    ( ~ class_Ring__and__Field_Opordered__ring(X3)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X5,X2,X3),X6,X3),X3)
    | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,X5,X3),X2,X3),X4,X3),X6,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2443]) ).

cnf(c_0_2444_0,axiom,
    ( c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),X4,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X3,tc_nat),X5,tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(X4,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),X3,tc_nat),X5,tc_nat),tc_nat)
    | ~ c_lessequals(X1,X2,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2444]) ).

cnf(c_0_2444_1,axiom,
    ( ~ c_lessequals(X1,X2,tc_nat)
    | c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),X4,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X3,tc_nat),X5,tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(X4,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),X3,tc_nat),X5,tc_nat),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2444]) ).

cnf(c_0_2445_0,axiom,
    ( c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X3,tc_nat),X4,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),X5,tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),X3,tc_nat),X4,tc_nat),X5,tc_nat)
    | ~ c_lessequals(X1,X2,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2445]) ).

cnf(c_0_2445_1,axiom,
    ( ~ c_lessequals(X1,X2,tc_nat)
    | c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X3,tc_nat),X4,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),X5,tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),X3,tc_nat),X4,tc_nat),X5,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2445]) ).

cnf(c_0_2446_0,axiom,
    ( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X4,X2,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,X4,tc_nat),X2,tc_nat),X3,tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),X3,tc_nat)
    | ~ c_lessequals(X4,X1,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2446]) ).

cnf(c_0_2446_1,axiom,
    ( ~ c_lessequals(X4,X1,tc_nat)
    | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X4,X2,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,X4,tc_nat),X2,tc_nat),X3,tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),X3,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2446]) ).

cnf(c_0_2447_0,axiom,
    ( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X3,X1,tc_nat),X2,tc_nat),X4,tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X2,tc_nat),X4,tc_nat)
    | ~ c_lessequals(X1,X3,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2447]) ).

cnf(c_0_2447_1,axiom,
    ( ~ c_lessequals(X1,X3,tc_nat)
    | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X3,X1,tc_nat),X2,tc_nat),X4,tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X2,tc_nat),X4,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2447]) ).

cnf(c_0_2448_0,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(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),X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2448]) ).

cnf(c_0_2448_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__ring__strict(X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(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),X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2448]) ).

cnf(c_0_2449_0,axiom,
    ( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X4,X1,X3),X2,X3),X5,X3),X3) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X4,X2,X3),X5,X3)
    | ~ class_Ring__and__Field_Oring(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2449]) ).

cnf(c_0_2449_1,axiom,
    ( ~ class_Ring__and__Field_Oring(X3)
    | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X4,X1,X3),X2,X3),X5,X3),X3) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X4,X2,X3),X5,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2449]) ).

cnf(c_0_2450_0,axiom,
    ( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X5,X2,X3),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,X5,X3),X2,X3),X4,X3),X3) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3)
    | ~ class_Ring__and__Field_Oring(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2450]) ).

cnf(c_0_2450_1,axiom,
    ( ~ class_Ring__and__Field_Oring(X3)
    | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X5,X2,X3),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,X5,X3),X2,X3),X4,X3),X3) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2450]) ).

cnf(c_0_2451_0,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,c_Divides_Odiv__class_Omod(X4,X1,tc_nat),tc_nat),X2,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_2451]) ).

cnf(c_0_2451_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
    | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,c_Divides_Odiv__class_Omod(X4,X1,tc_nat),tc_nat),X2,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_2451]) ).

cnf(c_0_2451_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_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,c_Divides_Odiv__class_Omod(X4,X1,tc_nat),tc_nat),X2,tc_nat),c_HOL_Otimes__class_Otimes(X3,X1,tc_nat),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2451]) ).

cnf(c_0_2452_0,axiom,
    ( X1 = c_HOL_Ozero__class_Ozero(X2)
    | ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X1,X2),c_HOL_Otimes__class_Otimes(X3,X3,X2),X2),c_HOL_Ozero__class_Ozero(X2),X2)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2452]) ).

cnf(c_0_2452_1,axiom,
    ( ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X1,X2),c_HOL_Otimes__class_Otimes(X3,X3,X2),X2),c_HOL_Ozero__class_Ozero(X2),X2)
    | X1 = c_HOL_Ozero__class_Ozero(X2)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2452]) ).

cnf(c_0_2452_2,axiom,
    ( ~ class_Ring__and__Field_Oordered__ring__strict(X2)
    | ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X1,X2),c_HOL_Otimes__class_Otimes(X3,X3,X2),X2),c_HOL_Ozero__class_Ozero(X2),X2)
    | X1 = c_HOL_Ozero__class_Ozero(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2452]) ).

cnf(c_0_2453_0,axiom,
    ( X3 = c_HOL_Ozero__class_Ozero(X2)
    | ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X1,X2),c_HOL_Otimes__class_Otimes(X3,X3,X2),X2),c_HOL_Ozero__class_Ozero(X2),X2)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2453]) ).

cnf(c_0_2453_1,axiom,
    ( ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X1,X2),c_HOL_Otimes__class_Otimes(X3,X3,X2),X2),c_HOL_Ozero__class_Ozero(X2),X2)
    | X3 = c_HOL_Ozero__class_Ozero(X2)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2453]) ).

cnf(c_0_2453_2,axiom,
    ( ~ class_Ring__and__Field_Oordered__ring__strict(X2)
    | ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X1,X2),c_HOL_Otimes__class_Otimes(X3,X3,X2),X2),c_HOL_Ozero__class_Ozero(X2),X2)
    | X3 = c_HOL_Ozero__class_Ozero(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2453]) ).

cnf(c_0_2454_0,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X1,X2),c_HOL_Otimes__class_Otimes(X3,X3,X2),X2),c_HOL_Ozero__class_Ozero(X2),X2)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2454]) ).

cnf(c_0_2454_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__ring__strict(X2)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X1,X2),c_HOL_Otimes__class_Otimes(X3,X3,X2),X2),c_HOL_Ozero__class_Ozero(X2),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2454]) ).

cnf(c_0_2455_0,axiom,
    ( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),X3,tc_nat),X4,tc_nat) = X5
    | ~ c_lessequals(X2,X1,tc_nat)
    | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),X4,tc_nat) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X3,tc_nat),X5,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2455]) ).

cnf(c_0_2455_1,axiom,
    ( ~ c_lessequals(X2,X1,tc_nat)
    | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),X3,tc_nat),X4,tc_nat) = X5
    | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),X4,tc_nat) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X3,tc_nat),X5,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2455]) ).

cnf(c_0_2455_2,axiom,
    ( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),X4,tc_nat) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X3,tc_nat),X5,tc_nat)
    | ~ c_lessequals(X2,X1,tc_nat)
    | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),X3,tc_nat),X4,tc_nat) = X5 ),
    inference(literals_permutation,[status(thm)],[c_0_2455]) ).

cnf(c_0_2456_0,axiom,
    ( X1 = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X3,tc_nat),X4,tc_nat),X5,tc_nat)
    | ~ c_lessequals(X3,X2,tc_nat)
    | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X4,tc_nat),X1,tc_nat) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X4,tc_nat),X5,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2456]) ).

cnf(c_0_2456_1,axiom,
    ( ~ c_lessequals(X3,X2,tc_nat)
    | X1 = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X3,tc_nat),X4,tc_nat),X5,tc_nat)
    | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X4,tc_nat),X1,tc_nat) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X4,tc_nat),X5,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2456]) ).

cnf(c_0_2456_2,axiom,
    ( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X4,tc_nat),X1,tc_nat) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X4,tc_nat),X5,tc_nat)
    | ~ c_lessequals(X3,X2,tc_nat)
    | X1 = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X3,tc_nat),X4,tc_nat),X5,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2456]) ).

cnf(c_0_2457_0,axiom,
    ( c_lessequals(c_Orderings_Oord__class_Omax(c_Orderings_Oord__class_Omin(X1,X2,X3),c_Orderings_Oord__class_Omin(X1,X4,X3),X3),c_Orderings_Oord__class_Omin(X1,c_Orderings_Oord__class_Omax(X2,X4,X3),X3),X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2457]) ).

cnf(c_0_2457_1,axiom,
    ( ~ class_Orderings_Olinorder(X3)
    | c_lessequals(c_Orderings_Oord__class_Omax(c_Orderings_Oord__class_Omin(X1,X2,X3),c_Orderings_Oord__class_Omin(X1,X4,X3),X3),c_Orderings_Oord__class_Omin(X1,c_Orderings_Oord__class_Omax(X2,X4,X3),X3),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2457]) ).

cnf(c_0_2458_0,axiom,
    ( c_lessequals(c_Orderings_Oord__class_Omax(X1,c_Orderings_Oord__class_Omin(X2,X3,X4),X4),c_Orderings_Oord__class_Omin(c_Orderings_Oord__class_Omax(X1,X2,X4),c_Orderings_Oord__class_Omax(X1,X3,X4),X4),X4)
    | ~ class_Orderings_Olinorder(X4) ),
    inference(literals_permutation,[status(thm)],[c_0_2458]) ).

cnf(c_0_2458_1,axiom,
    ( ~ class_Orderings_Olinorder(X4)
    | c_lessequals(c_Orderings_Oord__class_Omax(X1,c_Orderings_Oord__class_Omin(X2,X3,X4),X4),c_Orderings_Oord__class_Omin(c_Orderings_Oord__class_Omax(X1,X2,X4),c_Orderings_Oord__class_Omax(X1,X3,X4),X4),X4) ),
    inference(literals_permutation,[status(thm)],[c_0_2458]) ).

cnf(c_0_2459_0,axiom,
    ( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,X2,X3),X4,X3),X5,X3) = X6
    | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X4,X3),X5,X3) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X4,X3),X6,X3)
    | ~ class_Ring__and__Field_Oring(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2459]) ).

cnf(c_0_2459_1,axiom,
    ( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X4,X3),X5,X3) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X4,X3),X6,X3)
    | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,X2,X3),X4,X3),X5,X3) = X6
    | ~ class_Ring__and__Field_Oring(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2459]) ).

cnf(c_0_2459_2,axiom,
    ( ~ class_Ring__and__Field_Oring(X3)
    | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X4,X3),X5,X3) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X4,X3),X6,X3)
    | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,X2,X3),X4,X3),X5,X3) = X6 ),
    inference(literals_permutation,[status(thm)],[c_0_2459]) ).

cnf(c_0_2460_0,axiom,
    ( X1 = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X3,X4),X5,X4),X6,X4)
    | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X5,X4),X1,X4) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X5,X4),X6,X4)
    | ~ class_Ring__and__Field_Oring(X4) ),
    inference(literals_permutation,[status(thm)],[c_0_2460]) ).

cnf(c_0_2460_1,axiom,
    ( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X5,X4),X1,X4) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X5,X4),X6,X4)
    | X1 = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X3,X4),X5,X4),X6,X4)
    | ~ class_Ring__and__Field_Oring(X4) ),
    inference(literals_permutation,[status(thm)],[c_0_2460]) ).

cnf(c_0_2460_2,axiom,
    ( ~ class_Ring__and__Field_Oring(X4)
    | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X5,X4),X1,X4) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X5,X4),X6,X4)
    | X1 = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X3,X4),X5,X4),X6,X4) ),
    inference(literals_permutation,[status(thm)],[c_0_2460]) ).

cnf(c_0_2461_0,axiom,
    ( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X4,X2,X3),X5,X3),X3) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X1,X4,X3),X2,X3),X5,X3)
    | ~ class_Ring__and__Field_Osemiring(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2461]) ).

cnf(c_0_2461_1,axiom,
    ( ~ class_Ring__and__Field_Osemiring(X3)
    | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X4,X2,X3),X5,X3),X3) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X1,X4,X3),X2,X3),X5,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2461]) ).

cnf(c_0_2462_0,axiom,
    ( X1 = X2
    | X3 = X4
    | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X3,X5),c_HOL_Otimes__class_Otimes(X2,X4,X5),X5) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X4,X5),c_HOL_Otimes__class_Otimes(X2,X3,X5),X5)
    | ~ class_Int_Onumber__ring(X5)
    | ~ class_Ring__and__Field_Oidom(X5) ),
    inference(literals_permutation,[status(thm)],[c_0_2462]) ).

cnf(c_0_2462_1,axiom,
    ( X3 = X4
    | X1 = X2
    | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X3,X5),c_HOL_Otimes__class_Otimes(X2,X4,X5),X5) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X4,X5),c_HOL_Otimes__class_Otimes(X2,X3,X5),X5)
    | ~ class_Int_Onumber__ring(X5)
    | ~ class_Ring__and__Field_Oidom(X5) ),
    inference(literals_permutation,[status(thm)],[c_0_2462]) ).

cnf(c_0_2462_2,axiom,
    ( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X3,X5),c_HOL_Otimes__class_Otimes(X2,X4,X5),X5) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X4,X5),c_HOL_Otimes__class_Otimes(X2,X3,X5),X5)
    | X3 = X4
    | X1 = X2
    | ~ class_Int_Onumber__ring(X5)
    | ~ class_Ring__and__Field_Oidom(X5) ),
    inference(literals_permutation,[status(thm)],[c_0_2462]) ).

cnf(c_0_2462_3,axiom,
    ( ~ class_Int_Onumber__ring(X5)
    | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X3,X5),c_HOL_Otimes__class_Otimes(X2,X4,X5),X5) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X4,X5),c_HOL_Otimes__class_Otimes(X2,X3,X5),X5)
    | X3 = X4
    | X1 = X2
    | ~ class_Ring__and__Field_Oidom(X5) ),
    inference(literals_permutation,[status(thm)],[c_0_2462]) ).

cnf(c_0_2462_4,axiom,
    ( ~ class_Ring__and__Field_Oidom(X5)
    | ~ class_Int_Onumber__ring(X5)
    | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X3,X5),c_HOL_Otimes__class_Otimes(X2,X4,X5),X5) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X4,X5),c_HOL_Otimes__class_Otimes(X2,X3,X5),X5)
    | X3 = X4
    | X1 = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_2462]) ).

cnf(c_0_2463_0,axiom,
    ( X1 = X2
    | X3 = X4
    | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X3,X5),c_HOL_Otimes__class_Otimes(X2,X4,X5),X5) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X4,X5),c_HOL_Otimes__class_Otimes(X2,X3,X5),X5)
    | ~ class_Int_Onumber__ring(X5)
    | ~ class_Ring__and__Field_Oidom(X5) ),
    inference(literals_permutation,[status(thm)],[c_0_2463]) ).

cnf(c_0_2463_1,axiom,
    ( X3 = X4
    | X1 = X2
    | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X3,X5),c_HOL_Otimes__class_Otimes(X2,X4,X5),X5) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X4,X5),c_HOL_Otimes__class_Otimes(X2,X3,X5),X5)
    | ~ class_Int_Onumber__ring(X5)
    | ~ class_Ring__and__Field_Oidom(X5) ),
    inference(literals_permutation,[status(thm)],[c_0_2463]) ).

cnf(c_0_2463_2,axiom,
    ( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X3,X5),c_HOL_Otimes__class_Otimes(X2,X4,X5),X5) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X4,X5),c_HOL_Otimes__class_Otimes(X2,X3,X5),X5)
    | X3 = X4
    | X1 = X2
    | ~ class_Int_Onumber__ring(X5)
    | ~ class_Ring__and__Field_Oidom(X5) ),
    inference(literals_permutation,[status(thm)],[c_0_2463]) ).

cnf(c_0_2463_3,axiom,
    ( ~ class_Int_Onumber__ring(X5)
    | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X3,X5),c_HOL_Otimes__class_Otimes(X2,X4,X5),X5) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X4,X5),c_HOL_Otimes__class_Otimes(X2,X3,X5),X5)
    | X3 = X4
    | X1 = X2
    | ~ class_Ring__and__Field_Oidom(X5) ),
    inference(literals_permutation,[status(thm)],[c_0_2463]) ).

cnf(c_0_2463_4,axiom,
    ( ~ class_Ring__and__Field_Oidom(X5)
    | ~ class_Int_Onumber__ring(X5)
    | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X3,X5),c_HOL_Otimes__class_Otimes(X2,X4,X5),X5) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X4,X5),c_HOL_Otimes__class_Otimes(X2,X3,X5),X5)
    | X3 = X4
    | X1 = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_2463]) ).

cnf(c_0_2464_0,axiom,
    ( X1 = X2
    | X3 = X4
    | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),c_HOL_Otimes__class_Otimes(X2,X4,tc_nat),tc_nat) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X4,tc_nat),c_HOL_Otimes__class_Otimes(X2,X3,tc_nat),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2464]) ).

cnf(c_0_2464_1,axiom,
    ( X3 = X4
    | X1 = X2
    | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),c_HOL_Otimes__class_Otimes(X2,X4,tc_nat),tc_nat) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X4,tc_nat),c_HOL_Otimes__class_Otimes(X2,X3,tc_nat),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2464]) ).

cnf(c_0_2464_2,axiom,
    ( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),c_HOL_Otimes__class_Otimes(X2,X4,tc_nat),tc_nat) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X4,tc_nat),c_HOL_Otimes__class_Otimes(X2,X3,tc_nat),tc_nat)
    | X3 = X4
    | X1 = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_2464]) ).

cnf(c_0_2465_0,axiom,
    ( X1 = X2
    | X3 = X4
    | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),c_HOL_Otimes__class_Otimes(X2,X4,tc_nat),tc_nat) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X4,tc_nat),c_HOL_Otimes__class_Otimes(X2,X3,tc_nat),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2465]) ).

cnf(c_0_2465_1,axiom,
    ( X3 = X4
    | X1 = X2
    | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),c_HOL_Otimes__class_Otimes(X2,X4,tc_nat),tc_nat) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X4,tc_nat),c_HOL_Otimes__class_Otimes(X2,X3,tc_nat),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2465]) ).

cnf(c_0_2465_2,axiom,
    ( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),c_HOL_Otimes__class_Otimes(X2,X4,tc_nat),tc_nat) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X4,tc_nat),c_HOL_Otimes__class_Otimes(X2,X3,tc_nat),tc_nat)
    | X3 = X4
    | X1 = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_2465]) ).

cnf(c_0_2466_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_2466]) ).

cnf(c_0_2466_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_2466]) ).

cnf(c_0_2467_0,axiom,
    ( c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(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_Oplus__class_Oplus(X1,X2,X3),X4,X3)
    | ~ class_Divides_Osemiring__div(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2467]) ).

cnf(c_0_2467_1,axiom,
    ( ~ class_Divides_Osemiring__div(X3)
    | c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(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_Oplus__class_Oplus(X1,X2,X3),X4,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2467]) ).

cnf(c_0_2468_0,axiom,
    ( c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(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_Ominus__class_Ominus(X1,X2,X3),X4,X3)
    | ~ class_Divides_Oring__div(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2468]) ).

cnf(c_0_2468_1,axiom,
    ( ~ class_Divides_Oring__div(X3)
    | c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(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_Ominus__class_Ominus(X1,X2,X3),X4,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2468]) ).

cnf(c_0_2469_0,axiom,
    ( c_Lambda_Osubst(c_Lambda_Osubst(X3,c_Lambda_Olift(X4,X1),c_Suc(X2)),c_Lambda_Osubst(X5,X4,X2),X1) = c_Lambda_Osubst(c_Lambda_Osubst(X3,X5,X1),X4,X2)
    | ~ c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(X2,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2469]) ).

cnf(c_0_2469_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(X2,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat)
    | c_Lambda_Osubst(c_Lambda_Osubst(X3,c_Lambda_Olift(X4,X1),c_Suc(X2)),c_Lambda_Osubst(X5,X4,X2),X1) = c_Lambda_Osubst(c_Lambda_Osubst(X3,X5,X1),X4,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2469]) ).

cnf(c_0_2470_0,axiom,
    ( c_Lambda_Osubst(c_Lambda_Olift(X3,c_HOL_Oplus__class_Oplus(X2,c_HOL_Oone__class_Oone(tc_nat),tc_nat)),c_Lambda_Olift(X4,X2),X1) = c_Lambda_Olift(c_Lambda_Osubst(X3,X4,X1),X2)
    | ~ c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(X2,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2470]) ).

cnf(c_0_2470_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(X2,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat)
    | c_Lambda_Osubst(c_Lambda_Olift(X3,c_HOL_Oplus__class_Oplus(X2,c_HOL_Oone__class_Oone(tc_nat),tc_nat)),c_Lambda_Olift(X4,X2),X1) = c_Lambda_Olift(c_Lambda_Osubst(X3,X4,X1),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2470]) ).

cnf(c_0_2471_0,axiom,
    ( c_lessequals(c_HOL_Oplus__class_Oplus(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),c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2471]) ).

cnf(c_0_2471_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__ring__strict(X1)
    | c_lessequals(c_HOL_Oplus__class_Oplus(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),c_HOL_Ozero__class_Ozero(X1),X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2471]) ).

cnf(c_0_2472_0,axiom,
    ( c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X1,X2,X3),X4,X3) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(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_2472]) ).

cnf(c_0_2472_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_Oplus__class_Oplus(X1,X2,X3),X4,X3) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(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_2472]) ).

cnf(c_0_2472_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_Oplus__class_Oplus(X1,X2,X3),X4,X3) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X5,X6,X3),X4,X3)
    | ~ class_Divides_Osemiring__div(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2472]) ).

cnf(c_0_2472_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_Oplus__class_Oplus(X1,X2,X3),X4,X3) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X5,X6,X3),X4,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2472]) ).

cnf(c_0_2473_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_2473]) ).

cnf(c_0_2473_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_2473]) ).

cnf(c_0_2473_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_2473]) ).

cnf(c_0_2473_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_2473]) ).

cnf(c_0_2474_0,axiom,
    ( c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X1,X2,X3),X4,X3) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(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_Oring__div(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2474]) ).

cnf(c_0_2474_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_Ominus__class_Ominus(X1,X2,X3),X4,X3) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X5,X6,X3),X4,X3)
    | c_Divides_Odiv__class_Omod(X2,X4,X3) != c_Divides_Odiv__class_Omod(X6,X4,X3)
    | ~ class_Divides_Oring__div(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2474]) ).

cnf(c_0_2474_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_Ominus__class_Ominus(X1,X2,X3),X4,X3) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X5,X6,X3),X4,X3)
    | ~ class_Divides_Oring__div(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2474]) ).

cnf(c_0_2474_3,axiom,
    ( ~ class_Divides_Oring__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_Ominus__class_Ominus(X1,X2,X3),X4,X3) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X5,X6,X3),X4,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2474]) ).

cnf(c_0_2475_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_2475]) ).

cnf(c_0_2475_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_2475]) ).

cnf(c_0_2476_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_2476]) ).

cnf(c_0_2476_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_2476]) ).

cnf(c_0_2477_0,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X2,X5,X3),X3)
    | ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | ~ c_HOL_Oord__class_Oless(X4,X5,X3)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
    | ~ class_Ring__and__Field_Oordered__semiring__strict(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2477]) ).

cnf(c_0_2477_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,X5,X3),X3)
    | ~ c_HOL_Oord__class_Oless(X4,X5,X3)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
    | ~ class_Ring__and__Field_Oordered__semiring__strict(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2477]) ).

cnf(c_0_2477_2,axiom,
    ( ~ c_HOL_Oord__class_Oless(X4,X5,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,X5,X3),X3)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
    | ~ class_Ring__and__Field_Oordered__semiring__strict(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2477]) ).

cnf(c_0_2477_3,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3)
    | ~ c_HOL_Oord__class_Oless(X4,X5,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,X5,X3),X3)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
    | ~ class_Ring__and__Field_Oordered__semiring__strict(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2477]) ).

cnf(c_0_2477_4,axiom,
    ( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3)
    | ~ c_HOL_Oord__class_Oless(X4,X5,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,X5,X3),X3)
    | ~ class_Ring__and__Field_Oordered__semiring__strict(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2477]) ).

cnf(c_0_2477_5,axiom,
    ( ~ class_Ring__and__Field_Oordered__semiring__strict(X3)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3)
    | ~ c_HOL_Oord__class_Oless(X4,X5,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,X5,X3),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2477]) ).

cnf(c_0_2478_0,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X2,X5,X3),X3)
    | ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | ~ c_lessequals(X4,X5,X3)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X1,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_2478]) ).

cnf(c_0_2478_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,X5,X3),X3)
    | ~ c_lessequals(X4,X5,X3)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X1,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_2478]) ).

cnf(c_0_2478_2,axiom,
    ( ~ c_lessequals(X4,X5,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,X5,X3),X3)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X1,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_2478]) ).

cnf(c_0_2478_3,axiom,
    ( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X1,X3)
    | ~ c_lessequals(X4,X5,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,X5,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_2478]) ).

cnf(c_0_2478_4,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X4,X3)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X1,X3)
    | ~ c_lessequals(X4,X5,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,X5,X3),X3)
    | ~ class_Ring__and__Field_Oordered__semiring__strict(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2478]) ).

cnf(c_0_2478_5,axiom,
    ( ~ class_Ring__and__Field_Oordered__semiring__strict(X3)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X4,X3)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X1,X3)
    | ~ c_lessequals(X4,X5,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,X5,X3),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2478]) ).

cnf(c_0_2479_0,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X2,X5,X3),X3)
    | ~ c_lessequals(X1,X2,X3)
    | ~ c_HOL_Oord__class_Oless(X4,X5,X3)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X1,X3)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
    | ~ class_Ring__and__Field_Oordered__semiring__strict(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2479]) ).

cnf(c_0_2479_1,axiom,
    ( ~ c_lessequals(X1,X2,X3)
    | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X2,X5,X3),X3)
    | ~ c_HOL_Oord__class_Oless(X4,X5,X3)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X1,X3)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
    | ~ class_Ring__and__Field_Oordered__semiring__strict(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2479]) ).

cnf(c_0_2479_2,axiom,
    ( ~ c_HOL_Oord__class_Oless(X4,X5,X3)
    | ~ c_lessequals(X1,X2,X3)
    | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X2,X5,X3),X3)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X1,X3)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
    | ~ class_Ring__and__Field_Oordered__semiring__strict(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2479]) ).

cnf(c_0_2479_3,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X1,X3)
    | ~ c_HOL_Oord__class_Oless(X4,X5,X3)
    | ~ c_lessequals(X1,X2,X3)
    | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X2,X5,X3),X3)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
    | ~ class_Ring__and__Field_Oordered__semiring__strict(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2479]) ).

cnf(c_0_2479_4,axiom,
    ( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X1,X3)
    | ~ c_HOL_Oord__class_Oless(X4,X5,X3)
    | ~ c_lessequals(X1,X2,X3)
    | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X2,X5,X3),X3)
    | ~ class_Ring__and__Field_Oordered__semiring__strict(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2479]) ).

cnf(c_0_2479_5,axiom,
    ( ~ class_Ring__and__Field_Oordered__semiring__strict(X3)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X1,X3)
    | ~ c_HOL_Oord__class_Oless(X4,X5,X3)
    | ~ c_lessequals(X1,X2,X3)
    | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X2,X5,X3),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2479]) ).

cnf(c_0_2480_0,axiom,
    ( c_lessequals(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X2,X5,X3),X3)
    | ~ c_lessequals(X1,X2,X3)
    | ~ c_lessequals(X4,X5,X3)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X2,X3)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
    | ~ class_Ring__and__Field_Opordered__semiring(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2480]) ).

cnf(c_0_2480_1,axiom,
    ( ~ c_lessequals(X1,X2,X3)
    | c_lessequals(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X2,X5,X3),X3)
    | ~ c_lessequals(X4,X5,X3)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X2,X3)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
    | ~ class_Ring__and__Field_Opordered__semiring(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2480]) ).

cnf(c_0_2480_2,axiom,
    ( ~ c_lessequals(X4,X5,X3)
    | ~ c_lessequals(X1,X2,X3)
    | c_lessequals(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X2,X5,X3),X3)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X2,X3)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
    | ~ class_Ring__and__Field_Opordered__semiring(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2480]) ).

cnf(c_0_2480_3,axiom,
    ( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X2,X3)
    | ~ c_lessequals(X4,X5,X3)
    | ~ c_lessequals(X1,X2,X3)
    | c_lessequals(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X2,X5,X3),X3)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
    | ~ class_Ring__and__Field_Opordered__semiring(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2480]) ).

cnf(c_0_2480_4,axiom,
    ( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X2,X3)
    | ~ c_lessequals(X4,X5,X3)
    | ~ c_lessequals(X1,X2,X3)
    | c_lessequals(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X2,X5,X3),X3)
    | ~ class_Ring__and__Field_Opordered__semiring(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2480]) ).

cnf(c_0_2480_5,axiom,
    ( ~ class_Ring__and__Field_Opordered__semiring(X3)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X2,X3)
    | ~ c_lessequals(X4,X5,X3)
    | ~ c_lessequals(X1,X2,X3)
    | c_lessequals(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X2,X5,X3),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2480]) ).

cnf(c_0_2481_0,axiom,
    ( c_lessequals(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X2,X5,X3),X3)
    | ~ c_lessequals(X1,X2,X3)
    | ~ c_lessequals(X4,X5,X3)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X1,X3)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
    | ~ class_Ring__and__Field_Opordered__semiring(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2481]) ).

cnf(c_0_2481_1,axiom,
    ( ~ c_lessequals(X1,X2,X3)
    | c_lessequals(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X2,X5,X3),X3)
    | ~ c_lessequals(X4,X5,X3)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X1,X3)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
    | ~ class_Ring__and__Field_Opordered__semiring(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2481]) ).

cnf(c_0_2481_2,axiom,
    ( ~ c_lessequals(X4,X5,X3)
    | ~ c_lessequals(X1,X2,X3)
    | c_lessequals(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X2,X5,X3),X3)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X1,X3)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
    | ~ class_Ring__and__Field_Opordered__semiring(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2481]) ).

cnf(c_0_2481_3,axiom,
    ( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X1,X3)
    | ~ c_lessequals(X4,X5,X3)
    | ~ c_lessequals(X1,X2,X3)
    | c_lessequals(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X2,X5,X3),X3)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
    | ~ class_Ring__and__Field_Opordered__semiring(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2481]) ).

cnf(c_0_2481_4,axiom,
    ( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X1,X3)
    | ~ c_lessequals(X4,X5,X3)
    | ~ c_lessequals(X1,X2,X3)
    | c_lessequals(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X2,X5,X3),X3)
    | ~ class_Ring__and__Field_Opordered__semiring(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2481]) ).

cnf(c_0_2481_5,axiom,
    ( ~ class_Ring__and__Field_Opordered__semiring(X3)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X1,X3)
    | ~ c_lessequals(X4,X5,X3)
    | ~ c_lessequals(X1,X2,X3)
    | c_lessequals(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X2,X5,X3),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2481]) ).

cnf(c_0_2482_0,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X2,X5,X3),X3)
    | ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | ~ c_HOL_Oord__class_Oless(X4,X5,X3)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X1,X3)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
    | ~ class_Ring__and__Field_Oordered__semiring__strict(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2482]) ).

cnf(c_0_2482_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,X5,X3),X3)
    | ~ c_HOL_Oord__class_Oless(X4,X5,X3)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X1,X3)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
    | ~ class_Ring__and__Field_Oordered__semiring__strict(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2482]) ).

cnf(c_0_2482_2,axiom,
    ( ~ c_HOL_Oord__class_Oless(X4,X5,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,X5,X3),X3)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X1,X3)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
    | ~ class_Ring__and__Field_Oordered__semiring__strict(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2482]) ).

cnf(c_0_2482_3,axiom,
    ( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X1,X3)
    | ~ c_HOL_Oord__class_Oless(X4,X5,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,X5,X3),X3)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
    | ~ class_Ring__and__Field_Oordered__semiring__strict(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2482]) ).

cnf(c_0_2482_4,axiom,
    ( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X1,X3)
    | ~ c_HOL_Oord__class_Oless(X4,X5,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,X5,X3),X3)
    | ~ class_Ring__and__Field_Oordered__semiring__strict(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2482]) ).

cnf(c_0_2482_5,axiom,
    ( ~ class_Ring__and__Field_Oordered__semiring__strict(X3)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X1,X3)
    | ~ c_HOL_Oord__class_Oless(X4,X5,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,X5,X3),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2482]) ).

cnf(c_0_2483_0,axiom,
    ( c_lessequals(X2,X3,tc_nat)
    | ~ c_lessequals(X1,X2,tc_nat)
    | ~ c_lessequals(X1,X3,tc_nat)
    | ~ c_lessequals(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),c_HOL_Ominus__class_Ominus(X3,X1,tc_nat),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2483]) ).

cnf(c_0_2483_1,axiom,
    ( ~ c_lessequals(X1,X2,tc_nat)
    | c_lessequals(X2,X3,tc_nat)
    | ~ c_lessequals(X1,X3,tc_nat)
    | ~ c_lessequals(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),c_HOL_Ominus__class_Ominus(X3,X1,tc_nat),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2483]) ).

cnf(c_0_2483_2,axiom,
    ( ~ c_lessequals(X1,X3,tc_nat)
    | ~ c_lessequals(X1,X2,tc_nat)
    | c_lessequals(X2,X3,tc_nat)
    | ~ c_lessequals(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),c_HOL_Ominus__class_Ominus(X3,X1,tc_nat),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2483]) ).

cnf(c_0_2483_3,axiom,
    ( ~ c_lessequals(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),c_HOL_Ominus__class_Ominus(X3,X1,tc_nat),tc_nat)
    | ~ c_lessequals(X1,X3,tc_nat)
    | ~ c_lessequals(X1,X2,tc_nat)
    | c_lessequals(X2,X3,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2483]) ).

cnf(c_0_2484_0,axiom,
    ( c_HOL_Oord__class_Oless(X2,X3,tc_nat)
    | ~ c_lessequals(X1,X2,tc_nat)
    | ~ c_lessequals(X1,X3,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),c_HOL_Ominus__class_Ominus(X3,X1,tc_nat),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2484]) ).

cnf(c_0_2484_1,axiom,
    ( ~ c_lessequals(X1,X2,tc_nat)
    | c_HOL_Oord__class_Oless(X2,X3,tc_nat)
    | ~ c_lessequals(X1,X3,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),c_HOL_Ominus__class_Ominus(X3,X1,tc_nat),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2484]) ).

cnf(c_0_2484_2,axiom,
    ( ~ c_lessequals(X1,X3,tc_nat)
    | ~ c_lessequals(X1,X2,tc_nat)
    | c_HOL_Oord__class_Oless(X2,X3,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),c_HOL_Ominus__class_Ominus(X3,X1,tc_nat),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2484]) ).

cnf(c_0_2484_3,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),c_HOL_Ominus__class_Ominus(X3,X1,tc_nat),tc_nat)
    | ~ c_lessequals(X1,X3,tc_nat)
    | ~ c_lessequals(X1,X2,tc_nat)
    | c_HOL_Oord__class_Oless(X2,X3,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2484]) ).

cnf(c_0_2485_0,axiom,
    ( X1 = c_HOL_Ozero__class_Ozero(X2)
    | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X1,X2),c_HOL_Otimes__class_Otimes(X3,X3,X2),X2),X2)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2485]) ).

cnf(c_0_2485_1,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X1,X2),c_HOL_Otimes__class_Otimes(X3,X3,X2),X2),X2)
    | X1 = c_HOL_Ozero__class_Ozero(X2)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2485]) ).

cnf(c_0_2485_2,axiom,
    ( ~ class_Ring__and__Field_Oordered__ring__strict(X2)
    | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X1,X2),c_HOL_Otimes__class_Otimes(X3,X3,X2),X2),X2)
    | X1 = c_HOL_Ozero__class_Ozero(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2485]) ).

cnf(c_0_2486_0,axiom,
    ( X1 = c_HOL_Ozero__class_Ozero(X2)
    | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X3,X2),c_HOL_Otimes__class_Otimes(X1,X1,X2),X2),X2)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2486]) ).

cnf(c_0_2486_1,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X3,X2),c_HOL_Otimes__class_Otimes(X1,X1,X2),X2),X2)
    | X1 = c_HOL_Ozero__class_Ozero(X2)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2486]) ).

cnf(c_0_2486_2,axiom,
    ( ~ class_Ring__and__Field_Oordered__ring__strict(X2)
    | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X3,X2),c_HOL_Otimes__class_Otimes(X1,X1,X2),X2),X2)
    | X1 = c_HOL_Ozero__class_Ozero(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2486]) ).

cnf(c_0_2487_0,axiom,
    ( c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X2,X1),c_HOL_Otimes__class_Otimes(X3,X3,X1),X1),X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2487]) ).

cnf(c_0_2487_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__ring__strict(X1)
    | c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X2,X1),c_HOL_Otimes__class_Otimes(X3,X3,X1),X1),X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2487]) ).

cnf(c_0_2488_0,axiom,
    ( c_Divides_Odiv__class_Omod(X1,X2,tc_nat) = c_Divides_Odiv__class_Omod(X3,X2,tc_nat)
    | c_HOL_Oplus__class_Oplus(X1,c_HOL_Otimes__class_Otimes(X2,X4,tc_nat),tc_nat) != c_HOL_Oplus__class_Oplus(X3,c_HOL_Otimes__class_Otimes(X2,X5,tc_nat),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2488]) ).

cnf(c_0_2488_1,axiom,
    ( c_HOL_Oplus__class_Oplus(X1,c_HOL_Otimes__class_Otimes(X2,X4,tc_nat),tc_nat) != c_HOL_Oplus__class_Oplus(X3,c_HOL_Otimes__class_Otimes(X2,X5,tc_nat),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_2488]) ).

cnf(c_0_2489_0,axiom,
    ( c_Lambda_Osubst(c_Lambda_Olift(X3,X1),c_Lambda_Olift(X4,X1),c_HOL_Oplus__class_Oplus(X2,c_HOL_Oone__class_Oone(tc_nat),tc_nat)) = c_Lambda_Olift(c_Lambda_Osubst(X3,X4,X2),X1)
    | ~ c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(X2,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2489]) ).

cnf(c_0_2489_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(X2,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat)
    | c_Lambda_Osubst(c_Lambda_Olift(X3,X1),c_Lambda_Olift(X4,X1),c_HOL_Oplus__class_Oplus(X2,c_HOL_Oone__class_Oone(tc_nat),tc_nat)) = c_Lambda_Olift(c_Lambda_Osubst(X3,X4,X2),X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2489]) ).

cnf(c_0_2490_0,axiom,
    ( 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)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X2,X3)
    | ~ class_Ring__and__Field_Oordered__semiring__strict(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2490]) ).

cnf(c_0_2490_1,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(X1,X4,X3)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X2,X3)
    | ~ class_Ring__and__Field_Oordered__semiring__strict(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2490]) ).

cnf(c_0_2490_2,axiom,
    ( ~ c_lessequals(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)
    | c_HOL_Oord__class_Oless(X1,X4,X3)
    | ~ class_Ring__and__Field_Oordered__semiring__strict(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2490]) ).

cnf(c_0_2490_3,axiom,
    ( ~ class_Ring__and__Field_Oordered__semiring__strict(X3)
    | ~ c_lessequals(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)
    | c_HOL_Oord__class_Oless(X1,X4,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2490]) ).

cnf(c_0_2491_0,axiom,
    ( 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)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X1,X3)
    | ~ class_Ring__and__Field_Oordered__semiring__strict(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2491]) ).

cnf(c_0_2491_1,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(X2,X4,X3)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X1,X3)
    | ~ class_Ring__and__Field_Oordered__semiring__strict(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2491]) ).

cnf(c_0_2491_2,axiom,
    ( ~ c_lessequals(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)
    | c_HOL_Oord__class_Oless(X2,X4,X3)
    | ~ class_Ring__and__Field_Oordered__semiring__strict(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2491]) ).

cnf(c_0_2491_3,axiom,
    ( ~ class_Ring__and__Field_Oordered__semiring__strict(X3)
    | ~ c_lessequals(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)
    | c_HOL_Oord__class_Oless(X2,X4,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2491]) ).

cnf(c_0_2492_0,axiom,
    ( 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)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X2,X3)
    | ~ class_Ring__and__Field_Oordered__semiring(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2492]) ).

cnf(c_0_2492_1,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(X1,X4,X3)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X2,X3)
    | ~ class_Ring__and__Field_Oordered__semiring(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2492]) ).

cnf(c_0_2492_2,axiom,
    ( ~ c_lessequals(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)
    | c_HOL_Oord__class_Oless(X1,X4,X3)
    | ~ class_Ring__and__Field_Oordered__semiring(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2492]) ).

cnf(c_0_2492_3,axiom,
    ( ~ class_Ring__and__Field_Oordered__semiring(X3)
    | ~ c_lessequals(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)
    | c_HOL_Oord__class_Oless(X1,X4,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2492]) ).

cnf(c_0_2493_0,axiom,
    ( 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)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X1,X3)
    | ~ class_Ring__and__Field_Oordered__semiring(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2493]) ).

cnf(c_0_2493_1,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(X2,X4,X3)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X1,X3)
    | ~ class_Ring__and__Field_Oordered__semiring(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2493]) ).

cnf(c_0_2493_2,axiom,
    ( ~ c_lessequals(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)
    | c_HOL_Oord__class_Oless(X2,X4,X3)
    | ~ class_Ring__and__Field_Oordered__semiring(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2493]) ).

cnf(c_0_2493_3,axiom,
    ( ~ class_Ring__and__Field_Oordered__semiring(X3)
    | ~ c_lessequals(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)
    | c_HOL_Oord__class_Oless(X2,X4,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2493]) ).

cnf(c_0_2494_0,axiom,
    ( c_lessequals(X4,X3,X2)
    | ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
    | ~ c_lessequals(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_2494]) ).

cnf(c_0_2494_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
    | c_lessequals(X4,X3,X2)
    | ~ c_lessequals(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_2494]) ).

cnf(c_0_2494_2,axiom,
    ( ~ c_lessequals(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_lessequals(X4,X3,X2)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2494]) ).

cnf(c_0_2494_3,axiom,
    ( ~ class_Ring__and__Field_Oordered__ring__strict(X2)
    | ~ c_lessequals(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_lessequals(X4,X3,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2494]) ).

cnf(c_0_2495_0,axiom,
    ( c_lessequals(X3,X4,X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | ~ c_lessequals(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_2495]) ).

cnf(c_0_2495_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | c_lessequals(X3,X4,X1)
    | ~ c_lessequals(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_2495]) ).

cnf(c_0_2495_2,axiom,
    ( ~ c_lessequals(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_lessequals(X3,X4,X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2495]) ).

cnf(c_0_2495_3,axiom,
    ( ~ class_Ring__and__Field_Oordered__ring__strict(X1)
    | ~ c_lessequals(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_lessequals(X3,X4,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2495]) ).

cnf(c_0_2496_0,axiom,
    ( c_lessequals(X2,X4,X3)
    | ~ c_lessequals(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X1,X4,X3),X3)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X1,X3)
    | ~ class_Ring__and__Field_Oordered__semiring__strict(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2496]) ).

cnf(c_0_2496_1,axiom,
    ( ~ c_lessequals(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X1,X4,X3),X3)
    | c_lessequals(X2,X4,X3)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X1,X3)
    | ~ class_Ring__and__Field_Oordered__semiring__strict(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2496]) ).

cnf(c_0_2496_2,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X1,X3)
    | ~ c_lessequals(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X1,X4,X3),X3)
    | c_lessequals(X2,X4,X3)
    | ~ class_Ring__and__Field_Oordered__semiring__strict(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2496]) ).

cnf(c_0_2496_3,axiom,
    ( ~ class_Ring__and__Field_Oordered__semiring__strict(X3)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X1,X3)
    | ~ c_lessequals(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X1,X4,X3),X3)
    | c_lessequals(X2,X4,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2496]) ).

cnf(c_0_2497_0,axiom,
    ( c_lessequals(X1,X4,X3)
    | ~ c_lessequals(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X4,X2,X3),X3)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3)
    | ~ class_Ring__and__Field_Oordered__semiring__strict(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2497]) ).

cnf(c_0_2497_1,axiom,
    ( ~ c_lessequals(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X4,X2,X3),X3)
    | c_lessequals(X1,X4,X3)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3)
    | ~ class_Ring__and__Field_Oordered__semiring__strict(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2497]) ).

cnf(c_0_2497_2,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3)
    | ~ c_lessequals(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X4,X2,X3),X3)
    | c_lessequals(X1,X4,X3)
    | ~ class_Ring__and__Field_Oordered__semiring__strict(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2497]) ).

cnf(c_0_2497_3,axiom,
    ( ~ class_Ring__and__Field_Oordered__semiring__strict(X3)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3)
    | ~ c_lessequals(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X4,X2,X3),X3)
    | c_lessequals(X1,X4,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2497]) ).

