TSTP Solution File: SWV689-1 by iProverMo---2.5-0.1

%------------------------------------------------------------------------------
% File     : iProverMo---2.5-0.1
% Problem  : SWV689-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : iprover_modulo %s %d

% Computer : n010.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 : Wed Jul 20 19:21:20 EDT 2022

% Result   : Unsatisfiable 155.01s 155.24s
% Output   : CNFRefutation 155.08s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   28
%            Number of leaves      :  809
% Syntax   : Number of formulae    : 6096 ( 802 unt;   0 def)
%            Number of atoms       : 16602 (3222 equ)
%            Maximal formula atoms :    6 (   2 avg)
%            Number of connectives : 20307 (9801   ~;10506   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   12 (   5 avg)
%            Maximal term depth    :    6 (   1 avg)
%            Number of predicates  :   58 (  56 usr;   1 prp; 0-3 aty)
%            Number of functors    :   13 (  13 usr;   4 con; 0-3 aty)
%            Number of variables   : 17544 ( 574 sgn6675   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
% Axioms transformation by autotheo
% Orienting (remaining) axiom formulas using strategy ClausalAll
% CNF of (remaining) axioms:
% Start CNF derivation
fof(c_0_0,axiom,
    ! [X6,X7,X1,X2,X3] :
      ( ~ class_RealVector_Oreal__normed__algebra(X3)
      | c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X7,X6,X3),c_HOL_Otimes__class_Otimes(X2,X1,X3),X3) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X7,X2,X3),c_HOL_Ominus__class_Ominus(X6,X1,X3),X3),c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X7,X2,X3),X1,X3),X3),c_HOL_Otimes__class_Otimes(X2,c_HOL_Ominus__class_Ominus(X6,X1,X3),X3),X3) ),
    file('<stdin>',cls_mult_Oprod__diff__prod_0) ).

fof(c_0_1,axiom,
    ! [X20,X15,X1,X2,X3] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X3)
      | c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X2,X1,X3),c_HOL_Oplus__class_Oplus(X15,X20,X3),X3),X3),c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X2,X15,X3),X3),c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X1,X20,X3),X3),X3),X3) ),
    file('<stdin>',cls_abs__diff__triangle__ineq_0) ).

fof(c_0_2,axiom,
    ! [X17,X4,X5,X9,X10] :
      ( c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X10,X17,tc_nat),X5,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X9,X17,tc_nat),X4,tc_nat),tc_nat)
      | ~ c_lessequals(X5,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X9,X10,tc_nat),X17,tc_nat),X4,tc_nat),tc_nat)
      | ~ c_lessequals(X10,X9,tc_nat) ),
    file('<stdin>',cls_nat__le__add__iff2_1) ).

fof(c_0_3,axiom,
    ! [X17,X4,X5,X9,X10] :
      ( c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X10,X17,tc_nat),X5,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X9,X17,tc_nat),X4,tc_nat),tc_nat)
      | ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X10,X9,tc_nat),X17,tc_nat),X5,tc_nat),X4,tc_nat)
      | ~ c_lessequals(X9,X10,tc_nat) ),
    file('<stdin>',cls_nat__le__add__iff1_1) ).

fof(c_0_4,axiom,
    ! [X17,X4,X5,X9,X10] :
      ( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X10,X17,tc_nat),X5,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X9,X17,tc_nat),X4,tc_nat),tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X10,X9,tc_nat),X17,tc_nat),X5,tc_nat),X4,tc_nat)
      | ~ c_lessequals(X9,X10,tc_nat) ),
    file('<stdin>',cls_nat__less__add__iff1_1) ).

fof(c_0_5,axiom,
    ! [X17,X4,X5,X9,X10] :
      ( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X10,X17,tc_nat),X5,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X9,X17,tc_nat),X4,tc_nat),tc_nat)
      | ~ c_HOL_Oord__class_Oless(X5,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X9,X10,tc_nat),X17,tc_nat),X4,tc_nat),tc_nat)
      | ~ c_lessequals(X10,X9,tc_nat) ),
    file('<stdin>',cls_nat__less__add__iff2_1) ).

fof(c_0_6,axiom,
    ! [X19,X20,X15,X1,X2,X3] :
      ( ~ class_Ring__and__Field_Opordered__ring(X3)
      | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X19,X3),X15,X3),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X19,X3),X20,X3),X3)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X1,X3),X19,X3),X15,X3),X20,X3) ),
    file('<stdin>',cls_less__add__iff1_1) ).

fof(c_0_7,axiom,
    ! [X19,X20,X15,X1,X2,X3] :
      ( ~ class_Ring__and__Field_Opordered__ring(X3)
      | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X19,X3),X15,X3),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X19,X3),X20,X3),X3)
      | ~ c_HOL_Oord__class_Oless(X15,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,X2,X3),X19,X3),X20,X3),X3) ),
    file('<stdin>',cls_less__add__iff2_1) ).

fof(c_0_8,axiom,
    ! [X19,X20,X15,X1,X2,X3] :
      ( ~ class_Ring__and__Field_Opordered__ring(X3)
      | c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X19,X3),X15,X3),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X19,X3),X20,X3),X3)
      | ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X1,X3),X19,X3),X15,X3),X20,X3) ),
    file('<stdin>',cls_le__add__iff1_1) ).

fof(c_0_9,axiom,
    ! [X19,X20,X15,X1,X2,X3] :
      ( ~ class_Ring__and__Field_Opordered__ring(X3)
      | c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X19,X3),X15,X3),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X19,X3),X20,X3),X3)
      | ~ c_lessequals(X15,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,X2,X3),X19,X3),X20,X3),X3) ),
    file('<stdin>',cls_le__add__iff2_1) ).

fof(c_0_10,axiom,
    ! [X17,X4,X5,X9,X10] :
      ( c_lessequals(X5,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X9,X10,tc_nat),X17,tc_nat),X4,tc_nat),tc_nat)
      | ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X10,X17,tc_nat),X5,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X9,X17,tc_nat),X4,tc_nat),tc_nat)
      | ~ c_lessequals(X10,X9,tc_nat) ),
    file('<stdin>',cls_nat__le__add__iff2_0) ).

fof(c_0_11,axiom,
    ! [X17,X4,X5,X9,X10] :
      ( c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X10,X9,tc_nat),X17,tc_nat),X5,tc_nat),X4,tc_nat)
      | ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X10,X17,tc_nat),X5,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X9,X17,tc_nat),X4,tc_nat),tc_nat)
      | ~ c_lessequals(X9,X10,tc_nat) ),
    file('<stdin>',cls_nat__le__add__iff1_0) ).

fof(c_0_12,axiom,
    ! [X17,X4,X5,X9,X10] :
      ( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X10,X9,tc_nat),X17,tc_nat),X5,tc_nat),X4,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X10,X17,tc_nat),X5,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X9,X17,tc_nat),X4,tc_nat),tc_nat)
      | ~ c_lessequals(X9,X10,tc_nat) ),
    file('<stdin>',cls_nat__less__add__iff1_0) ).

fof(c_0_13,axiom,
    ! [X17,X4,X5,X9,X10] :
      ( c_HOL_Oord__class_Oless(X5,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X9,X10,tc_nat),X17,tc_nat),X4,tc_nat),tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X10,X17,tc_nat),X5,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X9,X17,tc_nat),X4,tc_nat),tc_nat)
      | ~ c_lessequals(X10,X9,tc_nat) ),
    file('<stdin>',cls_nat__less__add__iff2_0) ).

fof(c_0_14,axiom,
    ! [X19,X20,X15,X1,X2,X3] :
      ( ~ 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(X2,X1,X3),X19,X3),X15,X3),X20,X3)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X19,X3),X15,X3),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X19,X3),X20,X3),X3) ),
    file('<stdin>',cls_less__add__iff1_0) ).

fof(c_0_15,axiom,
    ! [X19,X20,X15,X1,X2,X3] :
      ( ~ class_Ring__and__Field_Opordered__ring(X3)
      | c_HOL_Oord__class_Oless(X15,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,X2,X3),X19,X3),X20,X3),X3)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X19,X3),X15,X3),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X19,X3),X20,X3),X3) ),
    file('<stdin>',cls_less__add__iff2_0) ).

fof(c_0_16,axiom,
    ! [X19,X20,X15,X1,X2,X3] :
      ( ~ class_Ring__and__Field_Opordered__ring(X3)
      | c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X1,X3),X19,X3),X15,X3),X20,X3)
      | ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X19,X3),X15,X3),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X19,X3),X20,X3),X3) ),
    file('<stdin>',cls_le__add__iff1_0) ).

fof(c_0_17,axiom,
    ! [X19,X20,X15,X1,X2,X3] :
      ( ~ class_Ring__and__Field_Opordered__ring(X3)
      | c_lessequals(X15,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,X2,X3),X19,X3),X20,X3),X3)
      | ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X19,X3),X15,X3),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X19,X3),X20,X3),X3) ),
    file('<stdin>',cls_le__add__iff2_0) ).

fof(c_0_18,axiom,
    ! [X17,X4,X5,X9,X10] :
      ( c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X10,X17,tc_nat),X5,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X9,X17,tc_nat),X4,tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(X5,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X9,X10,tc_nat),X17,tc_nat),X4,tc_nat),tc_nat)
      | ~ c_lessequals(X10,X9,tc_nat) ),
    file('<stdin>',cls_nat__diff__add__eq2_0) ).

fof(c_0_19,axiom,
    ! [X17,X4,X5,X9,X10] :
      ( c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X10,X17,tc_nat),X5,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X9,X17,tc_nat),X4,tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X10,X9,tc_nat),X17,tc_nat),X5,tc_nat),X4,tc_nat)
      | ~ c_lessequals(X9,X10,tc_nat) ),
    file('<stdin>',cls_nat__diff__add__eq1_0) ).

fof(c_0_20,axiom,
    ! [X7,X24,X8,X20,X25,X3] :
      ( ~ class_Ring__and__Field_Odvd(X3)
      | ~ class_Ring__and__Field_Ocomm__ring(X3)
      | c_Ring__and__Field_Odvd__class_Odvd(X20,c_HOL_Oplus__class_Oplus(X7,X24,X3),X3)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X20,c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X7,c_HOL_Otimes__class_Otimes(X8,X25,X3),X3),X24,X3),X3)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X20,X25,X3) ),
    file('<stdin>',cls_inf__period_I4_J_1) ).

fof(c_0_21,axiom,
    ! [X7,X24,X8,X20,X25,X3] :
      ( ~ class_Ring__and__Field_Odvd(X3)
      | ~ class_Ring__and__Field_Ocomm__ring(X3)
      | c_Ring__and__Field_Odvd__class_Odvd(X20,c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X7,c_HOL_Otimes__class_Otimes(X8,X25,X3),X3),X24,X3),X3)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X20,c_HOL_Oplus__class_Oplus(X7,X24,X3),X3)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X20,X25,X3) ),
    file('<stdin>',cls_inf__period_I4_J_0) ).

fof(c_0_22,axiom,
    ! [X17,X4,X9,X10] :
      ( ~ c_lessequals(X10,X9,tc_nat)
      | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X10,X17,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X9,X10,tc_nat),X17,tc_nat),X4,tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X9,X17,tc_nat),X4,tc_nat) ),
    file('<stdin>',cls_nat__eq__add__iff2_1) ).

fof(c_0_23,axiom,
    ! [X17,X5,X9,X10] :
      ( ~ c_lessequals(X9,X10,tc_nat)
      | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X10,X17,tc_nat),X5,tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X9,X17,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X10,X9,tc_nat),X17,tc_nat),X5,tc_nat),tc_nat) ),
    file('<stdin>',cls_nat__eq__add__iff1_1) ).

fof(c_0_24,axiom,
    ! [X3] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X3),c_HOL_Ozero__class_Ozero(X3),X3),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X3),c_HOL_Ozero__class_Ozero(X3),X3),X3),X3) ),
    file('<stdin>',cls_sum__squares__gt__zero__iff_0) ).

fof(c_0_25,axiom,
    ! [X19,X15,X1,X2,X3] :
      ( ~ class_Ring__and__Field_Oring(X3)
      | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X19,X3),X15,X3) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X19,X3),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X1,X3),X19,X3),X15,X3),X3) ),
    file('<stdin>',cls_eq__add__iff1_1) ).

fof(c_0_26,axiom,
    ! [X19,X20,X1,X2,X3] :
      ( ~ class_Ring__and__Field_Oring(X3)
      | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X19,X3),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,X2,X3),X19,X3),X20,X3),X3) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X19,X3),X20,X3) ),
    file('<stdin>',cls_eq__add__iff2_1) ).

fof(c_0_27,axiom,
    ! [X22,X23,X15,X1] :
      ( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,c_Divides_Odiv__class_Omod(X23,X15,tc_nat),tc_nat),X22,tc_nat),c_HOL_Otimes__class_Otimes(X1,X15,tc_nat),tc_nat)
      | ~ c_HOL_Oord__class_Oless(X22,X1,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X15,tc_nat) ),
    file('<stdin>',cls_mod__lemma_0) ).

fof(c_0_28,axiom,
    ! [X6,X7,X3] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
      | X7 = c_HOL_Ozero__class_Ozero(X3)
      | ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X7,X7,X3),c_HOL_Otimes__class_Otimes(X6,X6,X3),X3),c_HOL_Ozero__class_Ozero(X3),X3) ),
    file('<stdin>',cls_sum__squares__le__zero__iff_0) ).

fof(c_0_29,axiom,
    ! [X6,X7,X3] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
      | X6 = c_HOL_Ozero__class_Ozero(X3)
      | ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X7,X7,X3),c_HOL_Otimes__class_Otimes(X6,X6,X3),X3),c_HOL_Ozero__class_Ozero(X3),X3) ),
    file('<stdin>',cls_sum__squares__le__zero__iff_1) ).

fof(c_0_30,axiom,
    ! [X6,X7,X3] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X7,X7,X3),c_HOL_Otimes__class_Otimes(X6,X6,X3),X3),c_HOL_Ozero__class_Ozero(X3),X3) ),
    file('<stdin>',cls_not__sum__squares__lt__zero_0) ).

fof(c_0_31,axiom,
    ! [X17,X4,X5,X9,X10] :
      ( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X10,X17,tc_nat),X5,tc_nat) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X9,X17,tc_nat),X4,tc_nat)
      | ~ c_lessequals(X9,X10,tc_nat)
      | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X10,X9,tc_nat),X17,tc_nat),X5,tc_nat) = X4 ),
    file('<stdin>',cls_nat__eq__add__iff1_0) ).

fof(c_0_32,axiom,
    ! [X17,X4,X5,X9,X10] :
      ( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X10,X17,tc_nat),X5,tc_nat) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X9,X17,tc_nat),X4,tc_nat)
      | ~ c_lessequals(X10,X9,tc_nat)
      | X5 = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X9,X10,tc_nat),X17,tc_nat),X4,tc_nat) ),
    file('<stdin>',cls_nat__eq__add__iff2_0) ).

fof(c_0_33,axiom,
    ! [X19,X20,X15,X1,X2,X3] :
      ( ~ class_Ring__and__Field_Oring(X3)
      | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X19,X3),X15,X3) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X19,X3),X20,X3)
      | X15 = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,X2,X3),X19,X3),X20,X3) ),
    file('<stdin>',cls_eq__add__iff2_0) ).

fof(c_0_34,axiom,
    ! [X19,X20,X15,X1,X2,X3] :
      ( ~ class_Ring__and__Field_Oring(X3)
      | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X19,X3),X15,X3) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X19,X3),X20,X3)
      | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X1,X3),X19,X3),X15,X3) = X20 ),
    file('<stdin>',cls_eq__add__iff1_0) ).

fof(c_0_35,axiom,
    ! [X19,X15,X1,X2,X3] :
      ( ~ class_Ring__and__Field_Osemiring(X3)
      | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X19,X3),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X19,X3),X15,X3),X3) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X2,X1,X3),X19,X3),X15,X3) ),
    file('<stdin>',cls_combine__common__factor_0) ).

fof(c_0_36,axiom,
    ! [X16,X6,X7,X31,X3] :
      ( ~ class_Ring__and__Field_Oidom(X3)
      | ~ class_Int_Onumber__ring(X3)
      | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X31,X6,X3),c_HOL_Otimes__class_Otimes(X7,X16,X3),X3) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X31,X16,X3),c_HOL_Otimes__class_Otimes(X7,X6,X3),X3)
      | X6 = X16
      | X31 = X7 ),
    file('<stdin>',cls_class__ringb_Oadd__mul__solve_0) ).

fof(c_0_37,axiom,
    ! [X20,X15,X1,X2,X3] :
      ( ~ class_Ring__and__Field_Oidom(X3)
      | ~ class_Int_Onumber__ring(X3)
      | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X15,X3),c_HOL_Otimes__class_Otimes(X1,X20,X3),X3) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X20,X3),c_HOL_Otimes__class_Otimes(X1,X15,X3),X3)
      | X15 = X20
      | X2 = X1 ),
    file('<stdin>',cls_class__ringb_Onoteq__reduce_0) ).

fof(c_0_38,axiom,
    ! [X17,X8,X9,X10] : c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X10,X17,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X9,X17,tc_nat),X8,tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X10,X9,tc_nat),X17,tc_nat),X8,tc_nat),
    file('<stdin>',cls_left__add__mult__distrib_0) ).

fof(c_0_39,axiom,
    ! [X16,X6,X7,X31] :
      ( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X31,X6,tc_nat),c_HOL_Otimes__class_Otimes(X7,X16,tc_nat),tc_nat) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X31,X16,tc_nat),c_HOL_Otimes__class_Otimes(X7,X6,tc_nat),tc_nat)
      | X6 = X16
      | X31 = X7 ),
    file('<stdin>',cls_natgb_Oadd__mul__solve_0) ).

fof(c_0_40,axiom,
    ! [X20,X15,X1,X2] :
      ( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X15,tc_nat),c_HOL_Otimes__class_Otimes(X1,X20,tc_nat),tc_nat) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X20,tc_nat),c_HOL_Otimes__class_Otimes(X1,X15,tc_nat),tc_nat)
      | X15 = X20
      | X2 = X1 ),
    file('<stdin>',cls_natgb_Onoteq__reduce_0) ).

fof(c_0_41,axiom,
    ! [X7,X22,X2,X3] :
      ( ~ class_Ring__and__Field_Oordered__idom(X3)
      | c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X7,X2,X3),X3),X22,X3)
      | ~ c_HOL_Oord__class_Oless(X7,c_HOL_Oplus__class_Oplus(X2,X22,X3),X3)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X2,X22,X3),X7,X3) ),
    file('<stdin>',cls_abs__diff__less__iff_2) ).

fof(c_0_42,axiom,
    ! [X15,X1,X2,X3] :
      ( ~ class_Divides_Oring__div(X3)
      | c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X2,X1,X3),X15,X3) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(c_Divides_Odiv__class_Omod(X2,X15,X3),c_Divides_Odiv__class_Omod(X1,X15,X3),X3),X15,X3) ),
    file('<stdin>',cls_mod__diff__eq_0) ).

fof(c_0_43,axiom,
    ! [X15,X1,X2,X3] :
      ( ~ class_Divides_Osemiring__div(X3)
      | c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X2,X1,X3),X15,X3) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(X2,X15,X3),c_Divides_Odiv__class_Omod(X1,X15,X3),X3),X15,X3) ),
    file('<stdin>',cls_mod__mult__eq_0) ).

fof(c_0_44,axiom,
    ! [X15,X1,X2,X3] :
      ( ~ class_Divides_Osemiring__div(X3)
      | c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X2,X1,X3),X15,X3) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(X2,X15,X3),c_Divides_Odiv__class_Omod(X1,X15,X3),X3),X15,X3) ),
    file('<stdin>',cls_mod__add__eq_0) ).

fof(c_0_45,axiom,
    ! [X1,X2,X3] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X3)
      | c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(c_HOL_Oabs__class_Oabs(X2,X3),c_HOL_Oabs__class_Oabs(X1,X3),X3),X3),c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X2,X1,X3),X3),X3) ),
    file('<stdin>',cls_abs__triangle__ineq3_0) ).

fof(c_0_46,axiom,
    ! [X4,X5,X8] : c_Divides_Odiv__class_Omod(c_Suc(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X8,X4,tc_nat),X5,tc_nat)),X4,tc_nat) = c_Divides_Odiv__class_Omod(c_Suc(X5),X4,tc_nat),
    file('<stdin>',cls_mod__mult__self4_0) ).

fof(c_0_47,axiom,
    ! [X3] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
      | c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X3),c_HOL_Ozero__class_Ozero(X3),X3),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X3),c_HOL_Ozero__class_Ozero(X3),X3),X3),c_HOL_Ozero__class_Ozero(X3),X3) ),
    file('<stdin>',cls_sum__squares__le__zero__iff_2) ).

fof(c_0_48,axiom,
    ! [X15,X26,X1,X28,X2,X3] :
      ( ~ class_Divides_Oring__div(X3)
      | c_Divides_Odiv__class_Omod(X1,X15,X3) != c_Divides_Odiv__class_Omod(X26,X15,X3)
      | c_Divides_Odiv__class_Omod(X2,X15,X3) != c_Divides_Odiv__class_Omod(X28,X15,X3)
      | c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X2,X1,X3),X15,X3) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X28,X26,X3),X15,X3) ),
    file('<stdin>',cls_mod__diff__cong_0) ).

fof(c_0_49,axiom,
    ! [X15,X26,X1,X28,X2,X3] :
      ( ~ class_Divides_Osemiring__div(X3)
      | c_Divides_Odiv__class_Omod(X1,X15,X3) != c_Divides_Odiv__class_Omod(X26,X15,X3)
      | c_Divides_Odiv__class_Omod(X2,X15,X3) != c_Divides_Odiv__class_Omod(X28,X15,X3)
      | c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X2,X1,X3),X15,X3) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X28,X26,X3),X15,X3) ),
    file('<stdin>',cls_mod__mult__cong_0) ).

fof(c_0_50,axiom,
    ! [X15,X26,X1,X28,X2,X3] :
      ( ~ class_Divides_Osemiring__div(X3)
      | c_Divides_Odiv__class_Omod(X1,X15,X3) != c_Divides_Odiv__class_Omod(X26,X15,X3)
      | c_Divides_Odiv__class_Omod(X2,X15,X3) != c_Divides_Odiv__class_Omod(X28,X15,X3)
      | c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X2,X1,X3),X15,X3) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X28,X26,X3),X15,X3) ),
    file('<stdin>',cls_mod__add__cong_0) ).

fof(c_0_51,axiom,
    ! [X11,X12,X13,X14,X3] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
      | c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X14,X13,X3),c_HOL_Otimes__class_Otimes(X12,X11,X3),X3) = c_HOL_Otimes__class_Otimes(X12,c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X14,X13,X3),X11,X3),X3) ),
    file('<stdin>',cls_class__semiring_Osemiring__rules_I15_J_0) ).

fof(c_0_52,axiom,
    ! [X11,X12,X13,X14,X3] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
      | c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X14,X13,X3),c_HOL_Otimes__class_Otimes(X12,X11,X3),X3) = c_HOL_Otimes__class_Otimes(X14,c_HOL_Otimes__class_Otimes(X13,c_HOL_Otimes__class_Otimes(X12,X11,X3),X3),X3) ),
    file('<stdin>',cls_class__semiring_Osemiring__rules_I14_J_0) ).

fof(c_0_53,axiom,
    ! [X20,X15,X1,X2,X3] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X3)
      | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X15,X3),c_HOL_Otimes__class_Otimes(X1,X20,X3),X3)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X15,X3)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X2,X3)
      | ~ c_lessequals(X15,X20,X3)
      | ~ c_HOL_Oord__class_Oless(X2,X1,X3) ),
    file('<stdin>',cls_mult__less__le__imp__less_0) ).

fof(c_0_54,axiom,
    ! [X20,X15,X1,X2,X3] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X3)
      | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X15,X3),c_HOL_Otimes__class_Otimes(X1,X20,X3),X3)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X15,X3)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3)
      | ~ c_HOL_Oord__class_Oless(X15,X20,X3)
      | ~ c_lessequals(X2,X1,X3) ),
    file('<stdin>',cls_mult__le__less__imp__less_0) ).

fof(c_0_55,axiom,
    ! [X20,X15,X1,X2,X3] :
      ( ~ class_Ring__and__Field_Opordered__semiring(X3)
      | c_lessequals(c_HOL_Otimes__class_Otimes(X2,X15,X3),c_HOL_Otimes__class_Otimes(X1,X20,X3),X3)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X15,X3)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X2,X3)
      | ~ c_lessequals(X15,X20,X3)
      | ~ c_lessequals(X2,X1,X3) ),
    file('<stdin>',cls_mult__mono_H_0) ).

fof(c_0_56,axiom,
    ! [X20,X15,X1,X2,X3] :
      ( ~ class_Ring__and__Field_Opordered__semiring(X3)
      | c_lessequals(c_HOL_Otimes__class_Otimes(X2,X15,X3),c_HOL_Otimes__class_Otimes(X1,X20,X3),X3)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X15,X3)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X1,X3)
      | ~ c_lessequals(X15,X20,X3)
      | ~ c_lessequals(X2,X1,X3) ),
    file('<stdin>',cls_mult__mono_0) ).

fof(c_0_57,axiom,
    ! [X20,X15,X1,X2,X3] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X3)
      | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X15,X3),c_HOL_Otimes__class_Otimes(X1,X20,X3),X3)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X15,X3)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X2,X3)
      | ~ c_HOL_Oord__class_Oless(X15,X20,X3)
      | ~ c_HOL_Oord__class_Oless(X2,X1,X3) ),
    file('<stdin>',cls_mult__strict__mono_H_0) ).

fof(c_0_58,axiom,
    ! [X20,X15,X1,X2,X3] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X3)
      | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X15,X3),c_HOL_Otimes__class_Otimes(X1,X20,X3),X3)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X15,X3)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X1,X3)
      | ~ c_HOL_Oord__class_Oless(X15,X20,X3)
      | ~ c_HOL_Oord__class_Oless(X2,X1,X3) ),
    file('<stdin>',cls_mult__strict__mono_0) ).

fof(c_0_59,axiom,
    ! [X20,X15,X1,X2,X3] :
      ( ~ class_Ring__and__Field_Oordered__idom(X3)
      | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(X2,X3),c_HOL_Oabs__class_Oabs(X1,X3),X3),c_HOL_Otimes__class_Otimes(X15,X20,X3),X3)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(X1,X3),X20,X3)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(X2,X3),X15,X3) ),
    file('<stdin>',cls_abs__mult__less_0) ).

fof(c_0_60,axiom,
    ! [X7,X22,X2,X3] :
      ( ~ class_Ring__and__Field_Oordered__idom(X3)
      | c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X2,X22,X3),X7,X3)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X7,X2,X3),X3),X22,X3) ),
    file('<stdin>',cls_abs__diff__less__iff_0) ).

fof(c_0_61,axiom,
    ! [X7,X22,X2,X3] :
      ( ~ class_Ring__and__Field_Oordered__idom(X3)
      | c_HOL_Oord__class_Oless(X7,c_HOL_Oplus__class_Oplus(X2,X22,X3),X3)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X7,X2,X3),X3),X22,X3) ),
    file('<stdin>',cls_abs__diff__less__iff_1) ).

fof(c_0_62,axiom,
    ! [X4,X5,X8] :
      ( c_HOL_Oord__class_Oless(X5,X4,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X5,X8,tc_nat),c_HOL_Ominus__class_Ominus(X4,X8,tc_nat),tc_nat)
      | ~ c_lessequals(X8,X4,tc_nat)
      | ~ c_lessequals(X8,X5,tc_nat) ),
    file('<stdin>',cls_less__diff__iff_0) ).

fof(c_0_63,axiom,
    ! [X4,X5,X8] :
      ( c_lessequals(X5,X4,tc_nat)
      | ~ c_lessequals(c_HOL_Ominus__class_Ominus(X5,X8,tc_nat),c_HOL_Ominus__class_Ominus(X4,X8,tc_nat),tc_nat)
      | ~ c_lessequals(X8,X4,tc_nat)
      | ~ c_lessequals(X8,X5,tc_nat) ),
    file('<stdin>',cls_le__diff__iff_0) ).

fof(c_0_64,axiom,
    ! [X6,X7,X3] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X7,X7,X3),c_HOL_Otimes__class_Otimes(X6,X6,X3),X3),X3)
      | X7 = c_HOL_Ozero__class_Ozero(X3) ),
    file('<stdin>',cls_sum__squares__gt__zero__iff_1) ).

fof(c_0_65,axiom,
    ! [X6,X7,X3] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X7,X7,X3),c_HOL_Otimes__class_Otimes(X6,X6,X3),X3),X3)
      | X6 = c_HOL_Ozero__class_Ozero(X3) ),
    file('<stdin>',cls_sum__squares__gt__zero__iff_2) ).

fof(c_0_66,axiom,
    ! [X6,X7,X3] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
      | c_lessequals(c_HOL_Ozero__class_Ozero(X3),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X7,X7,X3),c_HOL_Otimes__class_Otimes(X6,X6,X3),X3),X3) ),
    file('<stdin>',cls_sum__squares__ge__zero_0) ).

fof(c_0_67,axiom,
    ! [X6,X34,X18,X7,X4] :
      ( c_HOL_Oplus__class_Oplus(X7,c_HOL_Otimes__class_Otimes(X4,X18,tc_nat),tc_nat) != c_HOL_Oplus__class_Oplus(X6,c_HOL_Otimes__class_Otimes(X4,X34,tc_nat),tc_nat)
      | c_Divides_Odiv__class_Omod(X7,X4,tc_nat) = c_Divides_Odiv__class_Omod(X6,X4,tc_nat) ),
    file('<stdin>',cls_nat__mod__eq__iff_1) ).

fof(c_0_68,axiom,
    ! [X15,X1,X2,X3] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
      | c_HOL_Oord__class_Oless(X1,X2,X3)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X15,X2,X3),c_HOL_Otimes__class_Otimes(X15,X1,X3),X3)
      | ~ c_HOL_Oord__class_Oless(X15,c_HOL_Ozero__class_Ozero(X3),X3) ),
    file('<stdin>',cls_mult__less__cancel__left__neg_0) ).

fof(c_0_69,axiom,
    ! [X15,X1,X2,X3] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
      | c_HOL_Oord__class_Oless(X2,X1,X3)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X15,X2,X3),c_HOL_Otimes__class_Otimes(X15,X1,X3),X3)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X15,X3) ),
    file('<stdin>',cls_mult__less__cancel__left__pos_0) ).

fof(c_0_70,axiom,
    ! [X15,X1,X2,X3] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
      | c_lessequals(X1,X2,X3)
      | ~ c_lessequals(c_HOL_Otimes__class_Otimes(X15,X2,X3),c_HOL_Otimes__class_Otimes(X15,X1,X3),X3)
      | ~ c_HOL_Oord__class_Oless(X15,c_HOL_Ozero__class_Ozero(X3),X3) ),
    file('<stdin>',cls_mult__le__cancel__left__neg_0) ).

fof(c_0_71,axiom,
    ! [X15,X1,X2,X3] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
      | c_lessequals(X2,X1,X3)
      | ~ c_lessequals(c_HOL_Otimes__class_Otimes(X15,X2,X3),c_HOL_Otimes__class_Otimes(X15,X1,X3),X3)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X15,X3) ),
    file('<stdin>',cls_mult__le__cancel__left__pos_0) ).

fof(c_0_72,axiom,
    ! [X15,X1,X2,X3] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X3)
      | c_lessequals(X2,X1,X3)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X15,X3)
      | ~ c_lessequals(c_HOL_Otimes__class_Otimes(X15,X2,X3),c_HOL_Otimes__class_Otimes(X15,X1,X3),X3) ),
    file('<stdin>',cls_mult__left__le__imp__le_0) ).

fof(c_0_73,axiom,
    ! [X15,X1,X2,X3] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X3)
      | c_lessequals(X2,X1,X3)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X15,X3)
      | ~ c_lessequals(c_HOL_Otimes__class_Otimes(X2,X15,X3),c_HOL_Otimes__class_Otimes(X1,X15,X3),X3) ),
    file('<stdin>',cls_mult__right__le__imp__le_0) ).

fof(c_0_74,axiom,
    ! [X15,X1,X2,X3] :
      ( ~ class_Ring__and__Field_Oordered__semiring(X3)
      | c_HOL_Oord__class_Oless(X2,X1,X3)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X15,X3)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X15,X2,X3),c_HOL_Otimes__class_Otimes(X15,X1,X3),X3) ),
    file('<stdin>',cls_mult__left__less__imp__less_0) ).

fof(c_0_75,axiom,
    ! [X15,X1,X2,X3] :
      ( ~ class_Ring__and__Field_Oordered__semiring(X3)
      | c_HOL_Oord__class_Oless(X2,X1,X3)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X15,X3)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X15,X3),c_HOL_Otimes__class_Otimes(X1,X15,X3),X3) ),
    file('<stdin>',cls_mult__right__less__imp__less_0) ).

fof(c_0_76,axiom,
    ! [X15,X1,X2,X3] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X3)
      | c_HOL_Oord__class_Oless(X2,X1,X3)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X15,X3)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X15,X2,X3),c_HOL_Otimes__class_Otimes(X15,X1,X3),X3) ),
    file('<stdin>',cls_mult__less__imp__less__left_0) ).

fof(c_0_77,axiom,
    ! [X15,X1,X2,X3] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X3)
      | c_HOL_Oord__class_Oless(X2,X1,X3)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X15,X3)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X15,X3),c_HOL_Otimes__class_Otimes(X1,X15,X3),X3) ),
    file('<stdin>',cls_mult__less__imp__less__right_0) ).