cnf(c_0_2498_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_2498]) ).

cnf(c_0_2498_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_2498]) ).

cnf(c_0_2498_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_2498]) ).

cnf(c_0_2498_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_2498]) ).

cnf(c_0_2499_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_2499]) ).

cnf(c_0_2499_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_2499]) ).

cnf(c_0_2499_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_2499]) ).

cnf(c_0_2499_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_2499]) ).

cnf(c_0_2500_0,axiom,
    ( c_lessequals(X1,X3,tc_nat)
    | ~ c_lessequals(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_2500]) ).

cnf(c_0_2500_1,axiom,
    ( ~ c_lessequals(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X3,X2,tc_nat),tc_nat)
    | c_lessequals(X1,X3,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2500]) ).

cnf(c_0_2500_2,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat)
    | ~ c_lessequals(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X3,X2,tc_nat),tc_nat)
    | c_lessequals(X1,X3,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2500]) ).

cnf(c_0_2501_0,axiom,
    ( c_lessequals(X2,X3,tc_nat)
    | ~ c_lessequals(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_2501]) ).

cnf(c_0_2501_1,axiom,
    ( ~ c_lessequals(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat)
    | c_lessequals(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_2501]) ).

cnf(c_0_2501_2,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
    | ~ c_lessequals(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat)
    | c_lessequals(X2,X3,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2501]) ).

cnf(c_0_2502_0,axiom,
    ( c_lessequals(X2,X3,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
    | ~ c_lessequals(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_2502]) ).

cnf(c_0_2502_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
    | c_lessequals(X2,X3,tc_nat)
    | ~ c_lessequals(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_2502]) ).

cnf(c_0_2502_2,axiom,
    ( ~ c_lessequals(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_lessequals(X2,X3,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2502]) ).

cnf(c_0_2503_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_2503]) ).

cnf(c_0_2503_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_2503]) ).

cnf(c_0_2503_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_2503]) ).

cnf(c_0_2504_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_2504]) ).

cnf(c_0_2504_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_2504]) ).

cnf(c_0_2504_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_2504]) ).

cnf(c_0_2504_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_2504]) ).

cnf(c_0_2505_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_2505]) ).

cnf(c_0_2505_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_2505]) ).

cnf(c_0_2505_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_2505]) ).

cnf(c_0_2505_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_2505]) ).

cnf(c_0_2506_0,axiom,
    ( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X1,X4,X3),X3) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X1,X2,X3),X3)
    | ~ class_Int_Onumber__ring(X3)
    | ~ class_Ring__and__Field_Oidom(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2506]) ).

cnf(c_0_2506_1,axiom,
    ( ~ class_Int_Onumber__ring(X3)
    | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X1,X4,X3),X3) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X1,X2,X3),X3)
    | ~ class_Ring__and__Field_Oidom(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2506]) ).

cnf(c_0_2506_2,axiom,
    ( ~ class_Ring__and__Field_Oidom(X3)
    | ~ class_Int_Onumber__ring(X3)
    | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X1,X4,X3),X3) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X1,X2,X3),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2506]) ).

cnf(c_0_2507_0,axiom,
    ( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X1,X4,X3),X3) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X1,X2,X3),X3)
    | ~ class_Int_Onumber__ring(X3)
    | ~ class_Ring__and__Field_Oidom(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2507]) ).

cnf(c_0_2507_1,axiom,
    ( ~ class_Int_Onumber__ring(X3)
    | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X1,X4,X3),X3) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X1,X2,X3),X3)
    | ~ class_Ring__and__Field_Oidom(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2507]) ).

cnf(c_0_2507_2,axiom,
    ( ~ class_Ring__and__Field_Oidom(X3)
    | ~ class_Int_Onumber__ring(X3)
    | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X1,X4,X3),X3) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X1,X2,X3),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2507]) ).

cnf(c_0_2508_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_2508]) ).

cnf(c_0_2508_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_2508]) ).

cnf(c_0_2508_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_2508]) ).

cnf(c_0_2508_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_2508]) ).

cnf(c_0_2509_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_2509]) ).

cnf(c_0_2509_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_2509]) ).

cnf(c_0_2509_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_2509]) ).

cnf(c_0_2509_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_2509]) ).

cnf(c_0_2510_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_2510]) ).

cnf(c_0_2510_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_2510]) ).

cnf(c_0_2510_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_2510]) ).

cnf(c_0_2510_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_2510]) ).

cnf(c_0_2511_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_2511]) ).

cnf(c_0_2511_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_2511]) ).

cnf(c_0_2511_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_2511]) ).

cnf(c_0_2511_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_2511]) ).

cnf(c_0_2512_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_2512]) ).

cnf(c_0_2512_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_2512]) ).

cnf(c_0_2513_0,axiom,
    ( c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(c_Divides_Odiv__class_Omod(X1,X4,X3),X2,X3),X4,X3) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X1,X2,X3),X4,X3)
    | ~ class_Divides_Oring__div(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2513]) ).

cnf(c_0_2513_1,axiom,
    ( ~ class_Divides_Oring__div(X3)
    | c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(c_Divides_Odiv__class_Omod(X1,X4,X3),X2,X3),X4,X3) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X1,X2,X3),X4,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2513]) ).

cnf(c_0_2514_0,axiom,
    ( c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X1,c_Divides_Odiv__class_Omod(X2,X4,X3),X3),X4,X3) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X1,X2,X3),X4,X3)
    | ~ class_Divides_Oring__div(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2514]) ).

cnf(c_0_2514_1,axiom,
    ( ~ class_Divides_Oring__div(X3)
    | c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X1,c_Divides_Odiv__class_Omod(X2,X4,X3),X3),X4,X3) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X1,X2,X3),X4,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2514]) ).

cnf(c_0_2515_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_2515]) ).

cnf(c_0_2515_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_2515]) ).

cnf(c_0_2516_0,axiom,
    ( c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(X1,X4,X3),X2,X3),X4,X3) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X1,X2,X3),X4,X3)
    | ~ class_Divides_Osemiring__div(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2516]) ).

cnf(c_0_2516_1,axiom,
    ( ~ class_Divides_Osemiring__div(X3)
    | c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(X1,X4,X3),X2,X3),X4,X3) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X1,X2,X3),X4,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2516]) ).

cnf(c_0_2517_0,axiom,
    ( c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X1,c_Divides_Odiv__class_Omod(X2,X4,X3),X3),X4,X3) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X1,X2,X3),X4,X3)
    | ~ class_Divides_Osemiring__div(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2517]) ).

cnf(c_0_2517_1,axiom,
    ( ~ class_Divides_Osemiring__div(X3)
    | c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X1,c_Divides_Odiv__class_Omod(X2,X4,X3),X3),X4,X3) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X1,X2,X3),X4,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2517]) ).

cnf(c_0_2518_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_2518]) ).

cnf(c_0_2518_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_2518]) ).

cnf(c_0_2519_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_2519]) ).

cnf(c_0_2519_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_2519]) ).

cnf(c_0_2520_0,axiom,
    ( c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X2,X3),c_HOL_Oplus__class_Oplus(X4,X5,X3),X3) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X4,X3),c_HOL_Oplus__class_Oplus(X2,X5,X3),X3)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2520]) ).

cnf(c_0_2520_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
    | c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X2,X3),c_HOL_Oplus__class_Oplus(X4,X5,X3),X3) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X4,X3),c_HOL_Oplus__class_Oplus(X2,X5,X3),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2520]) ).

cnf(c_0_2521_0,axiom,
    ( c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(X1,X2,X3),X4,X3),X2,X3) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X1,X4,X3),X2,X3)
    | ~ class_Divides_Osemiring__div(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2521]) ).

cnf(c_0_2521_1,axiom,
    ( ~ class_Divides_Osemiring__div(X3)
    | c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(X1,X2,X3),X4,X3),X2,X3) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X1,X4,X3),X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2521]) ).

cnf(c_0_2522_0,axiom,
    ( c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X1,c_Divides_Odiv__class_Omod(X2,X3,X4),X4),X3,X4) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X1,X2,X4),X3,X4)
    | ~ class_Divides_Osemiring__div(X4) ),
    inference(literals_permutation,[status(thm)],[c_0_2522]) ).

cnf(c_0_2522_1,axiom,
    ( ~ class_Divides_Osemiring__div(X4)
    | c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X1,c_Divides_Odiv__class_Omod(X2,X3,X4),X4),X3,X4) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X1,X2,X4),X3,X4) ),
    inference(literals_permutation,[status(thm)],[c_0_2522]) ).

cnf(c_0_2523_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_2523]) ).

cnf(c_0_2523_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_2523]) ).

cnf(c_0_2523_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_2523]) ).

cnf(c_0_2523_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_2523]) ).

cnf(c_0_2524_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_2524]) ).

cnf(c_0_2524_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_2524]) ).

cnf(c_0_2524_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_2524]) ).

cnf(c_0_2524_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_2524]) ).

cnf(c_0_2525_0,axiom,
    ( X1 = c_HOL_Ozero__class_Ozero(X2)
    | X3 = X4
    | c_HOL_Oplus__class_Oplus(X5,c_HOL_Otimes__class_Otimes(X1,X3,X2),X2) != c_HOL_Oplus__class_Oplus(X5,c_HOL_Otimes__class_Otimes(X1,X4,X2),X2)
    | ~ class_Int_Onumber__ring(X2)
    | ~ class_Ring__and__Field_Oidom(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2525]) ).

cnf(c_0_2525_1,axiom,
    ( X3 = X4
    | X1 = c_HOL_Ozero__class_Ozero(X2)
    | c_HOL_Oplus__class_Oplus(X5,c_HOL_Otimes__class_Otimes(X1,X3,X2),X2) != c_HOL_Oplus__class_Oplus(X5,c_HOL_Otimes__class_Otimes(X1,X4,X2),X2)
    | ~ class_Int_Onumber__ring(X2)
    | ~ class_Ring__and__Field_Oidom(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2525]) ).

cnf(c_0_2525_2,axiom,
    ( c_HOL_Oplus__class_Oplus(X5,c_HOL_Otimes__class_Otimes(X1,X3,X2),X2) != c_HOL_Oplus__class_Oplus(X5,c_HOL_Otimes__class_Otimes(X1,X4,X2),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_2525]) ).

cnf(c_0_2525_3,axiom,
    ( ~ class_Int_Onumber__ring(X2)
    | c_HOL_Oplus__class_Oplus(X5,c_HOL_Otimes__class_Otimes(X1,X3,X2),X2) != c_HOL_Oplus__class_Oplus(X5,c_HOL_Otimes__class_Otimes(X1,X4,X2),X2)
    | X3 = X4
    | X1 = c_HOL_Ozero__class_Ozero(X2)
    | ~ class_Ring__and__Field_Oidom(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2525]) ).

cnf(c_0_2525_4,axiom,
    ( ~ class_Ring__and__Field_Oidom(X2)
    | ~ class_Int_Onumber__ring(X2)
    | c_HOL_Oplus__class_Oplus(X5,c_HOL_Otimes__class_Otimes(X1,X3,X2),X2) != c_HOL_Oplus__class_Oplus(X5,c_HOL_Otimes__class_Otimes(X1,X4,X2),X2)
    | X3 = X4
    | X1 = c_HOL_Ozero__class_Ozero(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2525]) ).

cnf(c_0_2526_0,axiom,
    ( c_HOL_Ominus__class_Ominus(c_Suc(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat)),X3,tc_nat) = c_HOL_Ominus__class_Ominus(c_Suc(X2),c_HOL_Oplus__class_Oplus(X1,X3,tc_nat),tc_nat)
    | ~ c_lessequals(X1,X2,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2526]) ).

cnf(c_0_2526_1,axiom,
    ( ~ c_lessequals(X1,X2,tc_nat)
    | c_HOL_Ominus__class_Ominus(c_Suc(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat)),X3,tc_nat) = c_HOL_Ominus__class_Ominus(c_Suc(X2),c_HOL_Oplus__class_Oplus(X1,X3,tc_nat),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2526]) ).

cnf(c_0_2527_0,axiom,
    ( c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X3,X1,tc_nat),c_Suc(X2),tc_nat) = c_HOL_Ominus__class_Ominus(X3,c_Suc(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat)),tc_nat)
    | ~ c_lessequals(X1,X2,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2527]) ).

cnf(c_0_2527_1,axiom,
    ( ~ c_lessequals(X1,X2,tc_nat)
    | c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X3,X1,tc_nat),c_Suc(X2),tc_nat) = c_HOL_Ominus__class_Ominus(X3,c_Suc(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat)),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2527]) ).

cnf(c_0_2528_0,axiom,
    ( c_lessequals(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),c_HOL_Ominus__class_Ominus(X3,X1,tc_nat),tc_nat)
    | ~ c_lessequals(X1,X2,tc_nat)
    | ~ c_lessequals(X1,X3,tc_nat)
    | ~ c_lessequals(X2,X3,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2528]) ).

cnf(c_0_2528_1,axiom,
    ( ~ c_lessequals(X1,X2,tc_nat)
    | c_lessequals(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),c_HOL_Ominus__class_Ominus(X3,X1,tc_nat),tc_nat)
    | ~ c_lessequals(X1,X3,tc_nat)
    | ~ c_lessequals(X2,X3,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2528]) ).

cnf(c_0_2528_2,axiom,
    ( ~ c_lessequals(X1,X3,tc_nat)
    | ~ c_lessequals(X1,X2,tc_nat)
    | c_lessequals(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),c_HOL_Ominus__class_Ominus(X3,X1,tc_nat),tc_nat)
    | ~ c_lessequals(X2,X3,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2528]) ).

cnf(c_0_2528_3,axiom,
    ( ~ c_lessequals(X2,X3,tc_nat)
    | ~ c_lessequals(X1,X3,tc_nat)
    | ~ c_lessequals(X1,X2,tc_nat)
    | c_lessequals(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),c_HOL_Ominus__class_Ominus(X3,X1,tc_nat),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2528]) ).

cnf(c_0_2529_0,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),c_HOL_Ominus__class_Ominus(X3,X1,tc_nat),tc_nat)
    | ~ c_lessequals(X1,X2,tc_nat)
    | ~ c_lessequals(X1,X3,tc_nat)
    | ~ c_HOL_Oord__class_Oless(X2,X3,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2529]) ).

cnf(c_0_2529_1,axiom,
    ( ~ c_lessequals(X1,X2,tc_nat)
    | c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),c_HOL_Ominus__class_Ominus(X3,X1,tc_nat),tc_nat)
    | ~ c_lessequals(X1,X3,tc_nat)
    | ~ c_HOL_Oord__class_Oless(X2,X3,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2529]) ).

cnf(c_0_2529_2,axiom,
    ( ~ c_lessequals(X1,X3,tc_nat)
    | ~ c_lessequals(X1,X2,tc_nat)
    | c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),c_HOL_Ominus__class_Ominus(X3,X1,tc_nat),tc_nat)
    | ~ c_HOL_Oord__class_Oless(X2,X3,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2529]) ).

cnf(c_0_2529_3,axiom,
    ( ~ c_HOL_Oord__class_Oless(X2,X3,tc_nat)
    | ~ c_lessequals(X1,X3,tc_nat)
    | ~ c_lessequals(X1,X2,tc_nat)
    | c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),c_HOL_Ominus__class_Ominus(X3,X1,tc_nat),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2529]) ).

cnf(c_0_2530_0,axiom,
    ( c_lessequals(X1,c_HOL_Oplus__class_Oplus(X2,X5,X4),X4)
    | ~ c_lessequals(X1,c_HOL_Oplus__class_Oplus(X2,X3,X4),X4)
    | ~ c_lessequals(X3,X5,X4)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X4) ),
    inference(literals_permutation,[status(thm)],[c_0_2530]) ).

cnf(c_0_2530_1,axiom,
    ( ~ c_lessequals(X1,c_HOL_Oplus__class_Oplus(X2,X3,X4),X4)
    | c_lessequals(X1,c_HOL_Oplus__class_Oplus(X2,X5,X4),X4)
    | ~ c_lessequals(X3,X5,X4)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X4) ),
    inference(literals_permutation,[status(thm)],[c_0_2530]) ).

cnf(c_0_2530_2,axiom,
    ( ~ c_lessequals(X3,X5,X4)
    | ~ c_lessequals(X1,c_HOL_Oplus__class_Oplus(X2,X3,X4),X4)
    | c_lessequals(X1,c_HOL_Oplus__class_Oplus(X2,X5,X4),X4)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X4) ),
    inference(literals_permutation,[status(thm)],[c_0_2530]) ).

cnf(c_0_2530_3,axiom,
    ( ~ class_OrderedGroup_Opordered__ab__group__add(X4)
    | ~ c_lessequals(X3,X5,X4)
    | ~ c_lessequals(X1,c_HOL_Oplus__class_Oplus(X2,X3,X4),X4)
    | c_lessequals(X1,c_HOL_Oplus__class_Oplus(X2,X5,X4),X4) ),
    inference(literals_permutation,[status(thm)],[c_0_2530]) ).

cnf(c_0_2531_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_2531]) ).

cnf(c_0_2531_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_2531]) ).

cnf(c_0_2532_0,axiom,
    ( c_lessequals(X2,X3,tc_nat)
    | ~ c_lessequals(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_2532]) ).

cnf(c_0_2532_1,axiom,
    ( ~ c_lessequals(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_lessequals(X2,X3,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2532]) ).

cnf(c_0_2533_0,axiom,
    ( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
    | X2 = X3
    | c_HOL_Oplus__class_Oplus(X4,c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),tc_nat) != c_HOL_Oplus__class_Oplus(X4,c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2533]) ).

cnf(c_0_2533_1,axiom,
    ( X2 = X3
    | X1 = c_HOL_Ozero__class_Ozero(tc_nat)
    | c_HOL_Oplus__class_Oplus(X4,c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),tc_nat) != c_HOL_Oplus__class_Oplus(X4,c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2533]) ).

cnf(c_0_2533_2,axiom,
    ( c_HOL_Oplus__class_Oplus(X4,c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),tc_nat) != c_HOL_Oplus__class_Oplus(X4,c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat)
    | X2 = X3
    | X1 = c_HOL_Ozero__class_Ozero(tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2533]) ).

cnf(c_0_2534_0,axiom,
    ( c_lessequals(X3,c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),tc_nat)
    | ~ c_lessequals(X1,X2,tc_nat)
    | ~ c_lessequals(c_HOL_Oplus__class_Oplus(X3,X1,tc_nat),X2,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2534]) ).

cnf(c_0_2534_1,axiom,
    ( ~ c_lessequals(X1,X2,tc_nat)
    | c_lessequals(X3,c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),tc_nat)
    | ~ c_lessequals(c_HOL_Oplus__class_Oplus(X3,X1,tc_nat),X2,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2534]) ).

cnf(c_0_2534_2,axiom,
    ( ~ c_lessequals(c_HOL_Oplus__class_Oplus(X3,X1,tc_nat),X2,tc_nat)
    | ~ c_lessequals(X1,X2,tc_nat)
    | c_lessequals(X3,c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2534]) ).

cnf(c_0_2535_0,axiom,
    ( c_lessequals(c_HOL_Oplus__class_Oplus(X3,X1,tc_nat),X2,tc_nat)
    | ~ c_lessequals(X1,X2,tc_nat)
    | ~ c_lessequals(X3,c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2535]) ).

cnf(c_0_2535_1,axiom,
    ( ~ c_lessequals(X1,X2,tc_nat)
    | c_lessequals(c_HOL_Oplus__class_Oplus(X3,X1,tc_nat),X2,tc_nat)
    | ~ c_lessequals(X3,c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2535]) ).

cnf(c_0_2535_2,axiom,
    ( ~ c_lessequals(X3,c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),tc_nat)
    | ~ c_lessequals(X1,X2,tc_nat)
    | c_lessequals(c_HOL_Oplus__class_Oplus(X3,X1,tc_nat),X2,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2535]) ).

cnf(c_0_2536_0,axiom,
    ( c_lessequals(X1,X4,X3)
    | ~ c_lessequals(c_HOL_Oplus__class_Oplus(X1,X2,X3),c_HOL_Oplus__class_Oplus(X4,X2,X3),X3)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2536]) ).

cnf(c_0_2536_1,axiom,
    ( ~ c_lessequals(c_HOL_Oplus__class_Oplus(X1,X2,X3),c_HOL_Oplus__class_Oplus(X4,X2,X3),X3)
    | c_lessequals(X1,X4,X3)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2536]) ).

cnf(c_0_2536_2,axiom,
    ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
    | ~ c_lessequals(c_HOL_Oplus__class_Oplus(X1,X2,X3),c_HOL_Oplus__class_Oplus(X4,X2,X3),X3)
    | c_lessequals(X1,X4,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2536]) ).

cnf(c_0_2537_0,axiom,
    ( c_lessequals(X2,X4,X3)
    | ~ c_lessequals(c_HOL_Oplus__class_Oplus(X1,X2,X3),c_HOL_Oplus__class_Oplus(X1,X4,X3),X3)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2537]) ).

cnf(c_0_2537_1,axiom,
    ( ~ c_lessequals(c_HOL_Oplus__class_Oplus(X1,X2,X3),c_HOL_Oplus__class_Oplus(X1,X4,X3),X3)
    | c_lessequals(X2,X4,X3)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2537]) ).

cnf(c_0_2537_2,axiom,
    ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
    | ~ c_lessequals(c_HOL_Oplus__class_Oplus(X1,X2,X3),c_HOL_Oplus__class_Oplus(X1,X4,X3),X3)
    | c_lessequals(X2,X4,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2537]) ).

cnf(c_0_2538_0,axiom,
    ( c_HOL_Oord__class_Oless(X1,X4,X3)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X2,X3),c_HOL_Oplus__class_Oplus(X4,X2,X3),X3)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2538]) ).

cnf(c_0_2538_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X2,X3),c_HOL_Oplus__class_Oplus(X4,X2,X3),X3)
    | c_HOL_Oord__class_Oless(X1,X4,X3)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2538]) ).

cnf(c_0_2538_2,axiom,
    ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X2,X3),c_HOL_Oplus__class_Oplus(X4,X2,X3),X3)
    | c_HOL_Oord__class_Oless(X1,X4,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2538]) ).

cnf(c_0_2539_0,axiom,
    ( c_HOL_Oord__class_Oless(X2,X4,X3)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X2,X3),c_HOL_Oplus__class_Oplus(X1,X4,X3),X3)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2539]) ).

cnf(c_0_2539_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X2,X3),c_HOL_Oplus__class_Oplus(X1,X4,X3),X3)
    | c_HOL_Oord__class_Oless(X2,X4,X3)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2539]) ).

cnf(c_0_2539_2,axiom,
    ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X2,X3),c_HOL_Oplus__class_Oplus(X1,X4,X3),X3)
    | c_HOL_Oord__class_Oless(X2,X4,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2539]) ).

cnf(c_0_2540_0,axiom,
    ( c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),c_HOL_Ominus__class_Ominus(X3,X1,tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(X2,X3,tc_nat)
    | ~ c_lessequals(X1,X2,tc_nat)
    | ~ c_lessequals(X1,X3,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2540]) ).

cnf(c_0_2540_1,axiom,
    ( ~ c_lessequals(X1,X2,tc_nat)
    | c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),c_HOL_Ominus__class_Ominus(X3,X1,tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(X2,X3,tc_nat)
    | ~ c_lessequals(X1,X3,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2540]) ).

cnf(c_0_2540_2,axiom,
    ( ~ c_lessequals(X1,X3,tc_nat)
    | ~ c_lessequals(X1,X2,tc_nat)
    | c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),c_HOL_Ominus__class_Ominus(X3,X1,tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(X2,X3,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2540]) ).

cnf(c_0_2541_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_2541]) ).

cnf(c_0_2541_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_2541]) ).

cnf(c_0_2542_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_2542]) ).

cnf(c_0_2542_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_2542]) ).

cnf(c_0_2543_0,axiom,
    ( c_lessequals(X2,X3,tc_nat)
    | ~ c_lessequals(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),c_HOL_Oplus__class_Oplus(X1,X3,tc_nat),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2543]) ).

cnf(c_0_2543_1,axiom,
    ( ~ c_lessequals(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),c_HOL_Oplus__class_Oplus(X1,X3,tc_nat),tc_nat)
    | c_lessequals(X2,X3,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2543]) ).

cnf(c_0_2544_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_2544]) ).

cnf(c_0_2544_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_2544]) ).

cnf(c_0_2545_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_2545]) ).

cnf(c_0_2545_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_2545]) ).

cnf(c_0_2546_0,axiom,
    ( c_HOL_Oord__class_Oless(X2,X3,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),c_HOL_Oplus__class_Oplus(X1,X3,tc_nat),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2546]) ).

cnf(c_0_2546_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),c_HOL_Oplus__class_Oplus(X1,X3,tc_nat),tc_nat)
    | c_HOL_Oord__class_Oless(X2,X3,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2546]) ).

cnf(c_0_2547_0,axiom,
    ( c_lessequals(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_lessequals(X3,X4,X2)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2547]) ).

cnf(c_0_2547_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
    | c_lessequals(c_HOL_Otimes__class_Otimes(X1,X4,X2),c_HOL_Otimes__class_Otimes(X1,X3,X2),X2)
    | ~ c_lessequals(X3,X4,X2)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2547]) ).

cnf(c_0_2547_2,axiom,
    ( ~ c_lessequals(X3,X4,X2)
    | ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
    | c_lessequals(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_2547]) ).

cnf(c_0_2547_3,axiom,
    ( ~ class_Ring__and__Field_Oordered__ring__strict(X2)
    | ~ c_lessequals(X3,X4,X2)
    | ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
    | c_lessequals(c_HOL_Otimes__class_Otimes(X1,X4,X2),c_HOL_Otimes__class_Otimes(X1,X3,X2),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2547]) ).

cnf(c_0_2548_0,axiom,
    ( c_lessequals(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_lessequals(X3,X4,X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2548]) ).

cnf(c_0_2548_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | c_lessequals(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X2,X4,X1),X1)
    | ~ c_lessequals(X3,X4,X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2548]) ).

cnf(c_0_2548_2,axiom,
    ( ~ c_lessequals(X3,X4,X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | c_lessequals(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_2548]) ).

cnf(c_0_2548_3,axiom,
    ( ~ class_Ring__and__Field_Oordered__ring__strict(X1)
    | ~ c_lessequals(X3,X4,X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | c_lessequals(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X2,X4,X1),X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2548]) ).

cnf(c_0_2549_0,axiom,
    ( c_lessequals(c_HOL_Otimes__class_Otimes(X2,X4,X3),c_HOL_Otimes__class_Otimes(X1,X4,X3),X3)
    | ~ c_lessequals(X1,X2,X3)
    | ~ c_lessequals(X4,c_HOL_Ozero__class_Ozero(X3),X3)
    | ~ class_Ring__and__Field_Opordered__ring(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2549]) ).

cnf(c_0_2549_1,axiom,
    ( ~ c_lessequals(X1,X2,X3)
    | c_lessequals(c_HOL_Otimes__class_Otimes(X2,X4,X3),c_HOL_Otimes__class_Otimes(X1,X4,X3),X3)
    | ~ c_lessequals(X4,c_HOL_Ozero__class_Ozero(X3),X3)
    | ~ class_Ring__and__Field_Opordered__ring(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2549]) ).

cnf(c_0_2549_2,axiom,
    ( ~ c_lessequals(X4,c_HOL_Ozero__class_Ozero(X3),X3)
    | ~ c_lessequals(X1,X2,X3)
    | c_lessequals(c_HOL_Otimes__class_Otimes(X2,X4,X3),c_HOL_Otimes__class_Otimes(X1,X4,X3),X3)
    | ~ class_Ring__and__Field_Opordered__ring(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2549]) ).

cnf(c_0_2549_3,axiom,
    ( ~ class_Ring__and__Field_Opordered__ring(X3)
    | ~ c_lessequals(X4,c_HOL_Ozero__class_Ozero(X3),X3)
    | ~ c_lessequals(X1,X2,X3)
    | c_lessequals(c_HOL_Otimes__class_Otimes(X2,X4,X3),c_HOL_Otimes__class_Otimes(X1,X4,X3),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2549]) ).

cnf(c_0_2550_0,axiom,
    ( c_lessequals(c_HOL_Otimes__class_Otimes(X4,X2,X3),c_HOL_Otimes__class_Otimes(X4,X1,X3),X3)
    | ~ c_lessequals(X1,X2,X3)
    | ~ c_lessequals(X4,c_HOL_Ozero__class_Ozero(X3),X3)
    | ~ class_Ring__and__Field_Opordered__ring(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2550]) ).

cnf(c_0_2550_1,axiom,
    ( ~ c_lessequals(X1,X2,X3)
    | c_lessequals(c_HOL_Otimes__class_Otimes(X4,X2,X3),c_HOL_Otimes__class_Otimes(X4,X1,X3),X3)
    | ~ c_lessequals(X4,c_HOL_Ozero__class_Ozero(X3),X3)
    | ~ class_Ring__and__Field_Opordered__ring(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2550]) ).

cnf(c_0_2550_2,axiom,
    ( ~ c_lessequals(X4,c_HOL_Ozero__class_Ozero(X3),X3)
    | ~ c_lessequals(X1,X2,X3)
    | c_lessequals(c_HOL_Otimes__class_Otimes(X4,X2,X3),c_HOL_Otimes__class_Otimes(X4,X1,X3),X3)
    | ~ class_Ring__and__Field_Opordered__ring(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2550]) ).

cnf(c_0_2550_3,axiom,
    ( ~ class_Ring__and__Field_Opordered__ring(X3)
    | ~ c_lessequals(X4,c_HOL_Ozero__class_Ozero(X3),X3)
    | ~ c_lessequals(X1,X2,X3)
    | c_lessequals(c_HOL_Otimes__class_Otimes(X4,X2,X3),c_HOL_Otimes__class_Otimes(X4,X1,X3),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2550]) ).

cnf(c_0_2551_0,axiom,
    ( c_lessequals(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X2,X4,X3),X3)
    | ~ c_lessequals(X1,X2,X3)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
    | ~ class_Ring__and__Field_Omult__mono(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2551]) ).

cnf(c_0_2551_1,axiom,
    ( ~ c_lessequals(X1,X2,X3)
    | c_lessequals(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X2,X4,X3),X3)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
    | ~ class_Ring__and__Field_Omult__mono(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2551]) ).

cnf(c_0_2551_2,axiom,
    ( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
    | ~ c_lessequals(X1,X2,X3)
    | c_lessequals(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X2,X4,X3),X3)
    | ~ class_Ring__and__Field_Omult__mono(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2551]) ).

cnf(c_0_2551_3,axiom,
    ( ~ class_Ring__and__Field_Omult__mono(X3)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
    | ~ c_lessequals(X1,X2,X3)
    | c_lessequals(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X2,X4,X3),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2551]) ).

cnf(c_0_2552_0,axiom,
    ( c_lessequals(c_HOL_Otimes__class_Otimes(X4,X1,X3),c_HOL_Otimes__class_Otimes(X4,X2,X3),X3)
    | ~ c_lessequals(X1,X2,X3)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
    | ~ class_Ring__and__Field_Omult__mono(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2552]) ).

cnf(c_0_2552_1,axiom,
    ( ~ c_lessequals(X1,X2,X3)
    | c_lessequals(c_HOL_Otimes__class_Otimes(X4,X1,X3),c_HOL_Otimes__class_Otimes(X4,X2,X3),X3)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
    | ~ class_Ring__and__Field_Omult__mono(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2552]) ).

cnf(c_0_2552_2,axiom,
    ( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
    | ~ c_lessequals(X1,X2,X3)
    | c_lessequals(c_HOL_Otimes__class_Otimes(X4,X1,X3),c_HOL_Otimes__class_Otimes(X4,X2,X3),X3)
    | ~ class_Ring__and__Field_Omult__mono(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2552]) ).

cnf(c_0_2552_3,axiom,
    ( ~ class_Ring__and__Field_Omult__mono(X3)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
    | ~ c_lessequals(X1,X2,X3)
    | c_lessequals(c_HOL_Otimes__class_Otimes(X4,X1,X3),c_HOL_Otimes__class_Otimes(X4,X2,X3),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2552]) ).

cnf(c_0_2553_0,axiom,
    ( c_lessequals(c_HOL_Otimes__class_Otimes(X4,X1,X3),c_HOL_Otimes__class_Otimes(X4,X2,X3),X3)
    | ~ c_lessequals(X1,X2,X3)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
    | ~ class_Ring__and__Field_Omult__mono1(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2553]) ).

cnf(c_0_2553_1,axiom,
    ( ~ c_lessequals(X1,X2,X3)
    | c_lessequals(c_HOL_Otimes__class_Otimes(X4,X1,X3),c_HOL_Otimes__class_Otimes(X4,X2,X3),X3)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
    | ~ class_Ring__and__Field_Omult__mono1(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2553]) ).

cnf(c_0_2553_2,axiom,
    ( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
    | ~ c_lessequals(X1,X2,X3)
    | c_lessequals(c_HOL_Otimes__class_Otimes(X4,X1,X3),c_HOL_Otimes__class_Otimes(X4,X2,X3),X3)
    | ~ class_Ring__and__Field_Omult__mono1(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2553]) ).

cnf(c_0_2553_3,axiom,
    ( ~ class_Ring__and__Field_Omult__mono1(X3)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
    | ~ c_lessequals(X1,X2,X3)
    | c_lessequals(c_HOL_Otimes__class_Otimes(X4,X1,X3),c_HOL_Otimes__class_Otimes(X4,X2,X3),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2553]) ).

cnf(c_0_2554_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_2554]) ).

cnf(c_0_2554_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_2554]) ).

cnf(c_0_2554_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_2554]) ).

cnf(c_0_2554_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_2554]) ).

cnf(c_0_2555_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_2555]) ).

cnf(c_0_2555_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_2555]) ).

cnf(c_0_2555_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_2555]) ).

cnf(c_0_2555_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_2555]) ).

cnf(c_0_2556_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_2556]) ).

cnf(c_0_2556_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_2556]) ).

cnf(c_0_2556_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_2556]) ).

cnf(c_0_2556_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_2556]) ).

cnf(c_0_2557_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_2557]) ).

cnf(c_0_2557_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_2557]) ).

cnf(c_0_2557_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_2557]) ).

cnf(c_0_2557_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_2557]) ).

cnf(c_0_2558_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_2558]) ).

cnf(c_0_2558_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_2558]) ).

cnf(c_0_2558_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_2558]) ).

cnf(c_0_2558_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_2558]) ).

cnf(c_0_2559_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_2559]) ).

cnf(c_0_2559_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_2559]) ).

cnf(c_0_2559_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_2559]) ).

cnf(c_0_2559_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_2559]) ).

cnf(c_0_2560_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_2560]) ).

cnf(c_0_2560_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_2560]) ).

cnf(c_0_2560_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_2560]) ).

cnf(c_0_2560_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_2560]) ).

cnf(c_0_2561_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_2561]) ).

cnf(c_0_2561_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_2561]) ).

cnf(c_0_2561_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_2561]) ).

cnf(c_0_2561_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_2561]) ).

cnf(c_0_2562_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_2562]) ).

cnf(c_0_2562_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_2562]) ).

cnf(c_0_2562_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_2562]) ).

cnf(c_0_2562_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_2562]) ).

cnf(c_0_2563_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_2563]) ).

cnf(c_0_2563_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_2563]) ).

cnf(c_0_2563_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_2563]) ).

cnf(c_0_2563_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_2563]) ).

cnf(c_0_2564_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_2564]) ).

cnf(c_0_2564_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_2564]) ).

cnf(c_0_2564_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_2564]) ).

cnf(c_0_2564_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_2564]) ).

cnf(c_0_2565_0,axiom,
    ( c_lessequals(c_HOL_Otimes__class_Otimes(X2,X3,X1),X2,X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
    | ~ c_lessequals(X3,c_HOL_Oone__class_Oone(X1),X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2565]) ).

cnf(c_0_2565_1,axiom,
    ( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | c_lessequals(c_HOL_Otimes__class_Otimes(X2,X3,X1),X2,X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
    | ~ c_lessequals(X3,c_HOL_Oone__class_Oone(X1),X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2565]) ).

cnf(c_0_2565_2,axiom,
    ( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | c_lessequals(c_HOL_Otimes__class_Otimes(X2,X3,X1),X2,X1)
    | ~ c_lessequals(X3,c_HOL_Oone__class_Oone(X1),X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2565]) ).

cnf(c_0_2565_3,axiom,
    ( ~ c_lessequals(X3,c_HOL_Oone__class_Oone(X1),X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | c_lessequals(c_HOL_Otimes__class_Otimes(X2,X3,X1),X2,X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2565]) ).

cnf(c_0_2565_4,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(X1)
    | ~ c_lessequals(X3,c_HOL_Oone__class_Oone(X1),X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | c_lessequals(c_HOL_Otimes__class_Otimes(X2,X3,X1),X2,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2565]) ).

cnf(c_0_2566_0,axiom,
    ( c_lessequals(c_HOL_Otimes__class_Otimes(X3,X2,X1),X2,X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
    | ~ c_lessequals(X3,c_HOL_Oone__class_Oone(X1),X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2566]) ).

cnf(c_0_2566_1,axiom,
    ( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | c_lessequals(c_HOL_Otimes__class_Otimes(X3,X2,X1),X2,X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
    | ~ c_lessequals(X3,c_HOL_Oone__class_Oone(X1),X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2566]) ).

cnf(c_0_2566_2,axiom,
    ( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | c_lessequals(c_HOL_Otimes__class_Otimes(X3,X2,X1),X2,X1)
    | ~ c_lessequals(X3,c_HOL_Oone__class_Oone(X1),X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2566]) ).

cnf(c_0_2566_3,axiom,
    ( ~ c_lessequals(X3,c_HOL_Oone__class_Oone(X1),X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | c_lessequals(c_HOL_Otimes__class_Otimes(X3,X2,X1),X2,X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2566]) ).

cnf(c_0_2566_4,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(X1)
    | ~ c_lessequals(X3,c_HOL_Oone__class_Oone(X1),X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | c_lessequals(c_HOL_Otimes__class_Otimes(X3,X2,X1),X2,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2566]) ).

cnf(c_0_2567_0,axiom,
    ( c_lessequals(X3,c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X2,X3,tc_nat),X1,tc_nat),tc_nat)
    | ~ c_lessequals(X1,X2,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2567]) ).

cnf(c_0_2567_1,axiom,
    ( ~ c_lessequals(X1,X2,tc_nat)
    | c_lessequals(X3,c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X2,X3,tc_nat),X1,tc_nat),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2567]) ).

cnf(c_0_2568_0,axiom,
    ( c_lessequals(c_HOL_Oplus__class_Oplus(X1,X4,X3),c_HOL_Oplus__class_Oplus(X2,X5,X3),X3)
    | ~ c_lessequals(X1,X2,X3)
    | ~ c_lessequals(X4,X5,X3)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2568]) ).

cnf(c_0_2568_1,axiom,
    ( ~ c_lessequals(X1,X2,X3)
    | c_lessequals(c_HOL_Oplus__class_Oplus(X1,X4,X3),c_HOL_Oplus__class_Oplus(X2,X5,X3),X3)
    | ~ c_lessequals(X4,X5,X3)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2568]) ).

cnf(c_0_2568_2,axiom,
    ( ~ c_lessequals(X4,X5,X3)
    | ~ c_lessequals(X1,X2,X3)
    | c_lessequals(c_HOL_Oplus__class_Oplus(X1,X4,X3),c_HOL_Oplus__class_Oplus(X2,X5,X3),X3)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2568]) ).

cnf(c_0_2568_3,axiom,
    ( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X3)
    | ~ c_lessequals(X4,X5,X3)
    | ~ c_lessequals(X1,X2,X3)
    | c_lessequals(c_HOL_Oplus__class_Oplus(X1,X4,X3),c_HOL_Oplus__class_Oplus(X2,X5,X3),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2568]) ).

cnf(c_0_2569_0,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X4,X3),c_HOL_Oplus__class_Oplus(X2,X5,X3),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_2569]) ).

cnf(c_0_2569_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X4,X3),c_HOL_Oplus__class_Oplus(X2,X5,X3),X3)
    | ~ c_HOL_Oord__class_Oless(X4,X5,X3)
    | ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2569]) ).

cnf(c_0_2569_2,axiom,
    ( ~ c_HOL_Oord__class_Oless(X4,X5,X3)
    | ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X4,X3),c_HOL_Oplus__class_Oplus(X2,X5,X3),X3)
    | ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2569]) ).

cnf(c_0_2569_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(c_HOL_Oplus__class_Oplus(X1,X4,X3),c_HOL_Oplus__class_Oplus(X2,X5,X3),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2569]) ).

cnf(c_0_2570_0,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X4,X3),c_HOL_Oplus__class_Oplus(X2,X5,X3),X3)
    | ~ c_lessequals(X1,X2,X3)
    | ~ c_HOL_Oord__class_Oless(X4,X5,X3)
    | ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2570]) ).

cnf(c_0_2570_1,axiom,
    ( ~ c_lessequals(X1,X2,X3)
    | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X4,X3),c_HOL_Oplus__class_Oplus(X2,X5,X3),X3)
    | ~ c_HOL_Oord__class_Oless(X4,X5,X3)
    | ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2570]) ).

cnf(c_0_2570_2,axiom,
    ( ~ c_HOL_Oord__class_Oless(X4,X5,X3)
    | ~ c_lessequals(X1,X2,X3)
    | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X4,X3),c_HOL_Oplus__class_Oplus(X2,X5,X3),X3)
    | ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2570]) ).

cnf(c_0_2570_3,axiom,
    ( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X3)
    | ~ c_HOL_Oord__class_Oless(X4,X5,X3)
    | ~ c_lessequals(X1,X2,X3)
    | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X4,X3),c_HOL_Oplus__class_Oplus(X2,X5,X3),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2570]) ).

cnf(c_0_2571_0,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X4,X3),c_HOL_Oplus__class_Oplus(X2,X5,X3),X3)
    | ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | ~ c_lessequals(X4,X5,X3)
    | ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2571]) ).

cnf(c_0_2571_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X4,X3),c_HOL_Oplus__class_Oplus(X2,X5,X3),X3)
    | ~ c_lessequals(X4,X5,X3)
    | ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2571]) ).

cnf(c_0_2571_2,axiom,
    ( ~ c_lessequals(X4,X5,X3)
    | ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X4,X3),c_HOL_Oplus__class_Oplus(X2,X5,X3),X3)
    | ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2571]) ).

cnf(c_0_2571_3,axiom,
    ( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X3)
    | ~ c_lessequals(X4,X5,X3)
    | ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X4,X3),c_HOL_Oplus__class_Oplus(X2,X5,X3),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2571]) ).

cnf(c_0_2572_0,axiom,
    ( X1 = c_HOL_Ozero__class_Ozero(X2)
    | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X3,X2),c_HOL_Otimes__class_Otimes(X1,X1,X2),X2) != c_HOL_Ozero__class_Ozero(X2)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2572]) ).

cnf(c_0_2572_1,axiom,
    ( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X3,X2),c_HOL_Otimes__class_Otimes(X1,X1,X2),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_2572]) ).

cnf(c_0_2572_2,axiom,
    ( ~ class_Ring__and__Field_Oordered__ring__strict(X2)
    | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X3,X2),c_HOL_Otimes__class_Otimes(X1,X1,X2),X2) != c_HOL_Ozero__class_Ozero(X2)
    | X1 = c_HOL_Ozero__class_Ozero(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2572]) ).

cnf(c_0_2573_0,axiom,
    ( X1 = c_HOL_Ozero__class_Ozero(X2)
    | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X1,X2),c_HOL_Otimes__class_Otimes(X3,X3,X2),X2) != c_HOL_Ozero__class_Ozero(X2)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2573]) ).

cnf(c_0_2573_1,axiom,
    ( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X1,X2),c_HOL_Otimes__class_Otimes(X3,X3,X2),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_2573]) ).

cnf(c_0_2573_2,axiom,
    ( ~ class_Ring__and__Field_Oordered__ring__strict(X2)
    | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X1,X2),c_HOL_Otimes__class_Otimes(X3,X3,X2),X2) != c_HOL_Ozero__class_Ozero(X2)
    | X1 = c_HOL_Ozero__class_Ozero(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2573]) ).

cnf(c_0_2574_0,axiom,
    ( c_Orderings_Oord__class_Omax(c_Orderings_Oord__class_Omin(X1,X4,X3),c_Orderings_Oord__class_Omin(X2,X4,X3),X3) = c_Orderings_Oord__class_Omin(c_Orderings_Oord__class_Omax(X1,X2,X3),X4,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2574]) ).

cnf(c_0_2574_1,axiom,
    ( ~ class_Orderings_Olinorder(X3)
    | c_Orderings_Oord__class_Omax(c_Orderings_Oord__class_Omin(X1,X4,X3),c_Orderings_Oord__class_Omin(X2,X4,X3),X3) = c_Orderings_Oord__class_Omin(c_Orderings_Oord__class_Omax(X1,X2,X3),X4,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2574]) ).

cnf(c_0_2575_0,axiom,
    ( c_Orderings_Oord__class_Omax(c_Orderings_Oord__class_Omin(X1,X2,X4),c_Orderings_Oord__class_Omin(X1,X3,X4),X4) = c_Orderings_Oord__class_Omin(X1,c_Orderings_Oord__class_Omax(X2,X3,X4),X4)
    | ~ class_Orderings_Olinorder(X4) ),
    inference(literals_permutation,[status(thm)],[c_0_2575]) ).

cnf(c_0_2575_1,axiom,
    ( ~ class_Orderings_Olinorder(X4)
    | c_Orderings_Oord__class_Omax(c_Orderings_Oord__class_Omin(X1,X2,X4),c_Orderings_Oord__class_Omin(X1,X3,X4),X4) = c_Orderings_Oord__class_Omin(X1,c_Orderings_Oord__class_Omax(X2,X3,X4),X4) ),
    inference(literals_permutation,[status(thm)],[c_0_2575]) ).

cnf(c_0_2576_0,axiom,
    ( c_Orderings_Oord__class_Omin(c_HOL_Ominus__class_Ominus(X1,X4,X3),c_HOL_Ominus__class_Ominus(X2,X4,X3),X3) = c_HOL_Ominus__class_Ominus(c_Orderings_Oord__class_Omin(X1,X2,X3),X4,X3)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2576]) ).

cnf(c_0_2576_1,axiom,
    ( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
    | c_Orderings_Oord__class_Omin(c_HOL_Ominus__class_Ominus(X1,X4,X3),c_HOL_Ominus__class_Ominus(X2,X4,X3),X3) = c_HOL_Ominus__class_Ominus(c_Orderings_Oord__class_Omin(X1,X2,X3),X4,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2576]) ).

cnf(c_0_2577_0,axiom,
    ( c_Orderings_Oord__class_Omax(c_HOL_Ominus__class_Ominus(X1,X4,X3),c_HOL_Ominus__class_Ominus(X2,X4,X3),X3) = c_HOL_Ominus__class_Ominus(c_Orderings_Oord__class_Omax(X1,X2,X3),X4,X3)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2577]) ).

cnf(c_0_2577_1,axiom,
    ( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
    | c_Orderings_Oord__class_Omax(c_HOL_Ominus__class_Ominus(X1,X4,X3),c_HOL_Ominus__class_Ominus(X2,X4,X3),X3) = c_HOL_Ominus__class_Ominus(c_Orderings_Oord__class_Omax(X1,X2,X3),X4,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2577]) ).

cnf(c_0_2578_0,axiom,
    ( c_Orderings_Oord__class_Omin(c_HOL_Oplus__class_Oplus(X1,X4,X3),c_HOL_Oplus__class_Oplus(X2,X4,X3),X3) = c_HOL_Oplus__class_Oplus(c_Orderings_Oord__class_Omin(X1,X2,X3),X4,X3)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2578]) ).

cnf(c_0_2578_1,axiom,
    ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
    | c_Orderings_Oord__class_Omin(c_HOL_Oplus__class_Oplus(X1,X4,X3),c_HOL_Oplus__class_Oplus(X2,X4,X3),X3) = c_HOL_Oplus__class_Oplus(c_Orderings_Oord__class_Omin(X1,X2,X3),X4,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2578]) ).

cnf(c_0_2579_0,axiom,
    ( c_Orderings_Oord__class_Omax(c_HOL_Oplus__class_Oplus(X1,X4,X3),c_HOL_Oplus__class_Oplus(X2,X4,X3),X3) = c_HOL_Oplus__class_Oplus(c_Orderings_Oord__class_Omax(X1,X2,X3),X4,X3)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2579]) ).

cnf(c_0_2579_1,axiom,
    ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
    | c_Orderings_Oord__class_Omax(c_HOL_Oplus__class_Oplus(X1,X4,X3),c_HOL_Oplus__class_Oplus(X2,X4,X3),X3) = c_HOL_Oplus__class_Oplus(c_Orderings_Oord__class_Omax(X1,X2,X3),X4,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2579]) ).

cnf(c_0_2580_0,axiom,
    ( c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X1,c_HOL_Otimes__class_Otimes(X2,X3,X4),X4),X3,X4) = c_Divides_Odiv__class_Omod(X1,X3,X4)
    | ~ class_Divides_Osemiring__div(X4) ),
    inference(literals_permutation,[status(thm)],[c_0_2580]) ).

cnf(c_0_2580_1,axiom,
    ( ~ class_Divides_Osemiring__div(X4)
    | c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X1,c_HOL_Otimes__class_Otimes(X2,X3,X4),X4),X3,X4) = c_Divides_Odiv__class_Omod(X1,X3,X4) ),
    inference(literals_permutation,[status(thm)],[c_0_2580]) ).

cnf(c_0_2581_0,axiom,
    ( c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X1,c_HOL_Otimes__class_Otimes(X2,X3,X4),X4),X2,X4) = c_Divides_Odiv__class_Omod(X1,X2,X4)
    | ~ class_Divides_Osemiring__div(X4) ),
    inference(literals_permutation,[status(thm)],[c_0_2581]) ).

cnf(c_0_2581_1,axiom,
    ( ~ class_Divides_Osemiring__div(X4)
    | c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X1,c_HOL_Otimes__class_Otimes(X2,X3,X4),X4),X2,X4) = c_Divides_Odiv__class_Omod(X1,X2,X4) ),
    inference(literals_permutation,[status(thm)],[c_0_2581]) ).

cnf(c_0_2582_0,axiom,
    ( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X4,X2,X3),X3) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X1,X4,X3),X2,X3)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2582]) ).

cnf(c_0_2582_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
    | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X4,X2,X3),X3) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X1,X4,X3),X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2582]) ).

cnf(c_0_2583_0,axiom,
    ( c_Orderings_Oord__class_Omin(c_Orderings_Oord__class_Omax(X1,X4,X3),c_Orderings_Oord__class_Omax(X2,X4,X3),X3) = c_Orderings_Oord__class_Omax(c_Orderings_Oord__class_Omin(X1,X2,X3),X4,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2583]) ).

cnf(c_0_2583_1,axiom,
    ( ~ class_Orderings_Olinorder(X3)
    | c_Orderings_Oord__class_Omin(c_Orderings_Oord__class_Omax(X1,X4,X3),c_Orderings_Oord__class_Omax(X2,X4,X3),X3) = c_Orderings_Oord__class_Omax(c_Orderings_Oord__class_Omin(X1,X2,X3),X4,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2583]) ).

cnf(c_0_2584_0,axiom,
    ( c_Orderings_Oord__class_Omin(c_Orderings_Oord__class_Omax(X1,X2,X4),c_Orderings_Oord__class_Omax(X1,X3,X4),X4) = c_Orderings_Oord__class_Omax(X1,c_Orderings_Oord__class_Omin(X2,X3,X4),X4)
    | ~ class_Orderings_Olinorder(X4) ),
    inference(literals_permutation,[status(thm)],[c_0_2584]) ).

cnf(c_0_2584_1,axiom,
    ( ~ class_Orderings_Olinorder(X4)
    | c_Orderings_Oord__class_Omin(c_Orderings_Oord__class_Omax(X1,X2,X4),c_Orderings_Oord__class_Omax(X1,X3,X4),X4) = c_Orderings_Oord__class_Omax(X1,c_Orderings_Oord__class_Omin(X2,X3,X4),X4) ),
    inference(literals_permutation,[status(thm)],[c_0_2584]) ).

cnf(c_0_2585_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_2585]) ).

cnf(c_0_2585_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_2585]) ).

cnf(c_0_2586_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_2586]) ).

cnf(c_0_2586_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_2586]) ).

cnf(c_0_2587_0,axiom,
    ( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X2,X4,X3),X3) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X1,X2,X3),X4,X3)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2587]) ).

cnf(c_0_2587_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
    | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X2,X4,X3),X3) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X1,X2,X3),X4,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2587]) ).

cnf(c_0_2588_0,axiom,
    ( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X2,X4,X3),X3) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X1,X2,X3),X4,X3)
    | ~ class_Ring__and__Field_Ocomm__semiring(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2588]) ).

cnf(c_0_2588_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring(X3)
    | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X2,X4,X3),X3) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X1,X2,X3),X4,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2588]) ).

cnf(c_0_2589_0,axiom,
    ( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,X4),c_HOL_Otimes__class_Otimes(X1,X3,X4),X4) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Oplus__class_Oplus(X2,X3,X4),X4)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X4) ),
    inference(literals_permutation,[status(thm)],[c_0_2589]) ).

cnf(c_0_2589_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__1(X4)
    | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,X4),c_HOL_Otimes__class_Otimes(X1,X3,X4),X4) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Oplus__class_Oplus(X2,X3,X4),X4) ),
    inference(literals_permutation,[status(thm)],[c_0_2589]) ).

cnf(c_0_2590_0,axiom,
    ( c_lessequals(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_lessequals(X2,X3,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2590]) ).

cnf(c_0_2590_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
    | c_lessequals(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat)
    | ~ c_lessequals(X2,X3,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2590]) ).

cnf(c_0_2590_2,axiom,
    ( ~ c_lessequals(X2,X3,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
    | c_lessequals(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_2590]) ).

cnf(c_0_2591_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_2591]) ).

cnf(c_0_2591_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_2591]) ).

cnf(c_0_2591_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_2591]) ).

cnf(c_0_2592_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_2592]) ).

cnf(c_0_2592_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_2592]) ).

cnf(c_0_2592_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_2592]) ).

cnf(c_0_2593_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_2593]) ).

cnf(c_0_2593_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_2593]) ).

cnf(c_0_2593_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_2593]) ).

cnf(c_0_2594_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_2594]) ).

cnf(c_0_2594_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_2594]) ).

cnf(c_0_2594_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_2594]) ).

cnf(c_0_2595_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_2595]) ).

cnf(c_0_2595_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_2595]) ).

cnf(c_0_2595_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_2595]) ).

cnf(c_0_2596_0,axiom,
    ( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
    | c_HOL_Oplus__class_Oplus(X2,c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X2,tc_nat),tc_nat) = c_HOL_Otimes__class_Otimes(X1,X2,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2596]) ).

cnf(c_0_2596_1,axiom,
    ( c_HOL_Oplus__class_Oplus(X2,c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X2,tc_nat),tc_nat) = c_HOL_Otimes__class_Otimes(X1,X2,tc_nat)
    | X1 = c_HOL_Ozero__class_Ozero(tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2596]) ).

cnf(c_0_2597_0,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X3,X2,tc_nat),c_HOL_Ominus__class_Ominus(X3,X1,tc_nat),tc_nat)
    | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | ~ c_HOL_Oord__class_Oless(X1,X3,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2597]) ).

cnf(c_0_2597_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X3,X2,tc_nat),c_HOL_Ominus__class_Ominus(X3,X1,tc_nat),tc_nat)
    | ~ c_HOL_Oord__class_Oless(X1,X3,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2597]) ).

cnf(c_0_2597_2,axiom,
    ( ~ c_HOL_Oord__class_Oless(X1,X3,tc_nat)
    | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X3,X2,tc_nat),c_HOL_Ominus__class_Ominus(X3,X1,tc_nat),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2597]) ).

cnf(c_0_2598_0,axiom,
    ( c_lessequals(c_HOL_Oplus__class_Oplus(X1,X3,tc_nat),c_HOL_Oplus__class_Oplus(X2,X4,tc_nat),tc_nat)
    | ~ c_lessequals(X1,X2,tc_nat)
    | ~ c_lessequals(X3,X4,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2598]) ).

cnf(c_0_2598_1,axiom,
    ( ~ c_lessequals(X1,X2,tc_nat)
    | c_lessequals(c_HOL_Oplus__class_Oplus(X1,X3,tc_nat),c_HOL_Oplus__class_Oplus(X2,X4,tc_nat),tc_nat)
    | ~ c_lessequals(X3,X4,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2598]) ).

cnf(c_0_2598_2,axiom,
    ( ~ c_lessequals(X3,X4,tc_nat)
    | ~ c_lessequals(X1,X2,tc_nat)
    | c_lessequals(c_HOL_Oplus__class_Oplus(X1,X3,tc_nat),c_HOL_Oplus__class_Oplus(X2,X4,tc_nat),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2598]) ).

cnf(c_0_2599_0,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,X3,tc_nat),c_HOL_Ominus__class_Ominus(X2,X3,tc_nat),tc_nat)
    | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | ~ c_lessequals(X3,X1,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2599]) ).

cnf(c_0_2599_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,X3,tc_nat),c_HOL_Ominus__class_Ominus(X2,X3,tc_nat),tc_nat)
    | ~ c_lessequals(X3,X1,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2599]) ).

cnf(c_0_2599_2,axiom,
    ( ~ c_lessequals(X3,X1,tc_nat)
    | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,X3,tc_nat),c_HOL_Ominus__class_Ominus(X2,X3,tc_nat),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2599]) ).

cnf(c_0_2600_0,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X3,tc_nat),c_HOL_Oplus__class_Oplus(X2,X4,tc_nat),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_2600]) ).

cnf(c_0_2600_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X3,tc_nat),c_HOL_Oplus__class_Oplus(X2,X4,tc_nat),tc_nat)
    | ~ c_HOL_Oord__class_Oless(X3,X4,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2600]) ).

cnf(c_0_2600_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(c_HOL_Oplus__class_Oplus(X1,X3,tc_nat),c_HOL_Oplus__class_Oplus(X2,X4,tc_nat),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2600]) ).

cnf(c_0_2601_0,axiom,
    ( c_lessequals(c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),c_HOL_Otimes__class_Otimes(X2,X4,tc_nat),tc_nat)
    | ~ c_lessequals(X1,X2,tc_nat)
    | ~ c_lessequals(X3,X4,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2601]) ).

cnf(c_0_2601_1,axiom,
    ( ~ c_lessequals(X1,X2,tc_nat)
    | c_lessequals(c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),c_HOL_Otimes__class_Otimes(X2,X4,tc_nat),tc_nat)
    | ~ c_lessequals(X3,X4,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2601]) ).

cnf(c_0_2601_2,axiom,
    ( ~ c_lessequals(X3,X4,tc_nat)
    | ~ c_lessequals(X1,X2,tc_nat)
    | c_lessequals(c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),c_HOL_Otimes__class_Otimes(X2,X4,tc_nat),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2601]) ).

cnf(c_0_2602_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_2602]) ).

cnf(c_0_2602_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_2602]) ).

cnf(c_0_2602_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_2602]) ).

cnf(c_0_2602_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_2602]) ).

cnf(c_0_2603_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_2603]) ).

cnf(c_0_2603_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_2603]) ).

cnf(c_0_2603_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_2603]) ).

cnf(c_0_2603_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_2603]) ).

cnf(c_0_2604_0,axiom,
    ( c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),X2,tc_nat) = X1
    | ~ c_lessequals(X2,c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2604]) ).

cnf(c_0_2604_1,axiom,
    ( ~ c_lessequals(X2,c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat)
    | c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),X2,tc_nat) = X1 ),
    inference(literals_permutation,[status(thm)],[c_0_2604]) ).

cnf(c_0_2605_0,axiom,
    ( c_lessequals(X1,c_HOL_Oplus__class_Oplus(X3,X2,tc_nat),tc_nat)
    | ~ c_lessequals(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),X3,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2605]) ).

cnf(c_0_2605_1,axiom,
    ( ~ c_lessequals(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),X3,tc_nat)
    | c_lessequals(X1,c_HOL_Oplus__class_Oplus(X3,X2,tc_nat),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2605]) ).

cnf(c_0_2606_0,axiom,
    ( c_lessequals(c_HOL_Ominus__class_Ominus(X1,X3,tc_nat),X2,tc_nat)
    | ~ c_lessequals(X1,c_HOL_Oplus__class_Oplus(X2,X3,tc_nat),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2606]) ).

cnf(c_0_2606_1,axiom,
    ( ~ c_lessequals(X1,c_HOL_Oplus__class_Oplus(X2,X3,tc_nat),tc_nat)
    | c_lessequals(c_HOL_Ominus__class_Ominus(X1,X3,tc_nat),X2,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2606]) ).

cnf(c_0_2607_0,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X3,tc_nat),X2,tc_nat)
    | ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ominus__class_Ominus(X2,X3,tc_nat),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2607]) ).

cnf(c_0_2607_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ominus__class_Ominus(X2,X3,tc_nat),tc_nat)
    | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X3,tc_nat),X2,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2607]) ).

cnf(c_0_2608_0,axiom,
    ( c_HOL_Oord__class_Oless(X1,c_HOL_Ominus__class_Ominus(X3,X2,tc_nat),tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),X3,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2608]) ).

cnf(c_0_2608_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),X3,tc_nat)
    | c_HOL_Oord__class_Oless(X1,c_HOL_Ominus__class_Ominus(X3,X2,tc_nat),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2608]) ).

cnf(c_0_2609_0,axiom,
    ( c_HOL_Oplus__class_Oplus(X1,X2,X3) = X4
    | c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X5,X2,X3),X3) != c_HOL_Oplus__class_Oplus(X5,X4,X3)
    | ~ class_OrderedGroup_Oab__group__add(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2609]) ).

cnf(c_0_2609_1,axiom,
    ( c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X5,X2,X3),X3) != c_HOL_Oplus__class_Oplus(X5,X4,X3)
    | c_HOL_Oplus__class_Oplus(X1,X2,X3) = X4
    | ~ class_OrderedGroup_Oab__group__add(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2609]) ).

cnf(c_0_2609_2,axiom,
    ( ~ class_OrderedGroup_Oab__group__add(X3)
    | c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X5,X2,X3),X3) != c_HOL_Oplus__class_Oplus(X5,X4,X3)
    | c_HOL_Oplus__class_Oplus(X1,X2,X3) = X4 ),
    inference(literals_permutation,[status(thm)],[c_0_2609]) ).

cnf(c_0_2610_0,axiom,
    ( c_HOL_Oplus__class_Oplus(X3,c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X3,X2,tc_nat),X1,tc_nat)
    | ~ c_lessequals(X1,X2,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2610]) ).

cnf(c_0_2610_1,axiom,
    ( ~ c_lessequals(X1,X2,tc_nat)
    | c_HOL_Oplus__class_Oplus(X3,c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X3,X2,tc_nat),X1,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2610]) ).

cnf(c_0_2611_0,axiom,
    ( c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),X3,tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X2,X3,tc_nat),X1,tc_nat)
    | ~ c_lessequals(X1,X2,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2611]) ).

cnf(c_0_2611_1,axiom,
    ( ~ c_lessequals(X1,X2,tc_nat)
    | c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),X3,tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X2,X3,tc_nat),X1,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2611]) ).

cnf(c_0_2612_0,axiom,
    ( c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X3,X1,tc_nat),X2,tc_nat) = c_HOL_Ominus__class_Ominus(X3,c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),tc_nat)
    | ~ c_lessequals(X1,X2,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2612]) ).

cnf(c_0_2612_1,axiom,
    ( ~ c_lessequals(X1,X2,tc_nat)
    | c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X3,X1,tc_nat),X2,tc_nat) = c_HOL_Ominus__class_Ominus(X3,c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2612]) ).

cnf(c_0_2613_0,axiom,
    ( c_HOL_Oplus__class_Oplus(X3,c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X3,X2,tc_nat),X1,tc_nat)
    | ~ c_lessequals(X1,X2,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2613]) ).

cnf(c_0_2613_1,axiom,
    ( ~ c_lessequals(X1,X2,tc_nat)
    | c_HOL_Oplus__class_Oplus(X3,c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X3,X2,tc_nat),X1,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2613]) ).

cnf(c_0_2614_0,axiom,
    ( c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),X3,tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X2,X3,tc_nat),X1,tc_nat)
    | ~ c_lessequals(X1,X2,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2614]) ).

cnf(c_0_2614_1,axiom,
    ( ~ c_lessequals(X1,X2,tc_nat)
    | c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),X3,tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X2,X3,tc_nat),X1,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2614]) ).

cnf(c_0_2615_0,axiom,
    ( c_lessequals(X2,c_HOL_Ozero__class_Ozero(X3),X3)
    | c_lessequals(c_HOL_Ozero__class_Ozero(X3),X2,X3)
    | ~ c_lessequals(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2615]) ).

cnf(c_0_2615_1,axiom,
    ( c_lessequals(c_HOL_Ozero__class_Ozero(X3),X2,X3)
    | c_lessequals(X2,c_HOL_Ozero__class_Ozero(X3),X3)
    | ~ c_lessequals(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2615]) ).

cnf(c_0_2615_2,axiom,
    ( ~ c_lessequals(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
    | c_lessequals(c_HOL_Ozero__class_Ozero(X3),X2,X3)
    | c_lessequals(X2,c_HOL_Ozero__class_Ozero(X3),X3)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2615]) ).

cnf(c_0_2615_3,axiom,
    ( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
    | ~ c_lessequals(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
    | c_lessequals(c_HOL_Ozero__class_Ozero(X3),X2,X3)
    | c_lessequals(X2,c_HOL_Ozero__class_Ozero(X3),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2615]) ).

cnf(c_0_2616_0,axiom,
    ( c_lessequals(X2,c_HOL_Ozero__class_Ozero(X3),X3)
    | c_lessequals(X1,c_HOL_Ozero__class_Ozero(X3),X3)
    | ~ c_lessequals(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2616]) ).

cnf(c_0_2616_1,axiom,
    ( c_lessequals(X1,c_HOL_Ozero__class_Ozero(X3),X3)
    | c_lessequals(X2,c_HOL_Ozero__class_Ozero(X3),X3)
    | ~ c_lessequals(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2616]) ).

cnf(c_0_2616_2,axiom,
    ( ~ c_lessequals(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
    | c_lessequals(X1,c_HOL_Ozero__class_Ozero(X3),X3)
    | c_lessequals(X2,c_HOL_Ozero__class_Ozero(X3),X3)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2616]) ).

cnf(c_0_2616_3,axiom,
    ( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
    | ~ c_lessequals(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
    | c_lessequals(X1,c_HOL_Ozero__class_Ozero(X3),X3)
    | c_lessequals(X2,c_HOL_Ozero__class_Ozero(X3),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2616]) ).

cnf(c_0_2617_0,axiom,
    ( c_lessequals(c_HOL_Ozero__class_Ozero(X3),X1,X3)
    | c_lessequals(c_HOL_Ozero__class_Ozero(X3),X2,X3)
    | ~ c_lessequals(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2617]) ).

cnf(c_0_2617_1,axiom,
    ( c_lessequals(c_HOL_Ozero__class_Ozero(X3),X2,X3)
    | c_lessequals(c_HOL_Ozero__class_Ozero(X3),X1,X3)
    | ~ c_lessequals(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2617]) ).

cnf(c_0_2617_2,axiom,
    ( ~ c_lessequals(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
    | c_lessequals(c_HOL_Ozero__class_Ozero(X3),X2,X3)
    | c_lessequals(c_HOL_Ozero__class_Ozero(X3),X1,X3)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2617]) ).

cnf(c_0_2617_3,axiom,
    ( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
    | ~ c_lessequals(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
    | c_lessequals(c_HOL_Ozero__class_Ozero(X3),X2,X3)
    | c_lessequals(c_HOL_Ozero__class_Ozero(X3),X1,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2617]) ).

cnf(c_0_2618_0,axiom,
    ( c_lessequals(c_HOL_Ozero__class_Ozero(X3),X1,X3)
    | c_lessequals(X1,c_HOL_Ozero__class_Ozero(X3),X3)
    | ~ c_lessequals(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2618]) ).

cnf(c_0_2618_1,axiom,
    ( c_lessequals(X1,c_HOL_Ozero__class_Ozero(X3),X3)
    | c_lessequals(c_HOL_Ozero__class_Ozero(X3),X1,X3)
    | ~ c_lessequals(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2618]) ).

cnf(c_0_2618_2,axiom,
    ( ~ c_lessequals(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
    | c_lessequals(X1,c_HOL_Ozero__class_Ozero(X3),X3)
    | c_lessequals(c_HOL_Ozero__class_Ozero(X3),X1,X3)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2618]) ).

cnf(c_0_2618_3,axiom,
    ( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
    | ~ c_lessequals(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
    | c_lessequals(X1,c_HOL_Ozero__class_Ozero(X3),X3)
    | c_lessequals(c_HOL_Ozero__class_Ozero(X3),X1,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2618]) ).

cnf(c_0_2619_0,axiom,
    ( c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2619]) ).

cnf(c_0_2619_1,axiom,
    ( c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
    | c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2619]) ).

cnf(c_0_2619_2,axiom,
    ( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
    | c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
    | c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2619]) ).

cnf(c_0_2619_3,axiom,
    ( ~ class_Ring__and__Field_Oordered__ring__strict(X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
    | c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
    | c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2619]) ).

cnf(c_0_2620_0,axiom,
    ( c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2620]) ).

cnf(c_0_2620_1,axiom,
    ( c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
    | c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2620]) ).

cnf(c_0_2620_2,axiom,
    ( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
    | c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
    | c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2620]) ).

cnf(c_0_2620_3,axiom,
    ( ~ class_Ring__and__Field_Oordered__ring__strict(X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
    | c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
    | c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2620]) ).

cnf(c_0_2621_0,axiom,
    ( c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
    | c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2621]) ).

cnf(c_0_2621_1,axiom,
    ( c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
    | c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2621]) ).

cnf(c_0_2621_2,axiom,
    ( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
    | c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
    | c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2621]) ).

cnf(c_0_2621_3,axiom,
    ( ~ class_Ring__and__Field_Oordered__ring__strict(X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
    | c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
    | c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2621]) ).

cnf(c_0_2622_0,axiom,
    ( c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
    | c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2622]) ).

cnf(c_0_2622_1,axiom,
    ( c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
    | c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2622]) ).

cnf(c_0_2622_2,axiom,
    ( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
    | c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
    | c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2622]) ).

cnf(c_0_2622_3,axiom,
    ( ~ class_Ring__and__Field_Oordered__ring__strict(X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
    | c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
    | c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2622]) ).

cnf(c_0_2623_0,axiom,
    ( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
    | c_Suc(c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X2,tc_nat)) = c_HOL_Oplus__class_Oplus(X1,X2,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2623]) ).

cnf(c_0_2623_1,axiom,
    ( c_Suc(c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X2,tc_nat)) = c_HOL_Oplus__class_Oplus(X1,X2,tc_nat)
    | X1 = c_HOL_Ozero__class_Ozero(tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2623]) ).

cnf(c_0_2624_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_2624]) ).

cnf(c_0_2624_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_2624]) ).

cnf(c_0_2624_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_2624]) ).

cnf(c_0_2625_0,axiom,
    ( c_lessequals(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),tc_nat)
    | ~ c_lessequals(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X1,tc_nat)
    | ~ c_lessequals(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X2,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2625]) ).

cnf(c_0_2625_1,axiom,
    ( ~ c_lessequals(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X1,tc_nat)
    | c_lessequals(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),tc_nat)
    | ~ c_lessequals(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X2,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2625]) ).

cnf(c_0_2625_2,axiom,
    ( ~ c_lessequals(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X2,tc_nat)
    | ~ c_lessequals(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X1,tc_nat)
    | c_lessequals(c_Suc(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_2625]) ).

cnf(c_0_2626_0,axiom,
    ( c_lessequals(X1,X2,X4)
    | c_lessequals(X1,X3,X4)
    | ~ c_lessequals(X1,c_Orderings_Oord__class_Omax(X2,X3,X4),X4)
    | ~ class_Orderings_Olinorder(X4) ),
    inference(literals_permutation,[status(thm)],[c_0_2626]) ).

cnf(c_0_2626_1,axiom,
    ( c_lessequals(X1,X3,X4)
    | c_lessequals(X1,X2,X4)
    | ~ c_lessequals(X1,c_Orderings_Oord__class_Omax(X2,X3,X4),X4)
    | ~ class_Orderings_Olinorder(X4) ),
    inference(literals_permutation,[status(thm)],[c_0_2626]) ).

cnf(c_0_2626_2,axiom,
    ( ~ c_lessequals(X1,c_Orderings_Oord__class_Omax(X2,X3,X4),X4)
    | c_lessequals(X1,X3,X4)
    | c_lessequals(X1,X2,X4)
    | ~ class_Orderings_Olinorder(X4) ),
    inference(literals_permutation,[status(thm)],[c_0_2626]) ).

cnf(c_0_2626_3,axiom,
    ( ~ class_Orderings_Olinorder(X4)
    | ~ c_lessequals(X1,c_Orderings_Oord__class_Omax(X2,X3,X4),X4)
    | c_lessequals(X1,X3,X4)
    | c_lessequals(X1,X2,X4) ),
    inference(literals_permutation,[status(thm)],[c_0_2626]) ).

cnf(c_0_2627_0,axiom,
    ( c_lessequals(X1,X4,X3)
    | c_lessequals(X2,X4,X3)
    | ~ c_lessequals(c_Orderings_Oord__class_Omin(X1,X2,X3),X4,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2627]) ).

cnf(c_0_2627_1,axiom,
    ( c_lessequals(X2,X4,X3)
    | c_lessequals(X1,X4,X3)
    | ~ c_lessequals(c_Orderings_Oord__class_Omin(X1,X2,X3),X4,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2627]) ).

cnf(c_0_2627_2,axiom,
    ( ~ c_lessequals(c_Orderings_Oord__class_Omin(X1,X2,X3),X4,X3)
    | c_lessequals(X2,X4,X3)
    | c_lessequals(X1,X4,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2627]) ).

cnf(c_0_2627_3,axiom,
    ( ~ class_Orderings_Olinorder(X3)
    | ~ c_lessequals(c_Orderings_Oord__class_Omin(X1,X2,X3),X4,X3)
    | c_lessequals(X2,X4,X3)
    | c_lessequals(X1,X4,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2627]) ).

cnf(c_0_2628_0,axiom,
    ( c_HOL_Oord__class_Oless(X1,X2,X4)
    | c_HOL_Oord__class_Oless(X1,X3,X4)
    | ~ c_HOL_Oord__class_Oless(X1,c_Orderings_Oord__class_Omax(X2,X3,X4),X4)
    | ~ class_Orderings_Olinorder(X4) ),
    inference(literals_permutation,[status(thm)],[c_0_2628]) ).

cnf(c_0_2628_1,axiom,
    ( c_HOL_Oord__class_Oless(X1,X3,X4)
    | c_HOL_Oord__class_Oless(X1,X2,X4)
    | ~ c_HOL_Oord__class_Oless(X1,c_Orderings_Oord__class_Omax(X2,X3,X4),X4)
    | ~ class_Orderings_Olinorder(X4) ),
    inference(literals_permutation,[status(thm)],[c_0_2628]) ).

cnf(c_0_2628_2,axiom,
    ( ~ c_HOL_Oord__class_Oless(X1,c_Orderings_Oord__class_Omax(X2,X3,X4),X4)
    | c_HOL_Oord__class_Oless(X1,X3,X4)
    | c_HOL_Oord__class_Oless(X1,X2,X4)
    | ~ class_Orderings_Olinorder(X4) ),
    inference(literals_permutation,[status(thm)],[c_0_2628]) ).

cnf(c_0_2628_3,axiom,
    ( ~ class_Orderings_Olinorder(X4)
    | ~ c_HOL_Oord__class_Oless(X1,c_Orderings_Oord__class_Omax(X2,X3,X4),X4)
    | c_HOL_Oord__class_Oless(X1,X3,X4)
    | c_HOL_Oord__class_Oless(X1,X2,X4) ),
    inference(literals_permutation,[status(thm)],[c_0_2628]) ).

cnf(c_0_2629_0,axiom,
    ( c_HOL_Oord__class_Oless(X1,X4,X3)
    | c_HOL_Oord__class_Oless(X2,X4,X3)
    | ~ c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omin(X1,X2,X3),X4,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2629]) ).

cnf(c_0_2629_1,axiom,
    ( c_HOL_Oord__class_Oless(X2,X4,X3)
    | c_HOL_Oord__class_Oless(X1,X4,X3)
    | ~ c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omin(X1,X2,X3),X4,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2629]) ).

cnf(c_0_2629_2,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omin(X1,X2,X3),X4,X3)
    | c_HOL_Oord__class_Oless(X2,X4,X3)
    | c_HOL_Oord__class_Oless(X1,X4,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2629]) ).

cnf(c_0_2629_3,axiom,
    ( ~ class_Orderings_Olinorder(X3)
    | ~ c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omin(X1,X2,X3),X4,X3)
    | c_HOL_Oord__class_Oless(X2,X4,X3)
    | c_HOL_Oord__class_Oless(X1,X4,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2629]) ).

cnf(c_0_2630_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_2630]) ).

cnf(c_0_2630_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_2630]) ).

cnf(c_0_2631_0,axiom,
    ( c_lessequals(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_lessequals(X1,X2,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2631]) ).

cnf(c_0_2631_1,axiom,
    ( ~ c_lessequals(X1,X2,tc_nat)
    | c_lessequals(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_2631]) ).

cnf(c_0_2632_0,axiom,
    ( c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(X2,X3,X1),X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
    | ~ class_OrderedGroup_Opordered__comm__monoid__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2632]) ).

cnf(c_0_2632_1,axiom,
    ( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(X2,X3,X1),X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
    | ~ class_OrderedGroup_Opordered__comm__monoid__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2632]) ).

cnf(c_0_2632_2,axiom,
    ( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(X2,X3,X1),X1)
    | ~ class_OrderedGroup_Opordered__comm__monoid__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2632]) ).

cnf(c_0_2632_3,axiom,
    ( ~ class_OrderedGroup_Opordered__comm__monoid__add(X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(X2,X3,X1),X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2632]) ).

cnf(c_0_2633_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_2633]) ).

cnf(c_0_2633_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_2633]) ).

cnf(c_0_2633_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_2633]) ).

cnf(c_0_2633_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_2633]) ).

cnf(c_0_2634_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_2634]) ).

cnf(c_0_2634_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_2634]) ).

cnf(c_0_2634_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_2634]) ).

cnf(c_0_2634_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_2634]) ).

cnf(c_0_2635_0,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X3,X2),c_HOL_Ozero__class_Ozero(X2),X2)
    | ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
    | ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X2),X2)
    | ~ class_OrderedGroup_Opordered__comm__monoid__add(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2635]) ).

cnf(c_0_2635_1,axiom,
    ( ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
    | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X3,X2),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_2635]) ).

cnf(c_0_2635_2,axiom,
    ( ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X2),X2)
    | ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
    | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X3,X2),c_HOL_Ozero__class_Ozero(X2),X2)
    | ~ class_OrderedGroup_Opordered__comm__monoid__add(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2635]) ).

cnf(c_0_2635_3,axiom,
    ( ~ class_OrderedGroup_Opordered__comm__monoid__add(X2)
    | ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X2),X2)
    | ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
    | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X3,X2),c_HOL_Ozero__class_Ozero(X2),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2635]) ).

cnf(c_0_2636_0,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X3,X2),c_HOL_Ozero__class_Ozero(X2),X2)
    | ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
    | ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X2),X2)
    | ~ class_OrderedGroup_Opordered__comm__monoid__add(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2636]) ).

cnf(c_0_2636_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
    | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X3,X2),c_HOL_Ozero__class_Ozero(X2),X2)
    | ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X2),X2)
    | ~ class_OrderedGroup_Opordered__comm__monoid__add(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2636]) ).

cnf(c_0_2636_2,axiom,
    ( ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X2),X2)
    | ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
    | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X3,X2),c_HOL_Ozero__class_Ozero(X2),X2)
    | ~ class_OrderedGroup_Opordered__comm__monoid__add(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2636]) ).

cnf(c_0_2636_3,axiom,
    ( ~ class_OrderedGroup_Opordered__comm__monoid__add(X2)
    | ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X2),X2)
    | ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
    | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X3,X2),c_HOL_Ozero__class_Ozero(X2),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2636]) ).

cnf(c_0_2637_0,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(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(X3,c_HOL_Ozero__class_Ozero(X2),X2)
    | ~ class_OrderedGroup_Opordered__comm__monoid__add(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2637]) ).

cnf(c_0_2637_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
    | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X3,X2),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_2637]) ).

cnf(c_0_2637_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_Oplus__class_Oplus(X1,X3,X2),c_HOL_Ozero__class_Ozero(X2),X2)
    | ~ class_OrderedGroup_Opordered__comm__monoid__add(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2637]) ).

cnf(c_0_2637_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(c_HOL_Oplus__class_Oplus(X1,X3,X2),c_HOL_Ozero__class_Ozero(X2),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2637]) ).

cnf(c_0_2638_0,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(X2,X3,X1),X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
    | ~ class_OrderedGroup_Opordered__comm__monoid__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2638]) ).

cnf(c_0_2638_1,axiom,
    ( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(X2,X3,X1),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_2638]) ).

cnf(c_0_2638_2,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(X2,X3,X1),X1)
    | ~ class_OrderedGroup_Opordered__comm__monoid__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2638]) ).

cnf(c_0_2638_3,axiom,
    ( ~ class_OrderedGroup_Opordered__comm__monoid__add(X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(X2,X3,X1),X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2638]) ).

cnf(c_0_2639_0,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(X2,X3,X1),X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
    | ~ class_OrderedGroup_Opordered__comm__monoid__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2639]) ).

cnf(c_0_2639_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_Oplus__class_Oplus(X2,X3,X1),X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
    | ~ class_OrderedGroup_Opordered__comm__monoid__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2639]) ).

cnf(c_0_2639_2,axiom,
    ( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(X2,X3,X1),X1)
    | ~ class_OrderedGroup_Opordered__comm__monoid__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2639]) ).

cnf(c_0_2639_3,axiom,
    ( ~ class_OrderedGroup_Opordered__comm__monoid__add(X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(X2,X3,X1),X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2639]) ).

cnf(c_0_2640_0,axiom,
    ( c_lessequals(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2640]) ).

cnf(c_0_2640_1,axiom,
    ( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | c_lessequals(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2640]) ).

cnf(c_0_2640_2,axiom,
    ( ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | c_lessequals(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2640]) ).

cnf(c_0_2640_3,axiom,
    ( ~ class_Ring__and__Field_Oordered__ring__strict(X1)
    | ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | c_lessequals(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Ozero__class_Ozero(X1),X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2640]) ).

cnf(c_0_2641_0,axiom,
    ( c_lessequals(c_HOL_Otimes__class_Otimes(X1,X3,X2),c_HOL_Ozero__class_Ozero(X2),X2)
    | ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X3,X2)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2641]) ).

cnf(c_0_2641_1,axiom,
    ( ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
    | c_lessequals(c_HOL_Otimes__class_Otimes(X1,X3,X2),c_HOL_Ozero__class_Ozero(X2),X2)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X3,X2)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2641]) ).

cnf(c_0_2641_2,axiom,
    ( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X3,X2)
    | ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
    | c_lessequals(c_HOL_Otimes__class_Otimes(X1,X3,X2),c_HOL_Ozero__class_Ozero(X2),X2)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2641]) ).

cnf(c_0_2641_3,axiom,
    ( ~ class_Ring__and__Field_Oordered__ring__strict(X2)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X3,X2)
    | ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
    | c_lessequals(c_HOL_Otimes__class_Otimes(X1,X3,X2),c_HOL_Ozero__class_Ozero(X2),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2641]) ).

cnf(c_0_2642_0,axiom,
    ( c_lessequals(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ class_Ring__and__Field_Opordered__cancel__semiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2642]) ).

cnf(c_0_2642_1,axiom,
    ( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | c_lessequals(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ class_Ring__and__Field_Opordered__cancel__semiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2642]) ).

cnf(c_0_2642_2,axiom,
    ( ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | c_lessequals(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ class_Ring__and__Field_Opordered__cancel__semiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2642]) ).

cnf(c_0_2642_3,axiom,
    ( ~ class_Ring__and__Field_Opordered__cancel__semiring(X1)
    | ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | c_lessequals(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Ozero__class_Ozero(X1),X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2642]) ).

cnf(c_0_2643_0,axiom,
    ( c_lessequals(c_HOL_Otimes__class_Otimes(X1,X3,X2),c_HOL_Ozero__class_Ozero(X2),X2)
    | ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X3,X2)
    | ~ class_Ring__and__Field_Opordered__cancel__semiring(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2643]) ).

cnf(c_0_2643_1,axiom,
    ( ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
    | c_lessequals(c_HOL_Otimes__class_Otimes(X1,X3,X2),c_HOL_Ozero__class_Ozero(X2),X2)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X3,X2)
    | ~ class_Ring__and__Field_Opordered__cancel__semiring(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2643]) ).

cnf(c_0_2643_2,axiom,
    ( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X3,X2)
    | ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
    | c_lessequals(c_HOL_Otimes__class_Otimes(X1,X3,X2),c_HOL_Ozero__class_Ozero(X2),X2)
    | ~ class_Ring__and__Field_Opordered__cancel__semiring(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2643]) ).

cnf(c_0_2643_3,axiom,
    ( ~ class_Ring__and__Field_Opordered__cancel__semiring(X2)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X3,X2)
    | ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
    | c_lessequals(c_HOL_Otimes__class_Otimes(X1,X3,X2),c_HOL_Ozero__class_Ozero(X2),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2643]) ).

cnf(c_0_2644_0,axiom,
    ( c_lessequals(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ class_Ring__and__Field_Opordered__cancel__semiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2644]) ).

cnf(c_0_2644_1,axiom,
    ( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | c_lessequals(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ class_Ring__and__Field_Opordered__cancel__semiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2644]) ).

cnf(c_0_2644_2,axiom,
    ( ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | c_lessequals(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ class_Ring__and__Field_Opordered__cancel__semiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2644]) ).

cnf(c_0_2644_3,axiom,
    ( ~ class_Ring__and__Field_Opordered__cancel__semiring(X1)
    | ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | c_lessequals(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Ozero__class_Ozero(X1),X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2644]) ).

cnf(c_0_2645_0,axiom,
    ( c_lessequals(c_HOL_Otimes__class_Otimes(X1,X3,X2),c_HOL_Ozero__class_Ozero(X2),X2)
    | ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X3,X2)
    | ~ class_Ring__and__Field_Opordered__cancel__semiring(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2645]) ).

cnf(c_0_2645_1,axiom,
    ( ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
    | c_lessequals(c_HOL_Otimes__class_Otimes(X1,X3,X2),c_HOL_Ozero__class_Ozero(X2),X2)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X3,X2)
    | ~ class_Ring__and__Field_Opordered__cancel__semiring(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2645]) ).

cnf(c_0_2645_2,axiom,
    ( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X3,X2)
    | ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
    | c_lessequals(c_HOL_Otimes__class_Otimes(X1,X3,X2),c_HOL_Ozero__class_Ozero(X2),X2)
    | ~ class_Ring__and__Field_Opordered__cancel__semiring(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2645]) ).

cnf(c_0_2645_3,axiom,
    ( ~ class_Ring__and__Field_Opordered__cancel__semiring(X2)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X3,X2)
    | ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
    | c_lessequals(c_HOL_Otimes__class_Otimes(X1,X3,X2),c_HOL_Ozero__class_Ozero(X2),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2645]) ).

cnf(c_0_2646_0,axiom,
    ( c_lessequals(c_HOL_Otimes__class_Otimes(X3,X2,X1),c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ class_Ring__and__Field_Opordered__cancel__semiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2646]) ).

cnf(c_0_2646_1,axiom,
    ( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | c_lessequals(c_HOL_Otimes__class_Otimes(X3,X2,X1),c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ class_Ring__and__Field_Opordered__cancel__semiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2646]) ).

cnf(c_0_2646_2,axiom,
    ( ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | c_lessequals(c_HOL_Otimes__class_Otimes(X3,X2,X1),c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ class_Ring__and__Field_Opordered__cancel__semiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2646]) ).

cnf(c_0_2646_3,axiom,
    ( ~ class_Ring__and__Field_Opordered__cancel__semiring(X1)
    | ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | c_lessequals(c_HOL_Otimes__class_Otimes(X3,X2,X1),c_HOL_Ozero__class_Ozero(X1),X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2646]) ).

cnf(c_0_2647_0,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(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_OrderedGroup_Opordered__comm__monoid__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2647]) ).

cnf(c_0_2647_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_Oplus__class_Oplus(X2,X3,X1),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_2647]) ).