fof(c_0_78,axiom,
    ! [X4,X5,X8] :
      ( c_Ring__and__Field_Odvd__class_Odvd(X5,X4,tc_nat)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X8,X5,tc_nat),c_HOL_Otimes__class_Otimes(X8,X4,tc_nat),tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X8,tc_nat) ),
    file('<stdin>',cls_nat__mult__dvd__cancel1_0) ).

fof(c_0_79,axiom,
    ! [X4,X5,X8] :
      ( c_Ring__and__Field_Odvd__class_Odvd(X5,X4,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X8,tc_nat)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X8,X5,tc_nat),c_HOL_Otimes__class_Otimes(X8,X4,tc_nat),tc_nat) ),
    file('<stdin>',cls_dvd__mult__cancel_0) ).

fof(c_0_80,axiom,
    ! [X4,X5,X8] :
      ( c_HOL_Oord__class_Oless(X5,X4,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X8,X5,tc_nat),c_HOL_Otimes__class_Otimes(X8,X4,tc_nat),tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X8,tc_nat) ),
    file('<stdin>',cls_nat__mult__less__cancel1_0) ).

fof(c_0_81,axiom,
    ! [X4,X5,X8] :
      ( c_lessequals(X5,X4,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X8,tc_nat)
      | ~ c_lessequals(c_HOL_Otimes__class_Otimes(X5,X8,tc_nat),c_HOL_Otimes__class_Otimes(X4,X8,tc_nat),tc_nat) ),
    file('<stdin>',cls_mult__le__cancel2_0) ).

fof(c_0_82,axiom,
    ! [X4,X5,X8] :
      ( c_lessequals(X5,X4,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X8,tc_nat)
      | ~ c_lessequals(c_HOL_Otimes__class_Otimes(X8,X5,tc_nat),c_HOL_Otimes__class_Otimes(X8,X4,tc_nat),tc_nat) ),
    file('<stdin>',cls_mult__le__cancel1_0) ).

fof(c_0_83,axiom,
    ! [X4,X5,X8] :
      ( c_lessequals(X5,X4,tc_nat)
      | ~ c_lessequals(c_HOL_Otimes__class_Otimes(X8,X5,tc_nat),c_HOL_Otimes__class_Otimes(X8,X4,tc_nat),tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X8,tc_nat) ),
    file('<stdin>',cls_nat__mult__le__cancel1_0) ).

fof(c_0_84,axiom,
    ! [X15,X1,X2,X3] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
      | c_HOL_Oord__class_Oless(X15,c_HOL_Ozero__class_Ozero(X3),X3)
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X15,X3)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X15,X3),c_HOL_Otimes__class_Otimes(X1,X15,X3),X3) ),
    file('<stdin>',cls_mult__less__cancel__right__disj_0) ).

fof(c_0_85,axiom,
    ! [X15,X1,X2,X3] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
      | c_HOL_Oord__class_Oless(X15,c_HOL_Ozero__class_Ozero(X3),X3)
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X15,X3)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X15,X2,X3),c_HOL_Otimes__class_Otimes(X15,X1,X3),X3) ),
    file('<stdin>',cls_mult__less__cancel__left__disj_0) ).

fof(c_0_86,axiom,
    ! [X7,X20,X15,X3] :
      ( ~ class_Ring__and__Field_Oidom(X3)
      | ~ class_Int_Onumber__ring(X3)
      | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X7,X15,X3),c_HOL_Otimes__class_Otimes(X7,X20,X3),X3) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X7,X20,X3),c_HOL_Otimes__class_Otimes(X7,X15,X3),X3) ),
    file('<stdin>',cls_class__ringb_Onoteq__reduce_1) ).

fof(c_0_87,axiom,
    ! [X16,X6,X7,X3] :
      ( ~ class_Ring__and__Field_Oidom(X3)
      | ~ class_Int_Onumber__ring(X3)
      | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X7,X6,X3),c_HOL_Otimes__class_Otimes(X7,X16,X3),X3) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X7,X16,X3),c_HOL_Otimes__class_Otimes(X7,X6,X3),X3) ),
    file('<stdin>',cls_class__ringb_Oadd__mul__solve_1) ).

fof(c_0_88,axiom,
    ! [X18] : ~ c_Parity_Oeven__odd__class_Oeven(c_Suc(c_HOL_Otimes__class_Otimes(c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),X18,tc_nat)),tc_nat),
    file('<stdin>',cls_odd__nat__equiv__def2_1) ).

fof(c_0_89,axiom,
    ! [X15,X1,X2,X3] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
      | c_HOL_Oord__class_Oless(X15,c_HOL_Ozero__class_Ozero(X3),X3)
      | c_HOL_Oord__class_Oless(X2,X1,X3)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X15,X3),c_HOL_Otimes__class_Otimes(X1,X15,X3),X3) ),
    file('<stdin>',cls_mult__less__cancel__right__disj_2) ).

fof(c_0_90,axiom,
    ! [X15,X1,X2,X3] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
      | c_HOL_Oord__class_Oless(X1,X2,X3)
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X15,X3)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X15,X3),c_HOL_Otimes__class_Otimes(X1,X15,X3),X3) ),
    file('<stdin>',cls_mult__less__cancel__right__disj_1) ).

fof(c_0_91,axiom,
    ! [X15,X1,X2,X3] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
      | c_HOL_Oord__class_Oless(X15,c_HOL_Ozero__class_Ozero(X3),X3)
      | c_HOL_Oord__class_Oless(X2,X1,X3)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X15,X2,X3),c_HOL_Otimes__class_Otimes(X15,X1,X3),X3) ),
    file('<stdin>',cls_mult__less__cancel__left__disj_2) ).

fof(c_0_92,axiom,
    ! [X15,X1,X2,X3] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
      | c_HOL_Oord__class_Oless(X1,X2,X3)
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X15,X3)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X15,X2,X3),c_HOL_Otimes__class_Otimes(X15,X1,X3),X3) ),
    file('<stdin>',cls_mult__less__cancel__left__disj_1) ).

fof(c_0_93,axiom,
    ! [X20,X15,X1,X2,X3] :
      ( ~ class_OrderedGroup_Oab__group__add(X3)
      | c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X2,X15,X3),c_HOL_Oplus__class_Oplus(X1,X20,X3),X3) = c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X2,X1,X3),c_HOL_Ominus__class_Ominus(X15,X20,X3),X3) ),
    file('<stdin>',cls_Deriv_Oadd__diff__add_0) ).

fof(c_0_94,axiom,
    ! [X15,X1,X2,X3] :
      ( ~ class_Divides_Oring__div(X3)
      | c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X2,X1,X3),X15,X3) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(c_Divides_Odiv__class_Omod(X2,X15,X3),X1,X3),X15,X3) ),
    file('<stdin>',cls_mod__diff__left__eq_0) ).

fof(c_0_95,axiom,
    ! [X15,X1,X2,X3] :
      ( ~ class_Divides_Oring__div(X3)
      | c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X2,X1,X3),X15,X3) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X2,c_Divides_Odiv__class_Omod(X1,X15,X3),X3),X15,X3) ),
    file('<stdin>',cls_mod__diff__right__eq_0) ).

fof(c_0_96,axiom,
    ! [X15,X1,X2,X3] :
      ( ~ class_Divides_Osemiring__div(X3)
      | c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X2,X1,X3),X15,X3) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(X2,X15,X3),X1,X3),X15,X3) ),
    file('<stdin>',cls_mod__mult__left__eq_0) ).

fof(c_0_97,axiom,
    ! [X15,X1,X2,X3] :
      ( ~ class_Divides_Osemiring__div(X3)
      | c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X2,X1,X3),X15,X3) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X2,c_Divides_Odiv__class_Omod(X1,X15,X3),X3),X15,X3) ),
    file('<stdin>',cls_mod__mult__right__eq_0) ).

fof(c_0_98,axiom,
    ! [X15,X1,X2,X3] :
      ( ~ class_Divides_Osemiring__div(X3)
      | c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X2,X1,X3),X15,X3) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(X2,X15,X3),X1,X3),X15,X3) ),
    file('<stdin>',cls_mod__add__left__eq_0) ).

fof(c_0_99,axiom,
    ! [X15,X1,X2,X3] :
      ( ~ class_Divides_Osemiring__div(X3)
      | c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X2,X1,X3),X15,X3) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X2,c_Divides_Odiv__class_Omod(X1,X15,X3),X3),X15,X3) ),
    file('<stdin>',cls_mod__add__right__eq_0) ).

fof(c_0_100,axiom,
    ! [X20,X15,X1,X2,X3] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
      | c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X2,X1,X3),c_HOL_Oplus__class_Oplus(X15,X20,X3),X3) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X2,X15,X3),c_HOL_Oplus__class_Oplus(X1,X20,X3),X3) ),
    file('<stdin>',cls_class__semiring_Osemiring__rules_I20_J_0) ).

fof(c_0_101,axiom,
    ! [X15,X1,X2,X3] :
      ( ~ class_Divides_Osemiring__div(X3)
      | c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(X2,X15,X3),X1,X3),X15,X3) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X2,X1,X3),X15,X3) ),
    file('<stdin>',cls_zmod__simps_I1_J_0) ).

fof(c_0_102,axiom,
    ! [X15,X1,X2,X3] :
      ( ~ class_Divides_Osemiring__div(X3)
      | c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X2,c_Divides_Odiv__class_Omod(X1,X15,X3),X3),X15,X3) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X2,X1,X3),X15,X3) ),
    file('<stdin>',cls_zmod__simps_I2_J_0) ).

fof(c_0_103,axiom,
    ! [X15,X1,X2,X3] :
      ( ~ class_Divides_Osemiring__div(X3)
      | c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(X2,X15,X3),X1,X3),X15,X3) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X2,X1,X3),X15,X3) ),
    file('<stdin>',cls_zmod__simps_I4_J_0) ).

fof(c_0_104,axiom,
    ! [X11,X12,X13,X14,X3] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
      | c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X14,X13,X3),c_HOL_Otimes__class_Otimes(X12,X11,X3),X3) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X14,X12,X3),c_HOL_Otimes__class_Otimes(X13,X11,X3),X3) ),
    file('<stdin>',cls_class__semiring_Osemiring__rules_I13_J_0) ).

fof(c_0_105,axiom,
    ! [X15,X1,X2,X3] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
      | c_HOL_Oord__class_Oless(X1,X2,X3)
      | c_HOL_Oord__class_Oless(X2,X1,X3)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X15,X2,X3),c_HOL_Otimes__class_Otimes(X15,X1,X3),X3) ),
    file('<stdin>',cls_mult__less__cancel__left__disj_3) ).

fof(c_0_106,axiom,
    ! [X15,X1,X2,X3] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
      | c_HOL_Oord__class_Oless(X1,X2,X3)
      | c_HOL_Oord__class_Oless(X2,X1,X3)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X15,X3),c_HOL_Otimes__class_Otimes(X1,X15,X3),X3) ),
    file('<stdin>',cls_mult__less__cancel__right__disj_3) ).

fof(c_0_107,axiom,
    ! [X7,X22,X20,X15,X3] :
      ( ~ class_Ring__and__Field_Oidom(X3)
      | ~ class_Int_Onumber__ring(X3)
      | c_HOL_Oplus__class_Oplus(X7,c_HOL_Otimes__class_Otimes(X22,X15,X3),X3) != c_HOL_Oplus__class_Oplus(X7,c_HOL_Otimes__class_Otimes(X22,X20,X3),X3)
      | X15 = X20
      | X22 = c_HOL_Ozero__class_Ozero(X3) ),
    file('<stdin>',cls_class__ringb_Oadd__scale__eq__noteq_0) ).

fof(c_0_108,axiom,
    ! [X7,X20,X15] : c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X7,X15,tc_nat),c_HOL_Otimes__class_Otimes(X7,X20,tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X7,X20,tc_nat),c_HOL_Otimes__class_Otimes(X7,X15,tc_nat),tc_nat),
    file('<stdin>',cls_natgb_Onoteq__reduce_1) ).

fof(c_0_109,axiom,
    ! [X16,X6,X7] : c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X7,X6,tc_nat),c_HOL_Otimes__class_Otimes(X7,X16,tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X7,X16,tc_nat),c_HOL_Otimes__class_Otimes(X7,X6,tc_nat),tc_nat),
    file('<stdin>',cls_natgb_Oadd__mul__solve_1) ).

fof(c_0_110,axiom,
    ! [X5,X8,X9] :
      ( c_HOL_Ominus__class_Ominus(c_Suc(c_HOL_Ominus__class_Ominus(X9,X8,tc_nat)),X5,tc_nat) = c_HOL_Ominus__class_Ominus(c_Suc(X9),c_HOL_Oplus__class_Oplus(X8,X5,tc_nat),tc_nat)
      | ~ c_lessequals(X8,X9,tc_nat) ),
    file('<stdin>',cls_diff__Suc__diff__eq2_0) ).

fof(c_0_111,axiom,
    ! [X5,X8,X9] :
      ( c_HOL_Ominus__class_Ominus(X5,c_Suc(c_HOL_Ominus__class_Ominus(X9,X8,tc_nat)),tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X5,X8,tc_nat),c_Suc(X9),tc_nat)
      | ~ c_lessequals(X8,X9,tc_nat) ),
    file('<stdin>',cls_diff__Suc__diff__eq1_0) ).

fof(c_0_112,axiom,
    ! [X4,X5,X8] :
      ( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X5,X8,tc_nat),c_HOL_Ominus__class_Ominus(X4,X8,tc_nat),tc_nat)
      | ~ c_HOL_Oord__class_Oless(X5,X4,tc_nat)
      | ~ c_lessequals(X8,X4,tc_nat)
      | ~ c_lessequals(X8,X5,tc_nat) ),
    file('<stdin>',cls_less__diff__iff_1) ).

fof(c_0_113,axiom,
    ! [X4,X5,X8] :
      ( c_lessequals(c_HOL_Ominus__class_Ominus(X5,X8,tc_nat),c_HOL_Ominus__class_Ominus(X4,X8,tc_nat),tc_nat)
      | ~ c_lessequals(X5,X4,tc_nat)
      | ~ c_lessequals(X8,X4,tc_nat)
      | ~ c_lessequals(X8,X5,tc_nat) ),
    file('<stdin>',cls_le__diff__iff_1) ).

fof(c_0_114,axiom,
    ! [X1,X2,X3] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X3)
      | c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X2,X1,X3),X3),c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(X2,X3),c_HOL_Oabs__class_Oabs(X1,X3),X3),X3) ),
    file('<stdin>',cls_abs__triangle__ineq4_0) ).

fof(c_0_115,axiom,
    ! [X1,X2,X3] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X3)
      | c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Oplus__class_Oplus(X2,X1,X3),X3),c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(X2,X3),c_HOL_Oabs__class_Oabs(X1,X3),X3),X3) ),
    file('<stdin>',cls_abs__triangle__ineq_0) ).

fof(c_0_116,axiom,
    ! [X1,X2,X3] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X3)
      | c_lessequals(c_HOL_Ominus__class_Ominus(c_HOL_Oabs__class_Oabs(X2,X3),c_HOL_Oabs__class_Oabs(X1,X3),X3),c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X2,X1,X3),X3),X3) ),
    file('<stdin>',cls_abs__triangle__ineq2_0) ).

fof(c_0_117,axiom,
    ! [X1,X2,X3] :
      ( ~ class_Ring__and__Field_Olordered__ring(X3)
      | c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(X2,X1,X3),X3),c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(X2,X3),c_HOL_Oabs__class_Oabs(X1,X3),X3),X3) ),
    file('<stdin>',cls_abs__le__mult_0) ).

fof(c_0_118,axiom,
    ! [X20,X15,X1,X2,X3] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
      | c_lessequals(X2,c_HOL_Oplus__class_Oplus(X1,X20,X3),X3)
      | ~ c_lessequals(X15,X20,X3)
      | ~ c_lessequals(X2,c_HOL_Oplus__class_Oplus(X1,X15,X3),X3) ),
    file('<stdin>',cls_le__add__right__mono_0) ).

fof(c_0_119,axiom,
    ! [X4,X5,X8] :
      ( c_lessequals(X5,X4,tc_nat)
      | ~ c_lessequals(c_HOL_Otimes__class_Otimes(c_Suc(X8),X5,tc_nat),c_HOL_Otimes__class_Otimes(c_Suc(X8),X4,tc_nat),tc_nat) ),
    file('<stdin>',cls_Suc__mult__le__cancel1_0) ).

fof(c_0_120,axiom,
    ! [X4,X5,X8] :
      ( c_HOL_Oord__class_Oless(X5,X4,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Suc(X8),X5,tc_nat),c_HOL_Otimes__class_Otimes(c_Suc(X8),X4,tc_nat),tc_nat) ),
    file('<stdin>',cls_Suc__mult__less__cancel1_0) ).

fof(c_0_121,axiom,
    ! [X7,X22,X20,X15] :
      ( c_HOL_Oplus__class_Oplus(X7,c_HOL_Otimes__class_Otimes(X22,X15,tc_nat),tc_nat) != c_HOL_Oplus__class_Oplus(X7,c_HOL_Otimes__class_Otimes(X22,X20,tc_nat),tc_nat)
      | X15 = X20
      | X22 = c_HOL_Ozero__class_Ozero(tc_nat) ),
    file('<stdin>',cls_natgb_Oadd__scale__eq__noteq_0) ).

fof(c_0_122,axiom,
    ! [X15,X1,X2,X3] :
      ( ~ class_Ring__and__Field_Oidom(X3)
      | c_Ring__and__Field_Odvd__class_Odvd(X2,X1,X3)
      | X15 = c_HOL_Ozero__class_Ozero(X3)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X15,X2,X3),c_HOL_Otimes__class_Otimes(X15,X1,X3),X3) ),
    file('<stdin>',cls_dvd__mult__cancel__left_0) ).

fof(c_0_123,axiom,
    ! [X15,X1,X2,X3] :
      ( ~ class_Ring__and__Field_Oidom(X3)
      | c_Ring__and__Field_Odvd__class_Odvd(X2,X1,X3)
      | X15 = c_HOL_Ozero__class_Ozero(X3)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X2,X15,X3),c_HOL_Otimes__class_Otimes(X1,X15,X3),X3) ),
    file('<stdin>',cls_dvd__mult__cancel__right_0) ).

fof(c_0_124,axiom,
    ! [X8,X9,X10] :
      ( c_lessequals(X10,c_HOL_Ominus__class_Ominus(X9,X8,tc_nat),tc_nat)
      | ~ c_lessequals(c_HOL_Oplus__class_Oplus(X10,X8,tc_nat),X9,tc_nat)
      | ~ c_lessequals(X8,X9,tc_nat) ),
    file('<stdin>',cls_le__diff__conv2_1) ).

fof(c_0_125,axiom,
    ! [X8,X9,X10] :
      ( c_lessequals(c_HOL_Oplus__class_Oplus(X10,X8,tc_nat),X9,tc_nat)
      | ~ c_lessequals(X10,c_HOL_Ominus__class_Ominus(X9,X8,tc_nat),tc_nat)
      | ~ c_lessequals(X8,X9,tc_nat) ),
    file('<stdin>',cls_le__diff__conv2_0) ).

fof(c_0_126,axiom,
    ! [X15,X1,X2,X3] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
      | c_HOL_Oord__class_Oless(X2,X1,X3)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X15,X2,X3),c_HOL_Oplus__class_Oplus(X15,X1,X3),X3) ),
    file('<stdin>',cls_add__less__cancel__left_0) ).

fof(c_0_127,axiom,
    ! [X15,X1,X2,X3] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
      | c_HOL_Oord__class_Oless(X2,X1,X3)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X2,X15,X3),c_HOL_Oplus__class_Oplus(X1,X15,X3),X3) ),
    file('<stdin>',cls_add__less__cancel__right_0) ).

fof(c_0_128,axiom,
    ! [X15,X1,X2,X3] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
      | c_lessequals(X2,X1,X3)
      | ~ c_lessequals(c_HOL_Oplus__class_Oplus(X2,X15,X3),c_HOL_Oplus__class_Oplus(X1,X15,X3),X3) ),
    file('<stdin>',cls_add__le__cancel__right_0) ).

fof(c_0_129,axiom,
    ! [X15,X1,X2,X3] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
      | c_lessequals(X2,X1,X3)
      | ~ c_lessequals(c_HOL_Oplus__class_Oplus(X15,X2,X3),c_HOL_Oplus__class_Oplus(X15,X1,X3),X3) ),
    file('<stdin>',cls_add__le__cancel__left_0) ).

fof(c_0_130,axiom,
    ! [X4,X5,X8] :
      ( c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X5,X8,tc_nat),c_HOL_Ominus__class_Ominus(X4,X8,tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(X5,X4,tc_nat)
      | ~ c_lessequals(X8,X4,tc_nat)
      | ~ c_lessequals(X8,X5,tc_nat) ),
    file('<stdin>',cls_Nat_Odiff__diff__eq_0) ).

fof(c_0_131,axiom,
    ! [X15,X1,X2,X3] :
      ( ~ class_OrderedGroup_Olordered__ab__group__add__abs(X3)
      | c_lessequals(X2,c_HOL_Oplus__class_Oplus(X15,c_HOL_Oabs__class_Oabs(X1,X3),X3),X3)
      | ~ c_lessequals(c_HOL_Oplus__class_Oplus(X2,X1,X3),X15,X3) ),
    file('<stdin>',cls_estimate__by__abs_0) ).

fof(c_0_132,axiom,
    ! [X4,X5,X8] :
      ( c_Ring__and__Field_Odvd__class_Odvd(X8,X5,tc_nat)
      | ~ c_lessequals(X4,X5,tc_nat)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X8,X4,tc_nat)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X8,c_HOL_Ominus__class_Ominus(X5,X4,tc_nat),tc_nat) ),
    file('<stdin>',cls_dvd__diffD_0) ).

fof(c_0_133,axiom,
    ! [X4,X5,X8] :
      ( c_Ring__and__Field_Odvd__class_Odvd(X8,X4,tc_nat)
      | ~ c_lessequals(X4,X5,tc_nat)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X8,X5,tc_nat)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X8,c_HOL_Ominus__class_Ominus(X5,X4,tc_nat),tc_nat) ),
    file('<stdin>',cls_dvd__diffD1_0) ).

fof(c_0_134,axiom,
    ! [X4,X5,X8] :
      ( c_Ring__and__Field_Odvd__class_Odvd(X5,X4,tc_nat)
      | X8 = c_HOL_Ozero__class_Ozero(tc_nat)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X8,X5,tc_nat),c_HOL_Otimes__class_Otimes(X8,X4,tc_nat),tc_nat) ),
    file('<stdin>',cls_nat__mult__dvd__cancel__disj_0) ).

fof(c_0_135,axiom,
    ! [X4,X5,X8] :
      ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X8,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X5,X8,tc_nat),c_HOL_Otimes__class_Otimes(X4,X8,tc_nat),tc_nat) ),
    file('<stdin>',cls_mult__less__cancel2_0) ).

fof(c_0_136,axiom,
    ! [X4,X5,X8] :
      ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X8,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X8,X5,tc_nat),c_HOL_Otimes__class_Otimes(X8,X4,tc_nat),tc_nat) ),
    file('<stdin>',cls_mult__less__cancel1_0) ).

fof(c_0_137,axiom,
    ! [X4,X5,X8] :
      ( c_HOL_Oord__class_Oless(X5,X4,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X5,X8,tc_nat),c_HOL_Otimes__class_Otimes(X4,X8,tc_nat),tc_nat) ),
    file('<stdin>',cls_mult__less__cancel2_1) ).

fof(c_0_138,axiom,
    ! [X4,X5,X8] :
      ( c_HOL_Oord__class_Oless(X5,X4,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X8,X5,tc_nat),c_HOL_Otimes__class_Otimes(X8,X4,tc_nat),tc_nat) ),
    file('<stdin>',cls_mult__less__cancel1_1) ).

fof(c_0_139,axiom,
    ! [X4,X5,X8] :
      ( c_HOL_Oord__class_Oless(X5,X4,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X8,X5,tc_nat),c_HOL_Oplus__class_Oplus(X8,X4,tc_nat),tc_nat) ),
    file('<stdin>',cls_nat__add__left__cancel__less_0) ).

fof(c_0_140,axiom,
    ! [X4,X5,X8] :
      ( c_lessequals(X5,X4,tc_nat)
      | ~ c_lessequals(c_HOL_Oplus__class_Oplus(X8,X5,tc_nat),c_HOL_Oplus__class_Oplus(X8,X4,tc_nat),tc_nat) ),
    file('<stdin>',cls_nat__add__left__cancel__le_0) ).

fof(c_0_141,axiom,
    ! [X15,X1,X2,X3] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
      | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X15,X2,X3),c_HOL_Otimes__class_Otimes(X15,X1,X3),X3)
      | ~ c_HOL_Oord__class_Oless(X1,X2,X3)
      | ~ c_HOL_Oord__class_Oless(X15,c_HOL_Ozero__class_Ozero(X3),X3) ),
    file('<stdin>',cls_mult__less__cancel__left__neg_1) ).

fof(c_0_142,axiom,
    ! [X15,X1,X2,X3] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
      | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X15,X2,X3),c_HOL_Otimes__class_Otimes(X15,X1,X3),X3)
      | ~ c_HOL_Oord__class_Oless(X2,X1,X3)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X15,X3) ),
    file('<stdin>',cls_mult__less__cancel__left__pos_1) ).

fof(c_0_143,axiom,
    ! [X15,X1,X2,X3] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
      | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X15,X2,X3),c_HOL_Otimes__class_Otimes(X15,X1,X3),X3)
      | ~ c_HOL_Oord__class_Oless(X15,c_HOL_Ozero__class_Ozero(X3),X3)
      | ~ c_HOL_Oord__class_Oless(X1,X2,X3) ),
    file('<stdin>',cls_mult__strict__left__mono__neg_0) ).

fof(c_0_144,axiom,
    ! [X15,X1,X2,X3] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X3)
      | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X15,X2,X3),c_HOL_Otimes__class_Otimes(X15,X1,X3),X3)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X15,X3)
      | ~ c_HOL_Oord__class_Oless(X2,X1,X3) ),
    file('<stdin>',cls_mult__strict__left__mono_0) ).

fof(c_0_145,axiom,
    ! [X15,X1,X2,X3] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
      | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X15,X2,X3),c_HOL_Otimes__class_Otimes(X15,X1,X3),X3)
      | ~ c_HOL_Oord__class_Oless(X2,X1,X3)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X15,X3) ),
    file('<stdin>',cls_mult__less__cancel__left__disj_4) ).

fof(c_0_146,axiom,
    ! [X15,X1,X2,X3] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
      | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X15,X2,X3),c_HOL_Otimes__class_Otimes(X15,X1,X3),X3)
      | ~ c_HOL_Oord__class_Oless(X1,X2,X3)
      | ~ c_HOL_Oord__class_Oless(X15,c_HOL_Ozero__class_Ozero(X3),X3) ),
    file('<stdin>',cls_mult__less__cancel__left__disj_5) ).

fof(c_0_147,axiom,
    ! [X15,X1,X2,X3] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
      | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X15,X3),c_HOL_Otimes__class_Otimes(X1,X15,X3),X3)
      | ~ c_HOL_Oord__class_Oless(X15,c_HOL_Ozero__class_Ozero(X3),X3)
      | ~ c_HOL_Oord__class_Oless(X1,X2,X3) ),
    file('<stdin>',cls_mult__strict__right__mono__neg_0) ).

fof(c_0_148,axiom,
    ! [X15,X1,X2,X3] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X3)
      | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X15,X3),c_HOL_Otimes__class_Otimes(X1,X15,X3),X3)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X15,X3)
      | ~ c_HOL_Oord__class_Oless(X2,X1,X3) ),
    file('<stdin>',cls_mult__strict__right__mono_0) ).

fof(c_0_149,axiom,
    ! [X15,X1,X2,X3] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
      | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X15,X3),c_HOL_Otimes__class_Otimes(X1,X15,X3),X3)
      | ~ c_HOL_Oord__class_Oless(X2,X1,X3)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X15,X3) ),
    file('<stdin>',cls_mult__less__cancel__right__disj_4) ).

fof(c_0_150,axiom,
    ! [X15,X1,X2,X3] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
      | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X15,X3),c_HOL_Otimes__class_Otimes(X1,X15,X3),X3)
      | ~ c_HOL_Oord__class_Oless(X1,X2,X3)
      | ~ c_HOL_Oord__class_Oless(X15,c_HOL_Ozero__class_Ozero(X3),X3) ),
    file('<stdin>',cls_mult__less__cancel__right__disj_5) ).

fof(c_0_151,axiom,
    ! [X15,X1,X2,X3] :
      ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X3)
      | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X15,X2,X3),c_HOL_Otimes__class_Otimes(X15,X1,X3),X3)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X15,X3)
      | ~ c_HOL_Oord__class_Oless(X2,X1,X3) ),
    file('<stdin>',cls_mult__strict__left__mono__comm_0) ).

fof(c_0_152,axiom,
    ! [X15,X1,X2,X3] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
      | c_lessequals(c_HOL_Otimes__class_Otimes(X15,X2,X3),c_HOL_Otimes__class_Otimes(X15,X1,X3),X3)
      | ~ c_lessequals(X1,X2,X3)
      | ~ c_HOL_Oord__class_Oless(X15,c_HOL_Ozero__class_Ozero(X3),X3) ),
    file('<stdin>',cls_mult__le__cancel__left__neg_1) ).

fof(c_0_153,axiom,
    ! [X15,X1,X2,X3] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
      | c_lessequals(c_HOL_Otimes__class_Otimes(X15,X2,X3),c_HOL_Otimes__class_Otimes(X15,X1,X3),X3)
      | ~ c_lessequals(X2,X1,X3)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X15,X3) ),
    file('<stdin>',cls_mult__le__cancel__left__pos_1) ).

fof(c_0_154,axiom,
    ! [X15,X1,X2,X3] :
      ( ~ class_Ring__and__Field_Opordered__ring(X3)
      | c_lessequals(c_HOL_Otimes__class_Otimes(X2,X15,X3),c_HOL_Otimes__class_Otimes(X1,X15,X3),X3)
      | ~ c_lessequals(X15,c_HOL_Ozero__class_Ozero(X3),X3)
      | ~ c_lessequals(X1,X2,X3) ),
    file('<stdin>',cls_mult__right__mono__neg_0) ).

fof(c_0_155,axiom,
    ! [X15,X1,X2,X3] :
      ( ~ class_Ring__and__Field_Opordered__ring(X3)
      | c_lessequals(c_HOL_Otimes__class_Otimes(X15,X2,X3),c_HOL_Otimes__class_Otimes(X15,X1,X3),X3)
      | ~ c_lessequals(X15,c_HOL_Ozero__class_Ozero(X3),X3)
      | ~ c_lessequals(X1,X2,X3) ),
    file('<stdin>',cls_mult__left__mono__neg_0) ).

fof(c_0_156,axiom,
    ! [X15,X1,X2,X3] :
      ( ~ class_Ring__and__Field_Omult__mono(X3)
      | c_lessequals(c_HOL_Otimes__class_Otimes(X2,X15,X3),c_HOL_Otimes__class_Otimes(X1,X15,X3),X3)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X15,X3)
      | ~ c_lessequals(X2,X1,X3) ),
    file('<stdin>',cls_mult__right__mono_0) ).

fof(c_0_157,axiom,
    ! [X15,X1,X2,X3] :
      ( ~ class_Ring__and__Field_Omult__mono(X3)
      | c_lessequals(c_HOL_Otimes__class_Otimes(X15,X2,X3),c_HOL_Otimes__class_Otimes(X15,X1,X3),X3)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X15,X3)
      | ~ c_lessequals(X2,X1,X3) ),
    file('<stdin>',cls_mult__left__mono_0) ).

fof(c_0_158,axiom,
    ! [X15,X1,X2,X3] :
      ( ~ class_Ring__and__Field_Omult__mono1(X3)
      | c_lessequals(c_HOL_Otimes__class_Otimes(X15,X2,X3),c_HOL_Otimes__class_Otimes(X15,X1,X3),X3)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X15,X3)
      | ~ c_lessequals(X2,X1,X3) ),
    file('<stdin>',cls_mult__mono1_0) ).

fof(c_0_159,axiom,
    ! [X4,X5,X8] :
      ( c_lessequals(X5,c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X4,X5,tc_nat),X8,tc_nat),tc_nat)
      | ~ c_lessequals(X8,X4,tc_nat) ),
    file('<stdin>',cls_le__add__diff_0) ).

fof(c_0_160,axiom,
    ! [X20,X15,X1,X2,X3] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
      | c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X2,X15,X3),c_HOL_Otimes__class_Otimes(X1,X20,X3),X3)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X15,X20,X3)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X1,X3) ),
    file('<stdin>',cls_mult__dvd__mono_0) ).

fof(c_0_161,axiom,
    ! [X20,X15,X1,X2,X3] :
      ( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X3)
      | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X2,X15,X3),c_HOL_Oplus__class_Oplus(X1,X20,X3),X3)
      | ~ c_HOL_Oord__class_Oless(X15,X20,X3)
      | ~ c_HOL_Oord__class_Oless(X2,X1,X3) ),
    file('<stdin>',cls_add__strict__mono_0) ).

fof(c_0_162,axiom,
    ! [X20,X15,X1,X2,X3] :
      ( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X3)
      | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X2,X15,X3),c_HOL_Oplus__class_Oplus(X1,X20,X3),X3)
      | ~ c_HOL_Oord__class_Oless(X15,X20,X3)
      | ~ c_lessequals(X2,X1,X3) ),
    file('<stdin>',cls_add__le__less__mono_0) ).