cnf(c_0_2647_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_Oplus__class_Oplus(X2,X3,X1),X1)
    | ~ class_OrderedGroup_Opordered__comm__monoid__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2647]) ).

cnf(c_0_2647_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),c_HOL_Oplus__class_Oplus(X2,X3,X1),X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2647]) ).

cnf(c_0_2648_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_2648]) ).

cnf(c_0_2648_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_2648]) ).

cnf(c_0_2648_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_2648]) ).

cnf(c_0_2648_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_2648]) ).

cnf(c_0_2649_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_2649]) ).

cnf(c_0_2649_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_2649]) ).

cnf(c_0_2649_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_2649]) ).

cnf(c_0_2649_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_2649]) ).

cnf(c_0_2650_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_2650]) ).

cnf(c_0_2650_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_2650]) ).

cnf(c_0_2650_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_2650]) ).

cnf(c_0_2650_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_2650]) ).

cnf(c_0_2651_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_2651]) ).

cnf(c_0_2651_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_2651]) ).

cnf(c_0_2651_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_2651]) ).

cnf(c_0_2651_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_2651]) ).

cnf(c_0_2652_0,axiom,
    ( c_lessequals(c_HOL_Oplus__class_Oplus(X1,X3,X2),c_HOL_Ozero__class_Ozero(X2),X2)
    | ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
    | ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X2),X2)
    | ~ class_OrderedGroup_Opordered__comm__monoid__add(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2652]) ).

cnf(c_0_2652_1,axiom,
    ( ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
    | c_lessequals(c_HOL_Oplus__class_Oplus(X1,X3,X2),c_HOL_Ozero__class_Ozero(X2),X2)
    | ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X2),X2)
    | ~ class_OrderedGroup_Opordered__comm__monoid__add(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2652]) ).

cnf(c_0_2652_2,axiom,
    ( ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X2),X2)
    | ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
    | c_lessequals(c_HOL_Oplus__class_Oplus(X1,X3,X2),c_HOL_Ozero__class_Ozero(X2),X2)
    | ~ class_OrderedGroup_Opordered__comm__monoid__add(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2652]) ).

cnf(c_0_2652_3,axiom,
    ( ~ class_OrderedGroup_Opordered__comm__monoid__add(X2)
    | ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X2),X2)
    | ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
    | c_lessequals(c_HOL_Oplus__class_Oplus(X1,X3,X2),c_HOL_Ozero__class_Ozero(X2),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2652]) ).

cnf(c_0_2653_0,axiom,
    ( c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
    | ~ class_Ring__and__Field_Opordered__cancel__semiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2653]) ).

cnf(c_0_2653_1,axiom,
    ( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
    | ~ class_Ring__and__Field_Opordered__cancel__semiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2653]) ).

cnf(c_0_2653_2,axiom,
    ( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
    | ~ class_Ring__and__Field_Opordered__cancel__semiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2653]) ).

cnf(c_0_2653_3,axiom,
    ( ~ class_Ring__and__Field_Opordered__cancel__semiring(X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2653]) ).

cnf(c_0_2654_0,axiom,
    ( c_lessequals(c_HOL_Ozero__class_Ozero(X2),c_HOL_Otimes__class_Otimes(X1,X3,X2),X2)
    | ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
    | ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X2),X2)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2654]) ).

cnf(c_0_2654_1,axiom,
    ( ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
    | c_lessequals(c_HOL_Ozero__class_Ozero(X2),c_HOL_Otimes__class_Otimes(X1,X3,X2),X2)
    | ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X2),X2)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2654]) ).

cnf(c_0_2654_2,axiom,
    ( ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X2),X2)
    | ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
    | c_lessequals(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_2654]) ).

cnf(c_0_2654_3,axiom,
    ( ~ class_Ring__and__Field_Oordered__ring__strict(X2)
    | ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X2),X2)
    | ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
    | c_lessequals(c_HOL_Ozero__class_Ozero(X2),c_HOL_Otimes__class_Otimes(X1,X3,X2),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2654]) ).

cnf(c_0_2655_0,axiom,
    ( c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2655]) ).

cnf(c_0_2655_1,axiom,
    ( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2655]) ).

cnf(c_0_2655_2,axiom,
    ( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2655]) ).

cnf(c_0_2655_3,axiom,
    ( ~ class_Ring__and__Field_Oordered__ring__strict(X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2655]) ).

cnf(c_0_2656_0,axiom,
    ( c_lessequals(c_HOL_Ozero__class_Ozero(X2),c_HOL_Otimes__class_Otimes(X1,X3,X2),X2)
    | ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
    | ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X2),X2)
    | ~ class_Ring__and__Field_Opordered__ring(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2656]) ).

cnf(c_0_2656_1,axiom,
    ( ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
    | c_lessequals(c_HOL_Ozero__class_Ozero(X2),c_HOL_Otimes__class_Otimes(X1,X3,X2),X2)
    | ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X2),X2)
    | ~ class_Ring__and__Field_Opordered__ring(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2656]) ).

cnf(c_0_2656_2,axiom,
    ( ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X2),X2)
    | ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
    | c_lessequals(c_HOL_Ozero__class_Ozero(X2),c_HOL_Otimes__class_Otimes(X1,X3,X2),X2)
    | ~ class_Ring__and__Field_Opordered__ring(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2656]) ).

cnf(c_0_2656_3,axiom,
    ( ~ class_Ring__and__Field_Opordered__ring(X2)
    | ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X2),X2)
    | ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
    | c_lessequals(c_HOL_Ozero__class_Ozero(X2),c_HOL_Otimes__class_Otimes(X1,X3,X2),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2656]) ).

cnf(c_0_2657_0,axiom,
    ( c_lessequals(c_HOL_Ozero__class_Ozero(X2),c_HOL_Otimes__class_Otimes(X1,X3,X2),X2)
    | ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
    | ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X2),X2)
    | ~ class_Ring__and__Field_Opordered__ring(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2657]) ).

cnf(c_0_2657_1,axiom,
    ( ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
    | c_lessequals(c_HOL_Ozero__class_Ozero(X2),c_HOL_Otimes__class_Otimes(X1,X3,X2),X2)
    | ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X2),X2)
    | ~ class_Ring__and__Field_Opordered__ring(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2657]) ).

cnf(c_0_2657_2,axiom,
    ( ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X2),X2)
    | ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
    | c_lessequals(c_HOL_Ozero__class_Ozero(X2),c_HOL_Otimes__class_Otimes(X1,X3,X2),X2)
    | ~ class_Ring__and__Field_Opordered__ring(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2657]) ).

cnf(c_0_2657_3,axiom,
    ( ~ class_Ring__and__Field_Opordered__ring(X2)
    | ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X2),X2)
    | ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
    | c_lessequals(c_HOL_Ozero__class_Ozero(X2),c_HOL_Otimes__class_Otimes(X1,X3,X2),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2657]) ).

cnf(c_0_2658_0,axiom,
    ( c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
    | ~ class_Ring__and__Field_Opordered__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2658]) ).

cnf(c_0_2658_1,axiom,
    ( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
    | ~ class_Ring__and__Field_Opordered__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2658]) ).

cnf(c_0_2658_2,axiom,
    ( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
    | ~ class_Ring__and__Field_Opordered__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2658]) ).

cnf(c_0_2658_3,axiom,
    ( ~ class_Ring__and__Field_Opordered__ring(X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2658]) ).

cnf(c_0_2659_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),c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2659]) ).

cnf(c_0_2659_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),c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2659]) ).

cnf(c_0_2659_2,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),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_2659]) ).

cnf(c_0_2660_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_2660]) ).

cnf(c_0_2660_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_2660]) ).

cnf(c_0_2660_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_2660]) ).

cnf(c_0_2661_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_2661]) ).

cnf(c_0_2661_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_2661]) ).

cnf(c_0_2661_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_2661]) ).

cnf(c_0_2662_0,axiom,
    ( c_lessequals(c_HOL_Oplus__class_Oplus(X1,X4,X3),c_HOL_Oplus__class_Oplus(X2,X4,X3),X3)
    | ~ c_lessequals(X1,X2,X3)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2662]) ).

cnf(c_0_2662_1,axiom,
    ( ~ c_lessequals(X1,X2,X3)
    | c_lessequals(c_HOL_Oplus__class_Oplus(X1,X4,X3),c_HOL_Oplus__class_Oplus(X2,X4,X3),X3)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2662]) ).

cnf(c_0_2662_2,axiom,
    ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
    | ~ c_lessequals(X1,X2,X3)
    | c_lessequals(c_HOL_Oplus__class_Oplus(X1,X4,X3),c_HOL_Oplus__class_Oplus(X2,X4,X3),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2662]) ).

cnf(c_0_2663_0,axiom,
    ( c_lessequals(c_HOL_Oplus__class_Oplus(X4,X1,X3),c_HOL_Oplus__class_Oplus(X4,X2,X3),X3)
    | ~ c_lessequals(X1,X2,X3)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2663]) ).

cnf(c_0_2663_1,axiom,
    ( ~ c_lessequals(X1,X2,X3)
    | c_lessequals(c_HOL_Oplus__class_Oplus(X4,X1,X3),c_HOL_Oplus__class_Oplus(X4,X2,X3),X3)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2663]) ).

cnf(c_0_2663_2,axiom,
    ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
    | ~ c_lessequals(X1,X2,X3)
    | c_lessequals(c_HOL_Oplus__class_Oplus(X4,X1,X3),c_HOL_Oplus__class_Oplus(X4,X2,X3),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2663]) ).

cnf(c_0_2664_0,axiom,
    ( c_lessequals(c_HOL_Oplus__class_Oplus(X1,X4,X3),c_HOL_Oplus__class_Oplus(X2,X4,X3),X3)
    | ~ c_lessequals(X1,X2,X3)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2664]) ).

cnf(c_0_2664_1,axiom,
    ( ~ c_lessequals(X1,X2,X3)
    | c_lessequals(c_HOL_Oplus__class_Oplus(X1,X4,X3),c_HOL_Oplus__class_Oplus(X2,X4,X3),X3)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2664]) ).

cnf(c_0_2664_2,axiom,
    ( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X3)
    | ~ c_lessequals(X1,X2,X3)
    | c_lessequals(c_HOL_Oplus__class_Oplus(X1,X4,X3),c_HOL_Oplus__class_Oplus(X2,X4,X3),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2664]) ).

cnf(c_0_2665_0,axiom,
    ( c_lessequals(c_HOL_Oplus__class_Oplus(X4,X1,X3),c_HOL_Oplus__class_Oplus(X4,X2,X3),X3)
    | ~ c_lessequals(X1,X2,X3)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2665]) ).

cnf(c_0_2665_1,axiom,
    ( ~ c_lessequals(X1,X2,X3)
    | c_lessequals(c_HOL_Oplus__class_Oplus(X4,X1,X3),c_HOL_Oplus__class_Oplus(X4,X2,X3),X3)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2665]) ).

cnf(c_0_2665_2,axiom,
    ( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X3)
    | ~ c_lessequals(X1,X2,X3)
    | c_lessequals(c_HOL_Oplus__class_Oplus(X4,X1,X3),c_HOL_Oplus__class_Oplus(X4,X2,X3),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2665]) ).

cnf(c_0_2666_0,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X4,X3),c_HOL_Oplus__class_Oplus(X2,X4,X3),X3)
    | ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2666]) ).

cnf(c_0_2666_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X4,X3),c_HOL_Oplus__class_Oplus(X2,X4,X3),X3)
    | ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2666]) ).

cnf(c_0_2666_2,axiom,
    ( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X3)
    | ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X4,X3),c_HOL_Oplus__class_Oplus(X2,X4,X3),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2666]) ).

cnf(c_0_2667_0,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X4,X3),c_HOL_Oplus__class_Oplus(X2,X4,X3),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_2667]) ).

cnf(c_0_2667_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X4,X3),c_HOL_Oplus__class_Oplus(X2,X4,X3),X3)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2667]) ).

cnf(c_0_2667_2,axiom,
    ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
    | ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X4,X3),c_HOL_Oplus__class_Oplus(X2,X4,X3),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2667]) ).

cnf(c_0_2668_0,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X4,X1,X3),c_HOL_Oplus__class_Oplus(X4,X2,X3),X3)
    | ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2668]) ).

cnf(c_0_2668_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X4,X1,X3),c_HOL_Oplus__class_Oplus(X4,X2,X3),X3)
    | ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2668]) ).

cnf(c_0_2668_2,axiom,
    ( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X3)
    | ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X4,X1,X3),c_HOL_Oplus__class_Oplus(X4,X2,X3),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2668]) ).

cnf(c_0_2669_0,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X4,X1,X3),c_HOL_Oplus__class_Oplus(X4,X2,X3),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_2669]) ).

cnf(c_0_2669_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X4,X1,X3),c_HOL_Oplus__class_Oplus(X4,X2,X3),X3)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2669]) ).

cnf(c_0_2669_2,axiom,
    ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
    | ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X4,X1,X3),c_HOL_Oplus__class_Oplus(X4,X2,X3),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2669]) ).

cnf(c_0_2670_0,axiom,
    ( c_lessequals(X3,c_HOL_Oplus__class_Oplus(X2,X4,X1),X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | ~ c_lessequals(X3,X4,X1)
    | ~ class_OrderedGroup_Ocomm__monoid__add(X1)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2670]) ).

cnf(c_0_2670_1,axiom,
    ( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | c_lessequals(X3,c_HOL_Oplus__class_Oplus(X2,X4,X1),X1)
    | ~ c_lessequals(X3,X4,X1)
    | ~ class_OrderedGroup_Ocomm__monoid__add(X1)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2670]) ).

cnf(c_0_2670_2,axiom,
    ( ~ c_lessequals(X3,X4,X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | c_lessequals(X3,c_HOL_Oplus__class_Oplus(X2,X4,X1),X1)
    | ~ class_OrderedGroup_Ocomm__monoid__add(X1)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2670]) ).

cnf(c_0_2670_3,axiom,
    ( ~ class_OrderedGroup_Ocomm__monoid__add(X1)
    | ~ c_lessequals(X3,X4,X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | c_lessequals(X3,c_HOL_Oplus__class_Oplus(X2,X4,X1),X1)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2670]) ).

cnf(c_0_2670_4,axiom,
    ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
    | ~ class_OrderedGroup_Ocomm__monoid__add(X1)
    | ~ c_lessequals(X3,X4,X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | c_lessequals(X3,c_HOL_Oplus__class_Oplus(X2,X4,X1),X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2670]) ).

cnf(c_0_2671_0,axiom,
    ( c_lessequals(X3,c_HOL_Oplus__class_Oplus(X4,X2,X1),X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | ~ c_lessequals(X3,X4,X1)
    | ~ class_OrderedGroup_Ocomm__monoid__add(X1)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2671]) ).

cnf(c_0_2671_1,axiom,
    ( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | c_lessequals(X3,c_HOL_Oplus__class_Oplus(X4,X2,X1),X1)
    | ~ c_lessequals(X3,X4,X1)
    | ~ class_OrderedGroup_Ocomm__monoid__add(X1)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2671]) ).

cnf(c_0_2671_2,axiom,
    ( ~ c_lessequals(X3,X4,X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | c_lessequals(X3,c_HOL_Oplus__class_Oplus(X4,X2,X1),X1)
    | ~ class_OrderedGroup_Ocomm__monoid__add(X1)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2671]) ).

cnf(c_0_2671_3,axiom,
    ( ~ class_OrderedGroup_Ocomm__monoid__add(X1)
    | ~ c_lessequals(X3,X4,X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | c_lessequals(X3,c_HOL_Oplus__class_Oplus(X4,X2,X1),X1)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2671]) ).

cnf(c_0_2671_4,axiom,
    ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
    | ~ class_OrderedGroup_Ocomm__monoid__add(X1)
    | ~ c_lessequals(X3,X4,X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | c_lessequals(X3,c_HOL_Oplus__class_Oplus(X4,X2,X1),X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2671]) ).

cnf(c_0_2672_0,axiom,
    ( c_HOL_Oord__class_Oless(X3,c_HOL_Oplus__class_Oplus(X2,X4,X1),X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | ~ c_lessequals(X3,X4,X1)
    | ~ class_OrderedGroup_Ocomm__monoid__add(X1)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2672]) ).

cnf(c_0_2672_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | c_HOL_Oord__class_Oless(X3,c_HOL_Oplus__class_Oplus(X2,X4,X1),X1)
    | ~ c_lessequals(X3,X4,X1)
    | ~ class_OrderedGroup_Ocomm__monoid__add(X1)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2672]) ).

cnf(c_0_2672_2,axiom,
    ( ~ c_lessequals(X3,X4,X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | c_HOL_Oord__class_Oless(X3,c_HOL_Oplus__class_Oplus(X2,X4,X1),X1)
    | ~ class_OrderedGroup_Ocomm__monoid__add(X1)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2672]) ).

cnf(c_0_2672_3,axiom,
    ( ~ class_OrderedGroup_Ocomm__monoid__add(X1)
    | ~ c_lessequals(X3,X4,X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | c_HOL_Oord__class_Oless(X3,c_HOL_Oplus__class_Oplus(X2,X4,X1),X1)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2672]) ).

cnf(c_0_2672_4,axiom,
    ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
    | ~ class_OrderedGroup_Ocomm__monoid__add(X1)
    | ~ c_lessequals(X3,X4,X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | c_HOL_Oord__class_Oless(X3,c_HOL_Oplus__class_Oplus(X2,X4,X1),X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2672]) ).

cnf(c_0_2673_0,axiom,
    ( c_HOL_Oord__class_Oless(X3,c_HOL_Oplus__class_Oplus(X2,X4,X1),X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | ~ c_HOL_Oord__class_Oless(X3,X4,X1)
    | ~ class_OrderedGroup_Ocomm__monoid__add(X1)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2673]) ).

cnf(c_0_2673_1,axiom,
    ( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | c_HOL_Oord__class_Oless(X3,c_HOL_Oplus__class_Oplus(X2,X4,X1),X1)
    | ~ c_HOL_Oord__class_Oless(X3,X4,X1)
    | ~ class_OrderedGroup_Ocomm__monoid__add(X1)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2673]) ).

cnf(c_0_2673_2,axiom,
    ( ~ c_HOL_Oord__class_Oless(X3,X4,X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | c_HOL_Oord__class_Oless(X3,c_HOL_Oplus__class_Oplus(X2,X4,X1),X1)
    | ~ class_OrderedGroup_Ocomm__monoid__add(X1)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2673]) ).

cnf(c_0_2673_3,axiom,
    ( ~ class_OrderedGroup_Ocomm__monoid__add(X1)
    | ~ c_HOL_Oord__class_Oless(X3,X4,X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | c_HOL_Oord__class_Oless(X3,c_HOL_Oplus__class_Oplus(X2,X4,X1),X1)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2673]) ).

cnf(c_0_2673_4,axiom,
    ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
    | ~ class_OrderedGroup_Ocomm__monoid__add(X1)
    | ~ c_HOL_Oord__class_Oless(X3,X4,X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | c_HOL_Oord__class_Oless(X3,c_HOL_Oplus__class_Oplus(X2,X4,X1),X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2673]) ).

cnf(c_0_2674_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_2674]) ).

cnf(c_0_2674_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_2674]) ).

cnf(c_0_2675_0,axiom,
    ( c_HOL_Oord__class_Oless(X3,c_HOL_Oplus__class_Oplus(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__semidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2675]) ).

cnf(c_0_2675_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | c_HOL_Oord__class_Oless(X3,c_HOL_Oplus__class_Oplus(X2,X4,X1),X1)
    | ~ c_HOL_Oord__class_Oless(X3,X4,X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2675]) ).

cnf(c_0_2675_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,c_HOL_Oplus__class_Oplus(X2,X4,X1),X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2675]) ).

cnf(c_0_2675_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,c_HOL_Oplus__class_Oplus(X2,X4,X1),X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2675]) ).

cnf(c_0_2676_0,axiom,
    ( c_lessequals(c_HOL_Ominus__class_Ominus(X3,X2,tc_nat),c_HOL_Ominus__class_Ominus(X3,X1,tc_nat),tc_nat)
    | ~ c_lessequals(X1,X2,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2676]) ).

cnf(c_0_2676_1,axiom,
    ( ~ c_lessequals(X1,X2,tc_nat)
    | c_lessequals(c_HOL_Ominus__class_Ominus(X3,X2,tc_nat),c_HOL_Ominus__class_Ominus(X3,X1,tc_nat),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2676]) ).

cnf(c_0_2677_0,axiom,
    ( c_lessequals(c_HOL_Ominus__class_Ominus(X1,X3,tc_nat),c_HOL_Ominus__class_Ominus(X2,X3,tc_nat),tc_nat)
    | ~ c_lessequals(X1,X2,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2677]) ).

cnf(c_0_2677_1,axiom,
    ( ~ c_lessequals(X1,X2,tc_nat)
    | c_lessequals(c_HOL_Ominus__class_Ominus(X1,X3,tc_nat),c_HOL_Ominus__class_Ominus(X2,X3,tc_nat),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2677]) ).

cnf(c_0_2678_0,axiom,
    ( c_lessequals(c_HOL_Oplus__class_Oplus(X1,X3,tc_nat),c_HOL_Oplus__class_Oplus(X2,X3,tc_nat),tc_nat)
    | ~ c_lessequals(X1,X2,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2678]) ).

cnf(c_0_2678_1,axiom,
    ( ~ c_lessequals(X1,X2,tc_nat)
    | c_lessequals(c_HOL_Oplus__class_Oplus(X1,X3,tc_nat),c_HOL_Oplus__class_Oplus(X2,X3,tc_nat),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2678]) ).

cnf(c_0_2679_0,axiom,
    ( c_lessequals(c_HOL_Oplus__class_Oplus(X3,X1,tc_nat),c_HOL_Oplus__class_Oplus(X3,X2,tc_nat),tc_nat)
    | ~ c_lessequals(X1,X2,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2679]) ).

cnf(c_0_2679_1,axiom,
    ( ~ c_lessequals(X1,X2,tc_nat)
    | c_lessequals(c_HOL_Oplus__class_Oplus(X3,X1,tc_nat),c_HOL_Oplus__class_Oplus(X3,X2,tc_nat),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2679]) ).

cnf(c_0_2680_0,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X3,tc_nat),c_HOL_Oplus__class_Oplus(X2,X3,tc_nat),tc_nat)
    | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2680]) ).

cnf(c_0_2680_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X3,tc_nat),c_HOL_Oplus__class_Oplus(X2,X3,tc_nat),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2680]) ).

cnf(c_0_2681_0,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X3,X1,tc_nat),c_HOL_Oplus__class_Oplus(X3,X2,tc_nat),tc_nat)
    | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2681]) ).

cnf(c_0_2681_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X3,X1,tc_nat),c_HOL_Oplus__class_Oplus(X3,X2,tc_nat),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2681]) ).

cnf(c_0_2682_0,axiom,
    ( c_lessequals(c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),c_HOL_Otimes__class_Otimes(X2,X3,tc_nat),tc_nat)
    | ~ c_lessequals(X1,X2,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2682]) ).

cnf(c_0_2682_1,axiom,
    ( ~ c_lessequals(X1,X2,tc_nat)
    | c_lessequals(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_2682]) ).

cnf(c_0_2683_0,axiom,
    ( c_lessequals(c_HOL_Otimes__class_Otimes(X3,X1,tc_nat),c_HOL_Otimes__class_Otimes(X3,X2,tc_nat),tc_nat)
    | ~ c_lessequals(X1,X2,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2683]) ).

cnf(c_0_2683_1,axiom,
    ( ~ c_lessequals(X1,X2,tc_nat)
    | c_lessequals(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_2683]) ).

cnf(c_0_2684_0,axiom,
    ( c_lessequals(c_HOL_Otimes__class_Otimes(X3,X1,tc_nat),c_HOL_Otimes__class_Otimes(X3,X2,tc_nat),tc_nat)
    | ~ c_lessequals(X1,X2,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2684]) ).

cnf(c_0_2684_1,axiom,
    ( ~ c_lessequals(X1,X2,tc_nat)
    | c_lessequals(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_2684]) ).

cnf(c_0_2685_0,axiom,
    ( c_lessequals(c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),c_HOL_Otimes__class_Otimes(X2,X3,tc_nat),tc_nat)
    | ~ c_lessequals(X1,X2,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2685]) ).

cnf(c_0_2685_1,axiom,
    ( ~ c_lessequals(X1,X2,tc_nat)
    | c_lessequals(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_2685]) ).

cnf(c_0_2686_0,axiom,
    ( c_Lambda_Olift(c_Lambda_Olift(X3,X1),c_Suc(X2)) = c_Lambda_Olift(c_Lambda_Olift(X3,X2),X1)
    | ~ c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(X2,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2686]) ).

cnf(c_0_2686_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(X2,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat)
    | c_Lambda_Olift(c_Lambda_Olift(X3,X1),c_Suc(X2)) = c_Lambda_Olift(c_Lambda_Olift(X3,X2),X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2686]) ).

cnf(c_0_2687_0,axiom,
    ( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,X3),X2,X3) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(X3),X3),X2,X3)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2687]) ).

cnf(c_0_2687_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
    | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,X3),X2,X3) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(X3),X3),X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2687]) ).

cnf(c_0_2688_0,axiom,
    ( c_HOL_Oplus__class_Oplus(X1,c_HOL_Otimes__class_Otimes(X2,X1,X3),X3) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X2,c_HOL_Oone__class_Oone(X3),X3),X1,X3)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2688]) ).

cnf(c_0_2688_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
    | c_HOL_Oplus__class_Oplus(X1,c_HOL_Otimes__class_Otimes(X2,X1,X3),X3) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X2,c_HOL_Oone__class_Oone(X3),X3),X1,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2688]) ).

cnf(c_0_2689_0,axiom,
    ( c_lessequals(c_Orderings_Oord__class_Omax(X1,X4,X3),X2,X3)
    | ~ c_lessequals(X1,X2,X3)
    | ~ c_lessequals(X4,X2,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2689]) ).

cnf(c_0_2689_1,axiom,
    ( ~ c_lessequals(X1,X2,X3)
    | c_lessequals(c_Orderings_Oord__class_Omax(X1,X4,X3),X2,X3)
    | ~ c_lessequals(X4,X2,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2689]) ).

cnf(c_0_2689_2,axiom,
    ( ~ c_lessequals(X4,X2,X3)
    | ~ c_lessequals(X1,X2,X3)
    | c_lessequals(c_Orderings_Oord__class_Omax(X1,X4,X3),X2,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2689]) ).

cnf(c_0_2689_3,axiom,
    ( ~ class_Orderings_Olinorder(X3)
    | ~ c_lessequals(X4,X2,X3)
    | ~ c_lessequals(X1,X2,X3)
    | c_lessequals(c_Orderings_Oord__class_Omax(X1,X4,X3),X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2689]) ).

cnf(c_0_2690_0,axiom,
    ( c_lessequals(c_Orderings_Oord__class_Omax(X1,X4,X3),X2,X3)
    | ~ c_lessequals(X1,X2,X3)
    | ~ c_lessequals(X4,X2,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2690]) ).

cnf(c_0_2690_1,axiom,
    ( ~ c_lessequals(X1,X2,X3)
    | c_lessequals(c_Orderings_Oord__class_Omax(X1,X4,X3),X2,X3)
    | ~ c_lessequals(X4,X2,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2690]) ).

cnf(c_0_2690_2,axiom,
    ( ~ c_lessequals(X4,X2,X3)
    | ~ c_lessequals(X1,X2,X3)
    | c_lessequals(c_Orderings_Oord__class_Omax(X1,X4,X3),X2,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2690]) ).

cnf(c_0_2690_3,axiom,
    ( ~ class_Orderings_Olinorder(X3)
    | ~ c_lessequals(X4,X2,X3)
    | ~ c_lessequals(X1,X2,X3)
    | c_lessequals(c_Orderings_Oord__class_Omax(X1,X4,X3),X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2690]) ).

cnf(c_0_2691_0,axiom,
    ( c_lessequals(c_Orderings_Oord__class_Omax(X1,X4,X3),X2,X3)
    | ~ c_lessequals(X1,X2,X3)
    | ~ c_lessequals(X4,X2,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2691]) ).

cnf(c_0_2691_1,axiom,
    ( ~ c_lessequals(X1,X2,X3)
    | c_lessequals(c_Orderings_Oord__class_Omax(X1,X4,X3),X2,X3)
    | ~ c_lessequals(X4,X2,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2691]) ).

cnf(c_0_2691_2,axiom,
    ( ~ c_lessequals(X4,X2,X3)
    | ~ c_lessequals(X1,X2,X3)
    | c_lessequals(c_Orderings_Oord__class_Omax(X1,X4,X3),X2,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2691]) ).

cnf(c_0_2691_3,axiom,
    ( ~ class_Orderings_Olinorder(X3)
    | ~ c_lessequals(X4,X2,X3)
    | ~ c_lessequals(X1,X2,X3)
    | c_lessequals(c_Orderings_Oord__class_Omax(X1,X4,X3),X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2691]) ).

cnf(c_0_2692_0,axiom,
    ( c_lessequals(X1,c_Orderings_Oord__class_Omin(X2,X4,X3),X3)
    | ~ c_lessequals(X1,X2,X3)
    | ~ c_lessequals(X1,X4,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2692]) ).

cnf(c_0_2692_1,axiom,
    ( ~ c_lessequals(X1,X2,X3)
    | c_lessequals(X1,c_Orderings_Oord__class_Omin(X2,X4,X3),X3)
    | ~ c_lessequals(X1,X4,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2692]) ).

cnf(c_0_2692_2,axiom,
    ( ~ c_lessequals(X1,X4,X3)
    | ~ c_lessequals(X1,X2,X3)
    | c_lessequals(X1,c_Orderings_Oord__class_Omin(X2,X4,X3),X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2692]) ).

cnf(c_0_2692_3,axiom,
    ( ~ class_Orderings_Olinorder(X3)
    | ~ c_lessequals(X1,X4,X3)
    | ~ c_lessequals(X1,X2,X3)
    | c_lessequals(X1,c_Orderings_Oord__class_Omin(X2,X4,X3),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2692]) ).

cnf(c_0_2693_0,axiom,
    ( c_lessequals(X1,c_Orderings_Oord__class_Omin(X2,X4,X3),X3)
    | ~ c_lessequals(X1,X2,X3)
    | ~ c_lessequals(X1,X4,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2693]) ).

cnf(c_0_2693_1,axiom,
    ( ~ c_lessequals(X1,X2,X3)
    | c_lessequals(X1,c_Orderings_Oord__class_Omin(X2,X4,X3),X3)
    | ~ c_lessequals(X1,X4,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2693]) ).

cnf(c_0_2693_2,axiom,
    ( ~ c_lessequals(X1,X4,X3)
    | ~ c_lessequals(X1,X2,X3)
    | c_lessequals(X1,c_Orderings_Oord__class_Omin(X2,X4,X3),X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2693]) ).

cnf(c_0_2693_3,axiom,
    ( ~ class_Orderings_Olinorder(X3)
    | ~ c_lessequals(X1,X4,X3)
    | ~ c_lessequals(X1,X2,X3)
    | c_lessequals(X1,c_Orderings_Oord__class_Omin(X2,X4,X3),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2693]) ).

cnf(c_0_2694_0,axiom,
    ( c_lessequals(X1,c_Orderings_Oord__class_Omin(X2,X4,X3),X3)
    | ~ c_lessequals(X1,X2,X3)
    | ~ c_lessequals(X1,X4,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2694]) ).

cnf(c_0_2694_1,axiom,
    ( ~ c_lessequals(X1,X2,X3)
    | c_lessequals(X1,c_Orderings_Oord__class_Omin(X2,X4,X3),X3)
    | ~ c_lessequals(X1,X4,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2694]) ).

cnf(c_0_2694_2,axiom,
    ( ~ c_lessequals(X1,X4,X3)
    | ~ c_lessequals(X1,X2,X3)
    | c_lessequals(X1,c_Orderings_Oord__class_Omin(X2,X4,X3),X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2694]) ).

cnf(c_0_2694_3,axiom,
    ( ~ class_Orderings_Olinorder(X3)
    | ~ c_lessequals(X1,X4,X3)
    | ~ c_lessequals(X1,X2,X3)
    | c_lessequals(X1,c_Orderings_Oord__class_Omin(X2,X4,X3),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2694]) ).

cnf(c_0_2695_0,axiom,
    ( c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omax(X1,X4,X3),X2,X3)
    | ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | ~ c_HOL_Oord__class_Oless(X4,X2,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2695]) ).

cnf(c_0_2695_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omax(X1,X4,X3),X2,X3)
    | ~ c_HOL_Oord__class_Oless(X4,X2,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2695]) ).

cnf(c_0_2695_2,axiom,
    ( ~ c_HOL_Oord__class_Oless(X4,X2,X3)
    | ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omax(X1,X4,X3),X2,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2695]) ).

cnf(c_0_2695_3,axiom,
    ( ~ class_Orderings_Olinorder(X3)
    | ~ c_HOL_Oord__class_Oless(X4,X2,X3)
    | ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omax(X1,X4,X3),X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2695]) ).

cnf(c_0_2696_0,axiom,
    ( c_HOL_Oord__class_Oless(X1,c_Orderings_Oord__class_Omin(X2,X4,X3),X3)
    | ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | ~ c_HOL_Oord__class_Oless(X1,X4,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2696]) ).

cnf(c_0_2696_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | c_HOL_Oord__class_Oless(X1,c_Orderings_Oord__class_Omin(X2,X4,X3),X3)
    | ~ c_HOL_Oord__class_Oless(X1,X4,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2696]) ).

cnf(c_0_2696_2,axiom,
    ( ~ c_HOL_Oord__class_Oless(X1,X4,X3)
    | ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | c_HOL_Oord__class_Oless(X1,c_Orderings_Oord__class_Omin(X2,X4,X3),X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2696]) ).

cnf(c_0_2696_3,axiom,
    ( ~ class_Orderings_Olinorder(X3)
    | ~ c_HOL_Oord__class_Oless(X1,X4,X3)
    | ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | c_HOL_Oord__class_Oless(X1,c_Orderings_Oord__class_Omin(X2,X4,X3),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2696]) ).

cnf(c_0_2697_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_2697]) ).

cnf(c_0_2697_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_2697]) ).

cnf(c_0_2697_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_2697]) ).

cnf(c_0_2698_0,axiom,
    ( X1 = X2
    | ~ c_lessequals(X3,X1,tc_nat)
    | ~ c_lessequals(X3,X2,tc_nat)
    | c_HOL_Ominus__class_Ominus(X1,X3,tc_nat) != c_HOL_Ominus__class_Ominus(X2,X3,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2698]) ).

cnf(c_0_2698_1,axiom,
    ( ~ c_lessequals(X3,X1,tc_nat)
    | X1 = X2
    | ~ c_lessequals(X3,X2,tc_nat)
    | c_HOL_Ominus__class_Ominus(X1,X3,tc_nat) != c_HOL_Ominus__class_Ominus(X2,X3,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2698]) ).

cnf(c_0_2698_2,axiom,
    ( ~ c_lessequals(X3,X2,tc_nat)
    | ~ c_lessequals(X3,X1,tc_nat)
    | X1 = X2
    | c_HOL_Ominus__class_Ominus(X1,X3,tc_nat) != c_HOL_Ominus__class_Ominus(X2,X3,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2698]) ).

cnf(c_0_2698_3,axiom,
    ( c_HOL_Ominus__class_Ominus(X1,X3,tc_nat) != c_HOL_Ominus__class_Ominus(X2,X3,tc_nat)
    | ~ c_lessequals(X3,X2,tc_nat)
    | ~ c_lessequals(X3,X1,tc_nat)
    | X1 = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_2698]) ).

cnf(c_0_2699_0,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X2,X1,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),X2,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2699]) ).

cnf(c_0_2699_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
    | c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(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_2699]) ).

cnf(c_0_2699_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_Ominus__class_Ominus(X2,X1,tc_nat),X2,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2699]) ).

cnf(c_0_2700_0,axiom,
    ( c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(X2,X2,X1),X1)
    | ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2700]) ).

cnf(c_0_2700_1,axiom,
    ( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(X2,X2,X1),X1)
    | c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2700]) ).

cnf(c_0_2700_2,axiom,
    ( ~ class_OrderedGroup_Olordered__ab__group__add(X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(X2,X2,X1),X1)
    | c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2700]) ).

cnf(c_0_2701_0,axiom,
    ( c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X1,X2),c_HOL_Ozero__class_Ozero(X2),X2)
    | ~ class_OrderedGroup_Olordered__ab__group__add(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2701]) ).

cnf(c_0_2701_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X1,X2),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_2701]) ).

cnf(c_0_2701_2,axiom,
    ( ~ class_OrderedGroup_Olordered__ab__group__add(X2)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X1,X2),c_HOL_Ozero__class_Ozero(X2),X2)
    | c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2701]) ).

cnf(c_0_2702_0,axiom,
    ( c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X1,X2),c_HOL_Ozero__class_Ozero(X2),X2)
    | ~ class_Ring__and__Field_Oordered__idom(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2702]) ).

cnf(c_0_2702_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X1,X2),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_2702]) ).

cnf(c_0_2702_2,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(X2)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X1,X2),c_HOL_Ozero__class_Ozero(X2),X2)
    | c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2702]) ).

cnf(c_0_2703_0,axiom,
    ( c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
    | ~ c_lessequals(c_HOL_Oplus__class_Oplus(X1,X1,X2),c_HOL_Ozero__class_Ozero(X2),X2)
    | ~ class_OrderedGroup_Olordered__ab__group__add(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2703]) ).

cnf(c_0_2703_1,axiom,
    ( ~ c_lessequals(c_HOL_Oplus__class_Oplus(X1,X1,X2),c_HOL_Ozero__class_Ozero(X2),X2)
    | c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
    | ~ class_OrderedGroup_Olordered__ab__group__add(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2703]) ).

cnf(c_0_2703_2,axiom,
    ( ~ class_OrderedGroup_Olordered__ab__group__add(X2)
    | ~ c_lessequals(c_HOL_Oplus__class_Oplus(X1,X1,X2),c_HOL_Ozero__class_Ozero(X2),X2)
    | c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2703]) ).

cnf(c_0_2704_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_Oplus__class_Oplus(X2,X2,X1),X1)
    | ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2704]) ).

cnf(c_0_2704_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(X2,X2,X1),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_2704]) ).

cnf(c_0_2704_2,axiom,
    ( ~ class_OrderedGroup_Olordered__ab__group__add(X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(X2,X2,X1),X1)
    | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2704]) ).

cnf(c_0_2705_0,axiom,
    ( c_lessequals(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X2,tc_nat)
    | ~ c_lessequals(c_Suc(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_2705]) ).

cnf(c_0_2705_1,axiom,
    ( ~ c_lessequals(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),tc_nat)
    | c_lessequals(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X2,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2705]) ).

cnf(c_0_2706_0,axiom,
    ( c_lessequals(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X1,tc_nat)
    | ~ c_lessequals(c_Suc(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_2706]) ).

cnf(c_0_2706_1,axiom,
    ( ~ c_lessequals(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),tc_nat)
    | c_lessequals(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X1,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2706]) ).

cnf(c_0_2707_0,axiom,
    ( c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X2,X4),X3,X4) = c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X2,X3,X4),X4)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X4) ),
    inference(literals_permutation,[status(thm)],[c_0_2707]) ).

cnf(c_0_2707_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__1(X4)
    | c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X2,X4),X3,X4) = c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X2,X3,X4),X4) ),
    inference(literals_permutation,[status(thm)],[c_0_2707]) ).

cnf(c_0_2708_0,axiom,
    ( c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X2,X3,X4),X4) = c_HOL_Oplus__class_Oplus(X2,c_HOL_Oplus__class_Oplus(X1,X3,X4),X4)
    | ~ class_OrderedGroup_Oab__group__add(X4) ),
    inference(literals_permutation,[status(thm)],[c_0_2708]) ).

cnf(c_0_2708_1,axiom,
    ( ~ class_OrderedGroup_Oab__group__add(X4)
    | c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X2,X3,X4),X4) = c_HOL_Oplus__class_Oplus(X2,c_HOL_Oplus__class_Oplus(X1,X3,X4),X4) ),
    inference(literals_permutation,[status(thm)],[c_0_2708]) ).

cnf(c_0_2709_0,axiom,
    ( c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X2,X3),X4,X3) = c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X2,X4,X3),X3)
    | ~ class_OrderedGroup_Ocomm__monoid__add(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2709]) ).

cnf(c_0_2709_1,axiom,
    ( ~ class_OrderedGroup_Ocomm__monoid__add(X3)
    | c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X2,X3),X4,X3) = c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X2,X4,X3),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2709]) ).

cnf(c_0_2710_0,axiom,
    ( c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X2,X3,X4),X4) = c_HOL_Oplus__class_Oplus(X2,c_HOL_Oplus__class_Oplus(X1,X3,X4),X4)
    | ~ class_OrderedGroup_Ocomm__monoid__add(X4) ),
    inference(literals_permutation,[status(thm)],[c_0_2710]) ).

cnf(c_0_2710_1,axiom,
    ( ~ class_OrderedGroup_Ocomm__monoid__add(X4)
    | c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X2,X3,X4),X4) = c_HOL_Oplus__class_Oplus(X2,c_HOL_Oplus__class_Oplus(X1,X3,X4),X4) ),
    inference(literals_permutation,[status(thm)],[c_0_2710]) ).

cnf(c_0_2711_0,axiom,
    ( c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X2,X3),X4,X3) = c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X2,X4,X3),X3)
    | ~ class_OrderedGroup_Oab__semigroup__add(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2711]) ).

cnf(c_0_2711_1,axiom,
    ( ~ class_OrderedGroup_Oab__semigroup__add(X3)
    | c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X2,X3),X4,X3) = c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X2,X4,X3),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2711]) ).

cnf(c_0_2712_0,axiom,
    ( c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X2,X4),X3,X4) = c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X2,X3,X4),X4)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X4) ),
    inference(literals_permutation,[status(thm)],[c_0_2712]) ).

cnf(c_0_2712_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__1(X4)
    | c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X2,X4),X3,X4) = c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X2,X3,X4),X4) ),
    inference(literals_permutation,[status(thm)],[c_0_2712]) ).

cnf(c_0_2713_0,axiom,
    ( c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X2,X3),X4,X3) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X4,X3),X2,X3)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2713]) ).

cnf(c_0_2713_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
    | c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X2,X3),X4,X3) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X4,X3),X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2713]) ).

cnf(c_0_2714_0,axiom,
    ( c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X2,X3,X4),X4) = c_HOL_Oplus__class_Oplus(X2,c_HOL_Oplus__class_Oplus(X1,X3,X4),X4)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X4) ),
    inference(literals_permutation,[status(thm)],[c_0_2714]) ).

cnf(c_0_2714_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__1(X4)
    | c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X2,X3,X4),X4) = c_HOL_Oplus__class_Oplus(X2,c_HOL_Oplus__class_Oplus(X1,X3,X4),X4) ),
    inference(literals_permutation,[status(thm)],[c_0_2714]) ).

cnf(c_0_2715_0,axiom,
    ( c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X2,X3),X4,X3) = c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X2,X4,X3),X3)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2715]) ).

cnf(c_0_2715_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
    | c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X2,X3),X4,X3) = c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X2,X4,X3),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2715]) ).

cnf(c_0_2716_0,axiom,
    ( c_Orderings_Oord__class_Omin(c_Orderings_Oord__class_Omin(X1,X2,X3),X4,X3) = c_Orderings_Oord__class_Omin(X1,c_Orderings_Oord__class_Omin(X2,X4,X3),X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2716]) ).

cnf(c_0_2716_1,axiom,
    ( ~ class_Orderings_Olinorder(X3)
    | c_Orderings_Oord__class_Omin(c_Orderings_Oord__class_Omin(X1,X2,X3),X4,X3) = c_Orderings_Oord__class_Omin(X1,c_Orderings_Oord__class_Omin(X2,X4,X3),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2716]) ).

cnf(c_0_2717_0,axiom,
    ( c_Orderings_Oord__class_Omin(X1,c_Orderings_Oord__class_Omin(X2,X3,X4),X4) = c_Orderings_Oord__class_Omin(X2,c_Orderings_Oord__class_Omin(X1,X3,X4),X4)
    | ~ class_Orderings_Olinorder(X4) ),
    inference(literals_permutation,[status(thm)],[c_0_2717]) ).

cnf(c_0_2717_1,axiom,
    ( ~ class_Orderings_Olinorder(X4)
    | c_Orderings_Oord__class_Omin(X1,c_Orderings_Oord__class_Omin(X2,X3,X4),X4) = c_Orderings_Oord__class_Omin(X2,c_Orderings_Oord__class_Omin(X1,X3,X4),X4) ),
    inference(literals_permutation,[status(thm)],[c_0_2717]) ).