fof(c_0_163,axiom,
    ! [X20,X15,X1,X2,X3] :
      ( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X3)
      | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X2,X15,X3),c_HOL_Oplus__class_Oplus(X1,X20,X3),X3)
      | ~ c_lessequals(X15,X20,X3)
      | ~ c_HOL_Oord__class_Oless(X2,X1,X3) ),
    file('<stdin>',cls_add__less__le__mono_0) ).

fof(c_0_164,axiom,
    ! [X20,X15,X1,X2,X3] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X3)
      | c_lessequals(c_HOL_Oplus__class_Oplus(X2,X15,X3),c_HOL_Oplus__class_Oplus(X1,X20,X3),X3)
      | ~ c_lessequals(X15,X20,X3)
      | ~ c_lessequals(X2,X1,X3) ),
    file('<stdin>',cls_add__mono_0) ).

fof(c_0_165,axiom,
    ! [X6,X7,X3] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
      | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X7,X7,X3),c_HOL_Otimes__class_Otimes(X6,X6,X3),X3) != c_HOL_Ozero__class_Ozero(X3)
      | X6 = c_HOL_Ozero__class_Ozero(X3) ),
    file('<stdin>',cls_sum__squares__eq__zero__iff_1) ).

fof(c_0_166,axiom,
    ! [X6,X7,X3] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
      | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X7,X7,X3),c_HOL_Otimes__class_Otimes(X6,X6,X3),X3) != c_HOL_Ozero__class_Ozero(X3)
      | X7 = c_HOL_Ozero__class_Ozero(X3) ),
    file('<stdin>',cls_sum__squares__eq__zero__iff_0) ).

fof(c_0_167,axiom,
    ! [X15,X1,X2,X3] :
      ( ~ class_Divides_Osemiring__div(X3)
      | c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X2,X15,X3),c_HOL_Otimes__class_Otimes(X1,X15,X3),X3) = c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(X2,X1,X3),X15,X3) ),
    file('<stdin>',cls_mod__mult__mult2_0) ).

fof(c_0_168,axiom,
    ! [X15,X1,X2,X3] :
      ( ~ class_Divides_Osemiring__div(X3)
      | c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X15,X2,X3),c_HOL_Otimes__class_Otimes(X15,X1,X3),X3) = c_HOL_Otimes__class_Otimes(X15,c_Divides_Odiv__class_Omod(X2,X1,X3),X3) ),
    file('<stdin>',cls_mod__mult__mult1_0) ).

fof(c_0_169,axiom,
    ! [X27,X6,X7,X3] :
      ( ~ class_RealVector_Oreal__normed__algebra(X3)
      | c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X7,X6,X3),X27,X3) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X7,X27,X3),c_HOL_Otimes__class_Otimes(X6,X27,X3),X3) ),
    file('<stdin>',cls_mult__left_Odiff_0) ).

fof(c_0_170,axiom,
    ! [X1,X28,X2,X3] :
      ( ~ class_RealVector_Oreal__normed__algebra(X3)
      | c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X28,X3),X1,X3) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X2,X1,X3),c_HOL_Otimes__class_Otimes(X28,X1,X3),X3) ),
    file('<stdin>',cls_mult_Odiff__left_0) ).

fof(c_0_171,axiom,
    ! [X26,X1,X2,X3] :
      ( ~ class_RealVector_Oreal__normed__algebra(X3)
      | c_HOL_Otimes__class_Otimes(X2,c_HOL_Ominus__class_Ominus(X1,X26,X3),X3) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X2,X1,X3),c_HOL_Otimes__class_Otimes(X2,X26,X3),X3) ),
    file('<stdin>',cls_mult_Odiff__right_0) ).

fof(c_0_172,axiom,
    ! [X6,X18,X7,X3] :
      ( ~ class_RealVector_Oreal__normed__algebra(X3)
      | c_HOL_Otimes__class_Otimes(X18,c_HOL_Ominus__class_Ominus(X7,X6,X3),X3) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X18,X7,X3),c_HOL_Otimes__class_Otimes(X18,X6,X3),X3) ),
    file('<stdin>',cls_mult__right_Odiff_0) ).

fof(c_0_173,axiom,
    ! [X16,X6,X7,X3] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
      | c_HOL_Ominus__class_Ominus(c_Orderings_Oord__class_Omin(X7,X6,X3),X16,X3) = c_Orderings_Oord__class_Omin(c_HOL_Ominus__class_Ominus(X7,X16,X3),c_HOL_Ominus__class_Ominus(X6,X16,X3),X3) ),
    file('<stdin>',cls_min__diff__distrib__left_0) ).

fof(c_0_174,axiom,
    ! [X15,X1,X2,X3] :
      ( ~ class_Divides_Osemiring__div(X3)
      | c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X2,c_HOL_Otimes__class_Otimes(X15,X1,X3),X3),X1,X3) = c_Divides_Odiv__class_Omod(X2,X1,X3) ),
    file('<stdin>',cls_mod__mult__self1_0) ).

fof(c_0_175,axiom,
    ! [X15,X1,X2,X3] :
      ( ~ class_Divides_Osemiring__div(X3)
      | c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X2,c_HOL_Otimes__class_Otimes(X1,X15,X3),X3),X1,X3) = c_Divides_Odiv__class_Omod(X2,X1,X3) ),
    file('<stdin>',cls_mod__mult__self2_0) ).

fof(c_0_176,axiom,
    ! [X16,X6,X7,X3] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
      | c_HOL_Oplus__class_Oplus(c_Orderings_Oord__class_Omin(X7,X6,X3),X16,X3) = c_Orderings_Oord__class_Omin(c_HOL_Oplus__class_Oplus(X7,X16,X3),c_HOL_Oplus__class_Oplus(X6,X16,X3),X3) ),
    file('<stdin>',cls_min__add__distrib__left_0) ).

fof(c_0_177,axiom,
    ! [X5,X1,X2,X3] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
      | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X5,X3),c_HOL_Otimes__class_Otimes(X1,X5,X3),X3) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X2,X1,X3),X5,X3) ),
    file('<stdin>',cls_class__semiring_Osemiring__rules_I1_J_0) ).

fof(c_0_178,axiom,
    ! [X15,X1,X2,X3] :
      ( ~ class_Ring__and__Field_Ocomm__semiring(X3)
      | c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X2,X1,X3),X15,X3) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X15,X3),c_HOL_Otimes__class_Otimes(X1,X15,X3),X3) ),
    file('<stdin>',cls_comm__semiring__class_Odistrib_0) ).

fof(c_0_179,axiom,
    ! [X16,X6,X7,X3] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
      | c_HOL_Otimes__class_Otimes(X7,c_HOL_Oplus__class_Oplus(X6,X16,X3),X3) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X7,X6,X3),c_HOL_Otimes__class_Otimes(X7,X16,X3),X3) ),
    file('<stdin>',cls_class__semiring_Omul__d_0) ).

fof(c_0_180,axiom,
    ! [X1,X28,X2,X3] :
      ( ~ class_RealVector_Oreal__normed__algebra(X3)
      | c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X2,X28,X3),X1,X3) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X1,X3),c_HOL_Otimes__class_Otimes(X28,X1,X3),X3) ),
    file('<stdin>',cls_mult_Oadd__left_0) ).

fof(c_0_181,axiom,
    ! [X27,X6,X7,X3] :
      ( ~ class_RealVector_Oreal__normed__algebra(X3)
      | c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X7,X6,X3),X27,X3) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X7,X27,X3),c_HOL_Otimes__class_Otimes(X6,X27,X3),X3) ),
    file('<stdin>',cls_mult__left_Oadd_0) ).

fof(c_0_182,axiom,
    ! [X26,X1,X2,X3] :
      ( ~ class_RealVector_Oreal__normed__algebra(X3)
      | c_HOL_Otimes__class_Otimes(X2,c_HOL_Oplus__class_Oplus(X1,X26,X3),X3) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X1,X3),c_HOL_Otimes__class_Otimes(X2,X26,X3),X3) ),
    file('<stdin>',cls_mult_Oadd__right_0) ).

fof(c_0_183,axiom,
    ! [X6,X18,X7,X3] :
      ( ~ class_RealVector_Oreal__normed__algebra(X3)
      | c_HOL_Otimes__class_Otimes(X18,c_HOL_Oplus__class_Oplus(X7,X6,X3),X3) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X18,X7,X3),c_HOL_Otimes__class_Otimes(X18,X6,X3),X3) ),
    file('<stdin>',cls_mult__right_Oadd_0) ).

fof(c_0_184,axiom,
    ! [X15,X1,X2,X3] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
      | c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X2,X1,X3),X15,X3) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X15,X3),c_HOL_Otimes__class_Otimes(X1,X15,X3),X3) ),
    file('<stdin>',cls_class__semiring_Osemiring__rules_I8_J_0) ).

fof(c_0_185,axiom,
    ! [X4,X5,X8] :
      ( c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X8,X5,tc_nat),c_HOL_Otimes__class_Otimes(X8,X4,tc_nat),tc_nat)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X5,X4,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X8,tc_nat) ),
    file('<stdin>',cls_nat__mult__dvd__cancel1_1) ).

fof(c_0_186,axiom,
    ! [X4,X5,X8] :
      ( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X5,X8,tc_nat),c_HOL_Otimes__class_Otimes(X4,X8,tc_nat),tc_nat)
      | ~ c_HOL_Oord__class_Oless(X5,X4,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X8,tc_nat) ),
    file('<stdin>',cls_mult__less__cancel2_2) ).

fof(c_0_187,axiom,
    ! [X4,X5,X8] :
      ( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X8,X5,tc_nat),c_HOL_Otimes__class_Otimes(X8,X4,tc_nat),tc_nat)
      | ~ c_HOL_Oord__class_Oless(X5,X4,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X8,tc_nat) ),
    file('<stdin>',cls_mult__less__cancel1_2) ).

fof(c_0_188,axiom,
    ! [X8,X9,X10] :
      ( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X8,X10,tc_nat),c_HOL_Otimes__class_Otimes(X8,X9,tc_nat),tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X8,tc_nat)
      | ~ c_HOL_Oord__class_Oless(X10,X9,tc_nat) ),
    file('<stdin>',cls_mult__less__mono2_0) ).

fof(c_0_189,axiom,
    ! [X8,X9,X10] :
      ( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X10,X8,tc_nat),c_HOL_Otimes__class_Otimes(X9,X8,tc_nat),tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X8,tc_nat)
      | ~ c_HOL_Oord__class_Oless(X10,X9,tc_nat) ),
    file('<stdin>',cls_mult__less__mono1_0) ).

fof(c_0_190,axiom,
    ! [X4,X5,X8] :
      ( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X8,X5,tc_nat),c_HOL_Otimes__class_Otimes(X8,X4,tc_nat),tc_nat)
      | ~ c_HOL_Oord__class_Oless(X5,X4,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X8,tc_nat) ),
    file('<stdin>',cls_nat__mult__less__cancel1_1) ).

fof(c_0_191,axiom,
    ! [X4,X5,X8] :
      ( c_lessequals(c_HOL_Otimes__class_Otimes(X8,X5,tc_nat),c_HOL_Otimes__class_Otimes(X8,X4,tc_nat),tc_nat)
      | ~ c_lessequals(X5,X4,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X8,tc_nat) ),
    file('<stdin>',cls_nat__mult__le__cancel1_1) ).

fof(c_0_192,axiom,
    ! [X4,X5,X29] :
      ( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X29,X4,tc_nat),c_HOL_Ominus__class_Ominus(X29,X5,tc_nat),tc_nat)
      | ~ c_HOL_Oord__class_Oless(X5,X29,tc_nat)
      | ~ c_HOL_Oord__class_Oless(X5,X4,tc_nat) ),
    file('<stdin>',cls_diff__less__mono2_0) ).

fof(c_0_193,axiom,
    ! [X15,X1,X2] :
      ( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X2,X15,tc_nat),c_HOL_Ominus__class_Ominus(X1,X15,tc_nat),tc_nat)
      | ~ c_lessequals(X15,X2,tc_nat)
      | ~ c_HOL_Oord__class_Oless(X2,X1,tc_nat) ),
    file('<stdin>',cls_diff__less__mono_0) ).

fof(c_0_194,axiom,
    ! [X29,X8,X9,X10] :
      ( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X10,X8,tc_nat),c_HOL_Oplus__class_Oplus(X9,X29,tc_nat),tc_nat)
      | ~ c_HOL_Oord__class_Oless(X8,X29,tc_nat)
      | ~ c_HOL_Oord__class_Oless(X10,X9,tc_nat) ),
    file('<stdin>',cls_add__less__mono_0) ).

fof(c_0_195,axiom,
    ! [X29,X8,X9,X10] :
      ( c_lessequals(c_HOL_Oplus__class_Oplus(X10,X8,tc_nat),c_HOL_Oplus__class_Oplus(X9,X29,tc_nat),tc_nat)
      | ~ c_lessequals(X8,X29,tc_nat)
      | ~ c_lessequals(X10,X9,tc_nat) ),
    file('<stdin>',cls_add__le__mono_0) ).

fof(c_0_196,axiom,
    ! [X29,X8,X9,X10] :
      ( c_lessequals(c_HOL_Otimes__class_Otimes(X10,X8,tc_nat),c_HOL_Otimes__class_Otimes(X9,X29,tc_nat),tc_nat)
      | ~ c_lessequals(X8,X29,tc_nat)
      | ~ c_lessequals(X10,X9,tc_nat) ),
    file('<stdin>',cls_mult__le__mono_0) ).

fof(c_0_197,axiom,
    ! [X1,X2,X3] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X3)
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X1,X3)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_HOL_Otimes__class_Otimes(X1,X2,X3),X3) ),
    file('<stdin>',cls_zero__less__mult__pos2_0) ).

fof(c_0_198,axiom,
    ! [X1,X2,X3] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X3)
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X1,X3)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_HOL_Otimes__class_Otimes(X2,X1,X3),X3) ),
    file('<stdin>',cls_zero__less__mult__pos_0) ).

fof(c_0_199,axiom,
    ! [X1,X2,X3] :
      ( ~ class_Ring__and__Field_Opordered__ring__abs(X3)
      | c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(X2,X1,X3),X3) = c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(X2,X3),c_HOL_Oabs__class_Oabs(X1,X3),X3)
      | ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X3),X3)
      | ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X3),X3) ),
    file('<stdin>',cls_abs__eq__mult_3) ).

fof(c_0_200,axiom,
    ! [X1,X2,X3] :
      ( ~ class_Ring__and__Field_Opordered__ring__abs(X3)
      | c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(X2,X1,X3),X3) = c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(X2,X3),c_HOL_Oabs__class_Oabs(X1,X3),X3)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X1,X3)
      | ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X3),X3) ),
    file('<stdin>',cls_abs__eq__mult_2) ).

fof(c_0_201,axiom,
    ! [X1,X2,X3] :
      ( ~ class_Ring__and__Field_Opordered__ring__abs(X3)
      | c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(X2,X1,X3),X3) = c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(X2,X3),c_HOL_Oabs__class_Oabs(X1,X3),X3)
      | ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X3),X3)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X2,X3) ),
    file('<stdin>',cls_abs__eq__mult_1) ).

fof(c_0_202,axiom,
    ! [X1,X2,X3] :
      ( ~ class_Ring__and__Field_Opordered__ring__abs(X3)
      | c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(X2,X1,X3),X3) = c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(X2,X3),c_HOL_Oabs__class_Oabs(X1,X3),X3)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X1,X3)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X2,X3) ),
    file('<stdin>',cls_abs__eq__mult_0) ).

fof(c_0_203,axiom,
    ! [X4,X5,X8] : c_HOL_Otimes__class_Otimes(X8,c_HOL_Ominus__class_Ominus(X5,X4,tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X8,X5,tc_nat),c_HOL_Otimes__class_Otimes(X8,X4,tc_nat),tc_nat),
    file('<stdin>',cls_diff__mult__distrib2_0) ).

fof(c_0_204,axiom,
    ! [X4,X5,X8] : c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X5,X4,tc_nat),X8,tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X5,X8,tc_nat),c_HOL_Otimes__class_Otimes(X4,X8,tc_nat),tc_nat),
    file('<stdin>',cls_diff__mult__distrib_0) ).

fof(c_0_205,axiom,
    ! [X4,X5,X10] : c_Orderings_Oord__class_Omin(c_HOL_Ominus__class_Ominus(X5,X10,tc_nat),c_HOL_Ominus__class_Ominus(X4,X10,tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(c_Orderings_Oord__class_Omin(X5,X4,tc_nat),X10,tc_nat),
    file('<stdin>',cls_min__diff_0) ).

fof(c_0_206,axiom,
    ! [X4,X5,X8] : c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X8,X4,tc_nat),X5,tc_nat),X4,tc_nat) = c_Divides_Odiv__class_Omod(X5,X4,tc_nat),
    file('<stdin>',cls_mod__mult__self3_0) ).

fof(c_0_207,axiom,
    ! [X4,X5,X8] : c_HOL_Otimes__class_Otimes(X8,c_Divides_Odiv__class_Omod(X5,X4,tc_nat),tc_nat) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X8,X5,tc_nat),c_HOL_Otimes__class_Otimes(X8,X4,tc_nat),tc_nat),
    file('<stdin>',cls_mod__mult__distrib2_0) ).

fof(c_0_208,axiom,
    ! [X4,X5,X8] : c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(X5,X4,tc_nat),X8,tc_nat) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X5,X8,tc_nat),c_HOL_Otimes__class_Otimes(X4,X8,tc_nat),tc_nat),
    file('<stdin>',cls_mod__mult__distrib_0) ).

fof(c_0_209,axiom,
    ! [X4,X5,X8] : c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X5,X4,tc_nat),X8,tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X5,X8,tc_nat),c_HOL_Otimes__class_Otimes(X4,X8,tc_nat),tc_nat),
    file('<stdin>',cls_add__mult__distrib_0) ).

fof(c_0_210,axiom,
    ! [X4,X5,X8] : c_HOL_Otimes__class_Otimes(X8,c_HOL_Oplus__class_Oplus(X5,X4,tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X8,X5,tc_nat),c_HOL_Otimes__class_Otimes(X8,X4,tc_nat),tc_nat),
    file('<stdin>',cls_add__mult__distrib2_0) ).

fof(c_0_211,axiom,
    ! [X8,X10] :
      ( ~ c_lessequals(X10,c_HOL_Oplus__class_Oplus(X8,X10,tc_nat),tc_nat)
      | c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X8,X10,tc_nat),X10,tc_nat) = X8 ),
    file('<stdin>',cls_le__imp__diff__is__add_1) ).

fof(c_0_212,axiom,
    ! [X8,X9,X10] :
      ( c_HOL_Oord__class_Oless(X10,c_HOL_Ominus__class_Ominus(X9,X8,tc_nat),tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X10,X8,tc_nat),X9,tc_nat) ),
    file('<stdin>',cls_less__diff__conv_1) ).

fof(c_0_213,axiom,
    ! [X8,X9,X10] :
      ( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X10,X8,tc_nat),X9,tc_nat)
      | ~ c_HOL_Oord__class_Oless(X10,c_HOL_Ominus__class_Ominus(X9,X8,tc_nat),tc_nat) ),
    file('<stdin>',cls_less__diff__conv_0) ).

fof(c_0_214,axiom,
    ! [X8,X9,X10] :
      ( c_lessequals(X9,c_HOL_Oplus__class_Oplus(X10,X8,tc_nat),tc_nat)
      | ~ c_lessequals(c_HOL_Ominus__class_Ominus(X9,X8,tc_nat),X10,tc_nat) ),
    file('<stdin>',cls_le__diff__conv_0) ).

fof(c_0_215,axiom,
    ! [X8,X9,X10] :
      ( c_lessequals(c_HOL_Ominus__class_Ominus(X9,X8,tc_nat),X10,tc_nat)
      | ~ c_lessequals(X9,c_HOL_Oplus__class_Oplus(X10,X8,tc_nat),tc_nat) ),
    file('<stdin>',cls_le__diff__conv_1) ).

fof(c_0_216,axiom,
    ! [X4,X5,X8,X3] :
      ( ~ class_Divides_Osemiring__div(X3)
      | c_Ring__and__Field_Odvd__class_Odvd(X8,X5,X3)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X8,c_Divides_Odiv__class_Omod(X5,X4,X3),X3)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X8,X4,X3) ),
    file('<stdin>',cls_dvd__mod__iff_0) ).

fof(c_0_217,axiom,
    ! [X4,X5,X8,X3] :
      ( ~ class_Divides_Osemiring__div(X3)
      | c_Ring__and__Field_Odvd__class_Odvd(X8,X5,X3)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X8,X4,X3)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X8,c_Divides_Odiv__class_Omod(X5,X4,X3),X3) ),
    file('<stdin>',cls_dvd__mod__imp__dvd_0) ).

fof(c_0_218,axiom,
    ! [X16,X6,X7,X17,X3] :
      ( ~ class_OrderedGroup_Oab__group__add(X3)
      | c_HOL_Oplus__class_Oplus(X7,c_HOL_Oplus__class_Oplus(X6,X16,X3),X3) != c_HOL_Oplus__class_Oplus(X6,X17,X3)
      | c_HOL_Oplus__class_Oplus(X7,X16,X3) = X17 ),
    file('<stdin>',cls_add__cancel__21_0) ).

fof(c_0_219,axiom,
    ! [X8,X9,X10] :
      ( c_HOL_Oplus__class_Oplus(X10,c_HOL_Ominus__class_Ominus(X9,X8,tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X10,X9,tc_nat),X8,tc_nat)
      | ~ c_lessequals(X8,X9,tc_nat) ),
    file('<stdin>',cls_add__diff__assoc_0) ).

fof(c_0_220,axiom,
    ! [X8,X9,X10] :
      ( c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X9,X8,tc_nat),X10,tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X9,X10,tc_nat),X8,tc_nat)
      | ~ c_lessequals(X8,X9,tc_nat) ),
    file('<stdin>',cls_add__diff__assoc2_0) ).

fof(c_0_221,axiom,
    ! [X8,X9,X10] :
      ( c_HOL_Ominus__class_Ominus(X10,c_HOL_Ominus__class_Ominus(X9,X8,tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X10,X8,tc_nat),X9,tc_nat)
      | ~ c_lessequals(X8,X9,tc_nat) ),
    file('<stdin>',cls_diff__diff__right_0) ).

fof(c_0_222,axiom,
    ! [X8,X9,X10] :
      ( c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X10,X9,tc_nat),X8,tc_nat) = c_HOL_Oplus__class_Oplus(X10,c_HOL_Ominus__class_Ominus(X9,X8,tc_nat),tc_nat)
      | ~ c_lessequals(X8,X9,tc_nat) ),
    file('<stdin>',cls_diff__add__assoc_0) ).

fof(c_0_223,axiom,
    ! [X8,X9,X10] :
      ( c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X9,X10,tc_nat),X8,tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X9,X8,tc_nat),X10,tc_nat)
      | ~ c_lessequals(X8,X9,tc_nat) ),
    file('<stdin>',cls_diff__add__assoc2_0) ).

fof(c_0_224,axiom,
    ! [X1,X2,X3] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
      | c_lessequals(X1,c_HOL_Ozero__class_Ozero(X3),X3)
      | c_lessequals(c_HOL_Ozero__class_Ozero(X3),X1,X3)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),c_HOL_Otimes__class_Otimes(X2,X1,X3),X3) ),
    file('<stdin>',cls_zero__le__mult__iff_3) ).

fof(c_0_225,axiom,
    ! [X1,X2,X3] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
      | c_lessequals(X2,c_HOL_Ozero__class_Ozero(X3),X3)
      | c_lessequals(c_HOL_Ozero__class_Ozero(X3),X1,X3)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),c_HOL_Otimes__class_Otimes(X2,X1,X3),X3) ),
    file('<stdin>',cls_zero__le__mult__iff_2) ).

fof(c_0_226,axiom,
    ! [X1,X2,X3] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
      | c_lessequals(X1,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),c_HOL_Otimes__class_Otimes(X2,X1,X3),X3) ),
    file('<stdin>',cls_zero__le__mult__iff_1) ).

fof(c_0_227,axiom,
    ! [X1,X2,X3] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
      | c_lessequals(X2,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),c_HOL_Otimes__class_Otimes(X2,X1,X3),X3) ),
    file('<stdin>',cls_zero__le__mult__iff_0) ).

fof(c_0_228,axiom,
    ! [X1,X2,X3] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
      | 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(X2,X1,X3),c_HOL_Ozero__class_Ozero(X3),X3) ),
    file('<stdin>',cls_mult__le__0__iff_3) ).

fof(c_0_229,axiom,
    ! [X1,X2,X3] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
      | 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(X2,X1,X3),c_HOL_Ozero__class_Ozero(X3),X3) ),
    file('<stdin>',cls_mult__le__0__iff_2) ).

fof(c_0_230,axiom,
    ! [X1,X2,X3] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
      | 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(X2,X1,X3),c_HOL_Ozero__class_Ozero(X3),X3) ),
    file('<stdin>',cls_mult__le__0__iff_1) ).

fof(c_0_231,axiom,
    ! [X1,X2,X3] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
      | 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(X2,X1,X3),c_HOL_Ozero__class_Ozero(X3),X3) ),
    file('<stdin>',cls_mult__le__0__iff_0) ).

fof(c_0_232,axiom,
    ! [X4,X5] :
      ( c_lessequals(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Otimes__class_Otimes(X5,X4,tc_nat),tc_nat)
      | ~ 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)),X5,tc_nat) ),
    file('<stdin>',cls_one__le__mult__iff_2) ).

fof(c_0_233,axiom,
    ! [X4,X5] :
      ( c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Otimes__class_Otimes(X5,X4,tc_nat),tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X5,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X4,tc_nat) ),
    file('<stdin>',cls_one__less__mult_0) ).

fof(c_0_234,axiom,
    ! [X16,X6,X7,X3] :
      ( ~ class_Orderings_Olinorder(X3)
      | c_HOL_Oord__class_Oless(X6,X16,X3)
      | c_HOL_Oord__class_Oless(X7,X16,X3)
      | ~ c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omin(X7,X6,X3),X16,X3) ),
    file('<stdin>',cls_min__less__iff__disj_0) ).

fof(c_0_235,axiom,
    ! [X16,X6,X7,X3] :
      ( ~ class_Orderings_Olinorder(X3)
      | c_lessequals(X6,X16,X3)
      | c_lessequals(X7,X16,X3)
      | ~ c_lessequals(c_Orderings_Oord__class_Omin(X7,X6,X3),X16,X3) ),
    file('<stdin>',cls_min__le__iff__disj_0) ).

fof(c_0_236,axiom,
    ! [X4,X5,X8] :
      ( c_lessequals(c_HOL_Otimes__class_Otimes(c_Suc(X8),X5,tc_nat),c_HOL_Otimes__class_Otimes(c_Suc(X8),X4,tc_nat),tc_nat)
      | ~ c_lessequals(X5,X4,tc_nat) ),
    file('<stdin>',cls_Suc__mult__le__cancel1_1) ).

fof(c_0_237,axiom,
    ! [X4,X5,X8] :
      ( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Suc(X8),X5,tc_nat),c_HOL_Otimes__class_Otimes(c_Suc(X8),X4,tc_nat),tc_nat)
      | ~ c_HOL_Oord__class_Oless(X5,X4,tc_nat) ),
    file('<stdin>',cls_Suc__mult__less__cancel1_1) ).

fof(c_0_238,axiom,
    ! [X1,X2,X3] :
      ( ~ class_OrderedGroup_Opordered__comm__monoid__add(X3)
      | c_lessequals(c_HOL_Oplus__class_Oplus(X2,X1,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) ),
    file('<stdin>',cls_add__nonpos__nonpos_0) ).

fof(c_0_239,axiom,
    ! [X1,X2,X3] :
      ( ~ class_OrderedGroup_Opordered__comm__monoid__add(X3)
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_HOL_Oplus__class_Oplus(X2,X1,X3),X3)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X1,X3)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3) ),
    file('<stdin>',cls_add__pos__pos_0) ).

fof(c_0_240,axiom,
    ! [X1,X2,X3] :
      ( ~ class_OrderedGroup_Opordered__comm__monoid__add(X3)
      | c_lessequals(c_HOL_Ozero__class_Ozero(X3),c_HOL_Oplus__class_Oplus(X2,X1,X3),X3)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X1,X3)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X2,X3) ),
    file('<stdin>',cls_add__nonneg__nonneg_0) ).

fof(c_0_241,axiom,
    ! [X1,X2,X3] :
      ( ~ class_OrderedGroup_Opordered__comm__monoid__add(X3)
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_HOL_Oplus__class_Oplus(X2,X1,X3),X3)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X1,X3)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3) ),
    file('<stdin>',cls_add__pos__nonneg_0) ).

fof(c_0_242,axiom,
    ! [X1,X2,X3] :
      ( ~ class_OrderedGroup_Opordered__comm__monoid__add(X3)
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_HOL_Oplus__class_Oplus(X2,X1,X3),X3)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X1,X3)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X2,X3) ),
    file('<stdin>',cls_add__nonneg__pos_0) ).

fof(c_0_243,axiom,
    ! [X1,X2,X3] :
      ( ~ class_Ring__and__Field_Opordered__cancel__semiring(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),X2,X3) ),
    file('<stdin>',cls_mult__nonneg__nonpos2_0) ).

fof(c_0_244,axiom,
    ! [X1,X2,X3] :
      ( ~ class_Ring__and__Field_Opordered__cancel__semiring(X3)
      | c_lessequals(c_HOL_Otimes__class_Otimes(X2,X1,X3),c_HOL_Ozero__class_Ozero(X3),X3)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X1,X3)
      | ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X3),X3) ),
    file('<stdin>',cls_mult__nonpos__nonneg_0) ).

fof(c_0_245,axiom,
    ! [X1,X2,X3] :
      ( ~ class_Ring__and__Field_Opordered__cancel__semiring(X3)
      | c_lessequals(c_HOL_Otimes__class_Otimes(X2,X1,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),X2,X3) ),
    file('<stdin>',cls_mult__nonneg__nonpos_0) ).

fof(c_0_246,axiom,
    ! [X1,X2,X3] :
      ( ~ class_Ring__and__Field_Opordered__cancel__semiring(X3)
      | c_lessequals(c_HOL_Otimes__class_Otimes(X2,X1,X3),c_HOL_Ozero__class_Ozero(X3),X3)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X1,X3)
      | ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X3),X3) ),
    file('<stdin>',cls_split__mult__neg__le_1) ).

fof(c_0_247,axiom,
    ! [X1,X2,X3] :
      ( ~ class_Ring__and__Field_Opordered__cancel__semiring(X3)
      | c_lessequals(c_HOL_Otimes__class_Otimes(X2,X1,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),X2,X3) ),
    file('<stdin>',cls_split__mult__neg__le_0) ).

fof(c_0_248,axiom,
    ! [X1,X2,X3] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
      | c_lessequals(c_HOL_Otimes__class_Otimes(X2,X1,X3),c_HOL_Ozero__class_Ozero(X3),X3)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X1,X3)
      | ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X3),X3) ),
    file('<stdin>',cls_mult__le__0__iff_5) ).

fof(c_0_249,axiom,
    ! [X1,X2,X3] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
      | c_lessequals(c_HOL_Otimes__class_Otimes(X2,X1,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),X2,X3) ),
    file('<stdin>',cls_mult__le__0__iff_4) ).

fof(c_0_250,axiom,
    ! [X1,X2,X3] :
      ( ~ class_OrderedGroup_Opordered__comm__monoid__add(X3)
      | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X2,X1,X3),c_HOL_Ozero__class_Ozero(X3),X3)
      | ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X3),X3)
      | ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X3),X3) ),
    file('<stdin>',cls_add__neg__neg_0) ).

fof(c_0_251,axiom,
    ! [X1,X2,X3] :
      ( ~ class_Ring__and__Field_Opordered__cancel__semiring(X3)
      | c_lessequals(c_HOL_Ozero__class_Ozero(X3),c_HOL_Otimes__class_Otimes(X2,X1,X3),X3)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X1,X3)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X2,X3) ),
    file('<stdin>',cls_mult__nonneg__nonneg_0) ).

fof(c_0_252,axiom,
    ! [X1,X2,X3] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
      | c_lessequals(c_HOL_Ozero__class_Ozero(X3),c_HOL_Otimes__class_Otimes(X2,X1,X3),X3)
      | ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X3),X3)
      | ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X3),X3) ),
    file('<stdin>',cls_zero__le__mult__iff_5) ).

fof(c_0_253,axiom,
    ! [X1,X2,X3] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
      | c_lessequals(c_HOL_Ozero__class_Ozero(X3),c_HOL_Otimes__class_Otimes(X2,X1,X3),X3)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X1,X3)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X2,X3) ),
    file('<stdin>',cls_zero__le__mult__iff_4) ).

fof(c_0_254,axiom,
    ! [X1,X2,X3] :
      ( ~ class_Ring__and__Field_Opordered__ring(X3)
      | c_lessequals(c_HOL_Ozero__class_Ozero(X3),c_HOL_Otimes__class_Otimes(X2,X1,X3),X3)
      | ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X3),X3)
      | ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X3),X3) ),
    file('<stdin>',cls_mult__nonpos__nonpos_0) ).

fof(c_0_255,axiom,
    ! [X1,X2,X3] :
      ( ~ class_Ring__and__Field_Opordered__ring(X3)
      | c_lessequals(c_HOL_Ozero__class_Ozero(X3),c_HOL_Otimes__class_Otimes(X2,X1,X3),X3)
      | ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X3),X3)
      | ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X3),X3) ),
    file('<stdin>',cls_split__mult__pos__le_1) ).