cnf(c_0_2718_0,axiom,
    ( c_Orderings_Oord__class_Omax(c_Orderings_Oord__class_Omax(X1,X2,X3),X4,X3) = c_Orderings_Oord__class_Omax(X1,c_Orderings_Oord__class_Omax(X2,X4,X3),X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2718]) ).

cnf(c_0_2718_1,axiom,
    ( ~ class_Orderings_Olinorder(X3)
    | c_Orderings_Oord__class_Omax(c_Orderings_Oord__class_Omax(X1,X2,X3),X4,X3) = c_Orderings_Oord__class_Omax(X1,c_Orderings_Oord__class_Omax(X2,X4,X3),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2718]) ).

cnf(c_0_2719_0,axiom,
    ( c_Orderings_Oord__class_Omax(X1,c_Orderings_Oord__class_Omax(X2,X3,X4),X4) = c_Orderings_Oord__class_Omax(X2,c_Orderings_Oord__class_Omax(X1,X3,X4),X4)
    | ~ class_Orderings_Olinorder(X4) ),
    inference(literals_permutation,[status(thm)],[c_0_2719]) ).

cnf(c_0_2719_1,axiom,
    ( ~ class_Orderings_Olinorder(X4)
    | c_Orderings_Oord__class_Omax(X1,c_Orderings_Oord__class_Omax(X2,X3,X4),X4) = c_Orderings_Oord__class_Omax(X2,c_Orderings_Oord__class_Omax(X1,X3,X4),X4) ),
    inference(literals_permutation,[status(thm)],[c_0_2719]) ).

cnf(c_0_2720_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_2720]) ).

cnf(c_0_2720_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_2720]) ).

cnf(c_0_2721_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_2721]) ).

cnf(c_0_2721_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_2721]) ).

cnf(c_0_2722_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_2722]) ).

cnf(c_0_2722_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_2722]) ).

cnf(c_0_2723_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_2723]) ).

cnf(c_0_2723_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_2723]) ).

cnf(c_0_2724_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_2724]) ).

cnf(c_0_2724_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_2724]) ).

cnf(c_0_2725_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_2725]) ).

cnf(c_0_2725_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_2725]) ).

cnf(c_0_2726_0,axiom,
    ( c_HOL_Oord__class_Oless(X2,c_HOL_Oplus__class_Oplus(X3,X1,tc_nat),tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
    | ~ c_lessequals(X2,X3,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2726]) ).

cnf(c_0_2726_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
    | c_HOL_Oord__class_Oless(X2,c_HOL_Oplus__class_Oplus(X3,X1,tc_nat),tc_nat)
    | ~ c_lessequals(X2,X3,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2726]) ).

cnf(c_0_2726_2,axiom,
    ( ~ c_lessequals(X2,X3,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
    | c_HOL_Oord__class_Oless(X2,c_HOL_Oplus__class_Oplus(X3,X1,tc_nat),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2726]) ).

cnf(c_0_2727_0,axiom,
    ( c_HOL_Oplus__class_Oplus(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) = c_HOL_Ozero__class_Ozero(X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2727]) ).

cnf(c_0_2727_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__ring__strict(X1)
    | c_HOL_Oplus__class_Oplus(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) = c_HOL_Ozero__class_Ozero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2727]) ).

cnf(c_0_2728_0,axiom,
    ( c_lessequals(X1,X2,X3)
    | ~ c_lessequals(c_HOL_Ominus__class_Ominus(X1,X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2728]) ).

cnf(c_0_2728_1,axiom,
    ( ~ c_lessequals(c_HOL_Ominus__class_Ominus(X1,X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
    | c_lessequals(X1,X2,X3)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2728]) ).

cnf(c_0_2728_2,axiom,
    ( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
    | ~ c_lessequals(c_HOL_Ominus__class_Ominus(X1,X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
    | c_lessequals(X1,X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2728]) ).

cnf(c_0_2729_0,axiom,
    ( c_HOL_Oord__class_Oless(X1,X2,X3)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2729]) ).

cnf(c_0_2729_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
    | c_HOL_Oord__class_Oless(X1,X2,X3)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2729]) ).

cnf(c_0_2729_2,axiom,
    ( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
    | c_HOL_Oord__class_Oless(X1,X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2729]) ).

cnf(c_0_2730_0,axiom,
    ( c_lessequals(X4,X5,X3)
    | ~ c_lessequals(X1,X2,X3)
    | c_HOL_Ominus__class_Ominus(X2,X1,X3) != c_HOL_Ominus__class_Ominus(X5,X4,X3)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2730]) ).

cnf(c_0_2730_1,axiom,
    ( ~ c_lessequals(X1,X2,X3)
    | c_lessequals(X4,X5,X3)
    | c_HOL_Ominus__class_Ominus(X2,X1,X3) != c_HOL_Ominus__class_Ominus(X5,X4,X3)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2730]) ).

cnf(c_0_2730_2,axiom,
    ( c_HOL_Ominus__class_Ominus(X2,X1,X3) != c_HOL_Ominus__class_Ominus(X5,X4,X3)
    | ~ c_lessequals(X1,X2,X3)
    | c_lessequals(X4,X5,X3)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2730]) ).

cnf(c_0_2730_3,axiom,
    ( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
    | c_HOL_Ominus__class_Ominus(X2,X1,X3) != c_HOL_Ominus__class_Ominus(X5,X4,X3)
    | ~ c_lessequals(X1,X2,X3)
    | c_lessequals(X4,X5,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2730]) ).

cnf(c_0_2731_0,axiom,
    ( c_lessequals(X4,X5,X3)
    | ~ c_lessequals(X1,X2,X3)
    | c_HOL_Ominus__class_Ominus(X5,X4,X3) != c_HOL_Ominus__class_Ominus(X2,X1,X3)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2731]) ).

cnf(c_0_2731_1,axiom,
    ( ~ c_lessequals(X1,X2,X3)
    | c_lessequals(X4,X5,X3)
    | c_HOL_Ominus__class_Ominus(X5,X4,X3) != c_HOL_Ominus__class_Ominus(X2,X1,X3)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2731]) ).

cnf(c_0_2731_2,axiom,
    ( c_HOL_Ominus__class_Ominus(X5,X4,X3) != c_HOL_Ominus__class_Ominus(X2,X1,X3)
    | ~ c_lessequals(X1,X2,X3)
    | c_lessequals(X4,X5,X3)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2731]) ).

cnf(c_0_2731_3,axiom,
    ( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
    | c_HOL_Ominus__class_Ominus(X5,X4,X3) != c_HOL_Ominus__class_Ominus(X2,X1,X3)
    | ~ c_lessequals(X1,X2,X3)
    | c_lessequals(X4,X5,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2731]) ).

cnf(c_0_2732_0,axiom,
    ( c_HOL_Oord__class_Oless(X4,X5,X3)
    | ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | c_HOL_Ominus__class_Ominus(X1,X2,X3) != c_HOL_Ominus__class_Ominus(X4,X5,X3)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2732]) ).

cnf(c_0_2732_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | c_HOL_Oord__class_Oless(X4,X5,X3)
    | c_HOL_Ominus__class_Ominus(X1,X2,X3) != c_HOL_Ominus__class_Ominus(X4,X5,X3)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2732]) ).

cnf(c_0_2732_2,axiom,
    ( c_HOL_Ominus__class_Ominus(X1,X2,X3) != c_HOL_Ominus__class_Ominus(X4,X5,X3)
    | ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | c_HOL_Oord__class_Oless(X4,X5,X3)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2732]) ).

cnf(c_0_2732_3,axiom,
    ( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
    | c_HOL_Ominus__class_Ominus(X1,X2,X3) != c_HOL_Ominus__class_Ominus(X4,X5,X3)
    | ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | c_HOL_Oord__class_Oless(X4,X5,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2732]) ).

cnf(c_0_2733_0,axiom,
    ( c_HOL_Oord__class_Oless(X4,X5,X3)
    | ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | c_HOL_Ominus__class_Ominus(X4,X5,X3) != c_HOL_Ominus__class_Ominus(X1,X2,X3)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2733]) ).

cnf(c_0_2733_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | c_HOL_Oord__class_Oless(X4,X5,X3)
    | c_HOL_Ominus__class_Ominus(X4,X5,X3) != c_HOL_Ominus__class_Ominus(X1,X2,X3)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2733]) ).

cnf(c_0_2733_2,axiom,
    ( c_HOL_Ominus__class_Ominus(X4,X5,X3) != c_HOL_Ominus__class_Ominus(X1,X2,X3)
    | ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | c_HOL_Oord__class_Oless(X4,X5,X3)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2733]) ).

cnf(c_0_2733_3,axiom,
    ( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
    | c_HOL_Ominus__class_Ominus(X4,X5,X3) != c_HOL_Ominus__class_Ominus(X1,X2,X3)
    | ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | c_HOL_Oord__class_Oless(X4,X5,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2733]) ).

cnf(c_0_2734_0,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
    | c_lessequals(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_2734]) ).

cnf(c_0_2734_1,axiom,
    ( c_lessequals(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) ),
    inference(literals_permutation,[status(thm)],[c_0_2734]) ).

cnf(c_0_2735_0,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
    | c_lessequals(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_2735]) ).

cnf(c_0_2735_1,axiom,
    ( c_lessequals(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_2735]) ).

cnf(c_0_2736_0,axiom,
    ( c_lessequals(X1,X3,X4)
    | ~ c_lessequals(X1,c_Orderings_Oord__class_Omin(X2,X3,X4),X4)
    | ~ class_Orderings_Olinorder(X4) ),
    inference(literals_permutation,[status(thm)],[c_0_2736]) ).

cnf(c_0_2736_1,axiom,
    ( ~ c_lessequals(X1,c_Orderings_Oord__class_Omin(X2,X3,X4),X4)
    | c_lessequals(X1,X3,X4)
    | ~ class_Orderings_Olinorder(X4) ),
    inference(literals_permutation,[status(thm)],[c_0_2736]) ).

cnf(c_0_2736_2,axiom,
    ( ~ class_Orderings_Olinorder(X4)
    | ~ c_lessequals(X1,c_Orderings_Oord__class_Omin(X2,X3,X4),X4)
    | c_lessequals(X1,X3,X4) ),
    inference(literals_permutation,[status(thm)],[c_0_2736]) ).

cnf(c_0_2737_0,axiom,
    ( c_lessequals(X1,X2,X4)
    | ~ c_lessequals(X1,c_Orderings_Oord__class_Omin(X2,X3,X4),X4)
    | ~ class_Orderings_Olinorder(X4) ),
    inference(literals_permutation,[status(thm)],[c_0_2737]) ).

cnf(c_0_2737_1,axiom,
    ( ~ c_lessequals(X1,c_Orderings_Oord__class_Omin(X2,X3,X4),X4)
    | c_lessequals(X1,X2,X4)
    | ~ class_Orderings_Olinorder(X4) ),
    inference(literals_permutation,[status(thm)],[c_0_2737]) ).

cnf(c_0_2737_2,axiom,
    ( ~ class_Orderings_Olinorder(X4)
    | ~ c_lessequals(X1,c_Orderings_Oord__class_Omin(X2,X3,X4),X4)
    | c_lessequals(X1,X2,X4) ),
    inference(literals_permutation,[status(thm)],[c_0_2737]) ).

cnf(c_0_2738_0,axiom,
    ( c_lessequals(X1,X3,X4)
    | ~ c_lessequals(X1,c_Orderings_Oord__class_Omin(X2,X3,X4),X4)
    | ~ class_Orderings_Olinorder(X4) ),
    inference(literals_permutation,[status(thm)],[c_0_2738]) ).

cnf(c_0_2738_1,axiom,
    ( ~ c_lessequals(X1,c_Orderings_Oord__class_Omin(X2,X3,X4),X4)
    | c_lessequals(X1,X3,X4)
    | ~ class_Orderings_Olinorder(X4) ),
    inference(literals_permutation,[status(thm)],[c_0_2738]) ).

cnf(c_0_2738_2,axiom,
    ( ~ class_Orderings_Olinorder(X4)
    | ~ c_lessequals(X1,c_Orderings_Oord__class_Omin(X2,X3,X4),X4)
    | c_lessequals(X1,X3,X4) ),
    inference(literals_permutation,[status(thm)],[c_0_2738]) ).

cnf(c_0_2739_0,axiom,
    ( c_lessequals(X1,X2,X4)
    | ~ c_lessequals(X1,c_Orderings_Oord__class_Omin(X2,X3,X4),X4)
    | ~ class_Orderings_Olinorder(X4) ),
    inference(literals_permutation,[status(thm)],[c_0_2739]) ).

cnf(c_0_2739_1,axiom,
    ( ~ c_lessequals(X1,c_Orderings_Oord__class_Omin(X2,X3,X4),X4)
    | c_lessequals(X1,X2,X4)
    | ~ class_Orderings_Olinorder(X4) ),
    inference(literals_permutation,[status(thm)],[c_0_2739]) ).

cnf(c_0_2739_2,axiom,
    ( ~ class_Orderings_Olinorder(X4)
    | ~ c_lessequals(X1,c_Orderings_Oord__class_Omin(X2,X3,X4),X4)
    | c_lessequals(X1,X2,X4) ),
    inference(literals_permutation,[status(thm)],[c_0_2739]) ).

cnf(c_0_2740_0,axiom,
    ( c_lessequals(X2,X4,X3)
    | ~ c_lessequals(c_Orderings_Oord__class_Omax(X1,X2,X3),X4,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2740]) ).

cnf(c_0_2740_1,axiom,
    ( ~ c_lessequals(c_Orderings_Oord__class_Omax(X1,X2,X3),X4,X3)
    | c_lessequals(X2,X4,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2740]) ).

cnf(c_0_2740_2,axiom,
    ( ~ class_Orderings_Olinorder(X3)
    | ~ c_lessequals(c_Orderings_Oord__class_Omax(X1,X2,X3),X4,X3)
    | c_lessequals(X2,X4,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2740]) ).

cnf(c_0_2741_0,axiom,
    ( c_lessequals(X1,X4,X3)
    | ~ c_lessequals(c_Orderings_Oord__class_Omax(X1,X2,X3),X4,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2741]) ).

cnf(c_0_2741_1,axiom,
    ( ~ c_lessequals(c_Orderings_Oord__class_Omax(X1,X2,X3),X4,X3)
    | c_lessequals(X1,X4,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2741]) ).

cnf(c_0_2741_2,axiom,
    ( ~ class_Orderings_Olinorder(X3)
    | ~ c_lessequals(c_Orderings_Oord__class_Omax(X1,X2,X3),X4,X3)
    | c_lessequals(X1,X4,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2741]) ).

cnf(c_0_2742_0,axiom,
    ( c_lessequals(X2,X4,X3)
    | ~ c_lessequals(c_Orderings_Oord__class_Omax(X1,X2,X3),X4,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2742]) ).

cnf(c_0_2742_1,axiom,
    ( ~ c_lessequals(c_Orderings_Oord__class_Omax(X1,X2,X3),X4,X3)
    | c_lessequals(X2,X4,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2742]) ).

cnf(c_0_2742_2,axiom,
    ( ~ class_Orderings_Olinorder(X3)
    | ~ c_lessequals(c_Orderings_Oord__class_Omax(X1,X2,X3),X4,X3)
    | c_lessequals(X2,X4,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2742]) ).

cnf(c_0_2743_0,axiom,
    ( c_lessequals(X1,X4,X3)
    | ~ c_lessequals(c_Orderings_Oord__class_Omax(X1,X2,X3),X4,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2743]) ).

cnf(c_0_2743_1,axiom,
    ( ~ c_lessequals(c_Orderings_Oord__class_Omax(X1,X2,X3),X4,X3)
    | c_lessequals(X1,X4,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2743]) ).

cnf(c_0_2743_2,axiom,
    ( ~ class_Orderings_Olinorder(X3)
    | ~ c_lessequals(c_Orderings_Oord__class_Omax(X1,X2,X3),X4,X3)
    | c_lessequals(X1,X4,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2743]) ).

cnf(c_0_2744_0,axiom,
    ( c_HOL_Oord__class_Oless(X1,X4,X3)
    | ~ c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omax(X1,X2,X3),X4,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2744]) ).

cnf(c_0_2744_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omax(X1,X2,X3),X4,X3)
    | c_HOL_Oord__class_Oless(X1,X4,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2744]) ).

cnf(c_0_2744_2,axiom,
    ( ~ class_Orderings_Olinorder(X3)
    | ~ c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omax(X1,X2,X3),X4,X3)
    | c_HOL_Oord__class_Oless(X1,X4,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2744]) ).

cnf(c_0_2745_0,axiom,
    ( c_HOL_Oord__class_Oless(X2,X4,X3)
    | ~ c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omax(X1,X2,X3),X4,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2745]) ).

cnf(c_0_2745_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omax(X1,X2,X3),X4,X3)
    | c_HOL_Oord__class_Oless(X2,X4,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2745]) ).

cnf(c_0_2745_2,axiom,
    ( ~ class_Orderings_Olinorder(X3)
    | ~ c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omax(X1,X2,X3),X4,X3)
    | c_HOL_Oord__class_Oless(X2,X4,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2745]) ).

cnf(c_0_2746_0,axiom,
    ( c_HOL_Oord__class_Oless(X1,X2,X4)
    | ~ c_HOL_Oord__class_Oless(X1,c_Orderings_Oord__class_Omin(X2,X3,X4),X4)
    | ~ class_Orderings_Olinorder(X4) ),
    inference(literals_permutation,[status(thm)],[c_0_2746]) ).

cnf(c_0_2746_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(X1,c_Orderings_Oord__class_Omin(X2,X3,X4),X4)
    | c_HOL_Oord__class_Oless(X1,X2,X4)
    | ~ class_Orderings_Olinorder(X4) ),
    inference(literals_permutation,[status(thm)],[c_0_2746]) ).

cnf(c_0_2746_2,axiom,
    ( ~ class_Orderings_Olinorder(X4)
    | ~ c_HOL_Oord__class_Oless(X1,c_Orderings_Oord__class_Omin(X2,X3,X4),X4)
    | c_HOL_Oord__class_Oless(X1,X2,X4) ),
    inference(literals_permutation,[status(thm)],[c_0_2746]) ).

cnf(c_0_2747_0,axiom,
    ( c_HOL_Oord__class_Oless(X1,X3,X4)
    | ~ c_HOL_Oord__class_Oless(X1,c_Orderings_Oord__class_Omin(X2,X3,X4),X4)
    | ~ class_Orderings_Olinorder(X4) ),
    inference(literals_permutation,[status(thm)],[c_0_2747]) ).

cnf(c_0_2747_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(X1,c_Orderings_Oord__class_Omin(X2,X3,X4),X4)
    | c_HOL_Oord__class_Oless(X1,X3,X4)
    | ~ class_Orderings_Olinorder(X4) ),
    inference(literals_permutation,[status(thm)],[c_0_2747]) ).

cnf(c_0_2747_2,axiom,
    ( ~ class_Orderings_Olinorder(X4)
    | ~ c_HOL_Oord__class_Oless(X1,c_Orderings_Oord__class_Omin(X2,X3,X4),X4)
    | c_HOL_Oord__class_Oless(X1,X3,X4) ),
    inference(literals_permutation,[status(thm)],[c_0_2747]) ).

cnf(c_0_2748_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_2748]) ).

cnf(c_0_2748_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_2748]) ).

cnf(c_0_2749_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_2749]) ).

cnf(c_0_2749_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_2749]) ).

cnf(c_0_2750_0,axiom,
    ( c_HOL_Oord__class_Oless(X2,X1,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2750]) ).

cnf(c_0_2750_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),tc_nat)
    | c_HOL_Oord__class_Oless(X2,X1,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2750]) ).

cnf(c_0_2751_0,axiom,
    ( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | ~ c_HOL_Oord__class_Oless(X3,X4,tc_nat)
    | c_HOL_Oplus__class_Oplus(X1,X4,tc_nat) != c_HOL_Oplus__class_Oplus(X3,X2,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2751]) ).

cnf(c_0_2751_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(X3,X4,tc_nat)
    | c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | c_HOL_Oplus__class_Oplus(X1,X4,tc_nat) != c_HOL_Oplus__class_Oplus(X3,X2,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2751]) ).

cnf(c_0_2751_2,axiom,
    ( c_HOL_Oplus__class_Oplus(X1,X4,tc_nat) != c_HOL_Oplus__class_Oplus(X3,X2,tc_nat)
    | ~ 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_2751]) ).

cnf(c_0_2752_0,axiom,
    ( c_HOL_Oord__class_Oless(X1,X3,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),X3,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2752]) ).

cnf(c_0_2752_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),X3,tc_nat)
    | c_HOL_Oord__class_Oless(X1,X3,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2752]) ).

cnf(c_0_2753_0,axiom,
    ( c_lessequals(X2,X3,tc_nat)
    | ~ c_lessequals(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),X3,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2753]) ).

cnf(c_0_2753_1,axiom,
    ( ~ c_lessequals(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),X3,tc_nat)
    | c_lessequals(X2,X3,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2753]) ).

cnf(c_0_2754_0,axiom,
    ( c_lessequals(X1,X3,tc_nat)
    | ~ c_lessequals(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),X3,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2754]) ).

cnf(c_0_2754_1,axiom,
    ( ~ c_lessequals(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),X3,tc_nat)
    | c_lessequals(X1,X3,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2754]) ).

cnf(c_0_2755_0,axiom,
    ( X1 = c_HOL_Ozero__class_Ozero(X2)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X3,X2)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X1,X2)
    | c_HOL_Oplus__class_Oplus(X3,X1,X2) != c_HOL_Ozero__class_Ozero(X2)
    | ~ class_OrderedGroup_Opordered__comm__monoid__add(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2755]) ).

cnf(c_0_2755_1,axiom,
    ( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X3,X2)
    | X1 = c_HOL_Ozero__class_Ozero(X2)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X1,X2)
    | c_HOL_Oplus__class_Oplus(X3,X1,X2) != c_HOL_Ozero__class_Ozero(X2)
    | ~ class_OrderedGroup_Opordered__comm__monoid__add(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2755]) ).

cnf(c_0_2755_2,axiom,
    ( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X1,X2)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X3,X2)
    | X1 = c_HOL_Ozero__class_Ozero(X2)
    | c_HOL_Oplus__class_Oplus(X3,X1,X2) != c_HOL_Ozero__class_Ozero(X2)
    | ~ class_OrderedGroup_Opordered__comm__monoid__add(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2755]) ).

cnf(c_0_2755_3,axiom,
    ( c_HOL_Oplus__class_Oplus(X3,X1,X2) != c_HOL_Ozero__class_Ozero(X2)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X1,X2)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X3,X2)
    | X1 = c_HOL_Ozero__class_Ozero(X2)
    | ~ class_OrderedGroup_Opordered__comm__monoid__add(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2755]) ).

cnf(c_0_2755_4,axiom,
    ( ~ class_OrderedGroup_Opordered__comm__monoid__add(X2)
    | c_HOL_Oplus__class_Oplus(X3,X1,X2) != c_HOL_Ozero__class_Ozero(X2)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X1,X2)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X3,X2)
    | X1 = c_HOL_Ozero__class_Ozero(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2755]) ).

cnf(c_0_2756_0,axiom,
    ( X1 = c_HOL_Ozero__class_Ozero(X2)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X1,X2)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X3,X2)
    | c_HOL_Oplus__class_Oplus(X1,X3,X2) != c_HOL_Ozero__class_Ozero(X2)
    | ~ class_OrderedGroup_Opordered__comm__monoid__add(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2756]) ).

cnf(c_0_2756_1,axiom,
    ( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X1,X2)
    | X1 = c_HOL_Ozero__class_Ozero(X2)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X3,X2)
    | c_HOL_Oplus__class_Oplus(X1,X3,X2) != c_HOL_Ozero__class_Ozero(X2)
    | ~ class_OrderedGroup_Opordered__comm__monoid__add(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2756]) ).

cnf(c_0_2756_2,axiom,
    ( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X3,X2)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X1,X2)
    | X1 = c_HOL_Ozero__class_Ozero(X2)
    | c_HOL_Oplus__class_Oplus(X1,X3,X2) != c_HOL_Ozero__class_Ozero(X2)
    | ~ class_OrderedGroup_Opordered__comm__monoid__add(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2756]) ).

cnf(c_0_2756_3,axiom,
    ( c_HOL_Oplus__class_Oplus(X1,X3,X2) != c_HOL_Ozero__class_Ozero(X2)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X3,X2)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X1,X2)
    | X1 = c_HOL_Ozero__class_Ozero(X2)
    | ~ class_OrderedGroup_Opordered__comm__monoid__add(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2756]) ).

cnf(c_0_2756_4,axiom,
    ( ~ class_OrderedGroup_Opordered__comm__monoid__add(X2)
    | c_HOL_Oplus__class_Oplus(X1,X3,X2) != c_HOL_Ozero__class_Ozero(X2)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X3,X2)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X1,X2)
    | X1 = c_HOL_Ozero__class_Ozero(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2756]) ).

cnf(c_0_2757_0,axiom,
    ( c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),X1,tc_nat) = c_Divides_Odiv__class_Omod(X2,X1,tc_nat)
    | ~ c_lessequals(X1,X2,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2757]) ).

cnf(c_0_2757_1,axiom,
    ( ~ c_lessequals(X1,X2,tc_nat)
    | c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),X1,tc_nat) = c_Divides_Odiv__class_Omod(X2,X1,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2757]) ).

cnf(c_0_2758_0,axiom,
    ( c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ozero__class_Ozero(X1),X1) = c_HOL_Ozero__class_Ozero(X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ class_OrderedGroup_Opordered__comm__monoid__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2758]) ).

cnf(c_0_2758_1,axiom,
    ( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ozero__class_Ozero(X1),X1)
    | c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ozero__class_Ozero(X1),X1) = c_HOL_Ozero__class_Ozero(X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ class_OrderedGroup_Opordered__comm__monoid__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2758]) ).

cnf(c_0_2758_2,axiom,
    ( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ozero__class_Ozero(X1),X1)
    | c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ozero__class_Ozero(X1),X1) = c_HOL_Ozero__class_Ozero(X1)
    | ~ class_OrderedGroup_Opordered__comm__monoid__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2758]) ).

cnf(c_0_2758_3,axiom,
    ( ~ class_OrderedGroup_Opordered__comm__monoid__add(X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ozero__class_Ozero(X1),X1)
    | c_HOL_Oplus__class_Oplus(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_2758]) ).

cnf(c_0_2759_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_2759]) ).

cnf(c_0_2759_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_2759]) ).

cnf(c_0_2760_0,axiom,
    ( c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(X2,X2,X1),X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2760]) ).

cnf(c_0_2760_1,axiom,
    ( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(X2,X2,X1),X1)
    | ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2760]) ).

cnf(c_0_2760_2,axiom,
    ( ~ class_OrderedGroup_Olordered__ab__group__add(X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(X2,X2,X1),X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2760]) ).

cnf(c_0_2761_0,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X1,X2),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_2761]) ).

cnf(c_0_2761_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
    | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X1,X2),c_HOL_Ozero__class_Ozero(X2),X2)
    | ~ class_OrderedGroup_Olordered__ab__group__add(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2761]) ).

cnf(c_0_2761_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(c_HOL_Oplus__class_Oplus(X1,X1,X2),c_HOL_Ozero__class_Ozero(X2),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2761]) ).

cnf(c_0_2762_0,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X1,X2),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_2762]) ).

cnf(c_0_2762_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
    | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X1,X2),c_HOL_Ozero__class_Ozero(X2),X2)
    | ~ class_Ring__and__Field_Oordered__idom(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2762]) ).

cnf(c_0_2762_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(c_HOL_Oplus__class_Oplus(X1,X1,X2),c_HOL_Ozero__class_Ozero(X2),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2762]) ).

cnf(c_0_2763_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_2763]) ).

cnf(c_0_2763_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_2763]) ).

cnf(c_0_2764_0,axiom,
    ( c_lessequals(c_HOL_Oplus__class_Oplus(X1,X1,X2),c_HOL_Ozero__class_Ozero(X2),X2)
    | ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
    | ~ class_OrderedGroup_Olordered__ab__group__add(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2764]) ).

cnf(c_0_2764_1,axiom,
    ( ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
    | c_lessequals(c_HOL_Oplus__class_Oplus(X1,X1,X2),c_HOL_Ozero__class_Ozero(X2),X2)
    | ~ class_OrderedGroup_Olordered__ab__group__add(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2764]) ).

cnf(c_0_2764_2,axiom,
    ( ~ class_OrderedGroup_Olordered__ab__group__add(X2)
    | ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
    | c_lessequals(c_HOL_Oplus__class_Oplus(X1,X1,X2),c_HOL_Ozero__class_Ozero(X2),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2764]) ).

cnf(c_0_2765_0,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(X2,X2,X1),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_2765]) ).

cnf(c_0_2765_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_Oplus__class_Oplus(X2,X2,X1),X1)
    | ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2765]) ).

cnf(c_0_2765_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),c_HOL_Oplus__class_Oplus(X2,X2,X1),X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2765]) ).

cnf(c_0_2766_0,axiom,
    ( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),X2,tc_nat) = c_Divides_Odiv__class_Omod(X1,X2,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2766]) ).

cnf(c_0_2766_1,axiom,
    ( c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),X2,tc_nat) = c_Divides_Odiv__class_Omod(X1,X2,tc_nat)
    | c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2766]) ).

cnf(c_0_2767_0,axiom,
    ( c_lessequals(c_HOL_Ominus__class_Ominus(X1,X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
    | ~ c_lessequals(X1,X2,X3)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2767]) ).

cnf(c_0_2767_1,axiom,
    ( ~ c_lessequals(X1,X2,X3)
    | c_lessequals(c_HOL_Ominus__class_Ominus(X1,X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2767]) ).

cnf(c_0_2767_2,axiom,
    ( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
    | ~ c_lessequals(X1,X2,X3)
    | c_lessequals(c_HOL_Ominus__class_Ominus(X1,X2,X3),c_HOL_Ozero__class_Ozero(X3),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2767]) ).

cnf(c_0_2768_0,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
    | ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2768]) ).

cnf(c_0_2768_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2768]) ).

cnf(c_0_2768_2,axiom,
    ( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
    | ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,X2,X3),c_HOL_Ozero__class_Ozero(X3),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2768]) ).

cnf(c_0_2769_0,axiom,
    ( c_Lambda_Osubst(c_Lambda_OdB_OVar(X2),X3,X1) = c_Lambda_OdB_OVar(c_HOL_Ominus__class_Ominus(X2,c_HOL_Oone__class_Oone(tc_nat),tc_nat))
    | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2769]) ).

cnf(c_0_2769_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | c_Lambda_Osubst(c_Lambda_OdB_OVar(X2),X3,X1) = c_Lambda_OdB_OVar(c_HOL_Ominus__class_Ominus(X2,c_HOL_Oone__class_Oone(tc_nat),tc_nat)) ),
    inference(literals_permutation,[status(thm)],[c_0_2769]) ).

cnf(c_0_2770_0,axiom,
    ( c_Lambda_Osubst(c_Lambda_OdB_OVar(X2),X3,X1) = c_Lambda_OdB_OVar(c_HOL_Ominus__class_Ominus(X2,c_HOL_Oone__class_Oone(tc_nat),tc_nat))
    | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2770]) ).

cnf(c_0_2770_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | c_Lambda_Osubst(c_Lambda_OdB_OVar(X2),X3,X1) = c_Lambda_OdB_OVar(c_HOL_Ominus__class_Ominus(X2,c_HOL_Oone__class_Oone(tc_nat),tc_nat)) ),
    inference(literals_permutation,[status(thm)],[c_0_2770]) ).

cnf(c_0_2771_0,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,c_Suc(X2),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_2771]) ).

cnf(c_0_2771_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
    | c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,c_Suc(X2),tc_nat),X1,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2771]) ).

cnf(c_0_2772_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_2772]) ).

cnf(c_0_2772_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_2772]) ).

cnf(c_0_2772_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_2772]) ).

cnf(c_0_2773_0,axiom,
    ( c_lessequals(c_Orderings_Oord__class_Omin(X4,X1,X3),X2,X3)
    | ~ c_lessequals(X1,X2,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2773]) ).

cnf(c_0_2773_1,axiom,
    ( ~ c_lessequals(X1,X2,X3)
    | c_lessequals(c_Orderings_Oord__class_Omin(X4,X1,X3),X2,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2773]) ).

cnf(c_0_2773_2,axiom,
    ( ~ class_Orderings_Olinorder(X3)
    | ~ c_lessequals(X1,X2,X3)
    | c_lessequals(c_Orderings_Oord__class_Omin(X4,X1,X3),X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2773]) ).

cnf(c_0_2774_0,axiom,
    ( c_lessequals(c_Orderings_Oord__class_Omin(X1,X4,X3),X2,X3)
    | ~ c_lessequals(X1,X2,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2774]) ).

cnf(c_0_2774_1,axiom,
    ( ~ c_lessequals(X1,X2,X3)
    | c_lessequals(c_Orderings_Oord__class_Omin(X1,X4,X3),X2,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2774]) ).

cnf(c_0_2774_2,axiom,
    ( ~ class_Orderings_Olinorder(X3)
    | ~ c_lessequals(X1,X2,X3)
    | c_lessequals(c_Orderings_Oord__class_Omin(X1,X4,X3),X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2774]) ).

cnf(c_0_2775_0,axiom,
    ( c_lessequals(c_Orderings_Oord__class_Omin(X4,X1,X3),X2,X3)
    | ~ c_lessequals(X1,X2,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2775]) ).

cnf(c_0_2775_1,axiom,
    ( ~ c_lessequals(X1,X2,X3)
    | c_lessequals(c_Orderings_Oord__class_Omin(X4,X1,X3),X2,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2775]) ).

cnf(c_0_2775_2,axiom,
    ( ~ class_Orderings_Olinorder(X3)
    | ~ c_lessequals(X1,X2,X3)
    | c_lessequals(c_Orderings_Oord__class_Omin(X4,X1,X3),X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2775]) ).

cnf(c_0_2776_0,axiom,
    ( c_lessequals(c_Orderings_Oord__class_Omin(X1,X4,X3),X2,X3)
    | ~ c_lessequals(X1,X2,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2776]) ).

cnf(c_0_2776_1,axiom,
    ( ~ c_lessequals(X1,X2,X3)
    | c_lessequals(c_Orderings_Oord__class_Omin(X1,X4,X3),X2,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2776]) ).

cnf(c_0_2776_2,axiom,
    ( ~ class_Orderings_Olinorder(X3)
    | ~ c_lessequals(X1,X2,X3)
    | c_lessequals(c_Orderings_Oord__class_Omin(X1,X4,X3),X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2776]) ).

cnf(c_0_2777_0,axiom,
    ( c_lessequals(X1,c_Orderings_Oord__class_Omax(X4,X2,X3),X3)
    | ~ c_lessequals(X1,X2,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2777]) ).

cnf(c_0_2777_1,axiom,
    ( ~ c_lessequals(X1,X2,X3)
    | c_lessequals(X1,c_Orderings_Oord__class_Omax(X4,X2,X3),X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2777]) ).

cnf(c_0_2777_2,axiom,
    ( ~ class_Orderings_Olinorder(X3)
    | ~ c_lessequals(X1,X2,X3)
    | c_lessequals(X1,c_Orderings_Oord__class_Omax(X4,X2,X3),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2777]) ).

cnf(c_0_2778_0,axiom,
    ( c_lessequals(X1,c_Orderings_Oord__class_Omax(X2,X4,X3),X3)
    | ~ c_lessequals(X1,X2,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2778]) ).

cnf(c_0_2778_1,axiom,
    ( ~ c_lessequals(X1,X2,X3)
    | c_lessequals(X1,c_Orderings_Oord__class_Omax(X2,X4,X3),X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2778]) ).

cnf(c_0_2778_2,axiom,
    ( ~ class_Orderings_Olinorder(X3)
    | ~ c_lessequals(X1,X2,X3)
    | c_lessequals(X1,c_Orderings_Oord__class_Omax(X2,X4,X3),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2778]) ).

cnf(c_0_2779_0,axiom,
    ( c_lessequals(X1,c_Orderings_Oord__class_Omax(X4,X2,X3),X3)
    | ~ c_lessequals(X1,X2,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2779]) ).

cnf(c_0_2779_1,axiom,
    ( ~ c_lessequals(X1,X2,X3)
    | c_lessequals(X1,c_Orderings_Oord__class_Omax(X4,X2,X3),X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2779]) ).

cnf(c_0_2779_2,axiom,
    ( ~ class_Orderings_Olinorder(X3)
    | ~ c_lessequals(X1,X2,X3)
    | c_lessequals(X1,c_Orderings_Oord__class_Omax(X4,X2,X3),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2779]) ).

cnf(c_0_2780_0,axiom,
    ( c_lessequals(X1,c_Orderings_Oord__class_Omax(X2,X4,X3),X3)
    | ~ c_lessequals(X1,X2,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2780]) ).

cnf(c_0_2780_1,axiom,
    ( ~ c_lessequals(X1,X2,X3)
    | c_lessequals(X1,c_Orderings_Oord__class_Omax(X2,X4,X3),X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2780]) ).

cnf(c_0_2780_2,axiom,
    ( ~ class_Orderings_Olinorder(X3)
    | ~ c_lessequals(X1,X2,X3)
    | c_lessequals(X1,c_Orderings_Oord__class_Omax(X2,X4,X3),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2780]) ).

cnf(c_0_2781_0,axiom,
    ( c_HOL_Oord__class_Oless(X1,c_Orderings_Oord__class_Omax(X2,X4,X3),X3)
    | ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2781]) ).

cnf(c_0_2781_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | c_HOL_Oord__class_Oless(X1,c_Orderings_Oord__class_Omax(X2,X4,X3),X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2781]) ).

cnf(c_0_2781_2,axiom,
    ( ~ class_Orderings_Olinorder(X3)
    | ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | c_HOL_Oord__class_Oless(X1,c_Orderings_Oord__class_Omax(X2,X4,X3),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2781]) ).

cnf(c_0_2782_0,axiom,
    ( c_HOL_Oord__class_Oless(X1,c_Orderings_Oord__class_Omax(X4,X2,X3),X3)
    | ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2782]) ).

cnf(c_0_2782_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | c_HOL_Oord__class_Oless(X1,c_Orderings_Oord__class_Omax(X4,X2,X3),X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2782]) ).

cnf(c_0_2782_2,axiom,
    ( ~ class_Orderings_Olinorder(X3)
    | ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | c_HOL_Oord__class_Oless(X1,c_Orderings_Oord__class_Omax(X4,X2,X3),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2782]) ).

cnf(c_0_2783_0,axiom,
    ( c_HOL_Oord__class_Oless(X1,c_Orderings_Oord__class_Omax(X2,X4,X3),X3)
    | ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2783]) ).

cnf(c_0_2783_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | c_HOL_Oord__class_Oless(X1,c_Orderings_Oord__class_Omax(X2,X4,X3),X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2783]) ).

cnf(c_0_2783_2,axiom,
    ( ~ class_Orderings_Olinorder(X3)
    | ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | c_HOL_Oord__class_Oless(X1,c_Orderings_Oord__class_Omax(X2,X4,X3),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2783]) ).

cnf(c_0_2784_0,axiom,
    ( c_HOL_Oord__class_Oless(X1,c_Orderings_Oord__class_Omax(X4,X2,X3),X3)
    | ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2784]) ).

cnf(c_0_2784_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | c_HOL_Oord__class_Oless(X1,c_Orderings_Oord__class_Omax(X4,X2,X3),X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2784]) ).

cnf(c_0_2784_2,axiom,
    ( ~ class_Orderings_Olinorder(X3)
    | ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | c_HOL_Oord__class_Oless(X1,c_Orderings_Oord__class_Omax(X4,X2,X3),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2784]) ).

cnf(c_0_2785_0,axiom,
    ( c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omin(X1,X4,X3),X2,X3)
    | ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2785]) ).

cnf(c_0_2785_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omin(X1,X4,X3),X2,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2785]) ).

cnf(c_0_2785_2,axiom,
    ( ~ class_Orderings_Olinorder(X3)
    | ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omin(X1,X4,X3),X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2785]) ).

cnf(c_0_2786_0,axiom,
    ( c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omin(X4,X1,X3),X2,X3)
    | ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2786]) ).

cnf(c_0_2786_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omin(X4,X1,X3),X2,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2786]) ).

cnf(c_0_2786_2,axiom,
    ( ~ class_Orderings_Olinorder(X3)
    | ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omin(X4,X1,X3),X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2786]) ).

cnf(c_0_2787_0,axiom,
    ( c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omin(X1,X4,X3),X2,X3)
    | ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2787]) ).

cnf(c_0_2787_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omin(X1,X4,X3),X2,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2787]) ).

cnf(c_0_2787_2,axiom,
    ( ~ class_Orderings_Olinorder(X3)
    | ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omin(X1,X4,X3),X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2787]) ).

cnf(c_0_2788_0,axiom,
    ( c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omin(X4,X1,X3),X2,X3)
    | ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2788]) ).

cnf(c_0_2788_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omin(X4,X1,X3),X2,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2788]) ).

cnf(c_0_2788_2,axiom,
    ( ~ class_Orderings_Olinorder(X3)
    | ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omin(X4,X1,X3),X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2788]) ).

cnf(c_0_2789_0,axiom,
    ( c_Suc(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat)) = c_HOL_Ominus__class_Ominus(c_Suc(X2),X1,tc_nat)
    | ~ c_lessequals(X1,X2,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2789]) ).

cnf(c_0_2789_1,axiom,
    ( ~ c_lessequals(X1,X2,tc_nat)
    | c_Suc(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat)) = c_HOL_Ominus__class_Ominus(c_Suc(X2),X1,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2789]) ).

cnf(c_0_2790_0,axiom,
    ( c_Lambda_Obeta(c_Lambda_Osubst(X1,X3,X4),c_Lambda_Osubst(X2,X3,X4))
    | ~ c_Lambda_Obeta(X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2790]) ).

cnf(c_0_2790_1,axiom,
    ( ~ c_Lambda_Obeta(X1,X2)
    | c_Lambda_Obeta(c_Lambda_Osubst(X1,X3,X4),c_Lambda_Osubst(X2,X3,X4)) ),
    inference(literals_permutation,[status(thm)],[c_0_2790]) ).

cnf(c_0_2791_0,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oplus__class_Oplus(X2,X1,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_2791]) ).

cnf(c_0_2791_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_Oplus__class_Oplus(X2,X1,tc_nat),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2791]) ).

cnf(c_0_2792_0,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oplus__class_Oplus(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_2792]) ).

cnf(c_0_2792_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_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2792]) ).

cnf(c_0_2793_0,axiom,
    ( c_HOL_Oplus__class_Oplus(X1,X1,X2) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(X2),c_HOL_Oone__class_Oone(X2),X2),X1,X2)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2793]) ).

cnf(c_0_2793_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__1(X2)
    | c_HOL_Oplus__class_Oplus(X1,X1,X2) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(X2),c_HOL_Oone__class_Oone(X2),X2),X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2793]) ).

cnf(c_0_2794_0,axiom,
    ( c_lessequals(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_2794]) ).

cnf(c_0_2794_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
    | c_lessequals(c_Divides_Odiv__class_Omod(X2,X1,tc_nat),X1,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2794]) ).

cnf(c_0_2795_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_2795]) ).

cnf(c_0_2795_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_2795]) ).

cnf(c_0_2796_0,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),tc_nat)
    | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2796]) ).

cnf(c_0_2796_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2796]) ).

cnf(c_0_2797_0,axiom,
    ( c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),X2,tc_nat) = X1
    | ~ c_lessequals(X2,X1,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2797]) ).

cnf(c_0_2797_1,axiom,
    ( ~ c_lessequals(X2,X1,tc_nat)
    | c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),X2,tc_nat) = X1 ),
    inference(literals_permutation,[status(thm)],[c_0_2797]) ).

cnf(c_0_2798_0,axiom,
    ( c_HOL_Oplus__class_Oplus(X1,c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),tc_nat) = X2
    | ~ c_lessequals(X1,X2,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2798]) ).

cnf(c_0_2798_1,axiom,
    ( ~ c_lessequals(X1,X2,tc_nat)
    | c_HOL_Oplus__class_Oplus(X1,c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),tc_nat) = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_2798]) ).

cnf(c_0_2799_0,axiom,
    ( c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),X1,tc_nat) = X2
    | ~ c_lessequals(X1,X2,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2799]) ).