fof(c_0_256,axiom,
    ! [X1,X2,X3] :
      ( ~ class_Ring__and__Field_Opordered__ring(X3)
      | c_lessequals(c_HOL_Ozero__class_Ozero(X3),c_HOL_Otimes__class_Otimes(X2,X1,X3),X3)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X1,X3)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X2,X3) ),
    file('<stdin>',cls_split__mult__pos__le_0) ).

fof(c_0_257,axiom,
    ! [X1,X2,X3] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_HOL_Otimes__class_Otimes(X2,X1,X3),X3)
      | ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X3),X3)
      | ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X3),X3) ),
    file('<stdin>',cls_mult__neg__neg_0) ).

fof(c_0_258,axiom,
    ! [X1,X2,X3] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X3)
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_HOL_Otimes__class_Otimes(X2,X1,X3),X3)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X1,X3)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3) ),
    file('<stdin>',cls_mult__pos__pos_0) ).

fof(c_0_259,axiom,
    ! [X1,X2,X3] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X3)
      | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Ozero__class_Ozero(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),X2,X3) ),
    file('<stdin>',cls_mult__pos__neg2_0) ).

fof(c_0_260,axiom,
    ! [X1,X2,X3] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X3)
      | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X1,X3),c_HOL_Ozero__class_Ozero(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),X2,X3) ),
    file('<stdin>',cls_mult__pos__neg_0) ).

fof(c_0_261,axiom,
    ! [X1,X2,X3] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X3)
      | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X1,X3),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(X2,c_HOL_Ozero__class_Ozero(X3),X3) ),
    file('<stdin>',cls_mult__neg__pos_0) ).

fof(c_0_262,axiom,
    ! [X1,X2,X3] :
      ( ~ class_OrderedGroup_Opordered__comm__monoid__add(X3)
      | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X2,X1,X3),c_HOL_Ozero__class_Ozero(X3),X3)
      | ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X3),X3)
      | ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X3),X3) ),
    file('<stdin>',cls_add__nonpos__neg_0) ).

fof(c_0_263,axiom,
    ! [X1,X2,X3] :
      ( ~ class_OrderedGroup_Opordered__comm__monoid__add(X3)
      | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X2,X1,X3),c_HOL_Ozero__class_Ozero(X3),X3)
      | ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X3),X3)
      | ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X3),X3) ),
    file('<stdin>',cls_add__neg__nonpos_0) ).

fof(c_0_264,axiom,
    ! [X4,X5] :
      ( 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),X5,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oplus__class_Oplus(X5,X4,tc_nat),tc_nat) ),
    file('<stdin>',cls_add__gr__0_0) ).

fof(c_0_265,axiom,
    ! [X5] : c_lessequals(X5,c_HOL_Otimes__class_Otimes(X5,c_HOL_Otimes__class_Otimes(X5,X5,tc_nat),tc_nat),tc_nat),
    file('<stdin>',cls_le__cube_0) ).

fof(c_0_266,axiom,
    ! [X4,X5] :
      ( c_HOL_Oord__class_Oless(X4,c_HOL_Otimes__class_Otimes(X5,X4,tc_nat),tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X5,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X4,tc_nat) ),
    file('<stdin>',cls_n__less__m__mult__n_0) ).

fof(c_0_267,axiom,
    ! [X4,X5] :
      ( c_HOL_Oord__class_Oless(X4,c_HOL_Otimes__class_Otimes(X4,X5,tc_nat),tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X5,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X4,tc_nat) ),
    file('<stdin>',cls_n__less__n__mult__m_0) ).

fof(c_0_268,axiom,
    ! [X15,X1,X2,X3] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
      | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X15,X2,X3),c_HOL_Oplus__class_Oplus(X15,X1,X3),X3)
      | ~ c_HOL_Oord__class_Oless(X2,X1,X3) ),
    file('<stdin>',cls_add__less__cancel__left_1) ).

fof(c_0_269,axiom,
    ! [X15,X1,X2,X3] :
      ( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X3)
      | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X15,X2,X3),c_HOL_Oplus__class_Oplus(X15,X1,X3),X3)
      | ~ c_HOL_Oord__class_Oless(X2,X1,X3) ),
    file('<stdin>',cls_add__strict__left__mono_0) ).

fof(c_0_270,axiom,
    ! [X15,X1,X2,X3] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
      | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X2,X15,X3),c_HOL_Oplus__class_Oplus(X1,X15,X3),X3)
      | ~ c_HOL_Oord__class_Oless(X2,X1,X3) ),
    file('<stdin>',cls_add__less__cancel__right_1) ).

fof(c_0_271,axiom,
    ! [X15,X1,X2,X3] :
      ( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X3)
      | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X2,X15,X3),c_HOL_Oplus__class_Oplus(X1,X15,X3),X3)
      | ~ c_HOL_Oord__class_Oless(X2,X1,X3) ),
    file('<stdin>',cls_add__strict__right__mono_0) ).

fof(c_0_272,axiom,
    ! [X15,X1,X2,X3] :
      ( ~ class_Ring__and__Field_Oidom(X3)
      | c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X2,X15,X3),c_HOL_Otimes__class_Otimes(X1,X15,X3),X3)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X1,X3) ),
    file('<stdin>',cls_dvd__mult__cancel__right_2) ).

fof(c_0_273,axiom,
    ! [X15,X1,X2,X3] :
      ( ~ class_Ring__and__Field_Oidom(X3)
      | c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X15,X2,X3),c_HOL_Otimes__class_Otimes(X15,X1,X3),X3)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X1,X3) ),
    file('<stdin>',cls_dvd__mult__cancel__left_2) ).

fof(c_0_274,axiom,
    ! [X15,X1,X2,X3] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
      | c_lessequals(c_HOL_Oplus__class_Oplus(X2,X15,X3),c_HOL_Oplus__class_Oplus(X1,X15,X3),X3)
      | ~ c_lessequals(X2,X1,X3) ),
    file('<stdin>',cls_add__le__cancel__right_1) ).

fof(c_0_275,axiom,
    ! [X15,X1,X2,X3] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
      | c_lessequals(c_HOL_Oplus__class_Oplus(X15,X2,X3),c_HOL_Oplus__class_Oplus(X15,X1,X3),X3)
      | ~ c_lessequals(X2,X1,X3) ),
    file('<stdin>',cls_add__le__cancel__left_1) ).

fof(c_0_276,axiom,
    ! [X15,X1,X2,X3] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X3)
      | c_lessequals(c_HOL_Oplus__class_Oplus(X2,X15,X3),c_HOL_Oplus__class_Oplus(X1,X15,X3),X3)
      | ~ c_lessequals(X2,X1,X3) ),
    file('<stdin>',cls_add__right__mono_0) ).

fof(c_0_277,axiom,
    ! [X15,X1,X2,X3] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X3)
      | c_lessequals(c_HOL_Oplus__class_Oplus(X15,X2,X3),c_HOL_Oplus__class_Oplus(X15,X1,X3),X3)
      | ~ c_lessequals(X2,X1,X3) ),
    file('<stdin>',cls_add__left__mono_0) ).

fof(c_0_278,axiom,
    ! [X16,X6,X7] :
      ( ~ c_Ring__and__Field_Odvd__class_Odvd(X16,X7,tc_nat)
      | c_Ring__and__Field_Odvd__class_Odvd(X16,X6,tc_nat)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X6,X16,tc_nat)
      | c_Ring__and__Field_Odvd__class_Odvd(X6,X7,tc_nat)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X7,X6,tc_nat) ),
    file('<stdin>',cls_dvd_Oless__trans_1) ).

fof(c_0_279,axiom,
    ! [X15,X1,X2,X3] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
      | ~ class_OrderedGroup_Ocomm__monoid__add(X3)
      | c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(X2,X15,X3),X3)
      | ~ c_lessequals(X1,X15,X3)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3) ),
    file('<stdin>',cls_add__strict__increasing_0) ).

fof(c_0_280,axiom,
    ! [X15,X1,X2,X3] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
      | ~ class_OrderedGroup_Ocomm__monoid__add(X3)
      | c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(X2,X15,X3),X3)
      | ~ c_HOL_Oord__class_Oless(X1,X15,X3)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X2,X3) ),
    file('<stdin>',cls_add__strict__increasing2_0) ).

fof(c_0_281,axiom,
    ! [X15,X1,X2,X3] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
      | ~ class_OrderedGroup_Ocomm__monoid__add(X3)
      | c_lessequals(X1,c_HOL_Oplus__class_Oplus(X2,X15,X3),X3)
      | ~ c_lessequals(X1,X15,X3)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X2,X3) ),
    file('<stdin>',cls_add__increasing_0) ).

fof(c_0_282,axiom,
    ! [X15,X1,X2,X3] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
      | ~ class_OrderedGroup_Ocomm__monoid__add(X3)
      | c_lessequals(X1,c_HOL_Oplus__class_Oplus(X2,X15,X3),X3)
      | ~ c_lessequals(X1,X2,X3)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X15,X3) ),
    file('<stdin>',cls_add__increasing2_0) ).

fof(c_0_283,axiom,
    ! [X15,X1,X2,X3] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X3)
      | c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(X2,X15,X3),X3)
      | ~ c_HOL_Oord__class_Oless(X1,X15,X3)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3) ),
    file('<stdin>',cls_pos__add__strict_0) ).

fof(c_0_284,axiom,
    ! [X4,X5,X29] :
      ( c_lessequals(c_HOL_Ominus__class_Ominus(X29,X4,tc_nat),c_HOL_Ominus__class_Ominus(X29,X5,tc_nat),tc_nat)
      | ~ c_lessequals(X5,X4,tc_nat) ),
    file('<stdin>',cls_diff__le__mono2_0) ).

fof(c_0_285,axiom,
    ! [X4,X5,X29] :
      ( c_lessequals(c_HOL_Ominus__class_Ominus(X5,X29,tc_nat),c_HOL_Ominus__class_Ominus(X4,X29,tc_nat),tc_nat)
      | ~ c_lessequals(X5,X4,tc_nat) ),
    file('<stdin>',cls_diff__le__mono_0) ).

fof(c_0_286,axiom,
    ! [X8,X9,X10] :
      ( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X10,X8,tc_nat),c_HOL_Oplus__class_Oplus(X9,X8,tc_nat),tc_nat)
      | ~ c_HOL_Oord__class_Oless(X10,X9,tc_nat) ),
    file('<stdin>',cls_add__less__mono1_0) ).

fof(c_0_287,axiom,
    ! [X4,X5,X8] :
      ( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X8,X5,tc_nat),c_HOL_Oplus__class_Oplus(X8,X4,tc_nat),tc_nat)
      | ~ c_HOL_Oord__class_Oless(X5,X4,tc_nat) ),
    file('<stdin>',cls_nat__add__left__cancel__less_1) ).

fof(c_0_288,axiom,
    ! [X4,X5,X8] :
      ( c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X8,X5,tc_nat),c_HOL_Otimes__class_Otimes(X8,X4,tc_nat),tc_nat)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X5,X4,tc_nat) ),
    file('<stdin>',cls_nat__mult__dvd__cancel__disj_2) ).

fof(c_0_289,axiom,
    ! [X8,X9,X10] :
      ( c_lessequals(c_HOL_Otimes__class_Otimes(X10,X8,tc_nat),c_HOL_Otimes__class_Otimes(X9,X8,tc_nat),tc_nat)
      | ~ c_lessequals(X10,X9,tc_nat) ),
    file('<stdin>',cls_mult__le__mono1_0) ).

fof(c_0_290,axiom,
    ! [X8,X9,X10] :
      ( c_lessequals(c_HOL_Otimes__class_Otimes(X8,X10,tc_nat),c_HOL_Otimes__class_Otimes(X8,X9,tc_nat),tc_nat)
      | ~ c_lessequals(X10,X9,tc_nat) ),
    file('<stdin>',cls_mult__le__mono2_0) ).

fof(c_0_291,axiom,
    ! [X4,X5,X8] :
      ( c_lessequals(c_HOL_Otimes__class_Otimes(X8,X5,tc_nat),c_HOL_Otimes__class_Otimes(X8,X4,tc_nat),tc_nat)
      | ~ c_lessequals(X5,X4,tc_nat) ),
    file('<stdin>',cls_mult__le__cancel1_2) ).

fof(c_0_292,axiom,
    ! [X4,X5,X8] :
      ( c_lessequals(c_HOL_Otimes__class_Otimes(X5,X8,tc_nat),c_HOL_Otimes__class_Otimes(X4,X8,tc_nat),tc_nat)
      | ~ c_lessequals(X5,X4,tc_nat) ),
    file('<stdin>',cls_mult__le__cancel2_2) ).

fof(c_0_293,axiom,
    ! [X8,X9,X10] :
      ( c_lessequals(c_HOL_Oplus__class_Oplus(X10,X8,tc_nat),c_HOL_Oplus__class_Oplus(X9,X8,tc_nat),tc_nat)
      | ~ c_lessequals(X10,X9,tc_nat) ),
    file('<stdin>',cls_add__le__mono1_0) ).

fof(c_0_294,axiom,
    ! [X4,X5,X8] :
      ( c_lessequals(c_HOL_Oplus__class_Oplus(X8,X5,tc_nat),c_HOL_Oplus__class_Oplus(X8,X4,tc_nat),tc_nat)
      | ~ c_lessequals(X5,X4,tc_nat) ),
    file('<stdin>',cls_nat__add__left__cancel__le_1) ).

fof(c_0_295,axiom,
    ! [X16,X6,X7,X3] :
      ( ~ class_Ring__and__Field_Ocomm__ring__1(X3)
      | c_Ring__and__Field_Odvd__class_Odvd(X7,c_HOL_Ominus__class_Ominus(X6,X16,X3),X3)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X7,X16,X3)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X7,X6,X3) ),
    file('<stdin>',cls_dvd__diff_0) ).

fof(c_0_296,axiom,
    ! [X16,X6,X7,X3] :
      ( ~ class_Orderings_Olinorder(X3)
      | c_HOL_Oord__class_Oless(X16,c_Orderings_Oord__class_Omin(X7,X6,X3),X3)
      | ~ c_HOL_Oord__class_Oless(X16,X6,X3)
      | ~ c_HOL_Oord__class_Oless(X16,X7,X3) ),
    file('<stdin>',cls_min__less__iff__conj_2) ).

fof(c_0_297,axiom,
    ! [X15,X1,X2,X3] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
      | c_Ring__and__Field_Odvd__class_Odvd(X2,c_HOL_Oplus__class_Oplus(X1,X15,X3),X3)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X15,X3)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X1,X3) ),
    file('<stdin>',cls_dvd__add_0) ).

fof(c_0_298,axiom,
    ! [X7,X1,X2,X3] :
      ( ~ class_Orderings_Olinorder(X3)
      | c_lessequals(X7,c_Orderings_Oord__class_Omin(X2,X1,X3),X3)
      | ~ c_lessequals(X7,X1,X3)
      | ~ c_lessequals(X7,X2,X3) ),
    file('<stdin>',cls_min__max_Ole__infI_0) ).

fof(c_0_299,axiom,
    ! [X16,X6,X7,X3] :
      ( ~ class_Orderings_Olinorder(X3)
      | c_lessequals(X7,c_Orderings_Oord__class_Omin(X6,X16,X3),X3)
      | ~ c_lessequals(X7,X16,X3)
      | ~ c_lessequals(X7,X6,X3) ),
    file('<stdin>',cls_min__max_Ole__inf__iff_2) ).

fof(c_0_300,axiom,
    ! [X16,X6,X7,X3] :
      ( ~ class_Orderings_Olinorder(X3)
      | c_lessequals(X7,c_Orderings_Oord__class_Omin(X6,X16,X3),X3)
      | ~ c_lessequals(X7,X16,X3)
      | ~ c_lessequals(X7,X6,X3) ),
    file('<stdin>',cls_min__max_Oinf__greatest_0) ).

fof(c_0_301,axiom,
    ! [X4,X5,X8,X3] :
      ( ~ class_Divides_Osemiring__div(X3)
      | c_Ring__and__Field_Odvd__class_Odvd(X8,c_Divides_Odiv__class_Omod(X5,X4,X3),X3)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X8,X4,X3)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X8,X5,X3) ),
    file('<stdin>',cls_dvd__mod_0) ).

fof(c_0_302,axiom,
    ! [X4,X5,X8,X3] :
      ( ~ class_Divides_Osemiring__div(X3)
      | c_Ring__and__Field_Odvd__class_Odvd(X8,c_Divides_Odiv__class_Omod(X5,X4,X3),X3)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X8,X5,X3)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X8,X4,X3) ),
    file('<stdin>',cls_dvd__mod__iff_1) ).

fof(c_0_303,axiom,
    ! [X1,X2,X3] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X3)
      | c_HOL_Oabs__class_Oabs(c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(X2,X3),c_HOL_Oabs__class_Oabs(X1,X3),X3),X3) = c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(X2,X3),c_HOL_Oabs__class_Oabs(X1,X3),X3) ),
    file('<stdin>',cls_abs__add__abs_0) ).

fof(c_0_304,axiom,
    ! [X4,X5] :
      ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Otimes__class_Otimes(X5,X4,tc_nat),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),X5,tc_nat) ),
    file('<stdin>',cls_nat__0__less__mult__iff_2) ).

fof(c_0_305,axiom,
    ! [X4,X5,X8] :
      ( c_HOL_Ominus__class_Ominus(X5,X8,tc_nat) != c_HOL_Ominus__class_Ominus(X4,X8,tc_nat)
      | ~ c_lessequals(X8,X4,tc_nat)
      | ~ c_lessequals(X8,X5,tc_nat)
      | X5 = X4 ),
    file('<stdin>',cls_eq__diff__iff_0) ).

fof(c_0_306,axiom,
    ! [X4,X5] :
      ( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X5,X4,tc_nat),X5,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X5,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat) ),
    file('<stdin>',cls_diff__less_0) ).

fof(c_0_307,axiom,
    ! [X2,X3] :
      ( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
      | c_lessequals(X2,c_HOL_Ozero__class_Ozero(X3),X3)
      | ~ c_lessequals(c_HOL_Oplus__class_Oplus(X2,X2,X3),c_HOL_Ozero__class_Ozero(X3),X3) ),
    file('<stdin>',cls_double__add__le__zero__iff__single__add__le__zero_0) ).

fof(c_0_308,axiom,
    ! [X2,X3] :
      ( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
      | c_lessequals(c_HOL_Ozero__class_Ozero(X3),X2,X3)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),c_HOL_Oplus__class_Oplus(X2,X2,X3),X3) ),
    file('<stdin>',cls_zero__le__double__add__iff__zero__le__single__add_0) ).

fof(c_0_309,axiom,
    ! [X2,X3] :
      ( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_HOL_Oplus__class_Oplus(X2,X2,X3),X3) ),
    file('<stdin>',cls_zero__less__double__add__iff__zero__less__single__add_0) ).

fof(c_0_310,axiom,
    ! [X2,X3] :
      ( ~ class_Ring__and__Field_Oordered__idom(X3)
      | c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X3),X3)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X2,X2,X3),c_HOL_Ozero__class_Ozero(X3),X3) ),
    file('<stdin>',cls_even__less__0__iff_0) ).

fof(c_0_311,axiom,
    ! [X2,X3] :
      ( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
      | c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X3),X3)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X2,X2,X3),c_HOL_Ozero__class_Ozero(X3),X3) ),
    file('<stdin>',cls_double__add__less__zero__iff__single__less__zero_0) ).

fof(c_0_312,axiom,
    ! [X4,X5,X8] : c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(c_Suc(X5),X4,tc_nat),c_Suc(X8),tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X5,X4,tc_nat),X8,tc_nat),
    file('<stdin>',cls_Suc__diff__diff_0) ).

fof(c_0_313,axiom,
    ! [X4,X5] :
      ( c_lessequals(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X5,tc_nat)
      | ~ c_lessequals(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Otimes__class_Otimes(X5,X4,tc_nat),tc_nat) ),
    file('<stdin>',cls_one__le__mult__iff_0) ).

fof(c_0_314,axiom,
    ! [X4,X5] :
      ( 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(X5,X4,tc_nat),tc_nat) ),
    file('<stdin>',cls_one__le__mult__iff_1) ).

fof(c_0_315,axiom,
    ! [X16,X6,X7,X3] :
      ( ~ class_Orderings_Olinorder(X3)
      | c_Orderings_Oord__class_Omin(X7,c_Orderings_Oord__class_Omin(X6,X16,X3),X3) = c_Orderings_Oord__class_Omin(X6,c_Orderings_Oord__class_Omin(X7,X16,X3),X3) ),
    file('<stdin>',cls_min__max_Oinf__left__commute_0) ).

fof(c_0_316,axiom,
    ! [X16,X6,X7,X3] :
      ( ~ class_Orderings_Olinorder(X3)
      | c_Orderings_Oord__class_Omin(c_Orderings_Oord__class_Omin(X7,X6,X3),X16,X3) = c_Orderings_Oord__class_Omin(X7,c_Orderings_Oord__class_Omin(X6,X16,X3),X3) ),
    file('<stdin>',cls_min__max_Oinf__assoc_0) ).

fof(c_0_317,axiom,
    ! [X15,X1,X2,X3] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
      | c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X2,X1,X3),X15,X3) = c_HOL_Oplus__class_Oplus(X2,c_HOL_Oplus__class_Oplus(X1,X15,X3),X3) ),
    file('<stdin>',cls_class__semiring_Osemiring__rules_I21_J_0) ).

fof(c_0_318,axiom,
    ! [X20,X15,X2,X3] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
      | c_HOL_Oplus__class_Oplus(X2,c_HOL_Oplus__class_Oplus(X15,X20,X3),X3) = c_HOL_Oplus__class_Oplus(X15,c_HOL_Oplus__class_Oplus(X2,X20,X3),X3) ),
    file('<stdin>',cls_class__semiring_Osemiring__rules_I22_J_0) ).

fof(c_0_319,axiom,
    ! [X15,X1,X2,X3] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
      | c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X2,X1,X3),X15,X3) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X2,X15,X3),X1,X3) ),
    file('<stdin>',cls_class__semiring_Osemiring__rules_I23_J_0) ).

fof(c_0_320,axiom,
    ! [X20,X15,X2,X3] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
      | c_HOL_Oplus__class_Oplus(X2,c_HOL_Oplus__class_Oplus(X15,X20,X3),X3) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X2,X15,X3),X20,X3) ),
    file('<stdin>',cls_class__semiring_Osemiring__rules_I25_J_0) ).

fof(c_0_321,axiom,
    ! [X15,X1,X2,X3] :
      ( ~ class_OrderedGroup_Oab__semigroup__add(X3)
      | c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X2,X1,X3),X15,X3) = c_HOL_Oplus__class_Oplus(X2,c_HOL_Oplus__class_Oplus(X1,X15,X3),X3) ),
    file('<stdin>',cls_ab__semigroup__add__class_Oadd__ac_I1_J_0) ).

fof(c_0_322,axiom,
    ! [X16,X6,X7,X3] :
      ( ~ class_OrderedGroup_Oab__group__add(X3)
      | c_HOL_Oplus__class_Oplus(X7,c_HOL_Oplus__class_Oplus(X6,X16,X3),X3) = c_HOL_Oplus__class_Oplus(X6,c_HOL_Oplus__class_Oplus(X7,X16,X3),X3) ),
    file('<stdin>',cls_add__cancel__21_1) ).

fof(c_0_323,axiom,
    ! [X16,X6,X7,X3] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
      | c_HOL_Oplus__class_Oplus(X7,c_HOL_Oplus__class_Oplus(X6,X16,X3),X3) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X7,X6,X3),X16,X3) ),
    file('<stdin>',cls_class__semiring_Oadd__a_0) ).

fof(c_0_324,axiom,
    ! [X16,X6,X7,X3] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
      | c_HOL_Otimes__class_Otimes(X7,c_HOL_Otimes__class_Otimes(X6,X16,X3),X3) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X7,X6,X3),X16,X3) ),
    file('<stdin>',cls_class__semiring_Omul__a_0) ).

fof(c_0_325,axiom,
    ! [X11,X12,X14,X3] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
      | c_HOL_Otimes__class_Otimes(X14,c_HOL_Otimes__class_Otimes(X12,X11,X3),X3) = c_HOL_Otimes__class_Otimes(X12,c_HOL_Otimes__class_Otimes(X14,X11,X3),X3) ),
    file('<stdin>',cls_class__semiring_Osemiring__rules_I19_J_0) ).

fof(c_0_326,axiom,
    ! [X11,X12,X14,X3] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
      | c_HOL_Otimes__class_Otimes(X14,c_HOL_Otimes__class_Otimes(X12,X11,X3),X3) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X14,X12,X3),X11,X3) ),
    file('<stdin>',cls_class__semiring_Osemiring__rules_I18_J_0) ).

fof(c_0_327,axiom,
    ! [X12,X13,X14,X3] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
      | c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X14,X13,X3),X12,X3) = c_HOL_Otimes__class_Otimes(X14,c_HOL_Otimes__class_Otimes(X13,X12,X3),X3) ),
    file('<stdin>',cls_class__semiring_Osemiring__rules_I17_J_0) ).

fof(c_0_328,axiom,
    ! [X12,X13,X14,X3] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
      | c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X14,X13,X3),X12,X3) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X14,X12,X3),X13,X3) ),
    file('<stdin>',cls_class__semiring_Osemiring__rules_I16_J_0) ).

fof(c_0_329,axiom,
    ! [X15,X1,X2,X3] :
      ( ~ class_OrderedGroup_Oab__semigroup__mult(X3)
      | c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X2,X1,X3),X15,X3) = c_HOL_Otimes__class_Otimes(X2,c_HOL_Otimes__class_Otimes(X1,X15,X3),X3) ),
    file('<stdin>',cls_ab__semigroup__mult__class_Omult__ac_I1_J_0) ).

fof(c_0_330,axiom,
    ! [X15,X1,X2,X3] :
      ( ~ class_OrderedGroup_Ocomm__monoid__add(X3)
      | c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X2,X1,X3),X15,X3) = c_HOL_Oplus__class_Oplus(X2,c_HOL_Oplus__class_Oplus(X1,X15,X3),X3) ),
    file('<stdin>',cls_comm__monoid__add_Omult__assoc_0) ).

fof(c_0_331,axiom,
    ! [X15,X1,X2,X3] :
      ( ~ class_OrderedGroup_Ocomm__monoid__add(X3)
      | c_HOL_Oplus__class_Oplus(X2,c_HOL_Oplus__class_Oplus(X1,X15,X3),X3) = c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X2,X15,X3),X3) ),
    file('<stdin>',cls_comm__monoid__add_Omult__left__commute_0) ).

fof(c_0_332,axiom,
    ! [X3] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
      | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X3),c_HOL_Ozero__class_Ozero(X3),X3),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X3),c_HOL_Ozero__class_Ozero(X3),X3),X3) = c_HOL_Ozero__class_Ozero(X3) ),
    file('<stdin>',cls_sum__squares__eq__zero__iff_2) ).

fof(c_0_333,axiom,
    ! [X16,X6,X7] :
      ( c_Ring__and__Field_Odvd__class_Odvd(X7,X16,tc_nat)
      | c_Ring__and__Field_Odvd__class_Odvd(X16,X6,tc_nat)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X6,X16,tc_nat)
      | c_Ring__and__Field_Odvd__class_Odvd(X6,X7,tc_nat)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X7,X6,tc_nat) ),
    file('<stdin>',cls_dvd_Oless__trans_0) ).

fof(c_0_334,axiom,
    ! [X1,X2,X3] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
      | c_HOL_Oord__class_Oless(X2,X1,X3)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X2,X1,X3),c_HOL_Ozero__class_Ozero(X3),X3) ),
    file('<stdin>',cls_less__iff__diff__less__0_1) ).

fof(c_0_335,axiom,
    ! [X1,X2,X3] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
      | c_lessequals(X2,X1,X3)
      | ~ c_lessequals(c_HOL_Ominus__class_Ominus(X2,X1,X3),c_HOL_Ozero__class_Ozero(X3),X3) ),
    file('<stdin>',cls_le__iff__diff__le__0_1) ).

fof(c_0_336,axiom,
    ! [X4,X5] : c_Divides_Odiv__class_Omod(c_Suc(X5),X4,tc_nat) = c_Divides_Odiv__class_Omod(c_Suc(c_Divides_Odiv__class_Omod(X5,X4,tc_nat)),X4,tc_nat),
    file('<stdin>',cls_mod__Suc__eq__Suc__mod_0) ).

fof(c_0_337,axiom,
    ! [X4,X5,X8] :
      ( c_Ring__and__Field_Odvd__class_Odvd(X8,c_HOL_Ominus__class_Ominus(X5,X4,tc_nat),tc_nat)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X8,X4,tc_nat)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X8,X5,tc_nat) ),
    file('<stdin>',cls_dvd__diff__nat_0) ).

fof(c_0_338,axiom,
    ! [X32,X6,X33,X7,X3] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
      | c_HOL_Ominus__class_Ominus(X7,X6,X3) != c_HOL_Ominus__class_Ominus(X33,X32,X3)
      | c_HOL_Oord__class_Oless(X7,X6,X3)
      | ~ c_HOL_Oord__class_Oless(X33,X32,X3) ),
    file('<stdin>',cls_less__eqI_1) ).

fof(c_0_339,axiom,
    ! [X32,X6,X33,X7,X3] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
      | c_HOL_Ominus__class_Ominus(X7,X6,X3) != c_HOL_Ominus__class_Ominus(X33,X32,X3)
      | c_HOL_Oord__class_Oless(X33,X32,X3)
      | ~ c_HOL_Oord__class_Oless(X7,X6,X3) ),
    file('<stdin>',cls_less__eqI_0) ).

fof(c_0_340,axiom,
    ! [X32,X6,X33,X7,X3] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
      | c_HOL_Ominus__class_Ominus(X7,X6,X3) != c_HOL_Ominus__class_Ominus(X33,X32,X3)
      | c_lessequals(X6,X7,X3)
      | ~ c_lessequals(X32,X33,X3) ),
    file('<stdin>',cls_le__eqI_1) ).

fof(c_0_341,axiom,
    ! [X32,X6,X33,X7,X3] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
      | c_HOL_Ominus__class_Ominus(X7,X6,X3) != c_HOL_Ominus__class_Ominus(X33,X32,X3)
      | c_lessequals(X32,X33,X3)
      | ~ c_lessequals(X6,X7,X3) ),
    file('<stdin>',cls_le__eqI_0) ).

fof(c_0_342,axiom,
    ! [X4,X5,X8] :
      ( c_lessequals(c_HOL_Otimes__class_Otimes(X5,X8,tc_nat),c_HOL_Otimes__class_Otimes(X4,X8,tc_nat),tc_nat)
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X8,tc_nat) ),
    file('<stdin>',cls_mult__le__cancel2_1) ).

fof(c_0_343,axiom,
    ! [X4,X5,X8] :
      ( c_lessequals(c_HOL_Otimes__class_Otimes(X8,X5,tc_nat),c_HOL_Otimes__class_Otimes(X8,X4,tc_nat),tc_nat)
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X8,tc_nat) ),
    file('<stdin>',cls_mult__le__cancel1_1) ).

fof(c_0_344,axiom,
    ! [X16,X6,X7,X3] :
      ( ~ class_Orderings_Olinorder(X3)
      | c_HOL_Oord__class_Oless(X16,X7,X3)
      | ~ c_HOL_Oord__class_Oless(X16,c_Orderings_Oord__class_Omin(X7,X6,X3),X3) ),
    file('<stdin>',cls_min__less__iff__conj_0) ).

fof(c_0_345,axiom,
    ! [X16,X6,X7,X3] :
      ( ~ class_Orderings_Olinorder(X3)
      | c_HOL_Oord__class_Oless(X16,X6,X3)
      | ~ c_HOL_Oord__class_Oless(X16,c_Orderings_Oord__class_Omin(X7,X6,X3),X3) ),
    file('<stdin>',cls_min__less__iff__conj_1) ).

fof(c_0_346,axiom,
    ! [X16,X6,X7,X3] :
      ( ~ class_Orderings_Olinorder(X3)
      | c_lessequals(X7,X16,X3)
      | ~ c_lessequals(X7,c_Orderings_Oord__class_Omin(X6,X16,X3),X3) ),
    file('<stdin>',cls_min__max_Ole__inf__iff_1) ).

fof(c_0_347,axiom,
    ! [X16,X6,X7,X3] :
      ( ~ class_Orderings_Olinorder(X3)
      | c_lessequals(X7,X6,X3)
      | ~ c_lessequals(X7,c_Orderings_Oord__class_Omin(X6,X16,X3),X3) ),
    file('<stdin>',cls_min__max_Ole__inf__iff_0) ).

fof(c_0_348,axiom,
    ! [X7,X1,X2,X3] :
      ( ~ class_Orderings_Olinorder(X3)
      | c_lessequals(X7,X1,X3)
      | ~ c_lessequals(X7,c_Orderings_Oord__class_Omin(X2,X1,X3),X3) ),
    file('<stdin>',cls_min__max_Ole__infE_1) ).

fof(c_0_349,axiom,
    ! [X7,X1,X2,X3] :
      ( ~ class_Orderings_Olinorder(X3)
      | c_lessequals(X7,X2,X3)
      | ~ c_lessequals(X7,c_Orderings_Oord__class_Omin(X2,X1,X3),X3) ),
    file('<stdin>',cls_min__max_Ole__infE_0) ).

fof(c_0_350,axiom,
    ! [X15,X1,X2,X3] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
      | c_Ring__and__Field_Odvd__class_Odvd(X1,X15,X3)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X2,X1,X3),X15,X3) ),
    file('<stdin>',cls_dvd__mult__right_0) ).

fof(c_0_351,axiom,
    ! [X15,X1,X2,X3] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
      | c_Ring__and__Field_Odvd__class_Odvd(X2,X15,X3)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X2,X1,X3),X15,X3) ),
    file('<stdin>',cls_dvd__mult__left_0) ).