cnf(c_0_2799_1,axiom,
    ( ~ c_lessequals(X1,X2,tc_nat)
    | c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),X1,tc_nat) = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_2799]) ).

cnf(c_0_2800_0,axiom,
    ( c_HOL_Ominus__class_Ominus(X2,c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),tc_nat) = X1
    | ~ c_lessequals(X1,X2,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2800]) ).

cnf(c_0_2800_1,axiom,
    ( ~ c_lessequals(X1,X2,tc_nat)
    | c_HOL_Ominus__class_Ominus(X2,c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),tc_nat) = X1 ),
    inference(literals_permutation,[status(thm)],[c_0_2800]) ).

cnf(c_0_2801_0,axiom,
    ( c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(X2,X3,tc_nat),tc_nat)
    | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2801]) ).

cnf(c_0_2801_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(X2,X3,tc_nat),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2801]) ).

cnf(c_0_2802_0,axiom,
    ( c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(X3,X2,tc_nat),tc_nat)
    | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2802]) ).

cnf(c_0_2802_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(X3,X2,tc_nat),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2802]) ).

cnf(c_0_2803_0,axiom,
    ( c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(X2,X3,tc_nat),tc_nat)
    | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2803]) ).

cnf(c_0_2803_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(X2,X3,tc_nat),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2803]) ).

cnf(c_0_2804_0,axiom,
    ( c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(X3,X2,tc_nat),tc_nat)
    | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2804]) ).

cnf(c_0_2804_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(X3,X2,tc_nat),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2804]) ).

cnf(c_0_2805_0,axiom,
    ( c_lessequals(X1,c_HOL_Oplus__class_Oplus(X3,X2,tc_nat),tc_nat)
    | ~ c_lessequals(X1,X2,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2805]) ).

cnf(c_0_2805_1,axiom,
    ( ~ c_lessequals(X1,X2,tc_nat)
    | c_lessequals(X1,c_HOL_Oplus__class_Oplus(X3,X2,tc_nat),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2805]) ).

cnf(c_0_2806_0,axiom,
    ( c_lessequals(X1,c_HOL_Oplus__class_Oplus(X2,X3,tc_nat),tc_nat)
    | ~ c_lessequals(X1,X2,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2806]) ).

cnf(c_0_2806_1,axiom,
    ( ~ c_lessequals(X1,X2,tc_nat)
    | c_lessequals(X1,c_HOL_Oplus__class_Oplus(X2,X3,tc_nat),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2806]) ).

cnf(c_0_2807_0,axiom,
    ( c_lessequals(X1,c_HOL_Oplus__class_Oplus(X3,X2,tc_nat),tc_nat)
    | ~ c_lessequals(X1,X2,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2807]) ).

cnf(c_0_2807_1,axiom,
    ( ~ c_lessequals(X1,X2,tc_nat)
    | c_lessequals(X1,c_HOL_Oplus__class_Oplus(X3,X2,tc_nat),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2807]) ).

cnf(c_0_2808_0,axiom,
    ( c_lessequals(X1,c_HOL_Oplus__class_Oplus(X2,X3,tc_nat),tc_nat)
    | ~ c_lessequals(X1,X2,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2808]) ).

cnf(c_0_2808_1,axiom,
    ( ~ c_lessequals(X1,X2,tc_nat)
    | c_lessequals(X1,c_HOL_Oplus__class_Oplus(X2,X3,tc_nat),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2808]) ).

cnf(c_0_2809_0,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,X3,tc_nat),X2,tc_nat)
    | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2809]) ).

cnf(c_0_2809_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,X3,tc_nat),X2,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2809]) ).

cnf(c_0_2810_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_2810]) ).

cnf(c_0_2810_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_2810]) ).

cnf(c_0_2810_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_2810]) ).

cnf(c_0_2810_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_2810]) ).

cnf(c_0_2811_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_2811]) ).

cnf(c_0_2811_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_2811]) ).

cnf(c_0_2811_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_2811]) ).

cnf(c_0_2811_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_2811]) ).

cnf(c_0_2812_0,axiom,
    ( c_lessequals(X4,X2,X3)
    | ~ c_lessequals(X1,X2,X3)
    | ~ c_lessequals(X4,X1,X3)
    | ~ class_Orderings_Oorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2812]) ).

cnf(c_0_2812_1,axiom,
    ( ~ c_lessequals(X1,X2,X3)
    | c_lessequals(X4,X2,X3)
    | ~ c_lessequals(X4,X1,X3)
    | ~ class_Orderings_Oorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2812]) ).

cnf(c_0_2812_2,axiom,
    ( ~ c_lessequals(X4,X1,X3)
    | ~ c_lessequals(X1,X2,X3)
    | c_lessequals(X4,X2,X3)
    | ~ class_Orderings_Oorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2812]) ).

cnf(c_0_2812_3,axiom,
    ( ~ class_Orderings_Oorder(X3)
    | ~ c_lessequals(X4,X1,X3)
    | ~ c_lessequals(X1,X2,X3)
    | c_lessequals(X4,X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2812]) ).

cnf(c_0_2813_0,axiom,
    ( c_HOL_Oord__class_Oless(X4,X2,X3)
    | ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | ~ c_lessequals(X4,X1,X3)
    | ~ class_Orderings_Oorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2813]) ).

cnf(c_0_2813_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | c_HOL_Oord__class_Oless(X4,X2,X3)
    | ~ c_lessequals(X4,X1,X3)
    | ~ class_Orderings_Oorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2813]) ).

cnf(c_0_2813_2,axiom,
    ( ~ c_lessequals(X4,X1,X3)
    | ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | c_HOL_Oord__class_Oless(X4,X2,X3)
    | ~ class_Orderings_Oorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2813]) ).

cnf(c_0_2813_3,axiom,
    ( ~ class_Orderings_Oorder(X3)
    | ~ c_lessequals(X4,X1,X3)
    | ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | c_HOL_Oord__class_Oless(X4,X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2813]) ).

cnf(c_0_2814_0,axiom,
    ( c_HOL_Oord__class_Oless(X4,X2,X3)
    | ~ c_lessequals(X1,X2,X3)
    | ~ c_HOL_Oord__class_Oless(X4,X1,X3)
    | ~ class_Orderings_Oorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2814]) ).

cnf(c_0_2814_1,axiom,
    ( ~ c_lessequals(X1,X2,X3)
    | c_HOL_Oord__class_Oless(X4,X2,X3)
    | ~ c_HOL_Oord__class_Oless(X4,X1,X3)
    | ~ class_Orderings_Oorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2814]) ).

cnf(c_0_2814_2,axiom,
    ( ~ c_HOL_Oord__class_Oless(X4,X1,X3)
    | ~ c_lessequals(X1,X2,X3)
    | c_HOL_Oord__class_Oless(X4,X2,X3)
    | ~ class_Orderings_Oorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2814]) ).

cnf(c_0_2814_3,axiom,
    ( ~ class_Orderings_Oorder(X3)
    | ~ c_HOL_Oord__class_Oless(X4,X1,X3)
    | ~ c_lessequals(X1,X2,X3)
    | c_HOL_Oord__class_Oless(X4,X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2814]) ).

cnf(c_0_2815_0,axiom,
    ( c_lessequals(X1,X4,X3)
    | ~ c_lessequals(X1,X2,X3)
    | ~ c_lessequals(X2,X4,X3)
    | ~ class_Orderings_Opreorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2815]) ).

cnf(c_0_2815_1,axiom,
    ( ~ c_lessequals(X1,X2,X3)
    | c_lessequals(X1,X4,X3)
    | ~ c_lessequals(X2,X4,X3)
    | ~ class_Orderings_Opreorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2815]) ).

cnf(c_0_2815_2,axiom,
    ( ~ c_lessequals(X2,X4,X3)
    | ~ c_lessequals(X1,X2,X3)
    | c_lessequals(X1,X4,X3)
    | ~ class_Orderings_Opreorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2815]) ).

cnf(c_0_2815_3,axiom,
    ( ~ class_Orderings_Opreorder(X3)
    | ~ c_lessequals(X2,X4,X3)
    | ~ c_lessequals(X1,X2,X3)
    | c_lessequals(X1,X4,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2815]) ).

cnf(c_0_2816_0,axiom,
    ( c_HOL_Oord__class_Oless(X1,X4,X3)
    | ~ c_lessequals(X1,X2,X3)
    | ~ c_HOL_Oord__class_Oless(X2,X4,X3)
    | ~ class_Orderings_Opreorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2816]) ).

cnf(c_0_2816_1,axiom,
    ( ~ c_lessequals(X1,X2,X3)
    | c_HOL_Oord__class_Oless(X1,X4,X3)
    | ~ c_HOL_Oord__class_Oless(X2,X4,X3)
    | ~ class_Orderings_Opreorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2816]) ).

cnf(c_0_2816_2,axiom,
    ( ~ c_HOL_Oord__class_Oless(X2,X4,X3)
    | ~ c_lessequals(X1,X2,X3)
    | c_HOL_Oord__class_Oless(X1,X4,X3)
    | ~ class_Orderings_Opreorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2816]) ).

cnf(c_0_2816_3,axiom,
    ( ~ class_Orderings_Opreorder(X3)
    | ~ c_HOL_Oord__class_Oless(X2,X4,X3)
    | ~ c_lessequals(X1,X2,X3)
    | c_HOL_Oord__class_Oless(X1,X4,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2816]) ).

cnf(c_0_2817_0,axiom,
    ( c_HOL_Oord__class_Oless(X1,X4,X3)
    | ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | ~ c_lessequals(X2,X4,X3)
    | ~ class_Orderings_Opreorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2817]) ).

cnf(c_0_2817_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | c_HOL_Oord__class_Oless(X1,X4,X3)
    | ~ c_lessequals(X2,X4,X3)
    | ~ class_Orderings_Opreorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2817]) ).

cnf(c_0_2817_2,axiom,
    ( ~ c_lessequals(X2,X4,X3)
    | ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | c_HOL_Oord__class_Oless(X1,X4,X3)
    | ~ class_Orderings_Opreorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2817]) ).

cnf(c_0_2817_3,axiom,
    ( ~ class_Orderings_Opreorder(X3)
    | ~ c_lessequals(X2,X4,X3)
    | ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | c_HOL_Oord__class_Oless(X1,X4,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2817]) ).

cnf(c_0_2818_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_2818]) ).

cnf(c_0_2818_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_2818]) ).

cnf(c_0_2819_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_2819]) ).

cnf(c_0_2819_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_2819]) ).

cnf(c_0_2819_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_2819]) ).

cnf(c_0_2820_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_2820]) ).

cnf(c_0_2820_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_2820]) ).

cnf(c_0_2821_0,axiom,
    ( c_Orderings_Oord__class_Omin(X1,c_Orderings_Oord__class_Omin(X1,X2,X3),X3) = c_Orderings_Oord__class_Omin(X1,X2,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2821]) ).

cnf(c_0_2821_1,axiom,
    ( ~ class_Orderings_Olinorder(X3)
    | c_Orderings_Oord__class_Omin(X1,c_Orderings_Oord__class_Omin(X1,X2,X3),X3) = c_Orderings_Oord__class_Omin(X1,X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2821]) ).

cnf(c_0_2822_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_2822]) ).

cnf(c_0_2822_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_2822]) ).

cnf(c_0_2823_0,axiom,
    ( c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(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_2823]) ).

cnf(c_0_2823_1,axiom,
    ( ~ class_Divides_Osemiring__div(X3)
    | c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X1,X2,X3),X2,X3) = c_Divides_Odiv__class_Omod(X1,X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2823]) ).

cnf(c_0_2824_0,axiom,
    ( c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X1,X2,X3),X1,X3) = c_Divides_Odiv__class_Omod(X2,X1,X3)
    | ~ class_Divides_Osemiring__div(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2824]) ).

cnf(c_0_2824_1,axiom,
    ( ~ class_Divides_Osemiring__div(X3)
    | c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X1,X2,X3),X1,X3) = c_Divides_Odiv__class_Omod(X2,X1,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2824]) ).

cnf(c_0_2825_0,axiom,
    ( c_Orderings_Oord__class_Omax(X1,c_Orderings_Oord__class_Omax(X1,X2,X3),X3) = c_Orderings_Oord__class_Omax(X1,X2,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2825]) ).

cnf(c_0_2825_1,axiom,
    ( ~ class_Orderings_Olinorder(X3)
    | c_Orderings_Oord__class_Omax(X1,c_Orderings_Oord__class_Omax(X1,X2,X3),X3) = c_Orderings_Oord__class_Omax(X1,X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2825]) ).

cnf(c_0_2826_0,axiom,
    ( c_Suc(c_HOL_Ominus__class_Ominus(X1,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat)) = X1
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2826]) ).

cnf(c_0_2826_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
    | c_Suc(c_HOL_Ominus__class_Ominus(X1,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat)) = X1 ),
    inference(literals_permutation,[status(thm)],[c_0_2826]) ).

cnf(c_0_2827_0,axiom,
    ( c_lessequals(X1,X3,tc_nat)
    | ~ c_lessequals(X1,X2,tc_nat)
    | ~ c_lessequals(X2,X3,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2827]) ).

cnf(c_0_2827_1,axiom,
    ( ~ c_lessequals(X1,X2,tc_nat)
    | c_lessequals(X1,X3,tc_nat)
    | ~ c_lessequals(X2,X3,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2827]) ).

cnf(c_0_2827_2,axiom,
    ( ~ c_lessequals(X2,X3,tc_nat)
    | ~ c_lessequals(X1,X2,tc_nat)
    | c_lessequals(X1,X3,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2827]) ).

cnf(c_0_2828_0,axiom,
    ( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | c_HOL_Oplus__class_Oplus(X2,c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),tc_nat) = X1 ),
    inference(literals_permutation,[status(thm)],[c_0_2828]) ).

cnf(c_0_2828_1,axiom,
    ( c_HOL_Oplus__class_Oplus(X2,c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),tc_nat) = X1
    | c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2828]) ).

cnf(c_0_2829_0,axiom,
    ( c_Suc(c_HOL_Ominus__class_Ominus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat)) = X1
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2829]) ).

cnf(c_0_2829_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
    | c_Suc(c_HOL_Ominus__class_Ominus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat)) = X1 ),
    inference(literals_permutation,[status(thm)],[c_0_2829]) ).

cnf(c_0_2830_0,axiom,
    ( c_Suc(c_HOL_Ominus__class_Ominus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat)) = X1
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2830]) ).

cnf(c_0_2830_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
    | c_Suc(c_HOL_Ominus__class_Ominus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat)) = X1 ),
    inference(literals_permutation,[status(thm)],[c_0_2830]) ).

cnf(c_0_2831_0,axiom,
    ( c_lessequals(X2,X1,X3)
    | c_HOL_Oord__class_Oless(X1,X2,X3)
    | ~ c_lessequals(X1,X2,X3)
    | ~ class_Orderings_Opreorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2831]) ).

cnf(c_0_2831_1,axiom,
    ( c_HOL_Oord__class_Oless(X1,X2,X3)
    | c_lessequals(X2,X1,X3)
    | ~ c_lessequals(X1,X2,X3)
    | ~ class_Orderings_Opreorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2831]) ).

cnf(c_0_2831_2,axiom,
    ( ~ c_lessequals(X1,X2,X3)
    | c_HOL_Oord__class_Oless(X1,X2,X3)
    | c_lessequals(X2,X1,X3)
    | ~ class_Orderings_Opreorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2831]) ).

cnf(c_0_2831_3,axiom,
    ( ~ class_Orderings_Opreorder(X3)
    | ~ c_lessequals(X1,X2,X3)
    | c_HOL_Oord__class_Oless(X1,X2,X3)
    | c_lessequals(X2,X1,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2831]) ).

cnf(c_0_2832_0,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(X1),c_HOL_Oone__class_Oone(X1),X1),X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2832]) ).

cnf(c_0_2832_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__semidom(X1)
    | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(X1),c_HOL_Oone__class_Oone(X1),X1),X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2832]) ).

cnf(c_0_2833_0,axiom,
    ( X1 = X2
    | c_HOL_Oplus__class_Oplus(X3,X1,X4) != c_HOL_Oplus__class_Oplus(X3,X2,X4)
    | ~ class_Int_Onumber__ring(X4)
    | ~ class_Ring__and__Field_Oidom(X4) ),
    inference(literals_permutation,[status(thm)],[c_0_2833]) ).

cnf(c_0_2833_1,axiom,
    ( c_HOL_Oplus__class_Oplus(X3,X1,X4) != c_HOL_Oplus__class_Oplus(X3,X2,X4)
    | X1 = X2
    | ~ class_Int_Onumber__ring(X4)
    | ~ class_Ring__and__Field_Oidom(X4) ),
    inference(literals_permutation,[status(thm)],[c_0_2833]) ).

cnf(c_0_2833_2,axiom,
    ( ~ class_Int_Onumber__ring(X4)
    | c_HOL_Oplus__class_Oplus(X3,X1,X4) != c_HOL_Oplus__class_Oplus(X3,X2,X4)
    | X1 = X2
    | ~ class_Ring__and__Field_Oidom(X4) ),
    inference(literals_permutation,[status(thm)],[c_0_2833]) ).

cnf(c_0_2833_3,axiom,
    ( ~ class_Ring__and__Field_Oidom(X4)
    | ~ class_Int_Onumber__ring(X4)
    | c_HOL_Oplus__class_Oplus(X3,X1,X4) != c_HOL_Oplus__class_Oplus(X3,X2,X4)
    | X1 = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_2833]) ).

cnf(c_0_2834_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_2834]) ).

cnf(c_0_2834_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_2834]) ).

cnf(c_0_2835_0,axiom,
    ( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | c_Lambda_Olift(c_Lambda_OdB_OVar(X1),X2) = c_Lambda_OdB_OVar(c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat)) ),
    inference(literals_permutation,[status(thm)],[c_0_2835]) ).

cnf(c_0_2835_1,axiom,
    ( c_Lambda_Olift(c_Lambda_OdB_OVar(X1),X2) = c_Lambda_OdB_OVar(c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat))
    | c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2835]) ).

cnf(c_0_2836_0,axiom,
    ( X1 = X2
    | ~ c_lessequals(X1,X2,X3)
    | ~ c_lessequals(X2,X1,X3)
    | ~ class_Orderings_Oorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2836]) ).

cnf(c_0_2836_1,axiom,
    ( ~ c_lessequals(X1,X2,X3)
    | X1 = X2
    | ~ c_lessequals(X2,X1,X3)
    | ~ class_Orderings_Oorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2836]) ).

cnf(c_0_2836_2,axiom,
    ( ~ c_lessequals(X2,X1,X3)
    | ~ c_lessequals(X1,X2,X3)
    | X1 = X2
    | ~ class_Orderings_Oorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2836]) ).

cnf(c_0_2836_3,axiom,
    ( ~ class_Orderings_Oorder(X3)
    | ~ c_lessequals(X2,X1,X3)
    | ~ c_lessequals(X1,X2,X3)
    | X1 = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_2836]) ).

cnf(c_0_2837_0,axiom,
    ( X1 = X2
    | ~ c_lessequals(X1,X2,X3)
    | ~ c_lessequals(X2,X1,X3)
    | ~ class_Orderings_Oorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2837]) ).

cnf(c_0_2837_1,axiom,
    ( ~ c_lessequals(X1,X2,X3)
    | X1 = X2
    | ~ c_lessequals(X2,X1,X3)
    | ~ class_Orderings_Oorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2837]) ).

cnf(c_0_2837_2,axiom,
    ( ~ c_lessequals(X2,X1,X3)
    | ~ c_lessequals(X1,X2,X3)
    | X1 = X2
    | ~ class_Orderings_Oorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2837]) ).

cnf(c_0_2837_3,axiom,
    ( ~ class_Orderings_Oorder(X3)
    | ~ c_lessequals(X2,X1,X3)
    | ~ c_lessequals(X1,X2,X3)
    | X1 = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_2837]) ).

cnf(c_0_2838_0,axiom,
    ( X2 = X1
    | ~ c_lessequals(X1,X2,X3)
    | ~ c_lessequals(X2,X1,X3)
    | ~ class_Orderings_Oorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2838]) ).

cnf(c_0_2838_1,axiom,
    ( ~ c_lessequals(X1,X2,X3)
    | X2 = X1
    | ~ c_lessequals(X2,X1,X3)
    | ~ class_Orderings_Oorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2838]) ).

cnf(c_0_2838_2,axiom,
    ( ~ c_lessequals(X2,X1,X3)
    | ~ c_lessequals(X1,X2,X3)
    | X2 = X1
    | ~ class_Orderings_Oorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2838]) ).

cnf(c_0_2838_3,axiom,
    ( ~ class_Orderings_Oorder(X3)
    | ~ c_lessequals(X2,X1,X3)
    | ~ c_lessequals(X1,X2,X3)
    | X2 = X1 ),
    inference(literals_permutation,[status(thm)],[c_0_2838]) ).

cnf(c_0_2839_0,axiom,
    ( c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(X2),X2),X2)
    | ~ class_Ring__and__Field_Oordered__semidom(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2839]) ).

cnf(c_0_2839_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__semidom(X2)
    | c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(X2),X2),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2839]) ).

cnf(c_0_2840_0,axiom,
    ( X1 = X2
    | c_HOL_Ominus__class_Ominus(X1,X2,X3) != c_HOL_Ominus__class_Ominus(X4,X4,X3)
    | ~ class_OrderedGroup_Oab__group__add(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2840]) ).

cnf(c_0_2840_1,axiom,
    ( c_HOL_Ominus__class_Ominus(X1,X2,X3) != c_HOL_Ominus__class_Ominus(X4,X4,X3)
    | X1 = X2
    | ~ class_OrderedGroup_Oab__group__add(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2840]) ).

cnf(c_0_2840_2,axiom,
    ( ~ class_OrderedGroup_Oab__group__add(X3)
    | c_HOL_Ominus__class_Ominus(X1,X2,X3) != c_HOL_Ominus__class_Ominus(X4,X4,X3)
    | X1 = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_2840]) ).

cnf(c_0_2841_0,axiom,
    ( X1 = X2
    | c_HOL_Ominus__class_Ominus(X3,X3,X4) != c_HOL_Ominus__class_Ominus(X1,X2,X4)
    | ~ class_OrderedGroup_Oab__group__add(X4) ),
    inference(literals_permutation,[status(thm)],[c_0_2841]) ).

cnf(c_0_2841_1,axiom,
    ( c_HOL_Ominus__class_Ominus(X3,X3,X4) != c_HOL_Ominus__class_Ominus(X1,X2,X4)
    | X1 = X2
    | ~ class_OrderedGroup_Oab__group__add(X4) ),
    inference(literals_permutation,[status(thm)],[c_0_2841]) ).

cnf(c_0_2841_2,axiom,
    ( ~ class_OrderedGroup_Oab__group__add(X4)
    | c_HOL_Ominus__class_Ominus(X3,X3,X4) != c_HOL_Ominus__class_Ominus(X1,X2,X4)
    | X1 = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_2841]) ).

cnf(c_0_2842_0,axiom,
    ( X1 = X2
    | c_HOL_Oplus__class_Oplus(X3,X1,X4) != c_HOL_Oplus__class_Oplus(X3,X2,X4)
    | ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X4) ),
    inference(literals_permutation,[status(thm)],[c_0_2842]) ).

cnf(c_0_2842_1,axiom,
    ( c_HOL_Oplus__class_Oplus(X3,X1,X4) != c_HOL_Oplus__class_Oplus(X3,X2,X4)
    | X1 = X2
    | ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X4) ),
    inference(literals_permutation,[status(thm)],[c_0_2842]) ).

cnf(c_0_2842_2,axiom,
    ( ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X4)
    | c_HOL_Oplus__class_Oplus(X3,X1,X4) != c_HOL_Oplus__class_Oplus(X3,X2,X4)
    | X1 = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_2842]) ).

cnf(c_0_2843_0,axiom,
    ( X1 = X2
    | c_HOL_Oplus__class_Oplus(X3,X1,X4) != c_HOL_Oplus__class_Oplus(X3,X2,X4)
    | ~ class_OrderedGroup_Ocancel__semigroup__add(X4) ),
    inference(literals_permutation,[status(thm)],[c_0_2843]) ).

cnf(c_0_2843_1,axiom,
    ( c_HOL_Oplus__class_Oplus(X3,X1,X4) != c_HOL_Oplus__class_Oplus(X3,X2,X4)
    | X1 = X2
    | ~ class_OrderedGroup_Ocancel__semigroup__add(X4) ),
    inference(literals_permutation,[status(thm)],[c_0_2843]) ).

cnf(c_0_2843_2,axiom,
    ( ~ class_OrderedGroup_Ocancel__semigroup__add(X4)
    | c_HOL_Oplus__class_Oplus(X3,X1,X4) != c_HOL_Oplus__class_Oplus(X3,X2,X4)
    | X1 = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_2843]) ).

cnf(c_0_2844_0,axiom,
    ( X1 = X2
    | c_HOL_Oplus__class_Oplus(X1,X3,X4) != c_HOL_Oplus__class_Oplus(X2,X3,X4)
    | ~ class_OrderedGroup_Ocancel__semigroup__add(X4) ),
    inference(literals_permutation,[status(thm)],[c_0_2844]) ).

cnf(c_0_2844_1,axiom,
    ( c_HOL_Oplus__class_Oplus(X1,X3,X4) != c_HOL_Oplus__class_Oplus(X2,X3,X4)
    | X1 = X2
    | ~ class_OrderedGroup_Ocancel__semigroup__add(X4) ),
    inference(literals_permutation,[status(thm)],[c_0_2844]) ).

cnf(c_0_2844_2,axiom,
    ( ~ class_OrderedGroup_Ocancel__semigroup__add(X4)
    | c_HOL_Oplus__class_Oplus(X1,X3,X4) != c_HOL_Oplus__class_Oplus(X2,X3,X4)
    | X1 = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_2844]) ).

cnf(c_0_2845_0,axiom,
    ( ~ c_HOL_Oord__class_Oless(X1,X1,X2)
    | ~ c_lessequals(X1,X1,X2)
    | ~ class_Orderings_Olinorder(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2845]) ).

cnf(c_0_2845_1,axiom,
    ( ~ c_lessequals(X1,X1,X2)
    | ~ c_HOL_Oord__class_Oless(X1,X1,X2)
    | ~ class_Orderings_Olinorder(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2845]) ).

cnf(c_0_2845_2,axiom,
    ( ~ class_Orderings_Olinorder(X2)
    | ~ c_lessequals(X1,X1,X2)
    | ~ c_HOL_Oord__class_Oless(X1,X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2845]) ).

cnf(c_0_2846_0,axiom,
    ( ~ c_lessequals(X1,X2,X3)
    | ~ c_HOL_Oord__class_Oless(X2,X1,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2846]) ).

cnf(c_0_2846_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(X2,X1,X3)
    | ~ c_lessequals(X1,X2,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2846]) ).

cnf(c_0_2846_2,axiom,
    ( ~ class_Orderings_Olinorder(X3)
    | ~ c_HOL_Oord__class_Oless(X2,X1,X3)
    | ~ c_lessequals(X1,X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2846]) ).

cnf(c_0_2847_0,axiom,
    ( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | ~ c_lessequals(X2,X1,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2847]) ).

cnf(c_0_2847_1,axiom,
    ( ~ c_lessequals(X2,X1,X3)
    | ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2847]) ).

cnf(c_0_2847_2,axiom,
    ( ~ class_Orderings_Olinorder(X3)
    | ~ c_lessequals(X2,X1,X3)
    | ~ c_HOL_Oord__class_Oless(X1,X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2847]) ).

cnf(c_0_2848_0,axiom,
    ( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | ~ c_lessequals(X2,X1,X3)
    | ~ class_Orderings_Opreorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2848]) ).

cnf(c_0_2848_1,axiom,
    ( ~ c_lessequals(X2,X1,X3)
    | ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | ~ class_Orderings_Opreorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2848]) ).

cnf(c_0_2848_2,axiom,
    ( ~ class_Orderings_Opreorder(X3)
    | ~ c_lessequals(X2,X1,X3)
    | ~ c_HOL_Oord__class_Oless(X1,X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2848]) ).

cnf(c_0_2849_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_2849]) ).

cnf(c_0_2849_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_2849]) ).

cnf(c_0_2849_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_2849]) ).

cnf(c_0_2850_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_2850]) ).

cnf(c_0_2850_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_2850]) ).

cnf(c_0_2850_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_2850]) ).

cnf(c_0_2851_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_2851]) ).

cnf(c_0_2851_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_2851]) ).

cnf(c_0_2851_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_2851]) ).

cnf(c_0_2852_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_2852]) ).

cnf(c_0_2852_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_2852]) ).

cnf(c_0_2852_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_2852]) ).

cnf(c_0_2853_0,axiom,
    ( X2 = X1
    | ~ c_lessequals(X1,X2,tc_nat)
    | ~ c_HOL_Oord__class_Oless(X2,c_Suc(X1),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2853]) ).

cnf(c_0_2853_1,axiom,
    ( ~ c_lessequals(X1,X2,tc_nat)
    | X2 = X1
    | ~ c_HOL_Oord__class_Oless(X2,c_Suc(X1),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2853]) ).

cnf(c_0_2853_2,axiom,
    ( ~ c_HOL_Oord__class_Oless(X2,c_Suc(X1),tc_nat)
    | ~ c_lessequals(X1,X2,tc_nat)
    | X2 = X1 ),
    inference(literals_permutation,[status(thm)],[c_0_2853]) ).

cnf(c_0_2854_0,axiom,
    ( ~ c_lessequals(c_Suc(X1),X2,tc_nat)
    | ~ c_lessequals(X2,X1,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2854]) ).

cnf(c_0_2854_1,axiom,
    ( ~ c_lessequals(X2,X1,tc_nat)
    | ~ c_lessequals(c_Suc(X1),X2,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2854]) ).

cnf(c_0_2855_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_2855]) ).

cnf(c_0_2855_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_2855]) ).

cnf(c_0_2856_0,axiom,
    ( X1 = X2
    | c_HOL_Ominus__class_Ominus(X1,X2,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)
    | c_HOL_Ominus__class_Ominus(X2,X1,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2856]) ).

cnf(c_0_2856_1,axiom,
    ( c_HOL_Ominus__class_Ominus(X1,X2,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)
    | X1 = X2
    | c_HOL_Ominus__class_Ominus(X2,X1,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2856]) ).

cnf(c_0_2856_2,axiom,
    ( c_HOL_Ominus__class_Ominus(X2,X1,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)
    | c_HOL_Ominus__class_Ominus(X1,X2,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)
    | X1 = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_2856]) ).

cnf(c_0_2857_0,axiom,
    ( c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X2,X1),X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2857]) ).

cnf(c_0_2857_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__ring__strict(X1)
    | c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X2,X1),X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2857]) ).

cnf(c_0_2858_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_2858]) ).

cnf(c_0_2858_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_2858]) ).

cnf(c_0_2858_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_2858]) ).

cnf(c_0_2859_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_2859]) ).

cnf(c_0_2859_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_2859]) ).

cnf(c_0_2859_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_2859]) ).

cnf(c_0_2860_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_2860]) ).

cnf(c_0_2860_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_2860]) ).

cnf(c_0_2860_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_2860]) ).

cnf(c_0_2861_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_2861]) ).

cnf(c_0_2861_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_2861]) ).

cnf(c_0_2862_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_2862]) ).

cnf(c_0_2862_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_2862]) ).

cnf(c_0_2863_0,axiom,
    ( X1 = X2
    | ~ c_lessequals(X1,X2,tc_nat)
    | ~ c_lessequals(X2,X1,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2863]) ).

cnf(c_0_2863_1,axiom,
    ( ~ c_lessequals(X1,X2,tc_nat)
    | X1 = X2
    | ~ c_lessequals(X2,X1,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2863]) ).

cnf(c_0_2863_2,axiom,
    ( ~ c_lessequals(X2,X1,tc_nat)
    | ~ c_lessequals(X1,X2,tc_nat)
    | X1 = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_2863]) ).

cnf(c_0_2864_0,axiom,
    ( c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X1,X2,X3),X2,X3) = X1
    | ~ class_OrderedGroup_Ogroup__add(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2864]) ).

cnf(c_0_2864_1,axiom,
    ( ~ class_OrderedGroup_Ogroup__add(X3)
    | c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X1,X2,X3),X2,X3) = X1 ),
    inference(literals_permutation,[status(thm)],[c_0_2864]) ).

cnf(c_0_2865_0,axiom,
    ( c_Orderings_Oord__class_Omin(X1,c_Orderings_Oord__class_Omax(X1,X2,X3),X3) = X1
    | ~ class_Orderings_Olinorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2865]) ).

cnf(c_0_2865_1,axiom,
    ( ~ class_Orderings_Olinorder(X3)
    | c_Orderings_Oord__class_Omin(X1,c_Orderings_Oord__class_Omax(X1,X2,X3),X3) = X1 ),
    inference(literals_permutation,[status(thm)],[c_0_2865]) ).

cnf(c_0_2866_0,axiom,
    ( c_Orderings_Oord__class_Omax(X1,c_Orderings_Oord__class_Omin(X1,X2,X3),X3) = X1
    | ~ class_Orderings_Olinorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2866]) ).

cnf(c_0_2866_1,axiom,
    ( ~ class_Orderings_Olinorder(X3)
    | c_Orderings_Oord__class_Omax(X1,c_Orderings_Oord__class_Omin(X1,X2,X3),X3) = X1 ),
    inference(literals_permutation,[status(thm)],[c_0_2866]) ).

cnf(c_0_2867_0,axiom,
    ( c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X1,X2,X3),X2,X3) = X1
    | ~ class_OrderedGroup_Ogroup__add(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2867]) ).

cnf(c_0_2867_1,axiom,
    ( ~ class_OrderedGroup_Ogroup__add(X3)
    | c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X1,X2,X3),X2,X3) = X1 ),
    inference(literals_permutation,[status(thm)],[c_0_2867]) ).

cnf(c_0_2868_0,axiom,
    ( c_lessequals(X1,c_Orderings_Oord__class_Omax(X1,X2,X3),X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2868]) ).

cnf(c_0_2868_1,axiom,
    ( ~ class_Orderings_Olinorder(X3)
    | c_lessequals(X1,c_Orderings_Oord__class_Omax(X1,X2,X3),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2868]) ).

cnf(c_0_2869_0,axiom,
    ( c_lessequals(X1,c_Orderings_Oord__class_Omax(X2,X1,X3),X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2869]) ).

cnf(c_0_2869_1,axiom,
    ( ~ class_Orderings_Olinorder(X3)
    | c_lessequals(X1,c_Orderings_Oord__class_Omax(X2,X1,X3),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2869]) ).

cnf(c_0_2870_0,axiom,
    ( c_lessequals(c_Orderings_Oord__class_Omin(X1,X2,X3),X1,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2870]) ).

cnf(c_0_2870_1,axiom,
    ( ~ class_Orderings_Olinorder(X3)
    | c_lessequals(c_Orderings_Oord__class_Omin(X1,X2,X3),X1,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2870]) ).

cnf(c_0_2871_0,axiom,
    ( c_lessequals(c_Orderings_Oord__class_Omin(X1,X2,X3),X2,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2871]) ).

cnf(c_0_2871_1,axiom,
    ( ~ class_Orderings_Olinorder(X3)
    | c_lessequals(c_Orderings_Oord__class_Omin(X1,X2,X3),X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2871]) ).

cnf(c_0_2872_0,axiom,
    ( X1 = X2
    | c_HOL_Oplus__class_Oplus(X3,X1,tc_nat) != c_HOL_Oplus__class_Oplus(X3,X2,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2872]) ).

cnf(c_0_2872_1,axiom,
    ( c_HOL_Oplus__class_Oplus(X3,X1,tc_nat) != c_HOL_Oplus__class_Oplus(X3,X2,tc_nat)
    | X1 = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_2872]) ).

cnf(c_0_2873_0,axiom,
    ( X1 = X2
    | c_HOL_Oplus__class_Oplus(X1,X3,tc_nat) != c_HOL_Oplus__class_Oplus(X2,X3,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2873]) ).

cnf(c_0_2873_1,axiom,
    ( c_HOL_Oplus__class_Oplus(X1,X3,tc_nat) != c_HOL_Oplus__class_Oplus(X2,X3,tc_nat)
    | X1 = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_2873]) ).

cnf(c_0_2874_0,axiom,
    ( X1 = X2
    | c_HOL_Oplus__class_Oplus(X3,X1,tc_nat) != c_HOL_Oplus__class_Oplus(X3,X2,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2874]) ).

cnf(c_0_2874_1,axiom,
    ( c_HOL_Oplus__class_Oplus(X3,X1,tc_nat) != c_HOL_Oplus__class_Oplus(X3,X2,tc_nat)
    | X1 = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_2874]) ).

cnf(c_0_2875_0,axiom,
    ( c_lessequals(X1,X2,tc_nat)
    | ~ c_lessequals(c_Suc(X1),c_Suc(X2),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2875]) ).

cnf(c_0_2875_1,axiom,
    ( ~ c_lessequals(c_Suc(X1),c_Suc(X2),tc_nat)
    | c_lessequals(X1,X2,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2875]) ).

cnf(c_0_2876_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_2876]) ).

cnf(c_0_2876_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_2876]) ).

cnf(c_0_2877_0,axiom,
    ( c_lessequals(X1,X2,tc_nat)
    | X1 = c_Suc(X2)
    | ~ c_lessequals(X1,c_Suc(X2),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2877]) ).

cnf(c_0_2877_1,axiom,
    ( X1 = c_Suc(X2)
    | c_lessequals(X1,X2,tc_nat)
    | ~ c_lessequals(X1,c_Suc(X2),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2877]) ).

cnf(c_0_2877_2,axiom,
    ( ~ c_lessequals(X1,c_Suc(X2),tc_nat)
    | X1 = c_Suc(X2)
    | c_lessequals(X1,X2,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2877]) ).

cnf(c_0_2878_0,axiom,
    ( X2 = X1
    | c_HOL_Oord__class_Oless(X1,X2,X3)
    | ~ c_lessequals(X1,X2,X3)
    | ~ class_Orderings_Oorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2878]) ).

cnf(c_0_2878_1,axiom,
    ( c_HOL_Oord__class_Oless(X1,X2,X3)
    | X2 = X1
    | ~ c_lessequals(X1,X2,X3)
    | ~ class_Orderings_Oorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2878]) ).

cnf(c_0_2878_2,axiom,
    ( ~ c_lessequals(X1,X2,X3)
    | c_HOL_Oord__class_Oless(X1,X2,X3)
    | X2 = X1
    | ~ class_Orderings_Oorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2878]) ).

cnf(c_0_2878_3,axiom,
    ( ~ class_Orderings_Oorder(X3)
    | ~ c_lessequals(X1,X2,X3)
    | c_HOL_Oord__class_Oless(X1,X2,X3)
    | X2 = X1 ),
    inference(literals_permutation,[status(thm)],[c_0_2878]) ).

cnf(c_0_2879_0,axiom,
    ( X1 = X2
    | c_HOL_Oord__class_Oless(X2,X1,X3)
    | ~ c_lessequals(X2,X1,X3)
    | ~ class_Orderings_Oorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2879]) ).

cnf(c_0_2879_1,axiom,
    ( c_HOL_Oord__class_Oless(X2,X1,X3)
    | X1 = X2
    | ~ c_lessequals(X2,X1,X3)
    | ~ class_Orderings_Oorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2879]) ).

cnf(c_0_2879_2,axiom,
    ( ~ c_lessequals(X2,X1,X3)
    | c_HOL_Oord__class_Oless(X2,X1,X3)
    | X1 = X2
    | ~ class_Orderings_Oorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2879]) ).

cnf(c_0_2879_3,axiom,
    ( ~ class_Orderings_Oorder(X3)
    | ~ c_lessequals(X2,X1,X3)
    | c_HOL_Oord__class_Oless(X2,X1,X3)
    | X1 = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_2879]) ).

cnf(c_0_2880_0,axiom,
    ( c_HOL_Oord__class_Oless(X1,X2,X3)
    | X1 = X2
    | ~ c_lessequals(X1,X2,X3)
    | ~ class_Orderings_Oorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2880]) ).

cnf(c_0_2880_1,axiom,
    ( X1 = X2
    | c_HOL_Oord__class_Oless(X1,X2,X3)
    | ~ c_lessequals(X1,X2,X3)
    | ~ class_Orderings_Oorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2880]) ).

cnf(c_0_2880_2,axiom,
    ( ~ c_lessequals(X1,X2,X3)
    | X1 = X2
    | c_HOL_Oord__class_Oless(X1,X2,X3)
    | ~ class_Orderings_Oorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2880]) ).

cnf(c_0_2880_3,axiom,
    ( ~ class_Orderings_Oorder(X3)
    | ~ c_lessequals(X1,X2,X3)
    | X1 = X2
    | c_HOL_Oord__class_Oless(X1,X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2880]) ).

cnf(c_0_2881_0,axiom,
    ( X1 = X2
    | c_HOL_Oord__class_Oless(X1,X2,X3)
    | ~ c_lessequals(X1,X2,X3)
    | ~ class_Orderings_Oorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2881]) ).

cnf(c_0_2881_1,axiom,
    ( c_HOL_Oord__class_Oless(X1,X2,X3)
    | X1 = X2
    | ~ c_lessequals(X1,X2,X3)
    | ~ class_Orderings_Oorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2881]) ).

cnf(c_0_2881_2,axiom,
    ( ~ c_lessequals(X1,X2,X3)
    | c_HOL_Oord__class_Oless(X1,X2,X3)
    | X1 = X2
    | ~ class_Orderings_Oorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2881]) ).

cnf(c_0_2881_3,axiom,
    ( ~ class_Orderings_Oorder(X3)
    | ~ c_lessequals(X1,X2,X3)
    | c_HOL_Oord__class_Oless(X1,X2,X3)
    | X1 = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_2881]) ).

cnf(c_0_2882_0,axiom,
    ( X1 = X2
    | c_HOL_Oord__class_Oless(X1,X2,X3)
    | ~ c_lessequals(X1,X2,X3)
    | ~ class_Orderings_Oorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2882]) ).

cnf(c_0_2882_1,axiom,
    ( c_HOL_Oord__class_Oless(X1,X2,X3)
    | X1 = X2
    | ~ c_lessequals(X1,X2,X3)
    | ~ class_Orderings_Oorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2882]) ).

cnf(c_0_2882_2,axiom,
    ( ~ c_lessequals(X1,X2,X3)
    | c_HOL_Oord__class_Oless(X1,X2,X3)
    | X1 = X2
    | ~ class_Orderings_Oorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2882]) ).

cnf(c_0_2882_3,axiom,
    ( ~ class_Orderings_Oorder(X3)
    | ~ c_lessequals(X1,X2,X3)
    | c_HOL_Oord__class_Oless(X1,X2,X3)
    | X1 = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_2882]) ).

cnf(c_0_2883_0,axiom,
    ( X1 = X2
    | c_HOL_Oord__class_Oless(X1,X2,X3)
    | ~ c_lessequals(X1,X2,X3)
    | ~ class_Orderings_Oorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2883]) ).

cnf(c_0_2883_1,axiom,
    ( c_HOL_Oord__class_Oless(X1,X2,X3)
    | X1 = X2
    | ~ c_lessequals(X1,X2,X3)
    | ~ class_Orderings_Oorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2883]) ).

cnf(c_0_2883_2,axiom,
    ( ~ c_lessequals(X1,X2,X3)
    | c_HOL_Oord__class_Oless(X1,X2,X3)
    | X1 = X2
    | ~ class_Orderings_Oorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2883]) ).

cnf(c_0_2883_3,axiom,
    ( ~ class_Orderings_Oorder(X3)
    | ~ c_lessequals(X1,X2,X3)
    | c_HOL_Oord__class_Oless(X1,X2,X3)
    | X1 = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_2883]) ).

cnf(c_0_2884_0,axiom,
    ( c_HOL_Oord__class_Oless(X1,X2,X3)
    | X1 = X2
    | ~ c_lessequals(X1,X2,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2884]) ).

cnf(c_0_2884_1,axiom,
    ( X1 = X2
    | c_HOL_Oord__class_Oless(X1,X2,X3)
    | ~ c_lessequals(X1,X2,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2884]) ).

cnf(c_0_2884_2,axiom,
    ( ~ c_lessequals(X1,X2,X3)
    | X1 = X2
    | c_HOL_Oord__class_Oless(X1,X2,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2884]) ).

cnf(c_0_2884_3,axiom,
    ( ~ class_Orderings_Olinorder(X3)
    | ~ c_lessequals(X1,X2,X3)
    | X1 = X2
    | c_HOL_Oord__class_Oless(X1,X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2884]) ).