fof(c_0_352,axiom,
    ! [X4,X5,X3] :
      ( ~ class_Ring__and__Field_Oring__1(X3)
      | c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Ominus__class_Ominus(X5,X4,tc_nat),X3) = c_HOL_Ominus__class_Ominus(c_Nat_Osemiring__1__class_Oof__nat(X5,X3),c_Nat_Osemiring__1__class_Oof__nat(X4,X3),X3)
      | ~ c_lessequals(X4,X5,tc_nat) ),
    file('<stdin>',cls_of__nat__diff_0) ).

fof(c_0_353,axiom,
    ! [X8,X9,X10] : c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X10,X9,tc_nat),X8,tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X10,X8,tc_nat),X9,tc_nat),
    file('<stdin>',cls_diff__commute_0) ).

fof(c_0_354,axiom,
    ! [X8,X9,X10] : c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X10,X9,tc_nat),X8,tc_nat) = c_HOL_Ominus__class_Ominus(X10,c_HOL_Oplus__class_Oplus(X9,X8,tc_nat),tc_nat),
    file('<stdin>',cls_diff__diff__left_0) ).

fof(c_0_355,axiom,
    ! [X4,X5,X8] : c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X5,X8,tc_nat),c_HOL_Oplus__class_Oplus(X4,X8,tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(X5,X4,tc_nat),
    file('<stdin>',cls_diff__cancel2_0) ).

fof(c_0_356,axiom,
    ! [X4,X5,X8] : c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X8,X5,tc_nat),c_HOL_Oplus__class_Oplus(X8,X4,tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(X5,X4,tc_nat),
    file('<stdin>',cls_diff__cancel_0) ).

fof(c_0_357,axiom,
    ! [X16,X6,X7] : c_HOL_Oplus__class_Oplus(X7,c_HOL_Oplus__class_Oplus(X6,X16,tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(X6,c_HOL_Oplus__class_Oplus(X7,X16,tc_nat),tc_nat),
    file('<stdin>',cls_nat__add__left__commute_0) ).

fof(c_0_358,axiom,
    ! [X4,X5,X8] : c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X5,X4,tc_nat),X8,tc_nat) = c_HOL_Oplus__class_Oplus(X5,c_HOL_Oplus__class_Oplus(X4,X8,tc_nat),tc_nat),
    file('<stdin>',cls_nat__add__assoc_0) ).

fof(c_0_359,axiom,
    ! [X4,X5,X8] : c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X5,X4,tc_nat),X8,tc_nat) = c_HOL_Otimes__class_Otimes(X5,c_HOL_Otimes__class_Otimes(X4,X8,tc_nat),tc_nat),
    file('<stdin>',cls_nat__mult__assoc_0) ).

fof(c_0_360,axiom,
    ! [X15,X1,X2,X3] :
      ( ~ class_Divides_Osemiring__div(X3)
      | c_Divides_Odiv__class_Omod(c_Divides_Odiv__class_Omod(X2,X1,X3),X15,X3) = c_Divides_Odiv__class_Omod(X2,X15,X3)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X15,X1,X3) ),
    file('<stdin>',cls_mod__mod__cancel_0) ).

fof(c_0_361,axiom,
    ! [X4,X5] :
      ( 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(X5,X4,tc_nat),tc_nat) ),
    file('<stdin>',cls_nat__0__less__mult__iff_1) ).

fof(c_0_362,axiom,
    ! [X4,X5] :
      ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X5,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Otimes__class_Otimes(X5,X4,tc_nat),tc_nat) ),
    file('<stdin>',cls_nat__0__less__mult__iff_0) ).

fof(c_0_363,axiom,
    ! [X4,X5] :
      ( c_HOL_Oord__class_Oless(X5,X4,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ominus__class_Ominus(X4,X5,tc_nat),tc_nat) ),
    file('<stdin>',cls_zero__less__diff_0) ).

fof(c_0_364,axiom,
    ! [X16,X6,X7] :
      ( ~ c_Ring__and__Field_Odvd__class_Odvd(X16,X7,tc_nat)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X6,X16,tc_nat)
      | c_Ring__and__Field_Odvd__class_Odvd(X6,X7,tc_nat)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X7,X6,tc_nat) ),
    file('<stdin>',cls_dvd_Oless__le__trans_1) ).

fof(c_0_365,axiom,
    ! [X16,X6,X7] :
      ( ~ c_Ring__and__Field_Odvd__class_Odvd(X16,X7,tc_nat)
      | c_Ring__and__Field_Odvd__class_Odvd(X16,X6,tc_nat)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X6,X16,tc_nat)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X7,X6,tc_nat) ),
    file('<stdin>',cls_dvd_Ole__less__trans_1) ).

fof(c_0_366,axiom,
    ! [X6,X7,X3] :
      ( ~ class_Ring__and__Field_Oordered__idom(X3)
      | c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(X6,X3),X7,X3) = c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(X6,X7,X3),X3)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X7,X3) ),
    file('<stdin>',cls_abs__mult__pos_0) ).

fof(c_0_367,axiom,
    ! [X4,X5,X29,X8] :
      ( c_HOL_Oplus__class_Oplus(X5,X29,tc_nat) != c_HOL_Oplus__class_Oplus(X8,X4,tc_nat)
      | ~ c_HOL_Oord__class_Oless(X8,X29,tc_nat)
      | c_HOL_Oord__class_Oless(X5,X4,tc_nat) ),
    file('<stdin>',cls_less__add__eq__less_0) ).

fof(c_0_368,axiom,
    ! [X8,X9,X10] :
      ( c_HOL_Oord__class_Oless(X10,X8,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X10,X9,tc_nat),X8,tc_nat) ),
    file('<stdin>',cls_add__lessD1_0) ).

fof(c_0_369,axiom,
    ! [X4,X8] :
      ( c_Ring__and__Field_Odvd__class_Odvd(X8,X4,tc_nat)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X8,c_HOL_Oplus__class_Oplus(X4,X8,tc_nat),tc_nat) ),
    file('<stdin>',cls_dvd__reduce_0) ).

fof(c_0_370,axiom,
    ! [X4,X5,X8] :
      ( c_lessequals(X8,X4,tc_nat)
      | ~ c_lessequals(c_HOL_Oplus__class_Oplus(X5,X8,tc_nat),X4,tc_nat) ),
    file('<stdin>',cls_add__leE_1) ).

fof(c_0_371,axiom,
    ! [X4,X5,X8] :
      ( c_lessequals(X5,X4,tc_nat)
      | ~ c_lessequals(c_HOL_Oplus__class_Oplus(X5,X8,tc_nat),X4,tc_nat) ),
    file('<stdin>',cls_add__leE_0) ).

fof(c_0_372,axiom,
    ! [X1,X2,X3] :
      ( ~ class_Ring__and__Field_Oidom(X3)
      | c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X2,c_HOL_Ozero__class_Ozero(X3),X3),c_HOL_Otimes__class_Otimes(X1,c_HOL_Ozero__class_Ozero(X3),X3),X3) ),
    file('<stdin>',cls_dvd__mult__cancel__right_1) ).

fof(c_0_373,axiom,
    ! [X1,X2,X3] :
      ( ~ class_Ring__and__Field_Oidom(X3)
      | c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X3),X2,X3),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X3),X1,X3),X3) ),
    file('<stdin>',cls_dvd__mult__cancel__left_1) ).

fof(c_0_374,axiom,
    ! [X6,X7,X3] :
      ( ~ class_OrderedGroup_Opordered__comm__monoid__add(X3)
      | c_HOL_Oplus__class_Oplus(X7,X6,X3) != c_HOL_Ozero__class_Ozero(X3)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X6,X3)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X7,X3)
      | X7 = c_HOL_Ozero__class_Ozero(X3) ),
    file('<stdin>',cls_add__nonneg__eq__0__iff_0) ).

fof(c_0_375,axiom,
    ! [X6,X7,X3] :
      ( ~ class_OrderedGroup_Opordered__comm__monoid__add(X3)
      | c_HOL_Oplus__class_Oplus(X7,X6,X3) != c_HOL_Ozero__class_Ozero(X3)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X6,X3)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X7,X3)
      | X6 = c_HOL_Ozero__class_Ozero(X3) ),
    file('<stdin>',cls_add__nonneg__eq__0__iff_1) ).

fof(c_0_376,axiom,
    ! [X4,X5] :
      ( c_Divides_Odiv__class_Omod(X5,X4,tc_nat) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X5,X4,tc_nat),X4,tc_nat)
      | ~ c_lessequals(X4,X5,tc_nat) ),
    file('<stdin>',cls_le__mod__geq_0) ).

fof(c_0_377,axiom,
    ! [X3] :
      ( ~ class_OrderedGroup_Opordered__comm__monoid__add(X3)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),c_HOL_Ozero__class_Ozero(X3),X3)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),c_HOL_Ozero__class_Ozero(X3),X3)
      | c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X3),c_HOL_Ozero__class_Ozero(X3),X3) = c_HOL_Ozero__class_Ozero(X3) ),
    file('<stdin>',cls_add__nonneg__eq__0__iff_2) ).

fof(c_0_378,axiom,
    ! [X4,X5] :
      ( c_Divides_Odiv__class_Omod(c_Suc(X5),X4,tc_nat) = c_Suc(c_Divides_Odiv__class_Omod(X5,X4,tc_nat))
      | c_Suc(c_Divides_Odiv__class_Omod(X5,X4,tc_nat)) = X4 ),
    file('<stdin>',cls_mod__Suc_1) ).

fof(c_0_379,axiom,
    ! [X16,X6,X7] :
      ( c_Ring__and__Field_Odvd__class_Odvd(X7,X16,tc_nat)
      | c_Ring__and__Field_Odvd__class_Odvd(X16,X6,tc_nat)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X6,X16,tc_nat)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X7,X6,tc_nat) ),
    file('<stdin>',cls_dvd_Ole__less__trans_0) ).

fof(c_0_380,axiom,
    ! [X16,X6,X7] :
      ( c_Ring__and__Field_Odvd__class_Odvd(X7,X16,tc_nat)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X6,X16,tc_nat)
      | c_Ring__and__Field_Odvd__class_Odvd(X6,X7,tc_nat)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X7,X6,tc_nat) ),
    file('<stdin>',cls_dvd_Oless__le__trans_0) ).

fof(c_0_381,axiom,
    ! [X4,X5] : c_Ring__and__Field_Odvd__class_Odvd(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),X4,tc_nat),tc_nat),
    file('<stdin>',cls_nat__mult__dvd__cancel__disj_1) ).

fof(c_0_382,axiom,
    ! [X2,X3] :
      ( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
      | c_lessequals(c_HOL_Oplus__class_Oplus(X2,X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
      | ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X3),X3) ),
    file('<stdin>',cls_double__add__le__zero__iff__single__add__le__zero_1) ).

fof(c_0_383,axiom,
    ! [X2,X3] :
      ( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
      | c_lessequals(c_HOL_Ozero__class_Ozero(X3),c_HOL_Oplus__class_Oplus(X2,X2,X3),X3)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X2,X3) ),
    file('<stdin>',cls_zero__le__double__add__iff__zero__le__single__add_1) ).

fof(c_0_384,axiom,
    ! [X2,X3] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X2,X3),c_HOL_Ozero__class_Ozero(X3),X3) ),
    file('<stdin>',cls_not__square__less__zero_0) ).

fof(c_0_385,axiom,
    ! [X2,X3] :
      ( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_HOL_Oplus__class_Oplus(X2,X2,X3),X3)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3) ),
    file('<stdin>',cls_zero__less__double__add__iff__zero__less__single__add_1) ).

fof(c_0_386,axiom,
    ! [X2,X3] :
      ( ~ class_Ring__and__Field_Oordered__idom(X3)
      | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X2,X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
      | ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X3),X3) ),
    file('<stdin>',cls_even__less__0__iff_1) ).

fof(c_0_387,axiom,
    ! [X2,X3] :
      ( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
      | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X2,X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
      | ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X3),X3) ),
    file('<stdin>',cls_double__add__less__zero__iff__single__less__zero_1) ).

fof(c_0_388,axiom,
    ! [X6,X7] :
      ( ~ c_Parity_Oeven__odd__class_Oeven(X6,tc_nat)
      | c_Parity_Oeven__odd__class_Oeven(X7,tc_nat)
      | c_HOL_Oord__class_Oless(X7,X6,tc_nat)
      | ~ c_Parity_Oeven__odd__class_Oeven(c_HOL_Ominus__class_Ominus(X7,X6,tc_nat),tc_nat) ),
    file('<stdin>',cls_even__difference__nat_0) ).

fof(c_0_389,axiom,
    ! [X6,X7] :
      ( ~ c_Parity_Oeven__odd__class_Oeven(X7,tc_nat)
      | c_Parity_Oeven__odd__class_Oeven(X6,tc_nat)
      | c_HOL_Oord__class_Oless(X7,X6,tc_nat)
      | ~ c_Parity_Oeven__odd__class_Oeven(c_HOL_Ominus__class_Ominus(X7,X6,tc_nat),tc_nat) ),
    file('<stdin>',cls_even__difference__nat_1) ).

fof(c_0_390,axiom,
    ! [X7,X5] : c_HOL_Oord__class_Oless(X5,c_Suc(c_HOL_Oplus__class_Oplus(X5,X7,tc_nat)),tc_nat),
    file('<stdin>',cls_less__iff__Suc__add_1) ).

fof(c_0_391,axiom,
    ! [X5,X10] : c_HOL_Oord__class_Oless(X10,c_Suc(c_HOL_Oplus__class_Oplus(X5,X10,tc_nat)),tc_nat),
    file('<stdin>',cls_less__add__Suc2_0) ).

fof(c_0_392,axiom,
    ! [X5,X10] : c_HOL_Oord__class_Oless(X10,c_Suc(c_HOL_Oplus__class_Oplus(X10,X5,tc_nat)),tc_nat),
    file('<stdin>',cls_less__add__Suc1_0) ).

fof(c_0_393,axiom,
    ! [X4,X5] :
      ( c_Divides_Odiv__class_Omod(X5,X4,tc_nat) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X5,X4,tc_nat),X4,tc_nat)
      | c_HOL_Oord__class_Oless(X5,X4,tc_nat) ),
    file('<stdin>',cls_mod__if_1) ).

fof(c_0_394,axiom,
    ! [X1,X2,X3] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
      | c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X2,X1,X3),c_HOL_Ozero__class_Ozero(X3),X3)
      | ~ c_HOL_Oord__class_Oless(X2,X1,X3) ),
    file('<stdin>',cls_less__iff__diff__less__0_0) ).

fof(c_0_395,axiom,
    ! [X1,X2,X3] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
      | c_lessequals(c_HOL_Ominus__class_Ominus(X2,X1,X3),c_HOL_Ozero__class_Ozero(X3),X3)
      | ~ c_lessequals(X2,X1,X3) ),
    file('<stdin>',cls_le__iff__diff__le__0_0) ).

fof(c_0_396,axiom,
    ! [X4,X10] :
      ( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X4,c_Suc(X10),tc_nat),X4,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat) ),
    file('<stdin>',cls_diff__Suc__less_0) ).

fof(c_0_397,axiom,
    ! [X4,X5,X8] :
      ( c_HOL_Otimes__class_Otimes(X8,X5,tc_nat) != c_HOL_Otimes__class_Otimes(X8,X4,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X8,tc_nat)
      | X5 = X4 ),
    file('<stdin>',cls_nat__mult__eq__cancel1_0) ).

fof(c_0_398,axiom,
    ! [X4,X5] :
      ( ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X5,tc_nat)
      | ~ c_HOL_Oord__class_Oless(X5,X4,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X5,tc_nat) ),
    file('<stdin>',cls_nat__dvd__not__less_0) ).

fof(c_0_399,axiom,
    ! [X7,X1,X2,X3] :
      ( ~ class_Orderings_Olinorder(X3)
      | c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omin(X2,X1,X3),X7,X3)
      | ~ c_HOL_Oord__class_Oless(X2,X7,X3) ),
    file('<stdin>',cls_min__max_Oless__infI1_0) ).

fof(c_0_400,axiom,
    ! [X7,X1,X2,X3] :
      ( ~ class_Orderings_Olinorder(X3)
      | c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omin(X2,X1,X3),X7,X3)
      | ~ c_HOL_Oord__class_Oless(X1,X7,X3) ),
    file('<stdin>',cls_min__max_Oless__infI2_0) ).

fof(c_0_401,axiom,
    ! [X16,X6,X7,X3] :
      ( ~ class_Orderings_Olinorder(X3)
      | c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omin(X7,X6,X3),X16,X3)
      | ~ c_HOL_Oord__class_Oless(X7,X16,X3) ),
    file('<stdin>',cls_min__less__iff__disj_1) ).

fof(c_0_402,axiom,
    ! [X16,X6,X7,X3] :
      ( ~ class_Orderings_Olinorder(X3)
      | c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omin(X7,X6,X3),X16,X3)
      | ~ c_HOL_Oord__class_Oless(X6,X16,X3) ),
    file('<stdin>',cls_min__less__iff__disj_2) ).

fof(c_0_403,axiom,
    ! [X16,X6,X7,X3] :
      ( ~ class_Orderings_Olinorder(X3)
      | c_lessequals(c_Orderings_Oord__class_Omin(X7,X6,X3),X16,X3)
      | ~ c_lessequals(X6,X16,X3) ),
    file('<stdin>',cls_min__le__iff__disj_2) ).

fof(c_0_404,axiom,
    ! [X16,X6,X7,X3] :
      ( ~ class_Orderings_Olinorder(X3)
      | c_lessequals(c_Orderings_Oord__class_Omin(X7,X6,X3),X16,X3)
      | ~ c_lessequals(X7,X16,X3) ),
    file('<stdin>',cls_min__le__iff__disj_1) ).

fof(c_0_405,axiom,
    ! [X7,X1,X2,X3] :
      ( ~ class_Orderings_Olinorder(X3)
      | c_lessequals(c_Orderings_Oord__class_Omin(X2,X1,X3),X7,X3)
      | ~ c_lessequals(X1,X7,X3) ),
    file('<stdin>',cls_min__max_Ole__infI2_0) ).

fof(c_0_406,axiom,
    ! [X7,X1,X2,X3] :
      ( ~ class_Orderings_Olinorder(X3)
      | c_lessequals(c_Orderings_Oord__class_Omin(X2,X1,X3),X7,X3)
      | ~ c_lessequals(X2,X7,X3) ),
    file('<stdin>',cls_min__max_Ole__infI1_0) ).

fof(c_0_407,axiom,
    ! [X15,X1,X2,X3] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
      | c_Ring__and__Field_Odvd__class_Odvd(X2,c_HOL_Otimes__class_Otimes(X1,X15,X3),X3)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X1,X3) ),
    file('<stdin>',cls_dvd__mult2_0) ).

fof(c_0_408,axiom,
    ! [X15,X1,X2,X3] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
      | c_Ring__and__Field_Odvd__class_Odvd(X2,c_HOL_Otimes__class_Otimes(X1,X15,X3),X3)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X15,X3) ),
    file('<stdin>',cls_dvd__mult_0) ).

fof(c_0_409,axiom,
    ! [X4,X5] :
      ( c_HOL_Ominus__class_Ominus(c_Suc(X5),X4,tc_nat) = c_Suc(c_HOL_Ominus__class_Ominus(X5,X4,tc_nat))
      | ~ c_lessequals(X4,X5,tc_nat) ),
    file('<stdin>',cls_Suc__diff__le_0) ).

fof(c_0_410,axiom,
    ! [X1,X2,X3] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X3)
      | c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X2,X1,X3),X3) = c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X1,X2,X3),X3) ),
    file('<stdin>',cls_abs__minus__commute_0) ).

fof(c_0_411,axiom,
    ! [X4,X5] :
      ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oplus__class_Oplus(X5,X4,tc_nat),tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X5,tc_nat) ),
    file('<stdin>',cls_add__gr__0_1) ).

fof(c_0_412,axiom,
    ! [X4,X5] :
      ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oplus__class_Oplus(X5,X4,tc_nat),tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat) ),
    file('<stdin>',cls_add__gr__0_2) ).

fof(c_0_413,axiom,
    ! [X9,X10] : ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X9,X10,tc_nat),X10,tc_nat),
    file('<stdin>',cls_not__add__less2_0) ).

fof(c_0_414,axiom,
    ! [X9,X10] : ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X10,X9,tc_nat),X10,tc_nat),
    file('<stdin>',cls_not__add__less1_0) ).

fof(c_0_415,axiom,
    ! [X4,X5] :
      ( c_HOL_Oord__class_Oless(c_Divides_Odiv__class_Omod(X5,X4,tc_nat),X4,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat) ),
    file('<stdin>',cls_mod__less__divisor_0) ).

fof(c_0_416,axiom,
    ! [X4,X5] :
      ( c_lessequals(c_Divides_Odiv__class_Omod(X5,X4,tc_nat),X4,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat) ),
    file('<stdin>',cls_mod__le__divisor_0) ).

fof(c_0_417,axiom,
    ! [X4,X5] :
      ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ominus__class_Ominus(X4,X5,tc_nat),tc_nat)
      | ~ c_HOL_Oord__class_Oless(X5,X4,tc_nat) ),
    file('<stdin>',cls_zero__less__diff_1) ).

fof(c_0_418,axiom,
    ! [X4,X10] :
      ( c_HOL_Ominus__class_Ominus(X4,c_HOL_Ominus__class_Ominus(X4,X10,tc_nat),tc_nat) = X10
      | ~ c_lessequals(X10,X4,tc_nat) ),
    file('<stdin>',cls_diff__diff__cancel_0) ).

fof(c_0_419,axiom,
    ! [X9,X10] :
      ( ~ c_lessequals(X10,X9,tc_nat)
      | X9 = c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X9,X10,tc_nat),X10,tc_nat) ),
    file('<stdin>',cls_le__imp__diff__is__add_0) ).

fof(c_0_420,axiom,
    ! [X4,X5] :
      ( c_HOL_Oplus__class_Oplus(X4,c_HOL_Ominus__class_Ominus(X5,X4,tc_nat),tc_nat) = X5
      | ~ c_lessequals(X4,X5,tc_nat) ),
    file('<stdin>',cls_le__add__diff__inverse_0) ).

fof(c_0_421,axiom,
    ! [X4,X5] :
      ( c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X5,X4,tc_nat),X4,tc_nat) = X5
      | ~ c_lessequals(X4,X5,tc_nat) ),
    file('<stdin>',cls_le__add__diff__inverse2_0) ).

fof(c_0_422,axiom,
    ! [X4,X8,X9] :
      ( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X9,X4,tc_nat),X8,tc_nat)
      | ~ c_HOL_Oord__class_Oless(X9,X8,tc_nat) ),
    file('<stdin>',cls_less__imp__diff__less_0) ).

fof(c_0_423,axiom,
    ! [X5,X9,X10] :
      ( c_HOL_Oord__class_Oless(X10,c_HOL_Oplus__class_Oplus(X5,X9,tc_nat),tc_nat)
      | ~ c_HOL_Oord__class_Oless(X10,X9,tc_nat) ),
    file('<stdin>',cls_trans__less__add2_0) ).

fof(c_0_424,axiom,
    ! [X5,X9,X10] :
      ( c_HOL_Oord__class_Oless(X10,c_HOL_Oplus__class_Oplus(X9,X5,tc_nat),tc_nat)
      | ~ c_HOL_Oord__class_Oless(X10,X9,tc_nat) ),
    file('<stdin>',cls_trans__less__add1_0) ).

fof(c_0_425,axiom,
    ! [X16,X6,X7] :
      ( c_HOL_Oord__class_Oless(X7,c_HOL_Oplus__class_Oplus(X6,X16,tc_nat),tc_nat)
      | ~ c_HOL_Oord__class_Oless(X7,X16,tc_nat) ),
    file('<stdin>',cls_termination__basic__simps_I2_J_0) ).

fof(c_0_426,axiom,
    ! [X16,X6,X7] :
      ( c_HOL_Oord__class_Oless(X7,c_HOL_Oplus__class_Oplus(X6,X16,tc_nat),tc_nat)
      | ~ c_HOL_Oord__class_Oless(X7,X6,tc_nat) ),
    file('<stdin>',cls_termination__basic__simps_I1_J_0) ).

fof(c_0_427,axiom,
    ! [X4,X8] :
      ( c_Ring__and__Field_Odvd__class_Odvd(X8,c_HOL_Oplus__class_Oplus(X4,X8,tc_nat),tc_nat)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X8,X4,tc_nat) ),
    file('<stdin>',cls_dvd__reduce_1) ).

fof(c_0_428,axiom,
    ! [X5,X9,X10] :
      ( c_lessequals(X10,c_HOL_Oplus__class_Oplus(X5,X9,tc_nat),tc_nat)
      | ~ c_lessequals(X10,X9,tc_nat) ),
    file('<stdin>',cls_trans__le__add2_0) ).

fof(c_0_429,axiom,
    ! [X5,X9,X10] :
      ( c_lessequals(X10,c_HOL_Oplus__class_Oplus(X9,X5,tc_nat),tc_nat)
      | ~ c_lessequals(X10,X9,tc_nat) ),
    file('<stdin>',cls_trans__le__add1_0) ).

fof(c_0_430,axiom,
    ! [X16,X6,X7] :
      ( c_lessequals(X7,c_HOL_Oplus__class_Oplus(X6,X16,tc_nat),tc_nat)
      | ~ c_lessequals(X7,X16,tc_nat) ),
    file('<stdin>',cls_termination__basic__simps_I4_J_0) ).

fof(c_0_431,axiom,
    ! [X16,X6,X7] :
      ( c_lessequals(X7,c_HOL_Oplus__class_Oplus(X6,X16,tc_nat),tc_nat)
      | ~ c_lessequals(X7,X6,tc_nat) ),
    file('<stdin>',cls_termination__basic__simps_I3_J_0) ).

fof(c_0_432,axiom,
    ! [X16,X6,X7,X3] :
      ( ~ class_Orderings_Opreorder(X3)
      | c_HOL_Oord__class_Oless(X7,X16,X3)
      | ~ c_HOL_Oord__class_Oless(X6,X16,X3)
      | ~ c_HOL_Oord__class_Oless(X7,X6,X3) ),
    file('<stdin>',cls_order__less__trans_0) ).

fof(c_0_433,axiom,
    ! [X16,X6,X7,X3] :
      ( ~ class_Orderings_Oorder(X3)
      | c_HOL_Oord__class_Oless(X16,X7,X3)
      | ~ c_HOL_Oord__class_Oless(X16,X6,X3)
      | ~ c_HOL_Oord__class_Oless(X6,X7,X3) ),
    file('<stdin>',cls_xt1_I10_J_0) ).

fof(c_0_434,axiom,
    ! [X16,X6,X7,X3] :
      ( ~ class_Orderings_Oorder(X3)
      | c_lessequals(X16,X7,X3)
      | ~ c_lessequals(X16,X6,X3)
      | ~ c_lessequals(X6,X7,X3) ),
    file('<stdin>',cls_xt1_I6_J_0) ).

fof(c_0_435,axiom,
    ! [X16,X6,X7,X3] :
      ( ~ class_Orderings_Opreorder(X3)
      | c_lessequals(X7,X16,X3)
      | ~ c_lessequals(X6,X16,X3)
      | ~ c_lessequals(X7,X6,X3) ),
    file('<stdin>',cls_order__trans_0) ).

fof(c_0_436,axiom,
    ! [X16,X6,X7,X3] :
      ( ~ class_Orderings_Opreorder(X3)
      | c_HOL_Oord__class_Oless(X7,X16,X3)
      | ~ c_HOL_Oord__class_Oless(X6,X16,X3)
      | ~ c_lessequals(X7,X6,X3) ),
    file('<stdin>',cls_order__le__less__trans_0) ).

fof(c_0_437,axiom,
    ! [X16,X6,X7,X3] :
      ( ~ class_Orderings_Opreorder(X3)
      | c_HOL_Oord__class_Oless(X7,X16,X3)
      | ~ c_lessequals(X6,X16,X3)
      | ~ c_HOL_Oord__class_Oless(X7,X6,X3) ),
    file('<stdin>',cls_order__less__le__trans_0) ).

fof(c_0_438,axiom,
    ! [X16,X6,X7,X3] :
      ( ~ class_Orderings_Oorder(X3)
      | c_HOL_Oord__class_Oless(X16,X7,X3)
      | ~ c_HOL_Oord__class_Oless(X16,X6,X3)
      | ~ c_lessequals(X6,X7,X3) ),
    file('<stdin>',cls_xt1_I8_J_0) ).

fof(c_0_439,axiom,
    ! [X16,X6,X7,X3] :
      ( ~ class_Orderings_Oorder(X3)
      | c_HOL_Oord__class_Oless(X16,X7,X3)
      | ~ c_lessequals(X16,X6,X3)
      | ~ c_HOL_Oord__class_Oless(X6,X7,X3) ),
    file('<stdin>',cls_xt1_I7_J_0) ).

fof(c_0_440,axiom,
    ! [X15,X1,X2,X3] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
      | c_Ring__and__Field_Odvd__class_Odvd(X2,X15,X3)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X15,X3)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X1,X3) ),
    file('<stdin>',cls_dvd__trans_0) ).

fof(c_0_441,axiom,
    ! [X1,X2,X3] :
      ( ~ class_Ring__and__Field_Oordered__idom(X3)
      | c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(X2,X1,X3),X3) = c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(X2,X3),c_HOL_Oabs__class_Oabs(X1,X3),X3) ),
    file('<stdin>',cls_abs__mult_0) ).

fof(c_0_442,axiom,
    ! [X4,X5] :
      ( c_Suc(c_Divides_Odiv__class_Omod(X5,X4,tc_nat)) != X4
      | c_Divides_Odiv__class_Omod(c_Suc(X5),X4,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat) ),
    file('<stdin>',cls_mod__Suc_0) ).

fof(c_0_443,axiom,
    ! [X4,X5,X3] :
      ( ~ class_Ring__and__Field_Osemiring__1(X3)
      | c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Otimes__class_Otimes(X5,X4,tc_nat),X3) = c_HOL_Otimes__class_Otimes(c_Nat_Osemiring__1__class_Oof__nat(X5,X3),c_Nat_Osemiring__1__class_Oof__nat(X4,X3),X3) ),
    file('<stdin>',cls_of__nat__mult_0) ).

fof(c_0_444,axiom,
    ! [X4,X5,X3] :
      ( ~ class_Ring__and__Field_Osemiring__1(X3)
      | c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Oplus__class_Oplus(X5,X4,tc_nat),X3) = c_HOL_Oplus__class_Oplus(c_Nat_Osemiring__1__class_Oof__nat(X5,X3),c_Nat_Osemiring__1__class_Oof__nat(X4,X3),X3) ),
    file('<stdin>',cls_of__nat__add_0) ).

fof(c_0_445,axiom,
    ! [X4,X5] :
      ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X5,tc_nat)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X5,X4,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat) ),
    file('<stdin>',cls_dvd__pos__nat_0) ).

fof(c_0_446,axiom,
    ! [X4,X5,X3] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X3)
      | c_HOL_Oord__class_Oless(X5,X4,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X5,X3),c_Nat_Osemiring__1__class_Oof__nat(X4,X3),X3) ),
    file('<stdin>',cls_of__nat__less__iff_0) ).

fof(c_0_447,axiom,
    ! [X4,X5,X3] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X3)
      | c_lessequals(X5,X4,tc_nat)
      | ~ c_lessequals(c_Nat_Osemiring__1__class_Oof__nat(X5,X3),c_Nat_Osemiring__1__class_Oof__nat(X4,X3),X3) ),
    file('<stdin>',cls_of__nat__le__iff_0) ).

fof(c_0_448,axiom,
    ! [X8,X9,X10] :
      ( c_HOL_Oord__class_Oless(c_Suc(X10),X8,tc_nat)
      | ~ c_HOL_Oord__class_Oless(X9,X8,tc_nat)
      | ~ c_HOL_Oord__class_Oless(X10,X9,tc_nat) ),
    file('<stdin>',cls_less__trans__Suc_0) ).

fof(c_0_449,axiom,
    ! [X4,X8] :
      ( c_lessequals(X8,X4,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X8,X4,tc_nat) ),
    file('<stdin>',cls_dvd__imp__le_0) ).

fof(c_0_450,axiom,
    ! [X1,X2,X3] :
      ( ~ class_Divides_Osemiring__div(X3)
      | c_Divides_Odiv__class_Omod(c_Divides_Odiv__class_Omod(X2,X1,X3),X1,X3) = c_Divides_Odiv__class_Omod(X2,X1,X3) ),
    file('<stdin>',cls_mod__mod__trivial_0) ).

fof(c_0_451,axiom,
    ! [X6,X7,X3] :
      ( ~ class_Orderings_Olinorder(X3)
      | c_Orderings_Oord__class_Omin(X7,c_Orderings_Oord__class_Omin(X7,X6,X3),X3) = c_Orderings_Oord__class_Omin(X7,X6,X3) ),
    file('<stdin>',cls_min__max_Oinf__left__idem_0) ).

fof(c_0_452,axiom,
    ! [X1,X2,X3] :
      ( ~ class_Divides_Osemiring__div(X3)
      | c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X2,X1,X3),X1,X3) = c_Divides_Odiv__class_Omod(X2,X1,X3) ),
    file('<stdin>',cls_mod__add__self2_0) ).

fof(c_0_453,axiom,
    ! [X1,X2,X3] :
      ( ~ 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) ),
    file('<stdin>',cls_mod__add__self1_0) ).