cnf(c_0_2885_0,axiom,
    ( c_HOL_Oord__class_Oless(X1,X2,X3)
    | X1 = X2
    | ~ c_lessequals(X1,X2,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2885]) ).

cnf(c_0_2885_1,axiom,
    ( X1 = X2
    | c_HOL_Oord__class_Oless(X1,X2,X3)
    | ~ c_lessequals(X1,X2,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2885]) ).

cnf(c_0_2885_2,axiom,
    ( ~ c_lessequals(X1,X2,X3)
    | X1 = X2
    | c_HOL_Oord__class_Oless(X1,X2,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2885]) ).

cnf(c_0_2885_3,axiom,
    ( ~ class_Orderings_Olinorder(X3)
    | ~ c_lessequals(X1,X2,X3)
    | X1 = X2
    | c_HOL_Oord__class_Oless(X1,X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2885]) ).

cnf(c_0_2886_0,axiom,
    ( c_lessequals(X1,X2,X3)
    | c_Orderings_Oord__class_Omax(X1,X2,X3) != X2
    | ~ class_Orderings_Olinorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2886]) ).

cnf(c_0_2886_1,axiom,
    ( c_Orderings_Oord__class_Omax(X1,X2,X3) != X2
    | c_lessequals(X1,X2,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2886]) ).

cnf(c_0_2886_2,axiom,
    ( ~ class_Orderings_Olinorder(X3)
    | c_Orderings_Oord__class_Omax(X1,X2,X3) != X2
    | c_lessequals(X1,X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2886]) ).

cnf(c_0_2887_0,axiom,
    ( c_lessequals(X1,X2,X3)
    | c_Orderings_Oord__class_Omin(X1,X2,X3) != X1
    | ~ class_Orderings_Olinorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2887]) ).

cnf(c_0_2887_1,axiom,
    ( c_Orderings_Oord__class_Omin(X1,X2,X3) != X1
    | c_lessequals(X1,X2,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2887]) ).

cnf(c_0_2887_2,axiom,
    ( ~ class_Orderings_Olinorder(X3)
    | c_Orderings_Oord__class_Omin(X1,X2,X3) != X1
    | c_lessequals(X1,X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2887]) ).

cnf(c_0_2888_0,axiom,
    ( c_lessequals(c_Suc(X1),c_Suc(X2),tc_nat)
    | ~ c_lessequals(X1,X2,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2888]) ).

cnf(c_0_2888_1,axiom,
    ( ~ c_lessequals(X1,X2,tc_nat)
    | c_lessequals(c_Suc(X1),c_Suc(X2),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2888]) ).

cnf(c_0_2889_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_2889]) ).

cnf(c_0_2889_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_2889]) ).

cnf(c_0_2890_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_2890]) ).

cnf(c_0_2890_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_2890]) ).

cnf(c_0_2891_0,axiom,
    ( c_Orderings_Oord__class_Omax(X1,X2,X3) = X2
    | ~ c_lessequals(X1,X2,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2891]) ).

cnf(c_0_2891_1,axiom,
    ( ~ c_lessequals(X1,X2,X3)
    | c_Orderings_Oord__class_Omax(X1,X2,X3) = X2
    | ~ class_Orderings_Olinorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2891]) ).

cnf(c_0_2891_2,axiom,
    ( ~ class_Orderings_Olinorder(X3)
    | ~ c_lessequals(X1,X2,X3)
    | c_Orderings_Oord__class_Omax(X1,X2,X3) = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_2891]) ).

cnf(c_0_2892_0,axiom,
    ( c_Orderings_Oord__class_Omax(X2,X1,X3) = X2
    | ~ c_lessequals(X1,X2,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2892]) ).

cnf(c_0_2892_1,axiom,
    ( ~ c_lessequals(X1,X2,X3)
    | c_Orderings_Oord__class_Omax(X2,X1,X3) = X2
    | ~ class_Orderings_Olinorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2892]) ).

cnf(c_0_2892_2,axiom,
    ( ~ class_Orderings_Olinorder(X3)
    | ~ c_lessequals(X1,X2,X3)
    | c_Orderings_Oord__class_Omax(X2,X1,X3) = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_2892]) ).

cnf(c_0_2893_0,axiom,
    ( c_Orderings_Oord__class_Omin(X1,X2,X3) = X1
    | ~ c_lessequals(X1,X2,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2893]) ).

cnf(c_0_2893_1,axiom,
    ( ~ c_lessequals(X1,X2,X3)
    | c_Orderings_Oord__class_Omin(X1,X2,X3) = X1
    | ~ class_Orderings_Olinorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2893]) ).

cnf(c_0_2893_2,axiom,
    ( ~ class_Orderings_Olinorder(X3)
    | ~ c_lessequals(X1,X2,X3)
    | c_Orderings_Oord__class_Omin(X1,X2,X3) = X1 ),
    inference(literals_permutation,[status(thm)],[c_0_2893]) ).

cnf(c_0_2894_0,axiom,
    ( c_Orderings_Oord__class_Omin(X2,X1,X3) = X1
    | ~ c_lessequals(X1,X2,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2894]) ).

cnf(c_0_2894_1,axiom,
    ( ~ c_lessequals(X1,X2,X3)
    | c_Orderings_Oord__class_Omin(X2,X1,X3) = X1
    | ~ class_Orderings_Olinorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2894]) ).

cnf(c_0_2894_2,axiom,
    ( ~ class_Orderings_Olinorder(X3)
    | ~ c_lessequals(X1,X2,X3)
    | c_Orderings_Oord__class_Omin(X2,X1,X3) = X1 ),
    inference(literals_permutation,[status(thm)],[c_0_2894]) ).

cnf(c_0_2895_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_2895]) ).

cnf(c_0_2895_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_2895]) ).

cnf(c_0_2895_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_2895]) ).

cnf(c_0_2896_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_2896]) ).

cnf(c_0_2896_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_2896]) ).

cnf(c_0_2896_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_2896]) ).

cnf(c_0_2897_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_2897]) ).

cnf(c_0_2897_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_2897]) ).

cnf(c_0_2897_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_2897]) ).

cnf(c_0_2898_0,axiom,
    ( 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_2898]) ).

cnf(c_0_2898_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | c_Lambda_Osubst(c_Lambda_OdB_OVar(X1),X3,X2) = c_Lambda_OdB_OVar(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2898]) ).

cnf(c_0_2899_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_2899]) ).

cnf(c_0_2899_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_2899]) ).

cnf(c_0_2899_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_2899]) ).

cnf(c_0_2900_0,axiom,
    ( c_lessequals(X1,X2,X3)
    | ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | ~ class_Orderings_Oorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2900]) ).

cnf(c_0_2900_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | c_lessequals(X1,X2,X3)
    | ~ class_Orderings_Oorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2900]) ).

cnf(c_0_2900_2,axiom,
    ( ~ class_Orderings_Oorder(X3)
    | ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | c_lessequals(X1,X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2900]) ).

cnf(c_0_2901_0,axiom,
    ( c_lessequals(X1,X2,X3)
    | ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | ~ class_Orderings_Opreorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2901]) ).

cnf(c_0_2901_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | c_lessequals(X1,X2,X3)
    | ~ class_Orderings_Opreorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2901]) ).

cnf(c_0_2901_2,axiom,
    ( ~ class_Orderings_Opreorder(X3)
    | ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | c_lessequals(X1,X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2901]) ).

cnf(c_0_2902_0,axiom,
    ( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | ~ c_lessequals(c_Suc(X1),X2,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2902]) ).

cnf(c_0_2902_1,axiom,
    ( ~ c_lessequals(c_Suc(X1),X2,tc_nat)
    | c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2902]) ).

cnf(c_0_2903_0,axiom,
    ( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | ~ c_lessequals(c_Suc(X1),X2,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2903]) ).

cnf(c_0_2903_1,axiom,
    ( ~ c_lessequals(c_Suc(X1),X2,tc_nat)
    | c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2903]) ).

cnf(c_0_2904_0,axiom,
    ( c_lessequals(X1,X2,tc_nat)
    | ~ c_HOL_Oord__class_Oless(X1,c_Suc(X2),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2904]) ).

cnf(c_0_2904_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(X1,c_Suc(X2),tc_nat)
    | c_lessequals(X1,X2,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2904]) ).

cnf(c_0_2905_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_2905]) ).

cnf(c_0_2905_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_2905]) ).

cnf(c_0_2906_0,axiom,
    ( c_lessequals(X1,X2,tc_nat)
    | ~ c_lessequals(c_Suc(X1),X2,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2906]) ).

cnf(c_0_2906_1,axiom,
    ( ~ c_lessequals(c_Suc(X1),X2,tc_nat)
    | c_lessequals(X1,X2,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2906]) ).

cnf(c_0_2907_0,axiom,
    ( c_lessequals(c_Suc(X1),X2,tc_nat)
    | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2907]) ).

cnf(c_0_2907_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | c_lessequals(c_Suc(X1),X2,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2907]) ).

cnf(c_0_2908_0,axiom,
    ( c_lessequals(c_Suc(X1),X2,tc_nat)
    | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2908]) ).

cnf(c_0_2908_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | c_lessequals(c_Suc(X1),X2,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2908]) ).

cnf(c_0_2909_0,axiom,
    ( c_HOL_Oord__class_Oless(X1,c_Suc(X2),tc_nat)
    | ~ c_lessequals(X1,X2,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2909]) ).

cnf(c_0_2909_1,axiom,
    ( ~ c_lessequals(X1,X2,tc_nat)
    | c_HOL_Oord__class_Oless(X1,c_Suc(X2),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2909]) ).

cnf(c_0_2910_0,axiom,
    ( c_HOL_Oord__class_Oless(X1,c_Suc(X1),tc_nat)
    | ~ c_lessequals(X1,X1,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2910]) ).

cnf(c_0_2910_1,axiom,
    ( ~ c_lessequals(X1,X1,tc_nat)
    | c_HOL_Oord__class_Oless(X1,c_Suc(X1),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2910]) ).

cnf(c_0_2911_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_2911]) ).

cnf(c_0_2911_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_2911]) ).

cnf(c_0_2912_0,axiom,
    ( c_lessequals(X1,c_Suc(X2),tc_nat)
    | ~ c_lessequals(X1,X2,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2912]) ).

cnf(c_0_2912_1,axiom,
    ( ~ c_lessequals(X1,X2,tc_nat)
    | c_lessequals(X1,c_Suc(X2),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2912]) ).

cnf(c_0_2913_0,axiom,
    ( c_lessequals(X1,X2,tc_nat)
    | c_HOL_Ominus__class_Ominus(X1,X2,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2913]) ).

cnf(c_0_2913_1,axiom,
    ( c_HOL_Ominus__class_Ominus(X1,X2,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)
    | c_lessequals(X1,X2,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2913]) ).

cnf(c_0_2914_0,axiom,
    ( c_HOL_Ominus__class_Ominus(X1,X2,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat)
    | ~ c_lessequals(X1,X2,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2914]) ).

cnf(c_0_2914_1,axiom,
    ( ~ c_lessequals(X1,X2,tc_nat)
    | c_HOL_Ominus__class_Ominus(X1,X2,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2914]) ).

cnf(c_0_2915_0,axiom,
    ( X1 = X2
    | c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | ~ c_lessequals(X1,X2,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2915]) ).

cnf(c_0_2915_1,axiom,
    ( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | X1 = X2
    | ~ c_lessequals(X1,X2,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2915]) ).

cnf(c_0_2915_2,axiom,
    ( ~ c_lessequals(X1,X2,tc_nat)
    | c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | X1 = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_2915]) ).

cnf(c_0_2916_0,axiom,
    ( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | X1 = X2
    | ~ c_lessequals(X1,X2,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2916]) ).

cnf(c_0_2916_1,axiom,
    ( X1 = X2
    | c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | ~ c_lessequals(X1,X2,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2916]) ).

cnf(c_0_2916_2,axiom,
    ( ~ c_lessequals(X1,X2,tc_nat)
    | X1 = X2
    | c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2916]) ).

cnf(c_0_2917_0,axiom,
    ( X1 = X2
    | c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | ~ c_lessequals(X1,X2,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2917]) ).

cnf(c_0_2917_1,axiom,
    ( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | X1 = X2
    | ~ c_lessequals(X1,X2,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2917]) ).

cnf(c_0_2917_2,axiom,
    ( ~ c_lessequals(X1,X2,tc_nat)
    | c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | X1 = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_2917]) ).

cnf(c_0_2918_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_2918]) ).

cnf(c_0_2918_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_2918]) ).

cnf(c_0_2919_0,axiom,
    ( c_lessequals(X1,X2,tc_nat)
    | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2919]) ).

cnf(c_0_2919_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | c_lessequals(X1,X2,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2919]) ).

cnf(c_0_2920_0,axiom,
    ( c_lessequals(X1,X2,tc_nat)
    | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2920]) ).

cnf(c_0_2920_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | c_lessequals(X1,X2,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2920]) ).

cnf(c_0_2921_0,axiom,
    ( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | X2 = X1
    | c_Lambda_Osubst(c_Lambda_OdB_OVar(X2),X3,X1) = c_Lambda_OdB_OVar(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2921]) ).

cnf(c_0_2921_1,axiom,
    ( X2 = X1
    | c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | c_Lambda_Osubst(c_Lambda_OdB_OVar(X2),X3,X1) = c_Lambda_OdB_OVar(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2921]) ).

cnf(c_0_2921_2,axiom,
    ( 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_2921]) ).

cnf(c_0_2922_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_2922]) ).

cnf(c_0_2922_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_2922]) ).

cnf(c_0_2922_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_2922]) ).

cnf(c_0_2922_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_2922]) ).

cnf(c_0_2923_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_2923]) ).

cnf(c_0_2923_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_2923]) ).

cnf(c_0_2923_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_2923]) ).

cnf(c_0_2923_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_2923]) ).

cnf(c_0_2924_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_2924]) ).

cnf(c_0_2924_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_2924]) ).

cnf(c_0_2924_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_2924]) ).

cnf(c_0_2924_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_2924]) ).

cnf(c_0_2925_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_2925]) ).

cnf(c_0_2925_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_2925]) ).

cnf(c_0_2925_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_2925]) ).

cnf(c_0_2925_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_2925]) ).

cnf(c_0_2926_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_2926]) ).

cnf(c_0_2926_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_2926]) ).

cnf(c_0_2926_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_2926]) ).

cnf(c_0_2926_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_2926]) ).

cnf(c_0_2927_0,axiom,
    ( c_lessequals(X1,X2,X3)
    | c_HOL_Oord__class_Oless(X2,X1,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2927]) ).

cnf(c_0_2927_1,axiom,
    ( c_HOL_Oord__class_Oless(X2,X1,X3)
    | c_lessequals(X1,X2,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2927]) ).

cnf(c_0_2927_2,axiom,
    ( ~ class_Orderings_Olinorder(X3)
    | c_HOL_Oord__class_Oless(X2,X1,X3)
    | c_lessequals(X1,X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2927]) ).

cnf(c_0_2928_0,axiom,
    ( c_lessequals(X1,X1,X2)
    | c_HOL_Oord__class_Oless(X1,X1,X2)
    | ~ class_Orderings_Olinorder(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2928]) ).

cnf(c_0_2928_1,axiom,
    ( c_HOL_Oord__class_Oless(X1,X1,X2)
    | c_lessequals(X1,X1,X2)
    | ~ class_Orderings_Olinorder(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2928]) ).

cnf(c_0_2928_2,axiom,
    ( ~ class_Orderings_Olinorder(X2)
    | c_HOL_Oord__class_Oless(X1,X1,X2)
    | c_lessequals(X1,X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2928]) ).

cnf(c_0_2929_0,axiom,
    ( c_HOL_Oord__class_Oless(X1,X2,X3)
    | c_lessequals(X2,X1,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2929]) ).

cnf(c_0_2929_1,axiom,
    ( c_lessequals(X2,X1,X3)
    | c_HOL_Oord__class_Oless(X1,X2,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2929]) ).

cnf(c_0_2929_2,axiom,
    ( ~ class_Orderings_Olinorder(X3)
    | c_lessequals(X2,X1,X3)
    | c_HOL_Oord__class_Oless(X1,X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2929]) ).

cnf(c_0_2930_0,axiom,
    ( c_lessequals(X1,X2,X3)
    | c_HOL_Oord__class_Oless(X2,X1,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2930]) ).

cnf(c_0_2930_1,axiom,
    ( c_HOL_Oord__class_Oless(X2,X1,X3)
    | c_lessequals(X1,X2,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2930]) ).

cnf(c_0_2930_2,axiom,
    ( ~ class_Orderings_Olinorder(X3)
    | c_HOL_Oord__class_Oless(X2,X1,X3)
    | c_lessequals(X1,X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2930]) ).

cnf(c_0_2931_0,axiom,
    ( c_lessequals(X1,X2,X3)
    | c_lessequals(X2,X1,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2931]) ).

cnf(c_0_2931_1,axiom,
    ( c_lessequals(X2,X1,X3)
    | c_lessequals(X1,X2,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2931]) ).

cnf(c_0_2931_2,axiom,
    ( ~ class_Orderings_Olinorder(X3)
    | c_lessequals(X2,X1,X3)
    | c_lessequals(X1,X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2931]) ).

cnf(c_0_2932_0,axiom,
    ( c_HOL_Oplus__class_Oplus(X1,X2,X3) = c_HOL_Oplus__class_Oplus(X2,X1,X3)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2932]) ).

cnf(c_0_2932_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
    | c_HOL_Oplus__class_Oplus(X1,X2,X3) = c_HOL_Oplus__class_Oplus(X2,X1,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2932]) ).

cnf(c_0_2933_0,axiom,
    ( c_HOL_Oplus__class_Oplus(X1,X2,X3) = c_HOL_Oplus__class_Oplus(X2,X1,X3)
    | ~ class_OrderedGroup_Ocomm__monoid__add(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2933]) ).

cnf(c_0_2933_1,axiom,
    ( ~ class_OrderedGroup_Ocomm__monoid__add(X3)
    | c_HOL_Oplus__class_Oplus(X1,X2,X3) = c_HOL_Oplus__class_Oplus(X2,X1,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2933]) ).

cnf(c_0_2934_0,axiom,
    ( c_HOL_Oplus__class_Oplus(X1,X2,X3) = c_HOL_Oplus__class_Oplus(X2,X1,X3)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2934]) ).

cnf(c_0_2934_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
    | c_HOL_Oplus__class_Oplus(X1,X2,X3) = c_HOL_Oplus__class_Oplus(X2,X1,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2934]) ).

cnf(c_0_2935_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_2935]) ).

cnf(c_0_2935_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_2935]) ).

cnf(c_0_2936_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_2936]) ).

cnf(c_0_2936_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_2936]) ).

cnf(c_0_2937_0,axiom,
    ( c_Orderings_Oord__class_Omin(X1,X2,X3) = c_Orderings_Oord__class_Omin(X2,X1,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2937]) ).

cnf(c_0_2937_1,axiom,
    ( ~ class_Orderings_Olinorder(X3)
    | c_Orderings_Oord__class_Omin(X1,X2,X3) = c_Orderings_Oord__class_Omin(X2,X1,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2937]) ).

cnf(c_0_2938_0,axiom,
    ( c_Orderings_Oord__class_Omax(X1,X2,X3) = c_Orderings_Oord__class_Omax(X2,X1,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2938]) ).

cnf(c_0_2938_1,axiom,
    ( ~ class_Orderings_Olinorder(X3)
    | c_Orderings_Oord__class_Omax(X1,X2,X3) = c_Orderings_Oord__class_Omax(X2,X1,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2938]) ).

cnf(c_0_2939_0,axiom,
    ( 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_2939]) ).

cnf(c_0_2939_1,axiom,
    ( c_HOL_Oord__class_Oless(X1,X1,tc_nat)
    | c_Lambda_Osubst(c_Lambda_OdB_OVar(X1),X2,X1) = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_2939]) ).

cnf(c_0_2940_0,axiom,
    ( c_lessequals(X1,X2,tc_nat)
    | c_lessequals(c_Suc(X2),X1,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2940]) ).

cnf(c_0_2940_1,axiom,
    ( c_lessequals(c_Suc(X2),X1,tc_nat)
    | c_lessequals(X1,X2,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2940]) ).

cnf(c_0_2941_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_2941]) ).

cnf(c_0_2941_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_2941]) ).

cnf(c_0_2942_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_2942]) ).

cnf(c_0_2942_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_2942]) ).

cnf(c_0_2943_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_2943]) ).

cnf(c_0_2943_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_2943]) ).

cnf(c_0_2944_0,axiom,
    ( ~ c_lessequals(c_HOL_Oone__class_Oone(X1),c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2944]) ).

cnf(c_0_2944_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__semidom(X1)
    | ~ c_lessequals(c_HOL_Oone__class_Oone(X1),c_HOL_Ozero__class_Ozero(X1),X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2944]) ).

cnf(c_0_2945_0,axiom,
    ( X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
    | X2 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
    | c_HOL_Oplus__class_Oplus(X1,X2,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
    inference(literals_permutation,[status(thm)],[c_0_2945]) ).

cnf(c_0_2945_1,axiom,
    ( X2 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
    | X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
    | c_HOL_Oplus__class_Oplus(X1,X2,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
    inference(literals_permutation,[status(thm)],[c_0_2945]) ).

cnf(c_0_2945_2,axiom,
    ( c_HOL_Oplus__class_Oplus(X1,X2,tc_nat) != 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_2945]) ).

cnf(c_0_2946_0,axiom,
    ( X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
    | X2 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
    | c_HOL_Oplus__class_Oplus(X1,X2,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
    inference(literals_permutation,[status(thm)],[c_0_2946]) ).

cnf(c_0_2946_1,axiom,
    ( X2 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
    | X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
    | c_HOL_Oplus__class_Oplus(X1,X2,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
    inference(literals_permutation,[status(thm)],[c_0_2946]) ).

cnf(c_0_2946_2,axiom,
    ( c_HOL_Oplus__class_Oplus(X1,X2,tc_nat) != 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_2946]) ).

cnf(c_0_2947_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_2947]) ).

cnf(c_0_2947_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_2947]) ).

cnf(c_0_2947_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_2947]) ).

cnf(c_0_2947_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_2947]) ).

cnf(c_0_2948_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_2948]) ).

cnf(c_0_2948_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_2948]) ).

cnf(c_0_2948_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_2948]) ).

cnf(c_0_2948_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_2948]) ).

cnf(c_0_2949_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_2949]) ).

cnf(c_0_2949_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_2949]) ).

cnf(c_0_2949_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_2949]) ).

cnf(c_0_2949_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_2949]) ).

cnf(c_0_2950_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_2950]) ).

cnf(c_0_2950_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_2950]) ).

cnf(c_0_2950_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_2950]) ).

cnf(c_0_2951_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_2951]) ).

cnf(c_0_2951_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_2951]) ).

cnf(c_0_2951_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_2951]) ).

cnf(c_0_2952_0,axiom,
    ( X1 = X2
    | c_HOL_Ominus__class_Ominus(X1,X2,X3) != c_HOL_Ozero__class_Ozero(X3)
    | ~ class_Int_Onumber__ring(X3)
    | ~ class_Ring__and__Field_Oidom(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2952]) ).

cnf(c_0_2952_1,axiom,
    ( c_HOL_Ominus__class_Ominus(X1,X2,X3) != c_HOL_Ozero__class_Ozero(X3)
    | X1 = X2
    | ~ class_Int_Onumber__ring(X3)
    | ~ class_Ring__and__Field_Oidom(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2952]) ).

cnf(c_0_2952_2,axiom,
    ( ~ class_Int_Onumber__ring(X3)
    | c_HOL_Ominus__class_Ominus(X1,X2,X3) != c_HOL_Ozero__class_Ozero(X3)
    | X1 = X2
    | ~ class_Ring__and__Field_Oidom(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2952]) ).

cnf(c_0_2952_3,axiom,
    ( ~ class_Ring__and__Field_Oidom(X3)
    | ~ class_Int_Onumber__ring(X3)
    | c_HOL_Ominus__class_Ominus(X1,X2,X3) != c_HOL_Ozero__class_Ozero(X3)
    | X1 = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_2952]) ).

cnf(c_0_2953_0,axiom,
    ( 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_2953]) ).

cnf(c_0_2953_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | c_Lambda_Olift(c_Lambda_OdB_OVar(X1),X2) = c_Lambda_OdB_OVar(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2953]) ).

cnf(c_0_2954_0,axiom,
    ( X1 = c_HOL_Ozero__class_Ozero(X2)
    | c_HOL_Oplus__class_Oplus(X3,X1,X2) != X3
    | ~ class_Int_Onumber__ring(X2)
    | ~ class_Ring__and__Field_Oidom(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2954]) ).

cnf(c_0_2954_1,axiom,
    ( c_HOL_Oplus__class_Oplus(X3,X1,X2) != 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_2954]) ).

cnf(c_0_2954_2,axiom,
    ( ~ class_Int_Onumber__ring(X2)
    | c_HOL_Oplus__class_Oplus(X3,X1,X2) != X3
    | X1 = c_HOL_Ozero__class_Ozero(X2)
    | ~ class_Ring__and__Field_Oidom(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2954]) ).

cnf(c_0_2954_3,axiom,
    ( ~ class_Ring__and__Field_Oidom(X2)
    | ~ class_Int_Onumber__ring(X2)
    | c_HOL_Oplus__class_Oplus(X3,X1,X2) != X3
    | X1 = c_HOL_Ozero__class_Ozero(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2954]) ).

cnf(c_0_2955_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_2955]) ).

cnf(c_0_2955_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_2955]) ).

cnf(c_0_2956_0,axiom,
    ( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
    | X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
    | c_HOL_Oplus__class_Oplus(X2,X1,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
    inference(literals_permutation,[status(thm)],[c_0_2956]) ).

cnf(c_0_2956_1,axiom,
    ( X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
    | X1 = c_HOL_Ozero__class_Ozero(tc_nat)
    | c_HOL_Oplus__class_Oplus(X2,X1,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
    inference(literals_permutation,[status(thm)],[c_0_2956]) ).

cnf(c_0_2956_2,axiom,
    ( c_HOL_Oplus__class_Oplus(X2,X1,tc_nat) != 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_2956]) ).

cnf(c_0_2957_0,axiom,
    ( X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
    | X1 = c_HOL_Ozero__class_Ozero(tc_nat)
    | c_HOL_Oplus__class_Oplus(X1,X2,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
    inference(literals_permutation,[status(thm)],[c_0_2957]) ).

cnf(c_0_2957_1,axiom,
    ( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
    | X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
    | c_HOL_Oplus__class_Oplus(X1,X2,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
    inference(literals_permutation,[status(thm)],[c_0_2957]) ).

cnf(c_0_2957_2,axiom,
    ( c_HOL_Oplus__class_Oplus(X1,X2,tc_nat) != 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_2957]) ).

cnf(c_0_2958_0,axiom,
    ( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
    | X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
    | c_HOL_Oplus__class_Oplus(X2,X1,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
    inference(literals_permutation,[status(thm)],[c_0_2958]) ).

cnf(c_0_2958_1,axiom,
    ( X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
    | X1 = c_HOL_Ozero__class_Ozero(tc_nat)
    | c_HOL_Oplus__class_Oplus(X2,X1,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
    inference(literals_permutation,[status(thm)],[c_0_2958]) ).

cnf(c_0_2958_2,axiom,
    ( c_HOL_Oplus__class_Oplus(X2,X1,tc_nat) != 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_2958]) ).

cnf(c_0_2959_0,axiom,
    ( X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
    | X1 = c_HOL_Ozero__class_Ozero(tc_nat)
    | c_HOL_Oplus__class_Oplus(X1,X2,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
    inference(literals_permutation,[status(thm)],[c_0_2959]) ).

cnf(c_0_2959_1,axiom,
    ( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
    | X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
    | c_HOL_Oplus__class_Oplus(X1,X2,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
    inference(literals_permutation,[status(thm)],[c_0_2959]) ).

cnf(c_0_2959_2,axiom,
    ( c_HOL_Oplus__class_Oplus(X1,X2,tc_nat) != 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_2959]) ).

cnf(c_0_2960_0,axiom,
    ( c_lessequals(X1,X2,tc_nat)
    | c_lessequals(X2,X1,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2960]) ).

cnf(c_0_2960_1,axiom,
    ( c_lessequals(X2,X1,tc_nat)
    | c_lessequals(X1,X2,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2960]) ).

cnf(c_0_2961_0,axiom,
    ( X1 = c_HOL_Ozero__class_Ozero(X2)
    | c_HOL_Oplus__class_Oplus(X1,X1,X2) != c_HOL_Ozero__class_Ozero(X2)
    | ~ class_OrderedGroup_Olordered__ab__group__add(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2961]) ).

cnf(c_0_2961_1,axiom,
    ( c_HOL_Oplus__class_Oplus(X1,X1,X2) != 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_2961]) ).

cnf(c_0_2961_2,axiom,
    ( ~ class_OrderedGroup_Olordered__ab__group__add(X2)
    | c_HOL_Oplus__class_Oplus(X1,X1,X2) != c_HOL_Ozero__class_Ozero(X2)
    | X1 = c_HOL_Ozero__class_Ozero(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2961]) ).

cnf(c_0_2962_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_2962]) ).

cnf(c_0_2962_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_2962]) ).

cnf(c_0_2963_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_2963]) ).

cnf(c_0_2963_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_2963]) ).

cnf(c_0_2964_0,axiom,
    ( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
    | X2 = c_HOL_Ozero__class_Ozero(tc_nat)
    | c_HOL_Oplus__class_Oplus(X2,X1,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
    inference(literals_permutation,[status(thm)],[c_0_2964]) ).

cnf(c_0_2964_1,axiom,
    ( X2 = c_HOL_Ozero__class_Ozero(tc_nat)
    | X1 = c_HOL_Ozero__class_Ozero(tc_nat)
    | c_HOL_Oplus__class_Oplus(X2,X1,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
    inference(literals_permutation,[status(thm)],[c_0_2964]) ).

cnf(c_0_2964_2,axiom,
    ( c_HOL_Oplus__class_Oplus(X2,X1,tc_nat) != 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_2964]) ).

cnf(c_0_2965_0,axiom,
    ( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
    | X2 = c_HOL_Ozero__class_Ozero(tc_nat)
    | c_HOL_Oplus__class_Oplus(X2,X1,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
    inference(literals_permutation,[status(thm)],[c_0_2965]) ).

cnf(c_0_2965_1,axiom,
    ( X2 = c_HOL_Ozero__class_Ozero(tc_nat)
    | X1 = c_HOL_Ozero__class_Ozero(tc_nat)
    | c_HOL_Oplus__class_Oplus(X2,X1,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
    inference(literals_permutation,[status(thm)],[c_0_2965]) ).

cnf(c_0_2965_2,axiom,
    ( c_HOL_Oplus__class_Oplus(X2,X1,tc_nat) != 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_2965]) ).

cnf(c_0_2966_0,axiom,
    ( X1 = X2
    | c_HOL_Ominus__class_Ominus(X1,X2,X3) != c_HOL_Ozero__class_Ozero(X3)
    | ~ class_OrderedGroup_Ogroup__add(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2966]) ).

cnf(c_0_2966_1,axiom,
    ( c_HOL_Ominus__class_Ominus(X1,X2,X3) != c_HOL_Ozero__class_Ozero(X3)
    | X1 = X2
    | ~ class_OrderedGroup_Ogroup__add(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2966]) ).

cnf(c_0_2966_2,axiom,
    ( ~ class_OrderedGroup_Ogroup__add(X3)
    | c_HOL_Ominus__class_Ominus(X1,X2,X3) != c_HOL_Ozero__class_Ozero(X3)
    | X1 = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_2966]) ).

cnf(c_0_2967_0,axiom,
    ( X1 = X2
    | c_HOL_Ominus__class_Ominus(X1,X2,X3) != c_HOL_Ozero__class_Ozero(X3)
    | ~ class_OrderedGroup_Oab__group__add(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2967]) ).

cnf(c_0_2967_1,axiom,
    ( c_HOL_Ominus__class_Ominus(X1,X2,X3) != c_HOL_Ozero__class_Ozero(X3)
    | X1 = X2
    | ~ class_OrderedGroup_Oab__group__add(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2967]) ).

cnf(c_0_2967_2,axiom,
    ( ~ class_OrderedGroup_Oab__group__add(X3)
    | c_HOL_Ominus__class_Ominus(X1,X2,X3) != c_HOL_Ozero__class_Ozero(X3)
    | X1 = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_2967]) ).

cnf(c_0_2968_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_2968]) ).

cnf(c_0_2968_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_2968]) ).

cnf(c_0_2968_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_2968]) ).

cnf(c_0_2969_0,axiom,
    ( ~ c_HOL_Oord__class_Oless(X1,X1,X2)
    | ~ class_Orderings_Oorder(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2969]) ).

cnf(c_0_2969_1,axiom,
    ( ~ class_Orderings_Oorder(X2)
    | ~ c_HOL_Oord__class_Oless(X1,X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2969]) ).

cnf(c_0_2970_0,axiom,
    ( ~ c_HOL_Oord__class_Oless(X1,X1,X2)
    | ~ class_Orderings_Olinorder(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2970]) ).

cnf(c_0_2970_1,axiom,
    ( ~ class_Orderings_Olinorder(X2)
    | ~ c_HOL_Oord__class_Oless(X1,X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2970]) ).

cnf(c_0_2971_0,axiom,
    ( ~ c_HOL_Oord__class_Oless(X1,X1,X2)
    | ~ class_Orderings_Opreorder(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2971]) ).

cnf(c_0_2971_1,axiom,
    ( ~ class_Orderings_Opreorder(X2)
    | ~ c_HOL_Oord__class_Oless(X1,X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2971]) ).

cnf(c_0_2972_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_2972]) ).

cnf(c_0_2972_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_2972]) ).

cnf(c_0_2972_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_2972]) ).

cnf(c_0_2973_0,axiom,
    ( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
    | ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2973]) ).

cnf(c_0_2973_1,axiom,
    ( ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)
    | X1 = c_HOL_Ozero__class_Ozero(tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2973]) ).

cnf(c_0_2974_0,axiom,
    ( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
    | c_HOL_Oplus__class_Oplus(X1,X2,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2974]) ).

cnf(c_0_2974_1,axiom,
    ( c_HOL_Oplus__class_Oplus(X1,X2,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)
    | X1 = c_HOL_Ozero__class_Ozero(tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2974]) ).

cnf(c_0_2975_0,axiom,
    ( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
    | c_HOL_Oplus__class_Oplus(X2,X1,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2975]) ).

cnf(c_0_2975_1,axiom,
    ( c_HOL_Oplus__class_Oplus(X2,X1,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)
    | X1 = c_HOL_Ozero__class_Ozero(tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2975]) ).

cnf(c_0_2976_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_2976]) ).

cnf(c_0_2976_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_2976]) ).

cnf(c_0_2977_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_2977]) ).

cnf(c_0_2977_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_2977]) ).

cnf(c_0_2978_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_2978]) ).

cnf(c_0_2978_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_2978]) ).

cnf(c_0_2979_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_2979]) ).

cnf(c_0_2979_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_2979]) ).

cnf(c_0_2980_0,axiom,
    ( c_Lambda_Obeta(c_Lambda_OdB_OApp(X3,X1),c_Lambda_OdB_OApp(X3,X2))
    | ~ c_Lambda_Obeta(X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2980]) ).

cnf(c_0_2980_1,axiom,
    ( ~ c_Lambda_Obeta(X1,X2)
    | c_Lambda_Obeta(c_Lambda_OdB_OApp(X3,X1),c_Lambda_OdB_OApp(X3,X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_2980]) ).

cnf(c_0_2981_0,axiom,
    ( c_Lambda_Obeta(c_Lambda_OdB_OApp(X1,X3),c_Lambda_OdB_OApp(X2,X3))
    | ~ c_Lambda_Obeta(X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2981]) ).

cnf(c_0_2981_1,axiom,
    ( ~ c_Lambda_Obeta(X1,X2)
    | c_Lambda_Obeta(c_Lambda_OdB_OApp(X1,X3),c_Lambda_OdB_OApp(X2,X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_2981]) ).

cnf(c_0_2982_0,axiom,
    ( c_Lambda_Obeta(c_Lambda_Olift(X1,X3),c_Lambda_Olift(X2,X3))
    | ~ c_Lambda_Obeta(X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2982]) ).

cnf(c_0_2982_1,axiom,
    ( ~ c_Lambda_Obeta(X1,X2)
    | c_Lambda_Obeta(c_Lambda_Olift(X1,X3),c_Lambda_Olift(X2,X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_2982]) ).

cnf(c_0_2983_0,axiom,
    ( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
    | c_HOL_Oplus__class_Oplus(X2,X1,tc_nat) != X2 ),
    inference(literals_permutation,[status(thm)],[c_0_2983]) ).

cnf(c_0_2983_1,axiom,
    ( c_HOL_Oplus__class_Oplus(X2,X1,tc_nat) != X2
    | X1 = c_HOL_Ozero__class_Ozero(tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2983]) ).

cnf(c_0_2984_0,axiom,
    ( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
    | c_HOL_Oplus__class_Oplus(X2,X1,tc_nat) != X2 ),
    inference(literals_permutation,[status(thm)],[c_0_2984]) ).

cnf(c_0_2984_1,axiom,
    ( c_HOL_Oplus__class_Oplus(X2,X1,tc_nat) != X2
    | X1 = c_HOL_Ozero__class_Ozero(tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2984]) ).

cnf(c_0_2985_0,axiom,
    ( c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ozero__class_Ozero(X1),X1) = c_HOL_Ozero__class_Ozero(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2985]) ).

cnf(c_0_2985_1,axiom,
    ( ~ class_OrderedGroup_Olordered__ab__group__add(X1)
    | c_HOL_Oplus__class_Oplus(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_2985]) ).

cnf(c_0_2986_0,axiom,
    ( c_HOL_Oplus__class_Oplus(X1,c_HOL_Ozero__class_Ozero(X2),X2) = X1
    | ~ class_Int_Onumber__ring(X2)
    | ~ class_Ring__and__Field_Oidom(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2986]) ).

cnf(c_0_2986_1,axiom,
    ( ~ class_Int_Onumber__ring(X2)
    | c_HOL_Oplus__class_Oplus(X1,c_HOL_Ozero__class_Ozero(X2),X2) = X1
    | ~ class_Ring__and__Field_Oidom(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2986]) ).

cnf(c_0_2986_2,axiom,
    ( ~ class_Ring__and__Field_Oidom(X2)
    | ~ class_Int_Onumber__ring(X2)
    | c_HOL_Oplus__class_Oplus(X1,c_HOL_Ozero__class_Ozero(X2),X2) = X1 ),
    inference(literals_permutation,[status(thm)],[c_0_2986]) ).

cnf(c_0_2987_0,axiom,
    ( c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oone__class_Oone(X1),X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2987]) ).

cnf(c_0_2987_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__semidom(X1)
    | c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oone__class_Oone(X1),X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2987]) ).

cnf(c_0_2988_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_2988]) ).

cnf(c_0_2988_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_2988]) ).

cnf(c_0_2989_0,axiom,
    ( c_HOL_Ominus__class_Ominus(X1,X1,X2) = c_HOL_Ozero__class_Ozero(X2)
    | ~ class_Int_Onumber__ring(X2)
    | ~ class_Ring__and__Field_Oidom(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2989]) ).

cnf(c_0_2989_1,axiom,
    ( ~ class_Int_Onumber__ring(X2)
    | c_HOL_Ominus__class_Ominus(X1,X1,X2) = c_HOL_Ozero__class_Ozero(X2)
    | ~ class_Ring__and__Field_Oidom(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2989]) ).

cnf(c_0_2989_2,axiom,
    ( ~ class_Ring__and__Field_Oidom(X2)
    | ~ class_Int_Onumber__ring(X2)
    | c_HOL_Ominus__class_Ominus(X1,X1,X2) = c_HOL_Ozero__class_Ozero(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2989]) ).

cnf(c_0_2990_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_2990]) ).

cnf(c_0_2990_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_2990]) ).

cnf(c_0_2991_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_2991]) ).

cnf(c_0_2991_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_2991]) ).

cnf(c_0_2992_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_2992]) ).

cnf(c_0_2992_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_2992]) ).

cnf(c_0_2993_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_2993]) ).

cnf(c_0_2993_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_2993]) ).

cnf(c_0_2994_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_2994]) ).

cnf(c_0_2994_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_2994]) ).

cnf(c_0_2995_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_2995]) ).

cnf(c_0_2995_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_2995]) ).

cnf(c_0_2996_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_2996]) ).

cnf(c_0_2996_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_2996]) ).

cnf(c_0_2997_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_2997]) ).

cnf(c_0_2997_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_2997]) ).

cnf(c_0_2998_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_2998]) ).

cnf(c_0_2998_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_2998]) ).

cnf(c_0_2999_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_2999]) ).

cnf(c_0_2999_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_2999]) ).

cnf(c_0_3000_0,axiom,
    ( c_HOL_Ominus__class_Ominus(X1,c_HOL_Ozero__class_Ozero(X2),X2) = X1
    | ~ class_OrderedGroup_Ogroup__add(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_3000]) ).

cnf(c_0_3000_1,axiom,
    ( ~ class_OrderedGroup_Ogroup__add(X2)
    | c_HOL_Ominus__class_Ominus(X1,c_HOL_Ozero__class_Ozero(X2),X2) = X1 ),
    inference(literals_permutation,[status(thm)],[c_0_3000]) ).

cnf(c_0_3001_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_3001]) ).

cnf(c_0_3001_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_3001]) ).

cnf(c_0_3002_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_3002]) ).

cnf(c_0_3002_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_3002]) ).

cnf(c_0_3003_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_3003]) ).

cnf(c_0_3003_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_3003]) ).

cnf(c_0_3004_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_3004]) ).

cnf(c_0_3004_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_3004]) ).

cnf(c_0_3005_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_3005]) ).

cnf(c_0_3005_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_3005]) ).

cnf(c_0_3006_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_3006]) ).

cnf(c_0_3006_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_3006]) ).

cnf(c_0_3007_0,axiom,
    ( c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X1),X2,X1) = X2
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3007]) ).

cnf(c_0_3007_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
    | c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X1),X2,X1) = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_3007]) ).

cnf(c_0_3008_0,axiom,
    ( c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X1),X2,X1) = X2
    | ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3008]) ).

cnf(c_0_3008_1,axiom,
    ( ~ class_OrderedGroup_Ocomm__monoid__add(X1)
    | c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X1),X2,X1) = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_3008]) ).

cnf(c_0_3009_0,axiom,
    ( c_HOL_Oplus__class_Oplus(X1,c_HOL_Ozero__class_Ozero(X2),X2) = X1
    | ~ class_OrderedGroup_Ocomm__monoid__add(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_3009]) ).

cnf(c_0_3009_1,axiom,
    ( ~ class_OrderedGroup_Ocomm__monoid__add(X2)
    | c_HOL_Oplus__class_Oplus(X1,c_HOL_Ozero__class_Ozero(X2),X2) = X1 ),
    inference(literals_permutation,[status(thm)],[c_0_3009]) ).

cnf(c_0_3010_0,axiom,
    ( c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X1),X2,X1) = X2
    | ~ class_OrderedGroup_Omonoid__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3010]) ).

cnf(c_0_3010_1,axiom,
    ( ~ class_OrderedGroup_Omonoid__add(X1)
    | c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X1),X2,X1) = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_3010]) ).

cnf(c_0_3011_0,axiom,
    ( c_HOL_Oplus__class_Oplus(X1,c_HOL_Ozero__class_Ozero(X2),X2) = X1
    | ~ class_OrderedGroup_Omonoid__add(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_3011]) ).

cnf(c_0_3011_1,axiom,
    ( ~ class_OrderedGroup_Omonoid__add(X2)
    | c_HOL_Oplus__class_Oplus(X1,c_HOL_Ozero__class_Ozero(X2),X2) = X1 ),
    inference(literals_permutation,[status(thm)],[c_0_3011]) ).

cnf(c_0_3012_0,axiom,
    ( c_HOL_Oplus__class_Oplus(X1,c_HOL_Ozero__class_Ozero(X2),X2) = X1
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_3012]) ).

cnf(c_0_3012_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__1(X2)
    | c_HOL_Oplus__class_Oplus(X1,c_HOL_Ozero__class_Ozero(X2),X2) = X1 ),
    inference(literals_permutation,[status(thm)],[c_0_3012]) ).

cnf(c_0_3013_0,axiom,
    ( c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X1),X2,X1) = X2
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3013]) ).

cnf(c_0_3013_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
    | c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X1),X2,X1) = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_3013]) ).

cnf(c_0_3014_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_3014]) ).

cnf(c_0_3014_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_3014]) ).

cnf(c_0_3015_0,axiom,
    ( c_HOL_Ominus__class_Ominus(X1,X1,X2) = c_HOL_Ozero__class_Ozero(X2)
    | ~ class_OrderedGroup_Oab__group__add(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_3015]) ).

cnf(c_0_3015_1,axiom,
    ( ~ class_OrderedGroup_Oab__group__add(X2)
    | c_HOL_Ominus__class_Ominus(X1,X1,X2) = c_HOL_Ozero__class_Ozero(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_3015]) ).

cnf(c_0_3016_0,axiom,
    ( c_HOL_Ominus__class_Ominus(X1,X1,X2) = c_HOL_Ozero__class_Ozero(X2)
    | ~ class_OrderedGroup_Ogroup__add(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_3016]) ).

cnf(c_0_3016_1,axiom,
    ( ~ class_OrderedGroup_Ogroup__add(X2)
    | c_HOL_Ominus__class_Ominus(X1,X1,X2) = c_HOL_Ozero__class_Ozero(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_3016]) ).

cnf(c_0_3017_0,axiom,
    ( c_HOL_Ominus__class_Ominus(X1,X1,X2) = c_HOL_Ozero__class_Ozero(X2)
    | ~ class_OrderedGroup_Ogroup__add(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_3017]) ).

cnf(c_0_3017_1,axiom,
    ( ~ class_OrderedGroup_Ogroup__add(X2)
    | c_HOL_Ominus__class_Ominus(X1,X1,X2) = c_HOL_Ozero__class_Ozero(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_3017]) ).

cnf(c_0_3018_0,axiom,
    ( c_Orderings_Oord__class_Omin(X1,X1,X2) = X1
    | ~ class_Orderings_Olinorder(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_3018]) ).

cnf(c_0_3018_1,axiom,
    ( ~ class_Orderings_Olinorder(X2)
    | c_Orderings_Oord__class_Omin(X1,X1,X2) = X1 ),
    inference(literals_permutation,[status(thm)],[c_0_3018]) ).

cnf(c_0_3019_0,axiom,
    ( c_Orderings_Oord__class_Omax(X1,X1,X2) = X1
    | ~ class_Orderings_Olinorder(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_3019]) ).

cnf(c_0_3019_1,axiom,
    ( ~ class_Orderings_Olinorder(X2)
    | c_Orderings_Oord__class_Omax(X1,X1,X2) = X1 ),
    inference(literals_permutation,[status(thm)],[c_0_3019]) ).

cnf(c_0_3020_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_3020]) ).

cnf(c_0_3020_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_3020]) ).

cnf(c_0_3021_0,axiom,
    ( c_lessequals(X1,X1,X2)
    | ~ class_Orderings_Oorder(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_3021]) ).

cnf(c_0_3021_1,axiom,
    ( ~ class_Orderings_Oorder(X2)
    | c_lessequals(X1,X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_3021]) ).

cnf(c_0_3022_0,axiom,
    ( c_lessequals(X1,X1,X2)
    | ~ class_Orderings_Opreorder(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_3022]) ).

cnf(c_0_3022_1,axiom,
    ( ~ class_Orderings_Opreorder(X2)
    | c_lessequals(X1,X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_3022]) ).

cnf(c_0_3023_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_3023]) ).

cnf(c_0_3023_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_3023]) ).

cnf(c_0_3024_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_3024]) ).

cnf(c_0_3024_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_3024]) ).

cnf(c_0_3025_0,axiom,
    ( X1 = X2
    | c_Lambda_OdB_OApp(X3,X1) != c_Lambda_OdB_OApp(X4,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_3025]) ).

cnf(c_0_3025_1,axiom,
    ( c_Lambda_OdB_OApp(X3,X1) != c_Lambda_OdB_OApp(X4,X2)
    | X1 = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_3025]) ).

cnf(c_0_3026_0,axiom,
    ( X1 = X2
    | c_Lambda_OdB_OApp(X1,X3) != c_Lambda_OdB_OApp(X2,X4) ),
    inference(literals_permutation,[status(thm)],[c_0_3026]) ).

cnf(c_0_3026_1,axiom,
    ( c_Lambda_OdB_OApp(X1,X3) != c_Lambda_OdB_OApp(X2,X4)
    | X1 = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_3026]) ).

cnf(c_0_3027_0,axiom,
    ( c_InductTermi_OIT(c_Lambda_Olift(X1,X2))
    | ~ c_InductTermi_OIT(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3027]) ).

cnf(c_0_3027_1,axiom,
    ( ~ c_InductTermi_OIT(X1)
    | c_InductTermi_OIT(c_Lambda_Olift(X1,X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_3027]) ).

cnf(c_0_3028_0,axiom,
    ( c_HOL_Ozero__class_Ozero(X1) != c_HOL_Oone__class_Oone(X1)
    | ~ class_Ring__and__Field_Ozero__neq__one(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3028]) ).

cnf(c_0_3028_1,axiom,
    ( ~ class_Ring__and__Field_Ozero__neq__one(X1)
    | c_HOL_Ozero__class_Ozero(X1) != c_HOL_Oone__class_Oone(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3028]) ).

cnf(c_0_3029_0,axiom,
    ( c_HOL_Ozero__class_Ozero(X1) != c_HOL_Oone__class_Oone(X1)
    | ~ class_Ring__and__Field_Ozero__neq__one(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3029]) ).

cnf(c_0_3029_1,axiom,
    ( ~ class_Ring__and__Field_Ozero__neq__one(X1)
    | c_HOL_Ozero__class_Ozero(X1) != c_HOL_Oone__class_Oone(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3029]) ).

cnf(c_0_3030_0,axiom,
    ( c_InductTermi_OIT(c_Lambda_OdB_OAbs(X1))
    | ~ c_InductTermi_OIT(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3030]) ).

cnf(c_0_3030_1,axiom,
    ( ~ c_InductTermi_OIT(X1)
    | c_InductTermi_OIT(c_Lambda_OdB_OAbs(X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_3030]) ).

cnf(c_0_3031_0,axiom,
    ( X1 = X2
    | c_Lambda_OdB_OVar(X1) != c_Lambda_OdB_OVar(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_3031]) ).

cnf(c_0_3031_1,axiom,
    ( c_Lambda_OdB_OVar(X1) != c_Lambda_OdB_OVar(X2)
    | X1 = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_3031]) ).

cnf(c_0_3032_0,axiom,
    ( X1 = X2
    | c_Lambda_OdB_OAbs(X1) != c_Lambda_OdB_OAbs(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_3032]) ).

cnf(c_0_3032_1,axiom,
    ( c_Lambda_OdB_OAbs(X1) != c_Lambda_OdB_OAbs(X2)
    | X1 = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_3032]) ).

cnf(c_0_3033_0,axiom,
    ( X1 = X2
    | c_Suc(X1) != c_Suc(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_3033]) ).

cnf(c_0_3033_1,axiom,
    ( c_Suc(X1) != c_Suc(X2)
    | X1 = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_3033]) ).

cnf(c_0_3034_0,axiom,
    ( X1 = X2
    | c_Suc(X1) != c_Suc(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_3034]) ).

cnf(c_0_3034_1,axiom,
    ( c_Suc(X1) != c_Suc(X2)
    | X1 = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_3034]) ).

% CNF of non-axioms
% Start CNF derivation
fof(c_0_0_726,negated_conjecture,
    ~ c_InductTermi_OIT(c_Lambda_OdB_OAbs(c_Lambda_Osubst(v_ra,c_Lambda_OdB_OVar(c_Suc(v_ia)),c_Suc(v_ja)))),
    file('<stdin>',cls_conjecture_2) ).

fof(c_0_1_727,negated_conjecture,
    ! [X1,X2] : c_InductTermi_OIT(c_Lambda_Osubst(v_ra,c_Lambda_OdB_OVar(X2),X1)),
    file('<stdin>',cls_conjecture_1) ).

fof(c_0_2_728,negated_conjecture,
    c_InductTermi_OIT(v_ra),
    file('<stdin>',cls_conjecture_0) ).

fof(c_0_3_729,negated_conjecture,
    ~ c_InductTermi_OIT(c_Lambda_OdB_OAbs(c_Lambda_Osubst(v_ra,c_Lambda_OdB_OVar(c_Suc(v_ia)),c_Suc(v_ja)))),
    inference(fof_simplification,[status(thm)],[c_0_0]) ).

fof(c_0_4_730,negated_conjecture,
    ! [X1,X2] : c_InductTermi_OIT(c_Lambda_Osubst(v_ra,c_Lambda_OdB_OVar(X2),X1)),
    c_0_1 ).

fof(c_0_5_731,negated_conjecture,
    c_InductTermi_OIT(v_ra),
    c_0_2 ).

fof(c_0_6_732,negated_conjecture,
    ~ c_InductTermi_OIT(c_Lambda_OdB_OAbs(c_Lambda_Osubst(v_ra,c_Lambda_OdB_OVar(c_Suc(v_ia)),c_Suc(v_ja)))),
    c_0_3 ).

fof(c_0_7_733,negated_conjecture,
    ! [X3,X4] : c_InductTermi_OIT(c_Lambda_Osubst(v_ra,c_Lambda_OdB_OVar(X4),X3)),
    inference(variable_rename,[status(thm)],[c_0_4]) ).

fof(c_0_8_734,negated_conjecture,
    c_InductTermi_OIT(v_ra),
    c_0_5 ).

cnf(c_0_9_735,negated_conjecture,
    ~ c_InductTermi_OIT(c_Lambda_OdB_OAbs(c_Lambda_Osubst(v_ra,c_Lambda_OdB_OVar(c_Suc(v_ia)),c_Suc(v_ja)))),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

cnf(c_0_10_736,negated_conjecture,
    c_InductTermi_OIT(c_Lambda_Osubst(v_ra,c_Lambda_OdB_OVar(X1),X2)),
    inference(split_conjunct,[status(thm)],[c_0_7]) ).

cnf(c_0_11_737,negated_conjecture,
    c_InductTermi_OIT(v_ra),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

cnf(c_0_12_738,negated_conjecture,
    ~ c_InductTermi_OIT(c_Lambda_OdB_OAbs(c_Lambda_Osubst(v_ra,c_Lambda_OdB_OVar(c_Suc(v_ia)),c_Suc(v_ja)))),
    c_0_9,
    [final] ).

cnf(c_0_13_739,negated_conjecture,
    c_InductTermi_OIT(c_Lambda_Osubst(v_ra,c_Lambda_OdB_OVar(X1),X2)),
    c_0_10,
    [final] ).

cnf(c_0_14_740,negated_conjecture,
    c_InductTermi_OIT(v_ra),
    c_0_11,
    [final] ).

% End CNF derivation

%-------------------------------------------------------------
% Proof by iprover

cnf(c_1861,negated_conjecture,
    ~ c_InductTermi_OIT(c_Lambda_OdB_OAbs(c_Lambda_Osubst(v_ra,c_Lambda_OdB_OVar(c_Suc(v_ia)),c_Suc(v_ja)))),
    file('/export/starexec/sandbox/tmp/iprover_modulo_ea6b13.p',c_0_12) ).

cnf(c_2192,negated_conjecture,
    ~ c_InductTermi_OIT(c_Lambda_OdB_OAbs(c_Lambda_Osubst(v_ra,c_Lambda_OdB_OVar(c_Suc(v_ia)),c_Suc(v_ja)))),
    inference(copy,[status(esa)],[c_1861]) ).

cnf(c_2204,negated_conjecture,
    ~ c_InductTermi_OIT(c_Lambda_OdB_OAbs(c_Lambda_Osubst(v_ra,c_Lambda_OdB_OVar(c_Suc(v_ia)),c_Suc(v_ja)))),
    inference(copy,[status(esa)],[c_2192]) ).

cnf(c_2209,negated_conjecture,
    ~ c_InductTermi_OIT(c_Lambda_OdB_OAbs(c_Lambda_Osubst(v_ra,c_Lambda_OdB_OVar(c_Suc(v_ia)),c_Suc(v_ja)))),
    inference(copy,[status(esa)],[c_2204]) ).

cnf(c_2210,negated_conjecture,
    ~ c_InductTermi_OIT(c_Lambda_OdB_OAbs(c_Lambda_Osubst(v_ra,c_Lambda_OdB_OVar(c_Suc(v_ia)),c_Suc(v_ja)))),
    inference(copy,[status(esa)],[c_2209]) ).

cnf(c_7735,negated_conjecture,
    ~ c_InductTermi_OIT(c_Lambda_OdB_OAbs(c_Lambda_Osubst(v_ra,c_Lambda_OdB_OVar(c_Suc(v_ia)),c_Suc(v_ja)))),
    inference(copy,[status(esa)],[c_2210]) ).

cnf(c_1706,plain,
    ( ~ c_InductTermi_OIT(X0)
    | c_InductTermi_OIT(c_Lambda_OdB_OAbs(X0)) ),
    file('/export/starexec/sandbox/tmp/iprover_modulo_ea6b13.p',c_0_3030_0) ).

cnf(c_7489,plain,
    ( ~ c_InductTermi_OIT(X0)
    | c_InductTermi_OIT(c_Lambda_OdB_OAbs(X0)) ),
    inference(copy,[status(esa)],[c_1706]) ).

cnf(c_7490,plain,
    ( c_InductTermi_OIT(c_Lambda_OdB_OAbs(X0))
    | ~ c_InductTermi_OIT(X0) ),
    inference(rewriting,[status(thm)],[c_7489]) ).

cnf(c_7747,plain,
    ~ c_InductTermi_OIT(c_Lambda_Osubst(v_ra,c_Lambda_OdB_OVar(c_Suc(v_ia)),c_Suc(v_ja))),
    inference(resolution,[status(thm)],[c_7735,c_7490]) ).

cnf(c_7748,plain,
    ~ c_InductTermi_OIT(c_Lambda_Osubst(v_ra,c_Lambda_OdB_OVar(c_Suc(v_ia)),c_Suc(v_ja))),
    inference(rewriting,[status(thm)],[c_7747]) ).

cnf(c_1862,negated_conjecture,
    c_InductTermi_OIT(c_Lambda_Osubst(v_ra,c_Lambda_OdB_OVar(X0),X1)),
    file('/export/starexec/sandbox/tmp/iprover_modulo_ea6b13.p',c_0_13) ).

cnf(c_2194,negated_conjecture,
    c_InductTermi_OIT(c_Lambda_Osubst(v_ra,c_Lambda_OdB_OVar(X0),X1)),
    inference(copy,[status(esa)],[c_1862]) ).

cnf(c_2205,negated_conjecture,
    c_InductTermi_OIT(c_Lambda_Osubst(v_ra,c_Lambda_OdB_OVar(X0),X1)),
    inference(copy,[status(esa)],[c_2194]) ).

cnf(c_2208,negated_conjecture,
    c_InductTermi_OIT(c_Lambda_Osubst(v_ra,c_Lambda_OdB_OVar(X0),X1)),
    inference(copy,[status(esa)],[c_2205]) ).

cnf(c_2211,negated_conjecture,
    c_InductTermi_OIT(c_Lambda_Osubst(v_ra,c_Lambda_OdB_OVar(X0),X1)),
    inference(copy,[status(esa)],[c_2208]) ).

cnf(c_7737,negated_conjecture,
    c_InductTermi_OIT(c_Lambda_Osubst(v_ra,c_Lambda_OdB_OVar(X0),X1)),
    inference(copy,[status(esa)],[c_2211]) ).

cnf(c_7750,plain,
    $false,
    inference(forward_subsumption_resolution,[status(thm)],[c_7748,c_7737]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : LCL755-1 : TPTP v8.1.0. Released v4.1.0.
% 0.07/0.13  % Command  : iprover_modulo %s %d
% 0.14/0.34  % Computer : n018.cluster.edu
% 0.14/0.34  % Model    : x86_64 x86_64
% 0.14/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34  % Memory   : 8042.1875MB
% 0.14/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34  % CPULimit : 300
% 0.14/0.34  % WCLimit  : 600
% 0.14/0.34  % DateTime : Mon Jul  4 18:35:51 EDT 2022
% 0.14/0.34  % CPUTime  : 
% 0.14/0.35  % Running in mono-core mode
% 0.35/0.53  % Orienting using strategy Equiv(ClausalAll)
% 0.35/0.53  % Orientation found
% 0.35/0.53  % 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_f91999.s --tptp_safe_out true --time_out_real 150 /export/starexec/sandbox/tmp/iprover_modulo_ea6b13.p | tee /export/starexec/sandbox/tmp/iprover_modulo_out_87db1d | grep -v "SZS"
% 0.39/0.56  
% 0.39/0.56  %---------------- iProver v2.5 (CASC-J8 2016) ----------------%
% 0.39/0.56  
% 0.39/0.56  % 
% 0.39/0.56  % ------  iProver source info 
% 0.39/0.56  
% 0.39/0.56  % git: sha1: 57accf6c58032223c7708532cf852a99fa48c1b3
% 0.39/0.56  % git: non_committed_changes: true
% 0.39/0.56  % git: last_make_outside_of_git: true
% 0.39/0.56  
% 0.39/0.56  % 
% 0.39/0.56  % ------ Input Options
% 0.39/0.56  
% 0.39/0.56  % --out_options                         all
% 0.39/0.56  % --tptp_safe_out                       true
% 0.39/0.56  % --problem_path                        ""
% 0.39/0.56  % --include_path                        ""
% 0.39/0.56  % --clausifier                          .//eprover
% 0.39/0.56  % --clausifier_options                  --tstp-format  
% 0.39/0.56  % --stdin                               false
% 0.39/0.56  % --dbg_backtrace                       false
% 0.39/0.56  % --dbg_dump_prop_clauses               false
% 0.39/0.56  % --dbg_dump_prop_clauses_file          -
% 0.39/0.56  % --dbg_out_stat                        false
% 0.39/0.56  
% 0.39/0.56  % ------ General Options
% 0.39/0.56  
% 0.39/0.56  % --fof                                 false
% 0.39/0.56  % --time_out_real                       150.
% 0.39/0.56  % --time_out_prep_mult                  0.2
% 0.39/0.56  % --time_out_virtual                    -1.
% 0.39/0.56  % --schedule                            none
% 0.39/0.56  % --ground_splitting                    input
% 0.39/0.56  % --splitting_nvd                       16
% 0.39/0.56  % --non_eq_to_eq                        false
% 0.39/0.56  % --prep_gs_sim                         true
% 0.39/0.56  % --prep_unflatten                      false
% 0.39/0.56  % --prep_res_sim                        true
% 0.39/0.56  % --prep_upred                          true
% 0.39/0.56  % --res_sim_input                       true
% 0.39/0.56  % --clause_weak_htbl                    true
% 0.39/0.56  % --gc_record_bc_elim                   false
% 0.39/0.56  % --symbol_type_check                   false
% 0.39/0.56  % --clausify_out                        false
% 0.39/0.56  % --large_theory_mode                   false
% 0.39/0.56  % --prep_sem_filter                     none
% 0.39/0.56  % --prep_sem_filter_out                 false
% 0.39/0.56  % --preprocessed_out                    false
% 0.39/0.56  % --sub_typing                          false
% 0.39/0.56  % --brand_transform                     false
% 0.39/0.56  % --pure_diseq_elim                     true
% 0.39/0.56  % --min_unsat_core                      false
% 0.39/0.56  % --pred_elim                           true
% 0.39/0.56  % --add_important_lit                   false
% 0.39/0.56  % --soft_assumptions                    false
% 0.39/0.56  % --reset_solvers                       false
% 0.39/0.56  % --bc_imp_inh                          []
% 0.39/0.56  % --conj_cone_tolerance                 1.5
% 0.39/0.56  % --prolific_symb_bound                 500
% 0.39/0.56  % --lt_threshold                        2000
% 0.39/0.56  
% 0.39/0.56  % ------ SAT Options
% 0.39/0.56  
% 0.39/0.56  % --sat_mode                            false
% 0.39/0.56  % --sat_fm_restart_options              ""
% 0.39/0.56  % --sat_gr_def                          false
% 0.39/0.56  % --sat_epr_types                       true
% 0.39/0.56  % --sat_non_cyclic_types                false
% 0.39/0.56  % --sat_finite_models                   false
% 0.39/0.56  % --sat_fm_lemmas                       false
% 0.39/0.56  % --sat_fm_prep                         false
% 0.39/0.56  % --sat_fm_uc_incr                      true
% 0.39/0.56  % --sat_out_model                       small
% 0.39/0.56  % --sat_out_clauses                     false
% 0.39/0.56  
% 0.39/0.56  % ------ QBF Options
% 0.39/0.56  
% 0.39/0.56  % --qbf_mode                            false
% 0.39/0.56  % --qbf_elim_univ                       true
% 0.39/0.56  % --qbf_sk_in                           true
% 0.39/0.56  % --qbf_pred_elim                       true
% 0.39/0.56  % --qbf_split                           32
% 0.39/0.56  
% 0.39/0.56  % ------ BMC1 Options
% 0.39/0.56  
% 0.39/0.56  % --bmc1_incremental                    false
% 0.39/0.56  % --bmc1_axioms                         reachable_all
% 0.39/0.56  % --bmc1_min_bound                      0
% 0.39/0.56  % --bmc1_max_bound                      -1
% 0.39/0.56  % --bmc1_max_bound_default              -1
% 0.39/0.56  % --bmc1_symbol_reachability            true
% 0.39/0.56  % --bmc1_property_lemmas                false
% 0.39/0.56  % --bmc1_k_induction                    false
% 0.39/0.56  % --bmc1_non_equiv_states               false
% 0.39/0.56  % --bmc1_deadlock                       false
% 0.39/0.56  % --bmc1_ucm                            false
% 0.39/0.56  % --bmc1_add_unsat_core                 none
% 0.39/0.56  % --bmc1_unsat_core_children            false
% 0.39/0.56  % --bmc1_unsat_core_extrapolate_axioms  false
% 0.39/0.56  % --bmc1_out_stat                       full
% 0.39/0.56  % --bmc1_ground_init                    false
% 0.39/0.56  % --bmc1_pre_inst_next_state            false
% 0.39/0.56  % --bmc1_pre_inst_state                 false
% 0.39/0.56  % --bmc1_pre_inst_reach_state           false
% 0.39/0.56  % --bmc1_out_unsat_core                 false
% 0.39/0.56  % --bmc1_aig_witness_out                false
% 0.39/0.56  % --bmc1_verbose                        false
% 0.39/0.56  % --bmc1_dump_clauses_tptp              false
% 3.06/3.32  % --bmc1_dump_unsat_core_tptp           false
% 3.06/3.32  % --bmc1_dump_file                      -
% 3.06/3.32  % --bmc1_ucm_expand_uc_limit            128
% 3.06/3.32  % --bmc1_ucm_n_expand_iterations        6
% 3.06/3.32  % --bmc1_ucm_extend_mode                1
% 3.06/3.32  % --bmc1_ucm_init_mode                  2
% 3.06/3.32  % --bmc1_ucm_cone_mode                  none
% 3.06/3.32  % --bmc1_ucm_reduced_relation_type      0
% 3.06/3.32  % --bmc1_ucm_relax_model                4
% 3.06/3.32  % --bmc1_ucm_full_tr_after_sat          true
% 3.06/3.32  % --bmc1_ucm_expand_neg_assumptions     false
% 3.06/3.32  % --bmc1_ucm_layered_model              none
% 3.06/3.32  % --bmc1_ucm_max_lemma_size             10
% 3.06/3.32  
% 3.06/3.32  % ------ AIG Options
% 3.06/3.32  
% 3.06/3.32  % --aig_mode                            false
% 3.06/3.32  
% 3.06/3.32  % ------ Instantiation Options
% 3.06/3.32  
% 3.06/3.32  % --instantiation_flag                  true
% 3.06/3.32  % --inst_lit_sel                        [+prop;+sign;+ground;-num_var;-num_symb]
% 3.06/3.32  % --inst_solver_per_active              750
% 3.06/3.32  % --inst_solver_calls_frac              0.5
% 3.06/3.32  % --inst_passive_queue_type             priority_queues
% 3.06/3.32  % --inst_passive_queues                 [[-conj_dist;+conj_symb;-num_var];[+age;-num_symb]]
% 3.06/3.32  % --inst_passive_queues_freq            [25;2]
% 3.06/3.32  % --inst_dismatching                    true
% 3.06/3.32  % --inst_eager_unprocessed_to_passive   true
% 3.06/3.32  % --inst_prop_sim_given                 true
% 3.06/3.32  % --inst_prop_sim_new                   false
% 3.06/3.32  % --inst_orphan_elimination             true
% 3.06/3.32  % --inst_learning_loop_flag             true
% 3.06/3.32  % --inst_learning_start                 3000
% 3.06/3.32  % --inst_learning_factor                2
% 3.06/3.32  % --inst_start_prop_sim_after_learn     3
% 3.06/3.32  % --inst_sel_renew                      solver
% 3.06/3.32  % --inst_lit_activity_flag              true
% 3.06/3.32  % --inst_out_proof                      true
% 3.06/3.32  
% 3.06/3.32  % ------ Resolution Options
% 3.06/3.32  
% 3.06/3.32  % --resolution_flag                     true
% 3.06/3.32  % --res_lit_sel                         kbo_max
% 3.06/3.32  % --res_to_prop_solver                  none
% 3.06/3.32  % --res_prop_simpl_new                  false
% 3.06/3.32  % --res_prop_simpl_given                false
% 3.06/3.32  % --res_passive_queue_type              priority_queues
% 3.06/3.32  % --res_passive_queues                  [[-conj_dist;+conj_symb;-num_symb];[+age;-num_symb]]
% 3.06/3.32  % --res_passive_queues_freq             [15;5]
% 3.06/3.32  % --res_forward_subs                    full
% 3.06/3.32  % --res_backward_subs                   full
% 3.06/3.32  % --res_forward_subs_resolution         true
% 3.06/3.32  % --res_backward_subs_resolution        true
% 3.06/3.32  % --res_orphan_elimination              false
% 3.06/3.32  % --res_time_limit                      1000.
% 3.06/3.32  % --res_out_proof                       true
% 3.06/3.32  % --proof_out_file                      /export/starexec/sandbox/tmp/iprover_proof_f91999.s
% 3.06/3.32  % --modulo                              true
% 3.06/3.32  
% 3.06/3.32  % ------ Combination Options
% 3.06/3.32  
% 3.06/3.32  % --comb_res_mult                       1000
% 3.06/3.32  % --comb_inst_mult                      300
% 3.06/3.32  % ------ 
% 3.06/3.32  
% 3.06/3.32  % ------ Parsing...% successful
% 3.06/3.32  
% 3.06/3.32  % ------ 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 % 
% 3.06/3.32  
% 3.06/3.32  % ------ Proving...
% 3.06/3.32  % ------ Problem Properties 
% 3.06/3.32  
% 3.06/3.32  % 
% 3.06/3.32  % EPR                                   false
% 3.06/3.32  % Horn                                  false
% 3.06/3.32  % Has equality                          true
% 3.06/3.32  
% 3.06/3.32  % % ------ Input Options Time Limit: Unbounded
% 3.06/3.32  
% 3.06/3.32  
% 3.06/3.32  Compiling...
% 3.06/3.32  Loading plugin: done.
% 3.06/3.32  Compiling...
% 3.06/3.32  Loading plugin: done.
% 3.06/3.32  Compiling...
% 3.06/3.32  Loading plugin: done.
% 3.06/3.32  Compiling...
% 3.06/3.32  Loading plugin: done.
% 3.06/3.32  Compiling...
% 3.06/3.32  Loading plugin: done.
% 3.06/3.32  Compiling...
% 3.06/3.32  Loading plugin: done.
% 3.06/3.32  Compiling...
% 3.06/3.32  Loading plugin: done.
% 3.06/3.32  Compiling...
% 3.06/3.32  Loading plugin: done.
% 3.06/3.32  Compiling...
% 3.06/3.32  Loading plugin: done.
% 3.06/3.32  Compiling...
% 3.06/3.32  Loading plugin: done.
% 3.06/3.32  Compiling...
% 3.06/3.32  Loading plugin: done.
% 3.06/3.32  Compiling...
% 3.06/3.32  Loading plugin: done.
% 3.06/3.32  Compiling...
% 3.06/3.32  Loading plugin: done.
% 3.06/3.32  Compiling...
% 3.06/3.32  Loading plugin: done.
% 3.06/3.32  Compiling...
% 3.06/3.32  Loading plugin: done.
% 3.06/3.32  Compiling...
% 3.06/3.32  Loading plugin: done.
% 3.06/3.32  Compiling...
% 3.06/3.32  Loading plugin: done.
% 3.06/3.32  % % ------ Current options:
% 3.06/3.32  
% 3.06/3.32  % ------ Input Options
% 3.06/3.32  
% 3.06/3.32  % --out_options                         all
% 3.06/3.32  % --tptp_safe_out                       true
% 3.06/3.32  % --problem_path                        ""
% 3.06/3.32  % --include_path                        ""
% 3.06/3.32  % --clausifier                          .//eprover
% 3.06/3.32  % --clausifier_options                  --tstp-format  
% 3.06/3.32  % --stdin                               false
% 3.06/3.32  % --dbg_backtrace                       false
% 3.06/3.32  % --dbg_dump_prop_clauses               false
% 3.06/3.32  % --dbg_dump_prop_clauses_file          -
% 3.06/3.32  % --dbg_out_stat                        false
% 3.06/3.32  
% 3.06/3.32  % ------ General Options
% 3.06/3.32  
% 3.06/3.32  % --fof                                 false
% 3.06/3.32  % --time_out_real                       150.
% 3.06/3.32  % --time_out_prep_mult                  0.2
% 3.06/3.32  % --time_out_virtual                    -1.
% 3.06/3.32  % --schedule                            none
% 3.06/3.32  % --ground_splitting                    input
% 3.06/3.32  % --splitting_nvd                       16
% 3.06/3.32  % --non_eq_to_eq                        false
% 3.06/3.32  % --prep_gs_sim                         true
% 3.06/3.32  % --prep_unflatten                      false
% 3.06/3.32  % --prep_res_sim                        true
% 3.06/3.32  % --prep_upred                          true
% 3.06/3.32  % --res_sim_input                       true
% 3.06/3.32  % --clause_weak_htbl                    true
% 3.06/3.32  % --gc_record_bc_elim                   false
% 3.06/3.32  % --symbol_type_check                   false
% 3.06/3.32  % --clausify_out                        false
% 3.06/3.32  % --large_theory_mode                   false
% 3.06/3.32  % --prep_sem_filter                     none
% 3.06/3.32  % --prep_sem_filter_out                 false
% 3.06/3.32  % --preprocessed_out                    false
% 3.06/3.32  % --sub_typing                          false
% 3.06/3.32  % --brand_transform                     false
% 3.06/3.32  % --pure_diseq_elim                     true
% 3.06/3.32  % --min_unsat_core                      false
% 3.06/3.32  % --pred_elim                           true
% 3.06/3.32  % --add_important_lit                   false
% 3.06/3.32  % --soft_assumptions                    false
% 3.06/3.32  % --reset_solvers                       false
% 3.06/3.32  % --bc_imp_inh                          []
% 3.06/3.32  % --conj_cone_tolerance                 1.5
% 3.06/3.32  % --prolific_symb_bound                 500
% 3.06/3.32  % --lt_threshold                        2000
% 3.06/3.32  
% 3.06/3.32  % ------ SAT Options
% 3.06/3.32  
% 3.06/3.32  % --sat_mode                            false
% 3.06/3.32  % --sat_fm_restart_options              ""
% 3.06/3.32  % --sat_gr_def                          false
% 3.06/3.32  % --sat_epr_types                       true
% 3.06/3.32  % --sat_non_cyclic_types                false
% 3.06/3.32  % --sat_finite_models                   false
% 3.06/3.32  % --sat_fm_lemmas                       false
% 3.06/3.32  % --sat_fm_prep                         false
% 3.06/3.32  % --sat_fm_uc_incr                      true
% 3.06/3.32  % --sat_out_model                       small
% 3.06/3.32  % --sat_out_clauses                     false
% 3.06/3.32  
% 3.06/3.32  % ------ QBF Options
% 3.06/3.32  
% 3.06/3.32  % --qbf_mode                            false
% 3.06/3.32  % --qbf_elim_univ                       true
% 3.06/3.32  % --qbf_sk_in                           true
% 3.06/3.32  % --qbf_pred_elim                       true
% 3.06/3.32  % --qbf_split                           32
% 3.06/3.32  
% 3.06/3.32  % ------ BMC1 Options
% 3.06/3.32  
% 3.06/3.32  % --bmc1_incremental                    false
% 3.06/3.32  % --bmc1_axioms                         reachable_all
% 3.06/3.32  % --bmc1_min_bound                      0
% 3.06/3.32  % --bmc1_max_bound                      -1
% 3.06/3.32  % --bmc1_max_bound_default              -1
% 3.06/3.32  % --bmc1_symbol_reachability            true
% 3.06/3.32  % --bmc1_property_lemmas                false
% 3.06/3.32  % --bmc1_k_induction                    false
% 3.06/3.32  % --bmc1_non_equiv_states               false
% 3.06/3.32  % --bmc1_deadlock                       false
% 3.06/3.32  % --bmc1_ucm                            false
% 3.06/3.32  % --bmc1_add_unsat_core                 none
% 3.06/3.32  % --bmc1_unsat_core_children            false
% 3.06/3.32  % --bmc1_unsat_core_extrapolate_axioms  false
% 3.06/3.32  % --bmc1_out_stat                       full
% 3.06/3.32  % --bmc1_ground_init                    false
% 3.06/3.32  % --bmc1_pre_inst_next_state            false
% 3.06/3.32  % --bmc1_pre_inst_state                 false
% 3.06/3.32  % --bmc1_pre_inst_reach_state           false
% 3.06/3.32  % --bmc1_out_unsat_core                 false
% 3.06/3.32  % --bmc1_aig_witness_out                false
% 3.06/3.32  % --bmc1_verbose                        false
% 3.06/3.32  % --bmc1_dump_clauses_tptp              false
% 3.06/3.32  % --bmc1_dump_unsat_core_tptp           false
% 3.06/3.32  % --bmc1_dump_file                      -
% 3.06/3.32  % --bmc1_ucm_expand_uc_limit            128
% 3.06/3.32  % --bmc1_ucm_n_expand_iterations        6
% 3.06/3.32  % --bmc1_ucm_extend_mode                1
% 3.06/3.32  % --bmc1_ucm_init_mode                  2
% 3.06/3.32  % --bmc1_ucm_cone_mode                  none
% 3.06/3.32  % --bmc1_ucm_reduced_relation_type      0
% 3.06/3.32  % --bmc1_ucm_relax_model                4
% 3.06/3.32  % --bmc1_ucm_full_tr_after_sat          true
% 3.06/3.32  % --bmc1_ucm_expand_neg_assumptions     false
% 3.06/3.32  % --bmc1_ucm_layered_model              none
% 3.06/3.32  % --bmc1_ucm_max_lemma_size             10
% 3.06/3.32  
% 3.06/3.32  % ------ AIG Options
% 3.06/3.32  
% 3.06/3.32  % --aig_mode                            false
% 3.06/3.33  
% 3.06/3.33  % ------ Instantiation Options
% 3.06/3.33  
% 3.06/3.33  % --instantiation_flag                  true
% 3.06/3.33  % --inst_lit_sel                        [+prop;+sign;+ground;-num_var;-num_symb]
% 3.06/3.33  % --inst_solver_per_active              750
% 3.06/3.33  % --inst_solver_calls_frac              0.5
% 3.06/3.33  % --inst_passive_queue_type             priority_queues
% 3.06/3.33  % --inst_passive_queues                 [[-conj_dist;+conj_symb;-num_var];[+age;-num_symb]]
% 3.06/3.33  % --inst_passive_queues_freq            [25;2]
% 3.06/3.33  % --inst_dismatching                    true
% 3.06/3.33  % --inst_eager_unprocessed_to_passive   true
% 3.06/3.33  % --inst_prop_sim_given                 true
% 3.06/3.33  % --inst_prop_sim_new                   false
% 3.06/3.33  % --inst_orphan_elimination             true
% 3.06/3.33  % --inst_learning_loop_flag             true
% 3.06/3.33  % --inst_learning_start                 3000
% 3.06/3.33  % --inst_learning_factor                2
% 3.06/3.33  % --inst_start_prop_sim_after_learn     3
% 3.06/3.33  % --inst_sel_renew                      solver
% 3.06/3.33  % --inst_lit_activity_flag              true
% 3.06/3.33  % --inst_out_proof                      true
% 3.06/3.33  
% 3.06/3.33  % ------ Resolution Options
% 3.06/3.33  
% 3.06/3.33  % --resolution_flag                     true
% 3.06/3.33  % --res_lit_sel                         kbo_max
% 3.06/3.33  % --res_to_prop_solver                  none
% 3.06/3.33  % --res_prop_simpl_new                  false
% 3.06/3.33  % --res_prop_simpl_given                false
% 3.06/3.33  % --res_passive_queue_type              priority_queues
% 3.06/3.33  % --res_passive_queues                  [[-conj_dist;+conj_symb;-num_symb];[+age;-num_symb]]
% 3.06/3.33  % --res_passive_queues_freq             [15;5]
% 3.06/3.33  % --res_forward_subs                    full
% 3.06/3.33  % --res_backward_subs                   full
% 3.06/3.33  % --res_forward_subs_resolution         true
% 3.06/3.33  % --res_backward_subs_resolution        true
% 3.06/3.33  % --res_orphan_elimination              false
% 3.06/3.33  % --res_time_limit                      1000.
% 3.06/3.33  % --res_out_proof                       true
% 3.06/3.33  % --proof_out_file                      /export/starexec/sandbox/tmp/iprover_proof_f91999.s
% 3.06/3.33  % --modulo                              true
% 3.06/3.33  
% 3.06/3.33  % ------ Combination Options
% 3.06/3.33  
% 3.06/3.33  % --comb_res_mult                       1000
% 3.06/3.33  % --comb_inst_mult                      300
% 3.06/3.33  % ------ 
% 3.06/3.33  
% 3.06/3.33  
% 3.06/3.33  
% 3.06/3.33  % ------ Proving...
% 3.06/3.33  % 
% 3.06/3.33  
% 3.06/3.33  
% 3.06/3.33  %  Resolution empty clause
% 3.06/3.33  
% 3.06/3.33  % ------                             Statistics
% 3.06/3.33  
% 3.06/3.33  % ------ General
% 3.06/3.33  
% 3.06/3.33  % num_of_input_clauses:                 1864
% 3.06/3.33  % num_of_input_neg_conjectures:         3
% 3.06/3.33  % num_of_splits:                        0
% 3.06/3.33  % num_of_split_atoms:                   0
% 3.06/3.33  % num_of_sem_filtered_clauses:          0
% 3.06/3.33  % num_of_subtypes:                      0
% 3.06/3.33  % monotx_restored_types:                0
% 3.06/3.33  % sat_num_of_epr_types:                 0
% 3.06/3.33  % sat_num_of_non_cyclic_types:          0
% 3.06/3.33  % sat_guarded_non_collapsed_types:      0
% 3.06/3.33  % is_epr:                               0
% 3.06/3.33  % is_horn:                              0
% 3.06/3.33  % has_eq:                               1
% 3.06/3.33  % num_pure_diseq_elim:                  0
% 3.06/3.33  % simp_replaced_by:                     0
% 3.06/3.33  % res_preprocessed:                     6
% 3.06/3.33  % prep_upred:                           0
% 3.06/3.33  % prep_unflattend:                      0
% 3.06/3.33  % pred_elim_cands:                      0
% 3.06/3.33  % pred_elim:                            0
% 3.06/3.33  % pred_elim_cl:                         0
% 3.06/3.33  % pred_elim_cycles:                     0
% 3.06/3.33  % forced_gc_time:                       0
% 3.06/3.33  % gc_basic_clause_elim:                 0
% 3.06/3.33  % parsing_time:                         0.098
% 3.06/3.33  % sem_filter_time:                      0.
% 3.06/3.33  % pred_elim_time:                       0.
% 3.06/3.33  % out_proof_time:                       0.
% 3.06/3.33  % monotx_time:                          0.
% 3.06/3.33  % subtype_inf_time:                     0.
% 3.06/3.33  % unif_index_cands_time:                0.
% 3.06/3.33  % unif_index_add_time:                  0.001
% 3.06/3.33  % total_time:                           2.785
% 3.06/3.33  % num_of_symbols:                       90
% 3.06/3.33  % num_of_terms:                         3840
% 3.06/3.33  
% 3.06/3.33  % ------ Propositional Solver
% 3.06/3.33  
% 3.06/3.33  % prop_solver_calls:                    1
% 3.06/3.33  % prop_fast_solver_calls:               9
% 3.06/3.33  % prop_num_of_clauses:                  1539
% 3.06/3.33  % prop_preprocess_simplified:           5861
% 3.06/3.33  % prop_fo_subsumed:                     0
% 3.06/3.33  % prop_solver_time:                     0.
% 3.06/3.33  % prop_fast_solver_time:                0.
% 3.06/3.33  % prop_unsat_core_time:                 0.
% 3.06/3.33  
% 3.06/3.33  % ------ QBF 
% 3.06/3.33  
% 3.06/3.33  % qbf_q_res:                            0
% 3.06/3.33  % qbf_num_tautologies:                  0
% 3.06/3.33  % qbf_prep_cycles:                      0
% 3.06/3.33  
% 3.06/3.33  % ------ BMC1
% 3.06/3.33  
% 3.06/3.33  % bmc1_current_bound:                   -1
% 3.06/3.33  % bmc1_last_solved_bound:               -1
% 3.06/3.33  % bmc1_unsat_core_size:                 -1
% 3.06/3.33  % bmc1_unsat_core_parents_size:         -1
% 3.06/3.33  % bmc1_merge_next_fun:                  0
% 3.06/3.33  % bmc1_unsat_core_clauses_time:         0.
% 3.06/3.33  
% 3.06/3.33  % ------ Instantiation
% 3.06/3.33  
% 3.06/3.33  % inst_num_of_clauses:                  1623
% 3.06/3.33  % inst_num_in_passive:                  0
% 3.06/3.33  % inst_num_in_active:                   0
% 3.06/3.33  % inst_num_in_unprocessed:              1864
% 3.06/3.33  % inst_num_of_loops:                    0
% 3.06/3.33  % inst_num_of_learning_restarts:        0
% 3.06/3.33  % inst_num_moves_active_passive:        0
% 3.06/3.33  % inst_lit_activity:                    0
% 3.06/3.33  % inst_lit_activity_moves:              0
% 3.06/3.33  % inst_num_tautologies:                 0
% 3.06/3.33  % inst_num_prop_implied:                0
% 3.06/3.33  % inst_num_existing_simplified:         0
% 3.06/3.33  % inst_num_eq_res_simplified:           0
% 3.06/3.33  % inst_num_child_elim:                  0
% 3.06/3.33  % inst_num_of_dismatching_blockings:    0
% 3.06/3.33  % inst_num_of_non_proper_insts:         0
% 3.06/3.33  % inst_num_of_duplicates:               0
% 3.06/3.33  % inst_inst_num_from_inst_to_res:       0
% 3.06/3.33  % inst_dismatching_checking_time:       0.
% 3.06/3.33  
% 3.06/3.33  % ------ Resolution
% 3.06/3.33  
% 3.06/3.33  % res_num_of_clauses:                   1835
% 3.06/3.33  % res_num_in_passive:                   0
% 3.06/3.33  % res_num_in_active:                    679
% 3.06/3.33  % res_num_of_loops:                     4
% 3.06/3.33  % res_forward_subset_subsumed:          1116
% 3.06/3.33  % res_backward_subset_subsumed:         5
% 3.06/3.33  % res_forward_subsumed:                 0
% 3.06/3.33  % res_backward_subsumed:                0
% 3.06/3.33  % res_forward_subsumption_resolution:   1
% 3.06/3.33  % res_backward_subsumption_resolution:  0
% 3.06/3.33  % res_clause_to_clause_subsumption:     1
% 3.06/3.33  % res_orphan_elimination:               0
% 3.06/3.33  % res_tautology_del:                    0
% 3.06/3.33  % res_num_eq_res_simplified:            0
% 3.06/3.33  % res_num_sel_changes:                  0
% 3.06/3.33  % res_moves_from_active_to_pass:        0
% 3.06/3.33  
% 3.06/3.33  % Status Unsatisfiable
% 3.06/3.33  % SZS status Unsatisfiable
% 3.06/3.33  % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------