fof(c_0_454,axiom,
    ! [X6,X7,X3] :
      ( ~ class_OrderedGroup_Oab__semigroup__idem__mult(X3)
      | c_HOL_Otimes__class_Otimes(X7,c_HOL_Otimes__class_Otimes(X7,X6,X3),X3) = c_HOL_Otimes__class_Otimes(X7,X6,X3) ),
    file('<stdin>',cls_mult__left__idem_0) ).

fof(c_0_455,axiom,
    ! [X4] :
      ( c_Suc(c_HOL_Ominus__class_Ominus(X4,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat)) = X4
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat) ),
    file('<stdin>',cls_Suc__pred_0) ).

fof(c_0_456,axiom,
    ! [X8,X9,X10] :
      ( c_lessequals(X10,X8,tc_nat)
      | ~ c_lessequals(X9,X8,tc_nat)
      | ~ c_lessequals(X10,X9,tc_nat) ),
    file('<stdin>',cls_le__trans_0) ).

fof(c_0_457,axiom,
    ! [X16,X6,X7] :
      ( c_Ring__and__Field_Odvd__class_Odvd(X7,X16,tc_nat)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X6,X16,tc_nat)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X7,X6,tc_nat) ),
    file('<stdin>',cls_dvd_Oorder__trans_0) ).

fof(c_0_458,axiom,
    ! [X4,X5] :
      ( ~ c_Parity_Oeven__odd__class_Oeven(c_HOL_Oplus__class_Oplus(X5,X4,tc_nat),tc_nat)
      | ~ c_Parity_Oeven__odd__class_Oeven(X4,tc_nat)
      | c_Parity_Oeven__odd__class_Oeven(X5,tc_nat) ),
    file('<stdin>',cls_odd__add_2) ).

fof(c_0_459,axiom,
    ! [X4,X5] :
      ( ~ c_Parity_Oeven__odd__class_Oeven(c_HOL_Oplus__class_Oplus(X5,X4,tc_nat),tc_nat)
      | c_Parity_Oeven__odd__class_Oeven(X4,tc_nat)
      | ~ c_Parity_Oeven__odd__class_Oeven(X5,tc_nat) ),
    file('<stdin>',cls_odd__add_3) ).

fof(c_0_460,axiom,
    ! [X4,X5] :
      ( c_Parity_Oeven__odd__class_Oeven(X4,tc_nat)
      | ~ c_Parity_Oeven__odd__class_Oeven(X5,tc_nat)
      | ~ c_Parity_Oeven__odd__class_Oeven(c_HOL_Oplus__class_Oplus(X5,X4,tc_nat),tc_nat) ),
    file('<stdin>',cls_even__add_0) ).

fof(c_0_461,axiom,
    ! [X4,X5] :
      ( c_Parity_Oeven__odd__class_Oeven(X5,tc_nat)
      | ~ c_Parity_Oeven__odd__class_Oeven(X4,tc_nat)
      | ~ c_Parity_Oeven__odd__class_Oeven(c_HOL_Oplus__class_Oplus(X5,X4,tc_nat),tc_nat) ),
    file('<stdin>',cls_even__add_1) ).

fof(c_0_462,axiom,
    ! [X6,X7] :
      ( ~ c_Parity_Oeven__odd__class_Oeven(X6,tc_nat)
      | c_Parity_Oeven__odd__class_Oeven(X7,tc_nat)
      | ~ c_Parity_Oeven__odd__class_Oeven(c_HOL_Oplus__class_Oplus(X7,X6,tc_nat),tc_nat) ),
    file('<stdin>',cls_even__sum__nat_0) ).

fof(c_0_463,axiom,
    ! [X6,X7] :
      ( ~ c_Parity_Oeven__odd__class_Oeven(X7,tc_nat)
      | c_Parity_Oeven__odd__class_Oeven(X6,tc_nat)
      | ~ c_Parity_Oeven__odd__class_Oeven(c_HOL_Oplus__class_Oplus(X7,X6,tc_nat),tc_nat) ),
    file('<stdin>',cls_even__sum__nat_1) ).

fof(c_0_464,axiom,
    ! [X4,X5] : c_HOL_Otimes__class_Otimes(X5,c_Suc(X4),tc_nat) = c_HOL_Oplus__class_Oplus(X5,c_HOL_Otimes__class_Otimes(X5,X4,tc_nat),tc_nat),
    file('<stdin>',cls_mult__Suc__right_0) ).

fof(c_0_465,axiom,
    ! [X4,X5] : c_HOL_Otimes__class_Otimes(c_Suc(X5),X4,tc_nat) = c_HOL_Oplus__class_Oplus(X4,c_HOL_Otimes__class_Otimes(X5,X4,tc_nat),tc_nat),
    file('<stdin>',cls_mult__Suc_0) ).

fof(c_0_466,axiom,
    ! [X4,X5] :
      ( c_HOL_Oplus__class_Oplus(X4,c_HOL_Ominus__class_Ominus(X5,X4,tc_nat),tc_nat) = X5
      | c_HOL_Oord__class_Oless(X5,X4,tc_nat) ),
    file('<stdin>',cls_add__diff__inverse_0) ).

fof(c_0_467,axiom,
    ! [X6,X7] :
      ( c_Parity_Oeven__odd__class_Oeven(X6,tc_nat)
      | c_Parity_Oeven__odd__class_Oeven(X7,tc_nat)
      | ~ c_Parity_Oeven__odd__class_Oeven(c_HOL_Otimes__class_Otimes(X7,X6,tc_nat),tc_nat) ),
    file('<stdin>',cls_even__product__nat_0) ).

fof(c_0_468,axiom,
    ! [X6,X7,X3] :
      ( ~ class_Orderings_Opreorder(X3)
      | c_HOL_Oord__class_Oless(X7,X6,X3)
      | c_lessequals(X6,X7,X3)
      | ~ c_lessequals(X7,X6,X3) ),
    file('<stdin>',cls_less__le__not__le_2) ).

fof(c_0_469,axiom,
    ! [X6,X7] :
      ( c_Parity_Oeven__odd__class_Oeven(c_HOL_Ominus__class_Ominus(X7,X6,tc_nat),tc_nat)
      | ~ c_HOL_Oord__class_Oless(X7,X6,tc_nat) ),
    file('<stdin>',cls_even__difference__nat_2) ).

fof(c_0_470,axiom,
    ! [X4,X3] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X3)
      | 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(X3),c_Nat_Osemiring__1__class_Oof__nat(X4,X3),X3) ),
    file('<stdin>',cls_of__nat__0__less__iff_0) ).

fof(c_0_471,axiom,
    ! [X4,X5,X3] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X3)
      | c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X5,X3),c_Nat_Osemiring__1__class_Oof__nat(X4,X3),X3)
      | ~ c_HOL_Oord__class_Oless(X5,X4,tc_nat) ),
    file('<stdin>',cls_of__nat__less__iff_1) ).

fof(c_0_472,axiom,
    ! [X4,X5,X3] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X3)
      | c_lessequals(c_Nat_Osemiring__1__class_Oof__nat(X5,X3),c_Nat_Osemiring__1__class_Oof__nat(X4,X3),X3)
      | ~ c_lessequals(X5,X4,tc_nat) ),
    file('<stdin>',cls_of__nat__le__iff_1) ).

fof(c_0_473,axiom,
    ! [X5,X8,X3] :
      ( ~ class_Ring__and__Field_Oordered__idom(X3)
      | c_Ring__and__Field_Odvd__class_Odvd(X5,X8,X3)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X5,c_HOL_Oabs__class_Oabs(X8,X3),X3) ),
    file('<stdin>',cls_dvd__abs__iff_0) ).

fof(c_0_474,axiom,
    ! [X5,X8,X3] :
      ( ~ class_Ring__and__Field_Oordered__idom(X3)
      | c_Ring__and__Field_Odvd__class_Odvd(X5,X8,X3)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oabs__class_Oabs(X5,X3),X8,X3) ),
    file('<stdin>',cls_abs__dvd__iff_0) ).

fof(c_0_475,axiom,
    ! [X1,X2,X3] :
      ( ~ class_Ring__and__Field_Oordered__idom(X3)
      | c_HOL_Oord__class_Oless(X2,X1,X3)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(X2,X3),X1,X3) ),
    file('<stdin>',cls_abs__less__iff_0) ).

fof(c_0_476,axiom,
    ! [X1,X2,X3] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X3)
      | c_lessequals(X2,X1,X3)
      | ~ c_lessequals(c_HOL_Oabs__class_Oabs(X2,X3),X1,X3) ),
    file('<stdin>',cls_abs__le__D1_0) ).

fof(c_0_477,axiom,
    ! [X16,X6,X7,X3] :
      ( ~ class_Ring__and__Field_Oidom(X3)
      | ~ class_Int_Onumber__ring(X3)
      | c_HOL_Oplus__class_Oplus(X7,X6,X3) != c_HOL_Oplus__class_Oplus(X7,X16,X3)
      | X6 = X16 ),
    file('<stdin>',cls_class__ringb_Oadd__cancel_0) ).

fof(c_0_478,axiom,
    ! [X4,X5,X8] :
      ( c_HOL_Otimes__class_Otimes(c_Suc(X8),X5,tc_nat) != c_HOL_Otimes__class_Otimes(c_Suc(X8),X4,tc_nat)
      | X5 = X4 ),
    file('<stdin>',cls_Suc__mult__cancel1_0) ).

fof(c_0_479,axiom,
    ! [X4,X3] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X3)
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_Nat_Osemiring__1__class_Oof__nat(X4,X3),X3)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat) ),
    file('<stdin>',cls_of__nat__0__less__iff_1) ).

fof(c_0_480,axiom,
    ! [X6,X7,X3] :
      ( ~ class_Orderings_Oorder(X3)
      | X7 = X6
      | ~ c_lessequals(X7,X6,X3)
      | ~ c_lessequals(X6,X7,X3) ),
    file('<stdin>',cls_order__antisym__conv_0) ).

fof(c_0_481,axiom,
    ! [X6,X7,X3] :
      ( ~ class_Orderings_Oorder(X3)
      | X7 = X6
      | ~ c_lessequals(X6,X7,X3)
      | ~ c_lessequals(X7,X6,X3) ),
    file('<stdin>',cls_order__eq__iff_2) ).

fof(c_0_482,axiom,
    ! [X6,X7,X3] :
      ( ~ class_Orderings_Oorder(X3)
      | X7 = X6
      | ~ c_lessequals(X6,X7,X3)
      | ~ c_lessequals(X7,X6,X3) ),
    file('<stdin>',cls_order__antisym_0) ).

fof(c_0_483,axiom,
    ! [X6,X18,X7,X3] :
      ( ~ class_OrderedGroup_Oab__group__add(X3)
      | c_HOL_Ominus__class_Ominus(X18,X6,X3) != c_HOL_Ominus__class_Ominus(X7,X7,X3)
      | X18 = X6 ),
    file('<stdin>',cls_eq__eqI_1) ).

fof(c_0_484,axiom,
    ! [X32,X33,X7,X3] :
      ( ~ class_OrderedGroup_Oab__group__add(X3)
      | c_HOL_Ominus__class_Ominus(X7,X7,X3) != c_HOL_Ominus__class_Ominus(X33,X32,X3)
      | X33 = X32 ),
    file('<stdin>',cls_eq__eqI_0) ).

fof(c_0_485,axiom,
    ! [X15,X1,X2,X3] :
      ( ~ class_OrderedGroup_Ocancel__semigroup__add(X3)
      | c_HOL_Oplus__class_Oplus(X1,X2,X3) != c_HOL_Oplus__class_Oplus(X15,X2,X3)
      | X1 = X15 ),
    file('<stdin>',cls_add__right__cancel_0) ).

fof(c_0_486,axiom,
    ! [X15,X1,X2,X3] :
      ( ~ class_OrderedGroup_Ocancel__semigroup__add(X3)
      | c_HOL_Oplus__class_Oplus(X2,X1,X3) != c_HOL_Oplus__class_Oplus(X2,X15,X3)
      | X1 = X15 ),
    file('<stdin>',cls_add__left__cancel_0) ).

fof(c_0_487,axiom,
    ! [X15,X1,X2,X3] :
      ( ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X3)
      | c_HOL_Oplus__class_Oplus(X2,X1,X3) != c_HOL_Oplus__class_Oplus(X2,X15,X3)
      | X1 = X15 ),
    file('<stdin>',cls_add__imp__eq_0) ).

fof(c_0_488,axiom,
    ! [X6,X7,X3] :
      ( ~ class_Orderings_Opreorder(X3)
      | ~ c_HOL_Oord__class_Oless(X6,X7,X3)
      | ~ c_HOL_Oord__class_Oless(X7,X6,X3) ),
    file('<stdin>',cls_order__less__asym_0) ).

fof(c_0_489,axiom,
    ! [X1,X2,X3] :
      ( ~ class_Orderings_Opreorder(X3)
      | ~ c_HOL_Oord__class_Oless(X1,X2,X3)
      | ~ c_HOL_Oord__class_Oless(X2,X1,X3) ),
    file('<stdin>',cls_order__less__asym_H_0) ).

fof(c_0_490,axiom,
    ! [X6,X7,X3] :
      ( ~ class_Orderings_Olinorder(X3)
      | ~ c_HOL_Oord__class_Oless(X7,X6,X3)
      | ~ c_HOL_Oord__class_Oless(X6,X7,X3) ),
    file('<stdin>',cls_not__less__iff__gr__or__eq_1) ).

fof(c_0_491,axiom,
    ! [X1,X2,X3] :
      ( ~ class_Orderings_Oorder(X3)
      | ~ c_HOL_Oord__class_Oless(X2,X1,X3)
      | ~ c_HOL_Oord__class_Oless(X1,X2,X3) ),
    file('<stdin>',cls_xt1_I9_J_0) ).

fof(c_0_492,axiom,
    ! [X6,X7,X3] :
      ( ~ class_Orderings_Olinorder(X3)
      | ~ c_lessequals(X7,X6,X3)
      | ~ c_HOL_Oord__class_Oless(X6,X7,X3) ),
    file('<stdin>',cls_linorder__not__le_1) ).

fof(c_0_493,axiom,
    ! [X6,X7,X3] :
      ( ~ class_Orderings_Olinorder(X3)
      | ~ c_HOL_Oord__class_Oless(X7,X6,X3)
      | ~ c_lessequals(X6,X7,X3) ),
    file('<stdin>',cls_linorder__not__less_1) ).

fof(c_0_494,axiom,
    ! [X7,X3] :
      ( ~ class_Orderings_Olinorder(X3)
      | ~ c_lessequals(X7,X7,X3)
      | ~ c_HOL_Oord__class_Oless(X7,X7,X3) ),
    file('<stdin>',cls_linorder__antisym__conv2_1) ).

fof(c_0_495,axiom,
    ! [X6,X7,X3] :
      ( ~ class_Orderings_Opreorder(X3)
      | ~ c_lessequals(X6,X7,X3)
      | ~ c_HOL_Oord__class_Oless(X7,X6,X3) ),
    file('<stdin>',cls_less__le__not__le_1) ).

fof(c_0_496,axiom,
    ! [X4,X5] :
      ( X4 = X5
      | ~ c_HOL_Oord__class_Oless(X4,c_Suc(X5),tc_nat)
      | ~ c_lessequals(X5,X4,tc_nat) ),
    file('<stdin>',cls_le__less__Suc__eq_0) ).

fof(c_0_497,axiom,
    ! [X18] : c_Parity_Oeven__odd__class_Oeven(c_HOL_Otimes__class_Otimes(c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),X18,tc_nat),tc_nat),
    file('<stdin>',cls_even__nat__equiv__def2_1) ).

fof(c_0_498,axiom,
    ! [X4,X5] :
      ( ~ c_HOL_Oord__class_Oless(X5,X4,tc_nat)
      | ~ c_HOL_Oord__class_Oless(X4,c_Suc(X5),tc_nat) ),
    file('<stdin>',cls_not__less__eq_1) ).

fof(c_0_499,axiom,
    ! [X4,X5] :
      ( ~ c_lessequals(X5,X4,tc_nat)
      | ~ c_lessequals(c_Suc(X4),X5,tc_nat) ),
    file('<stdin>',cls_not__less__eq__eq_1) ).

fof(c_0_500,axiom,
    ! [X4,X5] :
      ( c_HOL_Ominus__class_Ominus(X4,X5,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)
      | c_HOL_Ominus__class_Ominus(X5,X4,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)
      | X5 = X4 ),
    file('<stdin>',cls_diffs0__imp__equal_0) ).

fof(c_0_501,axiom,
    ! [X2,X3] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
      | c_lessequals(c_HOL_Ozero__class_Ozero(X3),c_HOL_Otimes__class_Otimes(X2,X2,X3),X3) ),
    file('<stdin>',cls_zero__le__square_0) ).

fof(c_0_502,axiom,
    ! [X5,X8,X3] :
      ( ~ class_Ring__and__Field_Oordered__idom(X3)
      | c_Ring__and__Field_Odvd__class_Odvd(X5,c_HOL_Oabs__class_Oabs(X8,X3),X3)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X5,X8,X3) ),
    file('<stdin>',cls_dvd__abs__iff_1) ).

fof(c_0_503,axiom,
    ! [X5,X8,X3] :
      ( ~ class_Ring__and__Field_Oordered__idom(X3)
      | c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oabs__class_Oabs(X5,X3),X8,X3)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X5,X8,X3) ),
    file('<stdin>',cls_abs__dvd__iff_1) ).

fof(c_0_504,axiom,
    ! [X4,X5] : c_Orderings_Oord__class_Omin(c_Suc(X5),c_Suc(X4),tc_nat) = c_Suc(c_Orderings_Oord__class_Omin(X5,X4,tc_nat)),
    file('<stdin>',cls_min__Suc__Suc_0) ).

fof(c_0_505,axiom,
    ! [X1,X2,X3] :
      ( ~ class_Divides_Osemiring__div(X3)
      | c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X2,X1,X3),X1,X3) = c_HOL_Ozero__class_Ozero(X3) ),
    file('<stdin>',cls_mod__mult__self2__is__0_0) ).

fof(c_0_506,axiom,
    ! [X1,X2,X3] :
      ( ~ 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) ),
    file('<stdin>',cls_mod__mult__self1__is__0_0) ).

fof(c_0_507,axiom,
    ! [X4,X5,X8] :
      ( c_HOL_Otimes__class_Otimes(X8,X5,tc_nat) != c_HOL_Otimes__class_Otimes(X8,X4,tc_nat)
      | X5 = X4
      | X8 = c_HOL_Ozero__class_Ozero(tc_nat) ),
    file('<stdin>',cls_nat__mult__eq__cancel__disj_0) ).

fof(c_0_508,axiom,
    ! [X4,X5,X8] :
      ( c_HOL_Otimes__class_Otimes(X8,X5,tc_nat) != c_HOL_Otimes__class_Otimes(X8,X4,tc_nat)
      | X8 = c_HOL_Ozero__class_Ozero(tc_nat)
      | X5 = X4 ),
    file('<stdin>',cls_mult__cancel1_0) ).

fof(c_0_509,axiom,
    ! [X4,X5,X8] :
      ( c_HOL_Otimes__class_Otimes(X5,X8,tc_nat) != c_HOL_Otimes__class_Otimes(X4,X8,tc_nat)
      | X8 = c_HOL_Ozero__class_Ozero(tc_nat)
      | X5 = X4 ),
    file('<stdin>',cls_mult__cancel2_0) ).

fof(c_0_510,axiom,
    ! [X6,X7] :
      ( X7 = X6
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X6,X7,tc_nat)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X7,X6,tc_nat) ),
    file('<stdin>',cls_dvd_Oeq__iff_2) ).

fof(c_0_511,axiom,
    ! [X4,X5] :
      ( X5 = X4
      | ~ c_lessequals(X4,X5,tc_nat)
      | ~ c_lessequals(X5,X4,tc_nat) ),
    file('<stdin>',cls_le__antisym_0) ).

fof(c_0_512,axiom,
    ! [X6,X7] :
      ( X7 = X6
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X6,X7,tc_nat)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X7,X6,tc_nat) ),
    file('<stdin>',cls_dvd_Oantisym_0) ).

fof(c_0_513,axiom,
    ! [X6,X7] :
      ( ~ c_Ring__and__Field_Odvd__class_Odvd(X6,X7,tc_nat)
      | X7 = X6
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X7,X6,tc_nat) ),
    file('<stdin>',cls_dvd_Oless__le_0) ).

fof(c_0_514,axiom,
    ! [X4,X5] :
      ( X5 = X4
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X5,tc_nat)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X5,X4,tc_nat) ),
    file('<stdin>',cls_dvd__antisym_0) ).

fof(c_0_515,axiom,
    ! [X6,X7] :
      ( X7 = X6
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X7,X6,tc_nat)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X6,X7,tc_nat) ),
    file('<stdin>',cls_dvd_Oantisym__conv_0) ).

fof(c_0_516,axiom,
    ! [X1,X2] :
      ( ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
      | X2 = X1
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X1,tc_nat) ),
    file('<stdin>',cls_dvd_Ole__neq__trans_0) ).

fof(c_0_517,axiom,
    ! [X1,X2] :
      ( ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X1,tc_nat)
      | X2 = X1 ),
    file('<stdin>',cls_dvd_Oneq__le__trans_0) ).

fof(c_0_518,axiom,
    ! [X1,X2,X3] :
      ( ~ class_OrderedGroup_Ogroup__add(X3)
      | c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X2,X1,X3),X1,X3) = X2 ),
    file('<stdin>',cls_add__diff__cancel_0) ).

fof(c_0_519,axiom,
    ! [X1,X2,X3] :
      ( ~ class_OrderedGroup_Ogroup__add(X3)
      | c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X2,X1,X3),X1,X3) = X2 ),
    file('<stdin>',cls_diff__add__cancel_0) ).

fof(c_0_520,axiom,
    ! [X16,X6,X7] :
      ( c_HOL_Oplus__class_Oplus(X7,X6,tc_nat) != c_HOL_Oplus__class_Oplus(X7,X16,tc_nat)
      | X6 = X16 ),
    file('<stdin>',cls_natgb_Oadd__cancel_0) ).

fof(c_0_521,axiom,
    ! [X4,X5,X8] :
      ( c_HOL_Oplus__class_Oplus(X8,X5,tc_nat) != c_HOL_Oplus__class_Oplus(X8,X4,tc_nat)
      | X5 = X4 ),
    file('<stdin>',cls_nat__add__left__cancel_0) ).

fof(c_0_522,axiom,
    ! [X4,X5,X8] :
      ( c_HOL_Oplus__class_Oplus(X5,X8,tc_nat) != c_HOL_Oplus__class_Oplus(X4,X8,tc_nat)
      | X5 = X4 ),
    file('<stdin>',cls_nat__add__right__cancel_0) ).

fof(c_0_523,axiom,
    ! [X8,X1,X3] :
      ( ~ class_Ring__and__Field_Odvd(X3)
      | c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Otimes__class_Otimes(X1,X8,X3),X3) ),
    file('<stdin>',cls_dvdI_0) ).

fof(c_0_524,axiom,
    ! [X1,X2,X3] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
      | c_Ring__and__Field_Odvd__class_Odvd(X2,c_HOL_Otimes__class_Otimes(X2,X1,X3),X3) ),
    file('<stdin>',cls_dvd__triv__left_0) ).

fof(c_0_525,axiom,
    ! [X1,X2,X3] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
      | c_Ring__and__Field_Odvd__class_Odvd(X2,c_HOL_Otimes__class_Otimes(X1,X2,X3),X3) ),
    file('<stdin>',cls_dvd__triv__right_0) ).

fof(c_0_526,axiom,
    ! [X6,X7,X3] :
      ( ~ class_Orderings_Olinorder(X3)
      | c_lessequals(c_Orderings_Oord__class_Omin(X7,X6,X3),X7,X3) ),
    file('<stdin>',cls_min__max_Oinf__le1_0) ).

fof(c_0_527,axiom,
    ! [X6,X7,X3] :
      ( ~ class_Orderings_Olinorder(X3)
      | c_lessequals(c_Orderings_Oord__class_Omin(X7,X6,X3),X6,X3) ),
    file('<stdin>',cls_min__max_Oinf__le2_0) ).

fof(c_0_528,axiom,
    ! [X2,X3] :
      ( ~ class_Ring__and__Field_Oordered__idom(X3)
      | c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(X2,X3),c_HOL_Oabs__class_Oabs(X2,X3),X3) = c_HOL_Otimes__class_Otimes(X2,X2,X3) ),
    file('<stdin>',cls_abs__mult__self_0) ).

fof(c_0_529,axiom,
    ! [X4,X5] : c_HOL_Oplus__class_Oplus(X5,c_Suc(X4),tc_nat) = c_Suc(c_HOL_Oplus__class_Oplus(X5,X4,tc_nat)),
    file('<stdin>',cls_add__Suc__right_0) ).

fof(c_0_530,axiom,
    ! [X4,X5] : c_HOL_Oplus__class_Oplus(c_Suc(X5),X4,tc_nat) = c_Suc(c_HOL_Oplus__class_Oplus(X5,X4,tc_nat)),
    file('<stdin>',cls_add__Suc_0) ).

fof(c_0_531,axiom,
    ! [X4,X5] : c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X5,X4,tc_nat),c_Suc(X5),tc_nat),
    file('<stdin>',cls_diff__less__Suc_0) ).

fof(c_0_532,axiom,
    ! [X3] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X3)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_HOL_Oabs__class_Oabs(c_HOL_Ozero__class_Ozero(X3),X3),X3) ),
    file('<stdin>',cls_zero__less__abs__iff_0) ).

fof(c_0_533,axiom,
    ! [X7] :
      ( c_Divides_Odiv__class_Omod(X7,c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
      | ~ c_Parity_Oeven__odd__class_Oeven(X7,tc_nat) ),
    file('<stdin>',cls_odd__nat__equiv__def_1) ).

fof(c_0_534,axiom,
    ! [X7,X20] : c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X20,X7,tc_nat),X20,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
    file('<stdin>',cls_mod__eq__0__iff_1) ).

fof(c_0_535,axiom,
    ! [X4,X5] : c_HOL_Ominus__class_Ominus(X4,c_HOL_Oplus__class_Oplus(X4,X5,tc_nat),tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
    file('<stdin>',cls_diff__add__0_0) ).

fof(c_0_536,axiom,
    ! [X4,X5] : c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X5,X4,tc_nat),X4,tc_nat) = X5,
    file('<stdin>',cls_diff__add__inverse2_0) ).

fof(c_0_537,axiom,
    ! [X4,X5] : c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X4,X5,tc_nat),X4,tc_nat) = X5,
    file('<stdin>',cls_diff__add__inverse_0) ).

fof(c_0_538,axiom,
    ! [X6,X7] :
      ( c_Parity_Oeven__odd__class_Oeven(c_HOL_Ominus__class_Ominus(X7,X6,tc_nat),tc_nat)
      | ~ c_Parity_Oeven__odd__class_Oeven(X6,tc_nat)
      | ~ c_Parity_Oeven__odd__class_Oeven(X7,tc_nat) ),
    file('<stdin>',cls_even__difference__nat_3) ).

fof(c_0_539,axiom,
    ! [X4,X5] :
      ( ~ c_Parity_Oeven__odd__class_Oeven(X4,tc_nat)
      | ~ c_Parity_Oeven__odd__class_Oeven(X5,tc_nat)
      | c_Parity_Oeven__odd__class_Oeven(c_HOL_Oplus__class_Oplus(X5,X4,tc_nat),tc_nat) ),
    file('<stdin>',cls_odd__add_0) ).

fof(c_0_540,axiom,
    ! [X4,X5] :
      ( c_Parity_Oeven__odd__class_Oeven(c_HOL_Oplus__class_Oplus(X5,X4,tc_nat),tc_nat)
      | ~ c_Parity_Oeven__odd__class_Oeven(X4,tc_nat)
      | ~ c_Parity_Oeven__odd__class_Oeven(X5,tc_nat) ),
    file('<stdin>',cls_even__add_3) ).

fof(c_0_541,axiom,
    ! [X6,X7] :
      ( c_Parity_Oeven__odd__class_Oeven(c_HOL_Oplus__class_Oplus(X7,X6,tc_nat),tc_nat)
      | ~ c_Parity_Oeven__odd__class_Oeven(X6,tc_nat)
      | ~ c_Parity_Oeven__odd__class_Oeven(X7,tc_nat) ),
    file('<stdin>',cls_even__sum__nat_2) ).

fof(c_0_542,axiom,
    ! [X4,X5] : c_lessequals(c_HOL_Ominus__class_Ominus(X5,X4,tc_nat),X5,tc_nat),
    file('<stdin>',cls_diff__le__self_0) ).

fof(c_0_543,axiom,
    ! [X4,X5] : c_lessequals(X4,c_HOL_Oplus__class_Oplus(X4,X5,tc_nat),tc_nat),
    file('<stdin>',cls_le__add1_0) ).

fof(c_0_544,axiom,
    ! [X4,X5] : c_lessequals(X4,c_HOL_Oplus__class_Oplus(X5,X4,tc_nat),tc_nat),
    file('<stdin>',cls_le__add2_0) ).

fof(c_0_545,axiom,
    ! [X7,X5] : c_lessequals(X5,c_HOL_Oplus__class_Oplus(X5,X7,tc_nat),tc_nat),
    file('<stdin>',cls_le__iff__add_1) ).

fof(c_0_546,axiom,
    ! [X7,X8] : c_lessequals(X8,c_HOL_Oplus__class_Oplus(X8,X7,tc_nat),tc_nat),
    file('<stdin>',cls_le__Suc__ex__iff_1) ).

fof(c_0_547,axiom,
    ! [X5] : c_lessequals(X5,c_HOL_Otimes__class_Otimes(X5,X5,tc_nat),tc_nat),
    file('<stdin>',cls_le__square_0) ).

fof(c_0_548,axiom,
    ! [X4,X5] : c_lessequals(c_Divides_Odiv__class_Omod(X5,X4,tc_nat),X5,tc_nat),
    file('<stdin>',cls_mod__less__eq__dividend_0) ).

fof(c_0_549,axiom,
    ! [X4,X5] :
      ( c_HOL_Oord__class_Oless(X5,X4,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_Suc(X5),c_Suc(X4),tc_nat) ),
    file('<stdin>',cls_Suc__less__eq_0) ).

fof(c_0_550,axiom,
    ! [X4,X5] :
      ( c_lessequals(X4,X5,tc_nat)
      | ~ c_lessequals(c_Suc(X4),c_Suc(X5),tc_nat) ),
    file('<stdin>',cls_Suc__le__mono_0) ).

fof(c_0_551,axiom,
    ! [X1,X2,X3] :
      ( ~ class_Divides_Osemiring__div(X3)
      | c_Divides_Odiv__class_Omod(X1,X2,X3) != c_HOL_Ozero__class_Ozero(X3)
      | c_Ring__and__Field_Odvd__class_Odvd(X2,X1,X3) ),
    file('<stdin>',cls_dvd__eq__mod__eq__0_1) ).

fof(c_0_552,axiom,
    ! [X1,X2,X3] :
      ( ~ class_Divides_Osemiring__div(X3)
      | c_Divides_Odiv__class_Omod(X1,X2,X3) = c_HOL_Ozero__class_Ozero(X3)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X1,X3) ),
    file('<stdin>',cls_dvd__imp__mod__0_0) ).

fof(c_0_553,axiom,
    ! [X4,X5] :
      ( X5 = c_Suc(X4)
      | c_lessequals(X5,X4,tc_nat)
      | ~ c_lessequals(X5,c_Suc(X4),tc_nat) ),
    file('<stdin>',cls_le__SucE_0) ).

fof(c_0_554,axiom,
    ! [X6,X7,X3] :
      ( ~ class_Orderings_Oorder(X3)
      | c_HOL_Oord__class_Oless(X7,X6,X3)
      | X7 = X6
      | ~ c_lessequals(X7,X6,X3) ),
    file('<stdin>',cls_order__less__le_2) ).

fof(c_0_555,axiom,
    ! [X6,X7,X3] :
      ( ~ class_Orderings_Oorder(X3)
      | X7 = X6
      | c_HOL_Oord__class_Oless(X7,X6,X3)
      | ~ c_lessequals(X7,X6,X3) ),
    file('<stdin>',cls_order__le__less_0) ).

fof(c_0_556,axiom,
    ! [X1,X2,X3] :
      ( ~ class_Orderings_Oorder(X3)
      | c_HOL_Oord__class_Oless(X2,X1,X3)
      | X2 = X1
      | ~ c_lessequals(X2,X1,X3) ),
    file('<stdin>',cls_order__le__neq__trans_0) ).

fof(c_0_557,axiom,
    ! [X1,X2,X3] :
      ( ~ class_Orderings_Oorder(X3)
      | c_HOL_Oord__class_Oless(X2,X1,X3)
      | ~ c_lessequals(X2,X1,X3)
      | X2 = X1 ),
    file('<stdin>',cls_order__neq__le__trans_0) ).

fof(c_0_558,axiom,
    ! [X6,X7,X3] :
      ( ~ class_Orderings_Olinorder(X3)
      | X7 = X6
      | ~ c_lessequals(X7,X6,X3)
      | c_HOL_Oord__class_Oless(X7,X6,X3) ),
    file('<stdin>',cls_linorder__antisym__conv1_0) ).

fof(c_0_559,axiom,
    ! [X6,X7,X3] :
      ( ~ class_Orderings_Olinorder(X3)
      | X7 = X6
      | c_HOL_Oord__class_Oless(X7,X6,X3)
      | ~ c_lessequals(X7,X6,X3) ),
    file('<stdin>',cls_linorder__antisym__conv2_0) ).

fof(c_0_560,axiom,
    ! [X1,X2,X3] :
      ( ~ class_Orderings_Oorder(X3)
      | c_HOL_Oord__class_Oless(X1,X2,X3)
      | ~ c_lessequals(X1,X2,X3)
      | X2 = X1 ),
    file('<stdin>',cls_xt1_I12_J_0) ).

fof(c_0_561,axiom,
    ! [X1,X2,X3] :
      ( ~ class_Orderings_Oorder(X3)
      | c_HOL_Oord__class_Oless(X1,X2,X3)
      | X2 = X1
      | ~ c_lessequals(X1,X2,X3) ),
    file('<stdin>',cls_xt1_I11_J_0) ).

fof(c_0_562,axiom,
    ! [X6,X7,X3] :
      ( ~ class_Orderings_Olinorder(X3)
      | c_Orderings_Oord__class_Omin(X7,X6,X3) != X7
      | c_lessequals(X7,X6,X3) ),
    file('<stdin>',cls_min__max_Ole__iff__inf_1) ).

fof(c_0_563,axiom,
    ! [X7,X4] :
      ( c_HOL_Oord__class_Oless(c_Suc(X7),c_Suc(X4),tc_nat)
      | ~ c_HOL_Oord__class_Oless(X7,X4,tc_nat) ),
    file('<stdin>',cls_less__Suc__eq__0__disj_3) ).

fof(c_0_564,axiom,
    ! [X4,X5] :
      ( c_HOL_Oord__class_Oless(c_Suc(X5),c_Suc(X4),tc_nat)
      | ~ c_HOL_Oord__class_Oless(X5,X4,tc_nat) ),
    file('<stdin>',cls_Suc__mono_0) ).

fof(c_0_565,axiom,
    ! [X4,X5] :
      ( c_lessequals(c_Suc(X4),c_Suc(X5),tc_nat)
      | ~ c_lessequals(X4,X5,tc_nat) ),
    file('<stdin>',cls_Suc__le__mono_1) ).

fof(c_0_566,axiom,
    ! [X4,X5] :
      ( X4 = X5
      | ~ c_HOL_Oord__class_Oless(X4,c_Suc(X5),tc_nat)
      | c_HOL_Oord__class_Oless(X4,X5,tc_nat) ),
    file('<stdin>',cls_not__less__less__Suc__eq_0) ).

fof(c_0_567,axiom,
    ! [X4,X5] :
      ( X5 = X4
      | ~ c_HOL_Oord__class_Oless(X4,c_Suc(X5),tc_nat)
      | c_HOL_Oord__class_Oless(X4,X5,tc_nat) ),
    file('<stdin>',cls_less__antisym_0) ).

fof(c_0_568,axiom,
    ! [X4,X5] :
      ( X5 = X4
      | c_HOL_Oord__class_Oless(X5,X4,tc_nat)
      | ~ c_HOL_Oord__class_Oless(X5,c_Suc(X4),tc_nat) ),
    file('<stdin>',cls_less__SucE_0) ).

fof(c_0_569,axiom,
    ! [X6,X7,X3] :
      ( ~ class_Orderings_Olinorder(X3)
      | c_Orderings_Oord__class_Omin(X7,X6,X3) = X6
      | ~ c_lessequals(X6,X7,X3) ),
    file('<stdin>',cls_min__max_Oinf__absorb2_0) ).

fof(c_0_570,axiom,
    ! [X6,X7,X3] :
      ( ~ class_Orderings_Olinorder(X3)
      | c_Orderings_Oord__class_Omin(X7,X6,X3) = X7
      | ~ c_lessequals(X7,X6,X3) ),
    file('<stdin>',cls_min__max_Ole__iff__inf_0) ).

fof(c_0_571,axiom,
    ! [X2,X3] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X3)
      | X2 = c_HOL_Ozero__class_Ozero(X3)
      | ~ c_lessequals(c_HOL_Oabs__class_Oabs(X2,X3),c_HOL_Ozero__class_Ozero(X3),X3) ),
    file('<stdin>',cls_abs__le__zero__iff_0) ).

fof(c_0_572,axiom,
    ! [X4,X5] :
      ( c_HOL_Oord__class_Oless(c_Suc(X5),X4,tc_nat)
      | c_Suc(X5) = X4
      | ~ c_HOL_Oord__class_Oless(X5,X4,tc_nat) ),
    file('<stdin>',cls_Suc__lessI_0) ).

fof(c_0_573,axiom,
    ! [X6,X7,X3] :
      ( ~ class_Orderings_Oorder(X3)
      | c_lessequals(X7,X6,X3)
      | ~ c_HOL_Oord__class_Oless(X7,X6,X3) ),
    file('<stdin>',cls_order__le__less_1) ).

fof(c_0_574,axiom,
    ! [X6,X7,X3] :
      ( ~ class_Orderings_Opreorder(X3)
      | c_lessequals(X7,X6,X3)
      | ~ c_HOL_Oord__class_Oless(X7,X6,X3) ),
    file('<stdin>',cls_order__less__imp__le_0) ).

fof(c_0_575,axiom,
    ! [X7] :
      ( c_Divides_Odiv__class_Omod(X7,c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)
      | c_Parity_Oeven__odd__class_Oeven(X7,tc_nat) ),
    file('<stdin>',cls_even__nat__equiv__def_1) ).

fof(c_0_576,axiom,
    ! [X4,X5] :
      ( c_HOL_Oord__class_Oless(X5,X4,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_Suc(X5),X4,tc_nat) ),
    file('<stdin>',cls_Suc__lessD_0) ).

fof(c_0_577,axiom,
    ! [X4,X5] :
      ( c_lessequals(X5,X4,tc_nat)
      | ~ c_lessequals(c_Suc(X5),X4,tc_nat) ),
    file('<stdin>',cls_Suc__leD_0) ).

fof(c_0_578,axiom,
    ! [X4,X5] :
      ( c_lessequals(X5,X4,tc_nat)
      | ~ c_HOL_Oord__class_Oless(X5,c_Suc(X4),tc_nat) ),
    file('<stdin>',cls_less__Suc__eq__le_0) ).

fof(c_0_579,axiom,
    ! [X4,X5] :
      ( c_HOL_Oord__class_Oless(X4,X5,tc_nat)
      | ~ c_lessequals(c_Suc(X4),X5,tc_nat) ),
    file('<stdin>',cls_less__eq__Suc__le_1) ).

fof(c_0_580,axiom,
    ! [X4,X5] :
      ( c_HOL_Oord__class_Oless(X5,X4,tc_nat)
      | ~ c_lessequals(c_Suc(X5),X4,tc_nat) ),
    file('<stdin>',cls_Suc__le__eq_0) ).

fof(c_0_581,axiom,
    ! [X7] :
      ( X7 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
      | X7 = c_HOL_Ozero__class_Ozero(tc_nat)
      | ~ c_HOL_Oord__class_Oless(X7,c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),tc_nat) ),
    file('<stdin>',cls_nat__lt__two__imp__zero__or__one_0) ).

fof(c_0_582,axiom,
    ! [X2,X3] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X3)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(X2,X3),c_HOL_Ozero__class_Ozero(X3),X3) ),
    file('<stdin>',cls_abs__not__less__zero_0) ).

fof(c_0_583,axiom,
    ! [X5,X3] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X3)
      | ~ c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X5,X3),c_HOL_Ozero__class_Ozero(X3),X3) ),
    file('<stdin>',cls_of__nat__less__0__iff_0) ).

fof(c_0_584,axiom,
    ! [X4,X5] :
      ( c_HOL_Oord__class_Oless(X5,c_Suc(X4),tc_nat)
      | ~ c_HOL_Oord__class_Oless(X5,X4,tc_nat) ),
    file('<stdin>',cls_less__SucI_0) ).

fof(c_0_585,axiom,
    ! [X4,X5] :
      ( c_lessequals(X5,c_Suc(X4),tc_nat)
      | ~ c_lessequals(X5,X4,tc_nat) ),
    file('<stdin>',cls_le__SucI_0) ).

fof(c_0_586,axiom,
    ! [X7] :
      ( ~ c_lessequals(X7,X7,tc_nat)
      | c_HOL_Oord__class_Oless(X7,c_Suc(X7),tc_nat) ),
    file('<stdin>',cls_le__less__Suc__eq_1) ).

fof(c_0_587,axiom,
    ! [X4,X5] :
      ( c_HOL_Oord__class_Oless(X5,c_Suc(X4),tc_nat)
      | ~ c_lessequals(X5,X4,tc_nat) ),
    file('<stdin>',cls_less__Suc__eq__le_1) ).

fof(c_0_588,axiom,
    ! [X4,X5] :
      ( c_lessequals(c_Suc(X4),X5,tc_nat)
      | ~ c_HOL_Oord__class_Oless(X4,X5,tc_nat) ),
    file('<stdin>',cls_less__eq__Suc__le_0) ).

fof(c_0_589,axiom,
    ! [X4,X5] :
      ( c_lessequals(c_Suc(X5),X4,tc_nat)
      | ~ c_HOL_Oord__class_Oless(X5,X4,tc_nat) ),
    file('<stdin>',cls_Suc__leI_0) ).

fof(c_0_590,axiom,
    ! [X6,X7] :
      ( c_Parity_Oeven__odd__class_Oeven(c_HOL_Ominus__class_Ominus(X7,X6,tc_nat),tc_nat)
      | c_Parity_Oeven__odd__class_Oeven(X6,tc_nat)
      | c_Parity_Oeven__odd__class_Oeven(X7,tc_nat) ),
    file('<stdin>',cls_even__difference__nat_4) ).

fof(c_0_591,axiom,
    ! [X4,X5] :
      ( c_Parity_Oeven__odd__class_Oeven(X5,tc_nat)
      | c_Parity_Oeven__odd__class_Oeven(X4,tc_nat)
      | c_Parity_Oeven__odd__class_Oeven(c_HOL_Oplus__class_Oplus(X5,X4,tc_nat),tc_nat) ),
    file('<stdin>',cls_odd__add_1) ).

fof(c_0_592,axiom,
    ! [X4,X5] :
      ( c_Parity_Oeven__odd__class_Oeven(c_HOL_Oplus__class_Oplus(X5,X4,tc_nat),tc_nat)
      | c_Parity_Oeven__odd__class_Oeven(X4,tc_nat)
      | c_Parity_Oeven__odd__class_Oeven(X5,tc_nat) ),
    file('<stdin>',cls_even__add_2) ).

fof(c_0_593,axiom,
    ! [X6,X7] :
      ( c_Parity_Oeven__odd__class_Oeven(c_HOL_Oplus__class_Oplus(X7,X6,tc_nat),tc_nat)
      | c_Parity_Oeven__odd__class_Oeven(X6,tc_nat)
      | c_Parity_Oeven__odd__class_Oeven(X7,tc_nat) ),
    file('<stdin>',cls_even__sum__nat_3) ).

fof(c_0_594,axiom,
    ! [X4,X5] :
      ( c_HOL_Ominus__class_Ominus(X5,X4,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)
      | c_lessequals(X5,X4,tc_nat) ),
    file('<stdin>',cls_diff__is__0__eq_0) ).

fof(c_0_595,axiom,
    ! [X4,X5] :
      ( c_HOL_Oord__class_Oless(X5,X4,tc_nat)
      | X5 = X4
      | ~ c_lessequals(X5,X4,tc_nat) ),
    file('<stdin>',cls_le__neq__implies__less_0) ).

fof(c_0_596,axiom,
    ! [X4,X5] :
      ( X5 = X4
      | c_HOL_Oord__class_Oless(X5,X4,tc_nat)
      | ~ c_lessequals(X5,X4,tc_nat) ),
    file('<stdin>',cls_le__eq__less__or__eq_0) ).

fof(c_0_597,axiom,
    ! [X4,X5] :
      ( c_HOL_Oord__class_Oless(X5,X4,tc_nat)
      | X5 = X4
      | ~ c_lessequals(X5,X4,tc_nat) ),
    file('<stdin>',cls_nat__less__le_2) ).

fof(c_0_598,axiom,
    ! [X4,X5] :
      ( c_HOL_Ominus__class_Ominus(X5,X4,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat)
      | ~ c_lessequals(X5,X4,tc_nat) ),
    file('<stdin>',cls_diff__is__0__eq_1) ).

fof(c_0_599,axiom,
    ! [X4,X5] :
      ( c_Divides_Odiv__class_Omod(X5,X4,tc_nat) = X5
      | ~ c_HOL_Oord__class_Oless(X5,X4,tc_nat) ),
    file('<stdin>',cls_mod__if_0) ).

fof(c_0_600,axiom,
    ! [X4,X5] :
      ( c_lessequals(X5,X4,tc_nat)
      | ~ c_HOL_Oord__class_Oless(X5,X4,tc_nat) ),
    file('<stdin>',cls_nat__less__le_0) ).

fof(c_0_601,axiom,
    ! [X6,X7] :
      ( c_lessequals(X7,X6,tc_nat)
      | ~ c_HOL_Oord__class_Oless(X7,X6,tc_nat) ),
    file('<stdin>',cls_termination__basic__simps_I5_J_0) ).

fof(c_0_602,axiom,
    ! [X6,X7] :
      ( c_Parity_Oeven__odd__class_Oeven(c_HOL_Otimes__class_Otimes(X7,X6,tc_nat),tc_nat)
      | ~ c_Parity_Oeven__odd__class_Oeven(X7,tc_nat) ),
    file('<stdin>',cls_even__product__nat_1) ).

fof(c_0_603,axiom,
    ! [X6,X7] :
      ( c_Parity_Oeven__odd__class_Oeven(c_HOL_Otimes__class_Otimes(X7,X6,tc_nat),tc_nat)
      | ~ c_Parity_Oeven__odd__class_Oeven(X6,tc_nat) ),
    file('<stdin>',cls_even__product__nat_2) ).

fof(c_0_604,axiom,
    ! [X6,X7,X3] :
      ( ~ class_Orderings_Olinorder(X3)
      | c_HOL_Oord__class_Oless(X6,X7,X3)
      | c_HOL_Oord__class_Oless(X7,X6,X3)
      | X7 = X6 ),
    file('<stdin>',cls_linorder__neqE_0) ).

fof(c_0_605,axiom,
    ! [X6,X7,X3] :
      ( ~ class_Orderings_Olinorder(X3)
      | c_HOL_Oord__class_Oless(X6,X7,X3)
      | X7 = X6
      | c_HOL_Oord__class_Oless(X7,X6,X3) ),
    file('<stdin>',cls_linorder__less__linear_0) ).

fof(c_0_606,axiom,
    ! [X6,X7,X3] :
      ( ~ class_Orderings_Olinorder(X3)
      | X7 = X6
      | c_HOL_Oord__class_Oless(X7,X6,X3)
      | c_HOL_Oord__class_Oless(X6,X7,X3) ),
    file('<stdin>',cls_linorder__antisym__conv3_0) ).

fof(c_0_607,axiom,
    ! [X6,X7,X3] :
      ( ~ class_Orderings_Olinorder(X3)
      | X7 = X6
      | c_HOL_Oord__class_Oless(X6,X7,X3)
      | c_HOL_Oord__class_Oless(X7,X6,X3) ),
    file('<stdin>',cls_not__less__iff__gr__or__eq_0) ).

fof(c_0_608,axiom,
    ! [X6,X7,X3] :
      ( ~ class_Ring__and__Field_Oordered__idom(X3)
      | c_HOL_Oord__class_Oless(X6,X7,X3)
      | c_HOL_Oord__class_Oless(X7,X6,X3)
      | X7 = X6 ),
    file('<stdin>',cls_linorder__neqE__ordered__idom_0) ).

fof(c_0_609,axiom,
    ! [X2,X3] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X3)
      | c_HOL_Oabs__class_Oabs(X2,X3) = X2
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3) ),
    file('<stdin>',cls_abs__of__pos_0) ).

fof(c_0_610,axiom,
    ! [X2,X3] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X3)
      | c_HOL_Oabs__class_Oabs(X2,X3) = X2
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X2,X3) ),
    file('<stdin>',cls_abs__of__nonneg_0) ).

fof(c_0_611,axiom,
    ! [X4,X5] : c_HOL_Ominus__class_Ominus(c_Suc(X5),c_Suc(X4),tc_nat) = c_HOL_Ominus__class_Ominus(X5,X4,tc_nat),
    file('<stdin>',cls_diff__Suc__Suc_0) ).

fof(c_0_612,axiom,
    ! [X4,X5] : c_HOL_Oplus__class_Oplus(c_Suc(X5),X4,tc_nat) = c_HOL_Oplus__class_Oplus(X5,c_Suc(X4),tc_nat),
    file('<stdin>',cls_add__Suc__shift_0) ).

fof(c_0_613,axiom,
    ! [X6,X7,X3] :
      ( ~ class_Orderings_Olinorder(X3)
      | c_lessequals(X6,X7,X3)
      | c_lessequals(X7,X6,X3) ),
    file('<stdin>',cls_linorder__linear_0) ).

fof(c_0_614,axiom,
    ! [X6,X7,X3] :
      ( ~ class_Orderings_Olinorder(X3)
      | c_HOL_Oord__class_Oless(X6,X7,X3)
      | c_lessequals(X7,X6,X3) ),
    file('<stdin>',cls_linorder__not__le_0) ).

fof(c_0_615,axiom,
    ! [X6,X7,X3] :
      ( ~ class_Orderings_Olinorder(X3)
      | c_lessequals(X6,X7,X3)
      | c_HOL_Oord__class_Oless(X7,X6,X3) ),
    file('<stdin>',cls_linorder__not__less_0) ).

fof(c_0_616,axiom,
    ! [X7,X3] :
      ( ~ class_Orderings_Olinorder(X3)
      | c_HOL_Oord__class_Oless(X7,X7,X3)
      | c_lessequals(X7,X7,X3) ),
    file('<stdin>',cls_linorder__antisym__conv1_1) ).

fof(c_0_617,axiom,
    ! [X6,X7,X3] :
      ( ~ class_Orderings_Olinorder(X3)
      | c_HOL_Oord__class_Oless(X7,X6,X3)
      | c_lessequals(X6,X7,X3) ),
    file('<stdin>',cls_not__leE_0) ).

fof(c_0_618,axiom,
    ! [X1,X2,X3] :
      ( ~ class_OrderedGroup_Ocomm__monoid__add(X3)
      | c_HOL_Oplus__class_Oplus(X2,X1,X3) = c_HOL_Oplus__class_Oplus(X1,X2,X3) ),
    file('<stdin>',cls_comm__monoid__add_Omult__commute_0) ).

fof(c_0_619,axiom,
    ! [X6,X7,X3] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
      | c_HOL_Oplus__class_Oplus(X7,X6,X3) = c_HOL_Oplus__class_Oplus(X6,X7,X3) ),
    file('<stdin>',cls_class__semiring_Oadd__c_0) ).

fof(c_0_620,axiom,
    ! [X15,X2,X3] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
      | c_HOL_Oplus__class_Oplus(X2,X15,X3) = c_HOL_Oplus__class_Oplus(X15,X2,X3) ),
    file('<stdin>',cls_class__semiring_Osemiring__rules_I24_J_0) ).

fof(c_0_621,axiom,
    ! [X6,X7,X3] :
      ( ~ class_Orderings_Olinorder(X3)
      | c_Orderings_Oord__class_Omin(X7,X6,X3) = c_Orderings_Oord__class_Omin(X6,X7,X3) ),
    file('<stdin>',cls_min__max_Oinf__commute_0) ).

fof(c_0_622,axiom,
    ! [X1,X2,X3] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
      | c_HOL_Otimes__class_Otimes(X2,X1,X3) = c_HOL_Otimes__class_Otimes(X1,X2,X3) ),
    file('<stdin>',cls_class__semiring_Osemiring__rules_I7_J_0) ).

fof(c_0_623,axiom,
    ! [X6,X7,X3] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
      | c_HOL_Otimes__class_Otimes(X7,X6,X3) = c_HOL_Otimes__class_Otimes(X6,X7,X3) ),
    file('<stdin>',cls_class__semiring_Omul__c_0) ).

fof(c_0_624,axiom,
    ! [X7] :
      ( c_HOL_Oord__class_Oless(X7,X7,tc_nat)
      | c_HOL_Oord__class_Oless(X7,c_Suc(X7),tc_nat) ),
    file('<stdin>',cls_not__less__less__Suc__eq_1) ).

fof(c_0_625,axiom,
    ! [X4,X5] :
      ( c_HOL_Oord__class_Oless(X4,c_Suc(X5),tc_nat)
      | c_HOL_Oord__class_Oless(X5,X4,tc_nat) ),
    file('<stdin>',cls_not__less__eq_0) ).

fof(c_0_626,axiom,
    ! [X4,X5] :
      ( c_lessequals(c_Suc(X4),X5,tc_nat)
      | c_lessequals(X5,X4,tc_nat) ),
    file('<stdin>',cls_not__less__eq__eq_0) ).

fof(c_0_627,axiom,
    ! [X4,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),X4,tc_nat),
    file('<stdin>',cls_mult__cancel1_1) ).

fof(c_0_628,axiom,
    ! [X4,X5] : c_HOL_Otimes__class_Otimes(X5,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = c_HOL_Otimes__class_Otimes(X4,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
    file('<stdin>',cls_mult__cancel2_1) ).

fof(c_0_629,axiom,
    ! [X4,X5] :
      ( c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != c_HOL_Oplus__class_Oplus(X5,X4,tc_nat)
      | X4 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
      | X5 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
    file('<stdin>',cls_one__is__add_1) ).

fof(c_0_630,axiom,
    ! [X5] :
      ( X5 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X5,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) ),
    file('<stdin>',cls_dvd__1__iff__1_0) ).

fof(c_0_631,axiom,
    ! [X4,X5] :
      ( c_HOL_Oplus__class_Oplus(X5,X4,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
      | X4 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
      | X5 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
    file('<stdin>',cls_add__is__1_1) ).

fof(c_0_632,axiom,
    ! [X1,X2,X3] :
      ( ~ class_Ring__and__Field_Ono__zero__divisors(X3)
      | c_HOL_Otimes__class_Otimes(X2,X1,X3) != c_HOL_Ozero__class_Ozero(X3)
      | X2 = c_HOL_Ozero__class_Ozero(X3)
      | X1 = c_HOL_Ozero__class_Ozero(X3) ),
    file('<stdin>',cls_no__zero__divirors__neq0_0) ).

fof(c_0_633,axiom,
    ! [X1,X2,X3] :
      ( ~ class_Ring__and__Field_Ono__zero__divisors(X3)
      | c_HOL_Otimes__class_Otimes(X2,X1,X3) != c_HOL_Ozero__class_Ozero(X3)
      | X1 = c_HOL_Ozero__class_Ozero(X3)
      | X2 = c_HOL_Ozero__class_Ozero(X3) ),
    file('<stdin>',cls_no__zero__divisors_0) ).

fof(c_0_634,axiom,
    ! [X1,X2,X3] :
      ( ~ class_Ring__and__Field_Oring__no__zero__divisors(X3)
      | c_HOL_Otimes__class_Otimes(X2,X1,X3) != c_HOL_Ozero__class_Ozero(X3)
      | X1 = c_HOL_Ozero__class_Ozero(X3)
      | X2 = c_HOL_Ozero__class_Ozero(X3) ),
    file('<stdin>',cls_mult__eq__0__iff_0) ).

fof(c_0_635,axiom,
    ! [X6,X7] :
      ( c_HOL_Oord__class_Oless(X6,X7,tc_nat)
      | c_HOL_Oord__class_Oless(X7,X6,tc_nat)
      | X7 = X6 ),
    file('<stdin>',cls_linorder__neqE__nat_0) ).

fof(c_0_636,axiom,
    ! [X4,X5] :
      ( c_HOL_Oord__class_Oless(X4,X5,tc_nat)
      | c_HOL_Oord__class_Oless(X5,X4,tc_nat)
      | X5 = X4 ),
    file('<stdin>',cls_nat__neq__iff_0) ).

fof(c_0_637,axiom,
    ! [X6,X7,X3] :
      ( ~ class_Ring__and__Field_Oidom(X3)
      | ~ class_Int_Onumber__ring(X3)
      | c_HOL_Ominus__class_Ominus(X7,X6,X3) != c_HOL_Ozero__class_Ozero(X3)
      | X7 = X6 ),
    file('<stdin>',cls_class__ringb_Osubr0__iff_0) ).

fof(c_0_638,axiom,
    ! [X2,X3] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
      | X2 = c_HOL_Ozero__class_Ozero(X3)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ozero__class_Ozero(X3),X2,X3) ),
    file('<stdin>',cls_dvd__0__left_0) ).

fof(c_0_639,axiom,
    ! [X7,X2,X3] :
      ( ~ class_Ring__and__Field_Oidom(X3)
      | ~ class_Int_Onumber__ring(X3)
      | X7 != c_HOL_Oplus__class_Oplus(X7,X2,X3)
      | X2 = c_HOL_Ozero__class_Ozero(X3) ),
    file('<stdin>',cls_class__ringb_Oadd__r0__iff_0) ).

fof(c_0_640,axiom,
    ! [X4,X5] :
      ( c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != c_HOL_Oplus__class_Oplus(X5,X4,tc_nat)
      | X5 = c_HOL_Ozero__class_Ozero(tc_nat)
      | X5 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
    file('<stdin>',cls_one__is__add_0) ).

fof(c_0_641,axiom,
    ! [X4,X5] :
      ( c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != c_HOL_Oplus__class_Oplus(X5,X4,tc_nat)
      | X4 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
      | X4 = c_HOL_Ozero__class_Ozero(tc_nat) ),
    file('<stdin>',cls_one__is__add_3) ).

fof(c_0_642,axiom,
    ! [X4,X5] :
      ( c_HOL_Oplus__class_Oplus(X5,X4,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
      | X4 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
      | X4 = c_HOL_Ozero__class_Ozero(tc_nat) ),
    file('<stdin>',cls_add__is__1_3) ).

fof(c_0_643,axiom,
    ! [X4,X5] :
      ( c_HOL_Oplus__class_Oplus(X5,X4,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
      | X5 = c_HOL_Ozero__class_Ozero(tc_nat)
      | X5 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
    file('<stdin>',cls_add__is__1_0) ).

fof(c_0_644,axiom,
    ! [X4] :
      ( X4 = c_HOL_Ozero__class_Ozero(tc_nat)
      | ~ c_HOL_Oord__class_Oless(X4,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) ),
    file('<stdin>',cls_less__Suc0_0) ).

fof(c_0_645,axiom,
    ! [X4,X5] :
      ( c_lessequals(X4,X5,tc_nat)
      | c_lessequals(X5,X4,tc_nat) ),
    file('<stdin>',cls_nat__le__linear_0) ).

fof(c_0_646,axiom,
    ! [X7] :
      ( c_Divides_Odiv__class_Omod(X7,c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat)
      | ~ c_Parity_Oeven__odd__class_Oeven(X7,tc_nat) ),
    file('<stdin>',cls_even__nat__equiv__def_0) ).

fof(c_0_647,axiom,
    ! [X29,X8,X3] :
      ( ~ class_Ring__and__Field_Oordered__idom(X3)
      | c_HOL_Oabs__class_Oabs(X29,X3) != c_HOL_Oabs__class_Oabs(X8,X3)
      | c_Ring__and__Field_Odvd__class_Odvd(X29,X8,X3) ),
    file('<stdin>',cls_dvd__if__abs__eq_0) ).

fof(c_0_648,axiom,
    ! [X3] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X3)
      | c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Ozero__class_Ozero(X3),X3),c_HOL_Ozero__class_Ozero(X3),X3) ),
    file('<stdin>',cls_abs__le__zero__iff_1) ).

fof(c_0_649,axiom,
    ! [X4,X5] : c_HOL_Oplus__class_Oplus(X5,X4,tc_nat) = c_HOL_Oplus__class_Oplus(X4,X5,tc_nat),
    file('<stdin>',cls_nat__add__commute_0) ).

fof(c_0_650,axiom,
    ! [X4,X5] : c_HOL_Otimes__class_Otimes(X5,X4,tc_nat) = c_HOL_Otimes__class_Otimes(X4,X5,tc_nat),
    file('<stdin>',cls_nat__mult__commute_0) ).

fof(c_0_651,axiom,
    ! [X2,X3] :
      ( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
      | c_HOL_Oplus__class_Oplus(X2,X2,X3) != c_HOL_Ozero__class_Ozero(X3)
      | X2 = c_HOL_Ozero__class_Ozero(X3) ),
    file('<stdin>',cls_double__eq__0__iff_0) ).

fof(c_0_652,axiom,
    ! [X7] :
      ( c_Divides_Odiv__class_Omod(X7,c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),tc_nat) = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
      | c_Parity_Oeven__odd__class_Oeven(X7,tc_nat) ),
    file('<stdin>',cls_odd__nat__equiv__def_0) ).

fof(c_0_653,axiom,
    ! [X4,X5] :
      ( c_HOL_Otimes__class_Otimes(X5,X4,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
      | X4 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
    file('<stdin>',cls_mult__eq__1__iff_1) ).

fof(c_0_654,axiom,
    ! [X4,X5] :
      ( c_HOL_Otimes__class_Otimes(X5,X4,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
      | X5 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
    file('<stdin>',cls_mult__eq__1__iff_0) ).

fof(c_0_655,axiom,
    ! [X4,X5] :
      ( c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != c_HOL_Oplus__class_Oplus(X5,X4,tc_nat)
      | X5 = c_HOL_Ozero__class_Ozero(tc_nat)
      | X4 = c_HOL_Ozero__class_Ozero(tc_nat) ),
    file('<stdin>',cls_one__is__add_2) ).

fof(c_0_656,axiom,
    ! [X4,X5] :
      ( c_HOL_Oplus__class_Oplus(X5,X4,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
      | X5 = c_HOL_Ozero__class_Ozero(tc_nat)
      | X4 = c_HOL_Ozero__class_Ozero(tc_nat) ),
    file('<stdin>',cls_add__is__1_2) ).

fof(c_0_657,axiom,
    ! [X1,X2,X3] :
      ( ~ class_OrderedGroup_Ogroup__add(X3)
      | c_HOL_Ominus__class_Ominus(X2,X1,X3) != c_HOL_Ozero__class_Ozero(X3)
      | X2 = X1 ),
    file('<stdin>',cls_right__minus__eq_0) ).

fof(c_0_658,axiom,
    ! [X1,X2,X3] :
      ( ~ class_OrderedGroup_Oab__group__add(X3)
      | c_HOL_Ominus__class_Ominus(X2,X1,X3) != c_HOL_Ozero__class_Ozero(X3)
      | X2 = X1 ),
    file('<stdin>',cls_eq__iff__diff__eq__0_1) ).

fof(c_0_659,axiom,
    ! [X2,X3] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X3)
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_HOL_Oabs__class_Oabs(X2,X3),X3)
      | X2 = c_HOL_Ozero__class_Ozero(X3) ),
    file('<stdin>',cls_zero__less__abs__iff_1) ).

fof(c_0_660,axiom,
    ! [X4,X5] :
      ( c_HOL_Otimes__class_Otimes(X5,X4,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)
      | X4 = c_HOL_Ozero__class_Ozero(tc_nat)
      | X5 = c_HOL_Ozero__class_Ozero(tc_nat) ),
    file('<stdin>',cls_mult__is__0_0) ).

fof(c_0_661,axiom,
    ! [X2,X3] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X3)
      | c_lessequals(c_HOL_Ozero__class_Ozero(X3),c_HOL_Oabs__class_Oabs(X2,X3),X3) ),
    file('<stdin>',cls_abs__ge__zero_0) ).

fof(c_0_662,axiom,
    ! [X4,X3] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X3)
      | c_lessequals(c_HOL_Ozero__class_Ozero(X3),c_Nat_Osemiring__1__class_Oof__nat(X4,X3),X3) ),
    file('<stdin>',cls_of__nat__0__le__iff_0) ).

fof(c_0_663,axiom,
    ! [X5,X3] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X3)
      | c_lessequals(c_HOL_Ozero__class_Ozero(X3),c_Nat_Osemiring__1__class_Oof__nat(X5,X3),X3) ),
    file('<stdin>',cls_zero__le__imp__of__nat_0) ).

fof(c_0_664,axiom,
    ! [X7,X3] :
      ( ~ class_Orderings_Oorder(X3)
      | ~ c_HOL_Oord__class_Oless(X7,X7,X3) ),
    file('<stdin>',cls_order__less__le_1) ).

fof(c_0_665,axiom,
    ! [X7,X3] :
      ( ~ class_Orderings_Olinorder(X3)
      | ~ c_HOL_Oord__class_Oless(X7,X7,X3) ),
    file('<stdin>',cls_linorder__neq__iff_1) ).

fof(c_0_666,axiom,
    ! [X7,X3] :
      ( ~ class_Orderings_Opreorder(X3)
      | ~ c_HOL_Oord__class_Oless(X7,X7,X3) ),
    file('<stdin>',cls_order__less__irrefl_0) ).

fof(c_0_667,axiom,
    ! [X4] : ~ c_lessequals(c_Suc(X4),X4,tc_nat),
    file('<stdin>',cls_Suc__n__not__le__n_0) ).

fof(c_0_668,axiom,
    ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
    file('<stdin>',cls_neq0__conv_1) ).

fof(c_0_669,axiom,
    ! [X4] :
      ( X4 = c_HOL_Ozero__class_Ozero(tc_nat)
      | ~ c_lessequals(X4,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ),
    file('<stdin>',cls_le__0__eq_0) ).

fof(c_0_670,axiom,
    ! [X4,X5] :
      ( c_HOL_Oplus__class_Oplus(X5,X4,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)
      | X4 = c_HOL_Ozero__class_Ozero(tc_nat) ),
    file('<stdin>',cls_add__is__0_1) ).

fof(c_0_671,axiom,
    ! [X4,X5] :
      ( c_HOL_Oplus__class_Oplus(X5,X4,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)
      | X5 = c_HOL_Ozero__class_Ozero(tc_nat) ),
    file('<stdin>',cls_add__is__0_0) ).

fof(c_0_672,axiom,
    ! [X2,X3] :
      ( ~ class_Orderings_Olinorder(X3)
      | ~ class_OrderedGroup_Olordered__ab__group__add__abs(X3)
      | c_HOL_Oabs__class_Oabs(X2,X3) = X2
      | c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X3),X3) ),
    file('<stdin>',cls_abs__if__lattice_1) ).

fof(c_0_673,axiom,
    ! [X4,X5] :
      ( c_HOL_Oplus__class_Oplus(X5,X4,tc_nat) != X5
      | X4 = c_HOL_Ozero__class_Ozero(tc_nat) ),
    file('<stdin>',cls_add__eq__self__zero_0) ).

fof(c_0_674,axiom,
    ! [X7,X2] :
      ( X7 != c_HOL_Oplus__class_Oplus(X7,X2,tc_nat)
      | X2 = c_HOL_Ozero__class_Ozero(tc_nat) ),
    file('<stdin>',cls_natgb_Oadd__r0__iff_0) ).

fof(c_0_675,axiom,
    ! [X5] : ~ c_HOL_Oord__class_Oless(X5,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
    file('<stdin>',cls_gr__implies__not0_0) ).

fof(c_0_676,axiom,
    ! [X4] : ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
    file('<stdin>',cls_not__less0_0) ).

fof(c_0_677,axiom,
    ! [X2,X3] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X3)
      | c_lessequals(X2,c_HOL_Oabs__class_Oabs(X2,X3),X3) ),
    file('<stdin>',cls_abs__ge__self_0) ).

fof(c_0_678,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)),
    file('<stdin>',cls_mult__eq__1__iff_2) ).

fof(c_0_679,axiom,
    ! [X4] : ~ c_HOL_Oord__class_Oless(X4,X4,tc_nat),
    file('<stdin>',cls_less__not__refl_0) ).

fof(c_0_680,axiom,
    ! [X7] : ~ c_HOL_Oord__class_Oless(X7,X7,tc_nat),
    file('<stdin>',cls_nat__less__le_1) ).

fof(c_0_681,axiom,
    ! [X2,X3] :
      ( ~ class_Ring__and__Field_Oabs__if(X3)
      | c_HOL_Oabs__class_Oabs(X2,X3) = X2
      | c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X3),X3) ),
    file('<stdin>',cls_abs__if_1) ).

fof(c_0_682,axiom,
    ! [X3] :
      ( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
      | c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X3),c_HOL_Ozero__class_Ozero(X3),X3) = c_HOL_Ozero__class_Ozero(X3) ),
    file('<stdin>',cls_double__eq__0__iff_1) ).

fof(c_0_683,axiom,
    c_Ring__and__Field_Odvd__class_Odvd(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),
    file('<stdin>',cls_dvd__1__iff__1_1) ).

fof(c_0_684,axiom,
    ! [X7,X3] :
      ( ~ class_Ring__and__Field_Oidom(X3)
      | ~ class_Int_Onumber__ring(X3)
      | X7 = c_HOL_Oplus__class_Oplus(X7,c_HOL_Ozero__class_Ozero(X3),X3) ),
    file('<stdin>',cls_class__ringb_Oadd__r0__iff_1) ).

fof(c_0_685,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)),
    file('<stdin>',cls_add__is__1_5) ).

fof(c_0_686,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),
    file('<stdin>',cls_one__is__add_4) ).

fof(c_0_687,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),
    file('<stdin>',cls_one__is__add_5) ).

fof(c_0_688,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)),
    file('<stdin>',cls_add__is__1_4) ).

fof(c_0_689,axiom,
    ! [X7,X3] :
      ( ~ class_Ring__and__Field_Oidom(X3)
      | ~ class_Int_Onumber__ring(X3)
      | c_HOL_Ominus__class_Ominus(X7,X7,X3) = c_HOL_Ozero__class_Ozero(X3) ),
    file('<stdin>',cls_class__ringb_Osubr0__iff_1) ).

fof(c_0_690,axiom,
    ! [X2,X3] :
      ( ~ class_Ring__and__Field_Oring__no__zero__divisors(X3)
      | c_HOL_Otimes__class_Otimes(X2,c_HOL_Ozero__class_Ozero(X3),X3) = c_HOL_Ozero__class_Ozero(X3) ),
    file('<stdin>',cls_mult__eq__0__iff_2) ).

fof(c_0_691,axiom,
    ! [X1,X3] :
      ( ~ class_Ring__and__Field_Oring__no__zero__divisors(X3)
      | c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X3),X1,X3) = c_HOL_Ozero__class_Ozero(X3) ),
    file('<stdin>',cls_mult__eq__0__iff_1) ).

fof(c_0_692,axiom,
    ! [X2,X3] :
      ( ~ class_Ring__and__Field_Omult__zero(X3)
      | c_HOL_Otimes__class_Otimes(X2,c_HOL_Ozero__class_Ozero(X3),X3) = c_HOL_Ozero__class_Ozero(X3) ),
    file('<stdin>',cls_mult__zero__right_0) ).

fof(c_0_693,axiom,
    ! [X2,X3] :
      ( ~ class_Ring__and__Field_Omult__zero(X3)
      | c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X3),X2,X3) = c_HOL_Ozero__class_Ozero(X3) ),
    file('<stdin>',cls_mult__zero__left_0) ).

fof(c_0_694,axiom,
    ! [X7,X3] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
      | c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X3),X7,X3) = c_HOL_Ozero__class_Ozero(X3) ),
    file('<stdin>',cls_class__semiring_Omul__0_0) ).

fof(c_0_695,axiom,
    ! [X7,X3] :
      ( ~ class_RealVector_Oreal__normed__algebra(X3)
      | c_HOL_Otimes__class_Otimes(X7,c_HOL_Ozero__class_Ozero(X3),X3) = c_HOL_Ozero__class_Ozero(X3) ),
    file('<stdin>',cls_mult__right_Ozero_0) ).

fof(c_0_696,axiom,
    ! [X2,X3] :
      ( ~ class_RealVector_Oreal__normed__algebra(X3)
      | c_HOL_Otimes__class_Otimes(X2,c_HOL_Ozero__class_Ozero(X3),X3) = c_HOL_Ozero__class_Ozero(X3) ),
    file('<stdin>',cls_mult_Ozero__right_0) ).

fof(c_0_697,axiom,
    ! [X1,X3] :
      ( ~ class_RealVector_Oreal__normed__algebra(X3)
      | c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X3),X1,X3) = c_HOL_Ozero__class_Ozero(X3) ),
    file('<stdin>',cls_mult_Ozero__left_0) ).

fof(c_0_698,axiom,
    ! [X6,X3] :
      ( ~ class_RealVector_Oreal__normed__algebra(X3)
      | c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X3),X6,X3) = c_HOL_Ozero__class_Ozero(X3) ),
    file('<stdin>',cls_mult__left_Ozero_0) ).

fof(c_0_699,axiom,
    ! [X2,X3] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
      | c_HOL_Otimes__class_Otimes(X2,c_HOL_Ozero__class_Ozero(X3),X3) = c_HOL_Ozero__class_Ozero(X3) ),
    file('<stdin>',cls_class__semiring_Osemiring__rules_I10_J_0) ).

fof(c_0_700,axiom,
    ! [X2,X3] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
      | c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X3),X2,X3) = c_HOL_Ozero__class_Ozero(X3) ),
    file('<stdin>',cls_class__semiring_Osemiring__rules_I9_J_0) ).

fof(c_0_701,axiom,
    ! [X2,X3] :
      ( ~ class_Divides_Osemiring__div(X3)
      | c_Divides_Odiv__class_Omod(c_HOL_Ozero__class_Ozero(X3),X2,X3) = c_HOL_Ozero__class_Ozero(X3) ),
    file('<stdin>',cls_mod__0_0) ).

fof(c_0_702,axiom,
    ! [X4] :
      ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat)
      | c_Parity_Oeven__odd__class_Oeven(X4,tc_nat) ),
    file('<stdin>',cls_odd__pos_0) ).

fof(c_0_703,axiom,
    ! [X2,X3] :
      ( ~ class_OrderedGroup_Ogroup__add(X3)
      | c_HOL_Ominus__class_Ominus(X2,c_HOL_Ozero__class_Ozero(X3),X3) = X2 ),
    file('<stdin>',cls_diff__0__right_0) ).

fof(c_0_704,axiom,
    ! [X2,X3] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
      | c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X3),X2,X3) = X2 ),
    file('<stdin>',cls_class__semiring_Osemiring__rules_I5_J_0) ).

fof(c_0_705,axiom,
    ! [X2,X3] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
      | c_HOL_Oplus__class_Oplus(X2,c_HOL_Ozero__class_Ozero(X3),X3) = X2 ),
    file('<stdin>',cls_class__semiring_Osemiring__rules_I6_J_0) ).

fof(c_0_706,axiom,
    ! [X2,X3] :
      ( ~ class_OrderedGroup_Ocomm__monoid__add(X3)
      | c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X3),X2,X3) = X2 ),
    file('<stdin>',cls_comm__monoid__add_Omult__1_0) ).

fof(c_0_707,axiom,
    ! [X7,X3] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
      | c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X3),X7,X3) = X7 ),
    file('<stdin>',cls_class__semiring_Oadd__0_0) ).

fof(c_0_708,axiom,
    ! [X2,X3] :
      ( ~ class_OrderedGroup_Ocomm__monoid__add(X3)
      | c_HOL_Oplus__class_Oplus(X2,c_HOL_Ozero__class_Ozero(X3),X3) = X2 ),
    file('<stdin>',cls_comm__monoid__add_Omult__1__right_0) ).

fof(c_0_709,axiom,
    ! [X2,X3] :
      ( ~ class_OrderedGroup_Omonoid__add(X3)
      | c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X3),X2,X3) = X2 ),
    file('<stdin>',cls_add__0__left_0) ).

fof(c_0_710,axiom,
    ! [X2,X3] :
      ( ~ class_OrderedGroup_Omonoid__add(X3)
      | c_HOL_Oplus__class_Oplus(X2,c_HOL_Ozero__class_Ozero(X3),X3) = X2 ),
    file('<stdin>',cls_monoid__add__class_Oadd__0__right_0) ).

fof(c_0_711,axiom,
    ! [X2,X3] :
      ( ~ class_Divides_Osemiring__div(X3)
      | c_Divides_Odiv__class_Omod(X2,c_HOL_Ozero__class_Ozero(X3),X3) = X2 ),
    file('<stdin>',cls_mod__by__0_0) ).

fof(c_0_712,axiom,
    c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),
    file('<stdin>',cls_less__Suc0_1) ).

fof(c_0_713,axiom,
    ! [X2,X3] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
      | c_Ring__and__Field_Odvd__class_Odvd(X2,c_HOL_Ozero__class_Ozero(X3),X3) ),
    file('<stdin>',cls_dvd__0__right_0) ).

fof(c_0_714,axiom,
    ! [X5] : c_Divides_Odiv__class_Omod(X5,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
    file('<stdin>',cls_mod__1_0) ).

fof(c_0_715,axiom,
    ! [X2,X3] :
      ( ~ class_OrderedGroup_Ogroup__add(X3)
      | c_HOL_Ominus__class_Ominus(X2,X2,X3) = c_HOL_Ozero__class_Ozero(X3) ),
    file('<stdin>',cls_diff__self_0) ).

fof(c_0_716,axiom,
    ! [X7,X3] :
      ( ~ class_OrderedGroup_Ogroup__add(X3)
      | c_HOL_Ominus__class_Ominus(X7,X7,X3) = c_HOL_Ozero__class_Ozero(X3) ),
    file('<stdin>',cls_right__minus__eq_1) ).

fof(c_0_717,axiom,
    ! [X7,X3] :
      ( ~ class_OrderedGroup_Oab__group__add(X3)
      | c_HOL_Ominus__class_Ominus(X7,X7,X3) = c_HOL_Ozero__class_Ozero(X3) ),
    file('<stdin>',cls_eq__iff__diff__eq__0_0) ).

fof(c_0_718,axiom,
    ! [X2,X3] :
      ( ~ class_Divides_Osemiring__div(X3)
      | c_Divides_Odiv__class_Omod(X2,X2,X3) = c_HOL_Ozero__class_Ozero(X3) ),
    file('<stdin>',cls_mod__self_0) ).

fof(c_0_719,axiom,
    ! [X4] : c_lessequals(c_Suc(X4),c_Suc(X4),tc_nat),
    file('<stdin>',cls_le__Suc__eq_2) ).

fof(c_0_720,axiom,
    ! [X8] : c_Ring__and__Field_Odvd__class_Odvd(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X8,tc_nat),
    file('<stdin>',cls_dvd__1__left_0) ).

fof(c_0_721,axiom,
    ! [X7,X3] :
      ( ~ class_OrderedGroup_Oab__semigroup__idem__mult(X3)
      | c_HOL_Otimes__class_Otimes(X7,X7,X3) = X7 ),
    file('<stdin>',cls_mult__idem_0) ).

fof(c_0_722,axiom,
    ! [X7,X3] :
      ( ~ class_Orderings_Olinorder(X3)
      | c_Orderings_Oord__class_Omin(X7,X7,X3) = X7 ),
    file('<stdin>',cls_min__max_Oinf__idem_0) ).

fof(c_0_723,axiom,
    ! [X4] : c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(X4),tc_nat),
    file('<stdin>',cls_zero__less__Suc_0) ).

fof(c_0_724,axiom,
    ! [X7] : c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(X7),tc_nat),
    file('<stdin>',cls_gr0__conv__Suc_1) ).

fof(c_0_725,axiom,
    ! [X7,X3] :
      ( ~ class_Orderings_Oorder(X3)
      | c_lessequals(X7,X7,X3) ),
    file('<stdin>',cls_order__eq__iff_0) ).

fof(c_0_726,axiom,
    ! [X7,X3] :
      ( ~ class_Orderings_Opreorder(X3)
      | c_lessequals(X7,X7,X3) ),
    file('<stdin>',cls_order__eq__refl_0) ).

fof(c_0_727,axiom,
    ! [X2,X3] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
      | c_Ring__and__Field_Odvd__class_Odvd(X2,X2,X3) ),
    file('<stdin>',cls_dvd__refl_0) ).

fof(c_0_728,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),
    file('<stdin>',cls_add__is__0_2) ).

fof(c_0_729,axiom,
    ! [X2,X3] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X3)
      | c_HOL_Oabs__class_Oabs(c_HOL_Oabs__class_Oabs(X2,X3),X3) = c_HOL_Oabs__class_Oabs(X2,X3) ),
    file('<stdin>',cls_abs__idempotent_0) ).

fof(c_0_730,axiom,
    ! [X4,X3] :
      ( ~ class_Ring__and__Field_Oordered__idom(X3)
      | c_HOL_Oabs__class_Oabs(c_Nat_Osemiring__1__class_Oof__nat(X4,X3),X3) = c_Nat_Osemiring__1__class_Oof__nat(X4,X3) ),
    file('<stdin>',cls_abs__of__nat_0) ).

fof(c_0_731,axiom,
    ! [X4] :
      ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat)
      | X4 = c_HOL_Ozero__class_Ozero(tc_nat) ),
    file('<stdin>',cls_gr0I_0) ).

fof(c_0_732,axiom,
    ! [X7] : c_HOL_Oord__class_Oless(X7,c_Suc(X7),tc_nat),
    file('<stdin>',cls_less__Suc__eq_2) ).

fof(c_0_733,axiom,
    ! [X4] : c_HOL_Oord__class_Oless(X4,c_Suc(X4),tc_nat),
    file('<stdin>',cls_lessI_0) ).

fof(c_0_734,axiom,
    c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
    file('<stdin>',cls_le__0__eq_1) ).

fof(c_0_735,axiom,
    ! [X4] : c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
    file('<stdin>',cls_diff__0__eq__0_0) ).

fof(c_0_736,axiom,
    ! [X4] : c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
    file('<stdin>',cls_mult__is__0_1) ).

fof(c_0_737,axiom,
    ! [X5] : c_HOL_Otimes__class_Otimes(X5,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
    file('<stdin>',cls_mult__is__0_2) ).

fof(c_0_738,axiom,
    ! [X4] : c_Orderings_Oord__class_Omin(X4,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
    file('<stdin>',cls_min__0R_0) ).

fof(c_0_739,axiom,
    ! [X4] : c_Orderings_Oord__class_Omin(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
    file('<stdin>',cls_min__0L_0) ).

fof(c_0_740,axiom,
    ! [X5] : c_HOL_Ominus__class_Ominus(X5,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = X5,
    file('<stdin>',cls_minus__nat_Odiff__0_0) ).

fof(c_0_741,axiom,
    ! [X4] : c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat) = X4,
    file('<stdin>',cls_plus__nat_Oadd__0_0) ).

fof(c_0_742,axiom,
    ! [X5] : c_HOL_Oplus__class_Oplus(X5,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = X5,
    file('<stdin>',cls_Nat_Oadd__0__right_0) ).

fof(c_0_743,axiom,
    ! [X7] : X7 = c_HOL_Oplus__class_Oplus(X7,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
    file('<stdin>',cls_natgb_Oadd__r0__iff_1) ).

fof(c_0_744,axiom,
    ! [X7] : c_Ring__and__Field_Odvd__class_Odvd(X7,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
    file('<stdin>',cls_gcd__lcm__complete__lattice__nat_Otop__greatest_0) ).

fof(c_0_745,axiom,
    ! [X4] : c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat),
    file('<stdin>',cls_le0_0) ).

fof(c_0_746,axiom,
    ! [X5] : c_HOL_Ominus__class_Ominus(X5,X5,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
    file('<stdin>',cls_diff__self__eq__0_0) ).

fof(c_0_747,axiom,
    ! [X4,X5,X3] :
      ( ~ class_Nat_Osemiring__char__0(X3)
      | c_Nat_Osemiring__1__class_Oof__nat(X5,X3) != c_Nat_Osemiring__1__class_Oof__nat(X4,X3)
      | X5 = X4 ),
    file('<stdin>',cls_of__nat__eq__iff_0) ).

fof(c_0_748,axiom,
    ! [X4] : c_lessequals(X4,X4,tc_nat),
    file('<stdin>',cls_le__refl_0) ).

fof(c_0_749,axiom,
    ! [X7] : c_lessequals(X7,X7,tc_nat),
    file('<stdin>',cls_eq__imp__le_0) ).

fof(c_0_750,axiom,
    ! [X7] : c_Ring__and__Field_Odvd__class_Odvd(X7,X7,tc_nat),
    file('<stdin>',cls_dvd_Oeq__iff_0) ).

fof(c_0_751,axiom,
    c_HOL_Oord__class_Oless(v_i,v_n,tc_nat),
    file('<stdin>',cls_CHAINED_0) ).

fof(c_0_752,axiom,
    c_HOL_Oord__class_Oless(v_i,v_n,tc_nat),
    file('<stdin>',cls_assms_0) ).

fof(c_0_753,axiom,
    ! [X7] :
      ( ~ c_Parity_Oeven__odd__class_Oeven(X7,tc_nat)
      | ~ c_Parity_Oeven__odd__class_Oeven(c_Suc(X7),tc_nat) ),
    file('<stdin>',cls_even__Suc_0) ).

fof(c_0_754,axiom,
    ! [X2,X3] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X3)
      | c_HOL_Oabs__class_Oabs(X2,X3) != c_HOL_Ozero__class_Ozero(X3)
      | X2 = c_HOL_Ozero__class_Ozero(X3) ),
    file('<stdin>',cls_abs__eq__0_0) ).

fof(c_0_755,axiom,
    ! [X7] :
      ( c_Parity_Oeven__odd__class_Oeven(c_Suc(X7),tc_nat)
      | c_Parity_Oeven__odd__class_Oeven(X7,tc_nat) ),
    file('<stdin>',cls_even__Suc_1) ).

fof(c_0_756,axiom,
    ! [X3] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X3)
      | c_HOL_Oabs__class_Oabs(c_HOL_Ozero__class_Ozero(X3),X3) = c_HOL_Ozero__class_Ozero(X3) ),
    file('<stdin>',cls_abs__eq__0_1) ).

fof(c_0_757,axiom,
    ! [X3] :
      ( ~ class_Ring__and__Field_Osemiring__1(X3)
      | c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Ozero__class_Ozero(tc_nat),X3) = c_HOL_Ozero__class_Ozero(X3) ),
    file('<stdin>',cls_of__nat__0_0) ).

fof(c_0_758,axiom,
    c_Parity_Oeven__odd__class_Oeven(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
    file('<stdin>',cls_even__zero__nat_0) ).

fof(c_0_759,axiom,
    ! [X6,X7] :
      ( c_Suc(X7) != c_Suc(X6)
      | X7 = X6 ),
    file('<stdin>',cls_Suc__inject_0) ).

fof(c_0_760,axiom,
    ! [X21,X30] :
      ( c_Suc(X30) != c_Suc(X21)
      | X30 = X21 ),
    file('<stdin>',cls_nat_Oinject_0) ).

fof(c_0_761,axiom,
    ! [X21] : c_Suc(X21) != c_HOL_Ozero__class_Ozero(tc_nat),
    file('<stdin>',cls_nat_Osimps_I3_J_0) ).

fof(c_0_762,axiom,
    ! [X5] : c_Suc(X5) != c_HOL_Ozero__class_Ozero(tc_nat),
    file('<stdin>',cls_Suc__neq__Zero_0) ).

fof(c_0_763,axiom,
    ! [X5] : c_HOL_Ozero__class_Ozero(tc_nat) != c_Suc(X5),
    file('<stdin>',cls_Zero__neq__Suc_0) ).

fof(c_0_764,axiom,
    ! [X21] : c_HOL_Ozero__class_Ozero(tc_nat) != c_Suc(X21),
    file('<stdin>',cls_nat_Osimps_I2_J_0) ).

fof(c_0_765,axiom,
    ! [X4] : c_Suc(X4) != X4,
    file('<stdin>',cls_Suc__n__not__n_0) ).

fof(c_0_766,axiom,
    ! [X4] : X4 != c_Suc(X4),
    file('<stdin>',cls_n__not__Suc__n_0) ).

fof(c_0_767,axiom,
    class_Orderings_Oorder(tc_nat),
    file('<stdin>',clsarity_nat__Orderings_Oorder) ).

fof(c_0_768,axiom,
    class_Orderings_Olinorder(tc_nat),
    file('<stdin>',clsarity_nat__Orderings_Olinorder) ).

fof(c_0_769,axiom,
    class_Orderings_Opreorder(tc_nat),
    file('<stdin>',clsarity_nat__Orderings_Opreorder) ).

fof(c_0_770,axiom,
    class_Ring__and__Field_Odvd(tc_nat),
    file('<stdin>',clsarity_nat__Ring__and__Field_Odvd) ).

fof(c_0_771,axiom,
    class_Nat_Osemiring__char__0(tc_nat),
    file('<stdin>',clsarity_nat__Nat_Osemiring__char__0) ).

fof(c_0_772,axiom,
    class_Divides_Osemiring__div(tc_nat),
    file('<stdin>',clsarity_nat__Divides_Osemiring__div) ).

fof(c_0_773,axiom,
    class_OrderedGroup_Omonoid__add(tc_nat),
    file('<stdin>',clsarity_nat__OrderedGroup_Omonoid__add) ).

fof(c_0_774,axiom,
    class_Ring__and__Field_Osemiring(tc_nat),
    file('<stdin>',clsarity_nat__Ring__and__Field_Osemiring) ).

fof(c_0_775,axiom,
    class_Ring__and__Field_Omult__mono(tc_nat),
    file('<stdin>',clsarity_nat__Ring__and__Field_Omult__mono) ).

fof(c_0_776,axiom,
    class_Ring__and__Field_Omult__zero(tc_nat),
    file('<stdin>',clsarity_nat__Ring__and__Field_Omult__zero) ).

fof(c_0_777,axiom,
    class_Ring__and__Field_Omult__mono1(tc_nat),
    file('<stdin>',clsarity_nat__Ring__and__Field_Omult__mono1) ).

fof(c_0_778,axiom,
    class_Ring__and__Field_Osemiring__1(tc_nat),
    file('<stdin>',clsarity_nat__Ring__and__Field_Osemiring__1) ).

fof(c_0_779,axiom,
    class_OrderedGroup_Ocomm__monoid__add(tc_nat),
    file('<stdin>',clsarity_nat__OrderedGroup_Ocomm__monoid__add) ).

fof(c_0_780,axiom,
    class_Ring__and__Field_Ocomm__semiring(tc_nat),
    file('<stdin>',clsarity_nat__Ring__and__Field_Ocomm__semiring) ).

fof(c_0_781,axiom,
    class_OrderedGroup_Oab__semigroup__add(tc_nat),
    file('<stdin>',clsarity_nat__OrderedGroup_Oab__semigroup__add) ).

fof(c_0_782,axiom,
    class_OrderedGroup_Oab__semigroup__mult(tc_nat),
    file('<stdin>',clsarity_nat__OrderedGroup_Oab__semigroup__mult) ).

fof(c_0_783,axiom,
    class_Ring__and__Field_Ocomm__semiring__1(tc_nat),
    file('<stdin>',clsarity_nat__Ring__and__Field_Ocomm__semiring__1) ).

fof(c_0_784,axiom,
    class_Ring__and__Field_Oordered__semidom(tc_nat),
    file('<stdin>',clsarity_nat__Ring__and__Field_Oordered__semidom) ).

fof(c_0_785,axiom,
    class_Ring__and__Field_Ono__zero__divisors(tc_nat),
    file('<stdin>',clsarity_nat__Ring__and__Field_Ono__zero__divisors) ).

fof(c_0_786,axiom,
    class_Ring__and__Field_Oordered__semiring(tc_nat),
    file('<stdin>',clsarity_nat__Ring__and__Field_Oordered__semiring) ).

fof(c_0_787,axiom,
    class_Ring__and__Field_Opordered__semiring(tc_nat),
    file('<stdin>',clsarity_nat__Ring__and__Field_Opordered__semiring) ).

fof(c_0_788,axiom,
    class_OrderedGroup_Ocancel__semigroup__add(tc_nat),
    file('<stdin>',clsarity_nat__OrderedGroup_Ocancel__semigroup__add) ).

fof(c_0_789,axiom,
    class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat),
    file('<stdin>',clsarity_nat__OrderedGroup_Ocancel__ab__semigroup__add) ).

fof(c_0_790,axiom,
    class_OrderedGroup_Opordered__comm__monoid__add(tc_nat),
    file('<stdin>',clsarity_nat__OrderedGroup_Opordered__comm__monoid__add) ).

fof(c_0_791,axiom,
    class_OrderedGroup_Opordered__ab__semigroup__add(tc_nat),
    file('<stdin>',clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add) ).

fof(c_0_792,axiom,
    class_Ring__and__Field_Oordered__semiring__strict(tc_nat),
    file('<stdin>',clsarity_nat__Ring__and__Field_Oordered__semiring__strict) ).

fof(c_0_793,axiom,
    class_Ring__and__Field_Opordered__cancel__semiring(tc_nat),
    file('<stdin>',clsarity_nat__Ring__and__Field_Opordered__cancel__semiring) ).

fof(c_0_794,axiom,
    class_Ring__and__Field_Oordered__comm__semiring__strict(tc_nat),
    file('<stdin>',clsarity_nat__Ring__and__Field_Oordered__comm__semiring__strict) ).

fof(c_0_795,axiom,
    class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat),
    file('<stdin>',clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add__imp__le) ).

fof(c_0_796,axiom,
    class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat),
    file('<stdin>',clsarity_nat__OrderedGroup_Opordered__cancel__ab__semigroup__add) ).

fof(c_0_797,plain,
    ! [X6,X7,X1,X2,X3] :
      ( ~ class_RealVector_Oreal__normed__algebra(X3)
      | c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X7,X6,X3),c_HOL_Otimes__class_Otimes(X2,X1,X3),X3) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X7,X2,X3),c_HOL_Ominus__class_Ominus(X6,X1,X3),X3),c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X7,X2,X3),X1,X3),X3),c_HOL_Otimes__class_Otimes(X2,c_HOL_Ominus__class_Ominus(X6,X1,X3),X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_0]) ).

fof(c_0_798,plain,
    ! [X20,X15,X1,X2,X3] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X3)
      | c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X2,X1,X3),c_HOL_Oplus__class_Oplus(X15,X20,X3),X3),X3),c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X2,X15,X3),X3),c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X1,X20,X3),X3),X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_1]) ).

fof(c_0_799,plain,
    ! [X17,X4,X5,X9,X10] :
      ( c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X10,X17,tc_nat),X5,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X9,X17,tc_nat),X4,tc_nat),tc_nat)
      | ~ c_lessequals(X5,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X9,X10,tc_nat),X17,tc_nat),X4,tc_nat),tc_nat)
      | ~ c_lessequals(X10,X9,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_2]) ).

fof(c_0_800,plain,
    ! [X17,X4,X5,X9,X10] :
      ( c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X10,X17,tc_nat),X5,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X9,X17,tc_nat),X4,tc_nat),tc_nat)
      | ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X10,X9,tc_nat),X17,tc_nat),X5,tc_nat),X4,tc_nat)
      | ~ c_lessequals(X9,X10,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_3]) ).

fof(c_0_801,plain,
    ! [X17,X4,X5,X9,X10] :
      ( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X10,X17,tc_nat),X5,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X9,X17,tc_nat),X4,tc_nat),tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X10,X9,tc_nat),X17,tc_nat),X5,tc_nat),X4,tc_nat)
      | ~ c_lessequals(X9,X10,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_4]) ).

fof(c_0_802,plain,
    ! [X17,X4,X5,X9,X10] :
      ( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X10,X17,tc_nat),X5,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X9,X17,tc_nat),X4,tc_nat),tc_nat)
      | ~ c_HOL_Oord__class_Oless(X5,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X9,X10,tc_nat),X17,tc_nat),X4,tc_nat),tc_nat)
      | ~ c_lessequals(X10,X9,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_5]) ).

fof(c_0_803,plain,
    ! [X19,X20,X15,X1,X2,X3] :
      ( ~ class_Ring__and__Field_Opordered__ring(X3)
      | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X19,X3),X15,X3),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X19,X3),X20,X3),X3)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X1,X3),X19,X3),X15,X3),X20,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_6]) ).

fof(c_0_804,plain,
    ! [X19,X20,X15,X1,X2,X3] :
      ( ~ class_Ring__and__Field_Opordered__ring(X3)
      | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X19,X3),X15,X3),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X19,X3),X20,X3),X3)
      | ~ c_HOL_Oord__class_Oless(X15,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,X2,X3),X19,X3),X20,X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_7]) ).

fof(c_0_805,plain,
    ! [X19,X20,X15,X1,X2,X3] :
      ( ~ class_Ring__and__Field_Opordered__ring(X3)
      | c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X19,X3),X15,X3),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X19,X3),X20,X3),X3)
      | ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X1,X3),X19,X3),X15,X3),X20,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_8]) ).

fof(c_0_806,plain,
    ! [X19,X20,X15,X1,X2,X3] :
      ( ~ class_Ring__and__Field_Opordered__ring(X3)
      | c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X19,X3),X15,X3),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X19,X3),X20,X3),X3)
      | ~ c_lessequals(X15,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,X2,X3),X19,X3),X20,X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_9]) ).

fof(c_0_807,plain,
    ! [X17,X4,X5,X9,X10] :
      ( c_lessequals(X5,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X9,X10,tc_nat),X17,tc_nat),X4,tc_nat),tc_nat)
      | ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X10,X17,tc_nat),X5,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X9,X17,tc_nat),X4,tc_nat),tc_nat)
      | ~ c_lessequals(X10,X9,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_10]) ).

fof(c_0_808,plain,
    ! [X17,X4,X5,X9,X10] :
      ( c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X10,X9,tc_nat),X17,tc_nat),X5,tc_nat),X4,tc_nat)
      | ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X10,X17,tc_nat),X5,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X9,X17,tc_nat),X4,tc_nat),tc_nat)
      | ~ c_lessequals(X9,X10,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_11]) ).

fof(c_0_809,plain,
    ! [X17,X4,X5,X9,X10] :
      ( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X10,X9,tc_nat),X17,tc_nat),X5,tc_nat),X4,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X10,X17,tc_nat),X5,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X9,X17,tc_nat),X4,tc_nat),tc_nat)
      | ~ c_lessequals(X9,X10,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_12]) ).

fof(c_0_810,plain,
    ! [X17,X4,X5,X9,X10] :
      ( c_HOL_Oord__class_Oless(X5,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X9,X10,tc_nat),X17,tc_nat),X4,tc_nat),tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X10,X17,tc_nat),X5,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X9,X17,tc_nat),X4,tc_nat),tc_nat)
      | ~ c_lessequals(X10,X9,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_13]) ).

fof(c_0_811,plain,
    ! [X19,X20,X15,X1,X2,X3] :
      ( ~ 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(X2,X1,X3),X19,X3),X15,X3),X20,X3)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X19,X3),X15,X3),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X19,X3),X20,X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_14]) ).

fof(c_0_812,plain,
    ! [X19,X20,X15,X1,X2,X3] :
      ( ~ class_Ring__and__Field_Opordered__ring(X3)
      | c_HOL_Oord__class_Oless(X15,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,X2,X3),X19,X3),X20,X3),X3)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X19,X3),X15,X3),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X19,X3),X20,X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_15]) ).

fof(c_0_813,plain,
    ! [X19,X20,X15,X1,X2,X3] :
      ( ~ class_Ring__and__Field_Opordered__ring(X3)
      | c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X1,X3),X19,X3),X15,X3),X20,X3)
      | ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X19,X3),X15,X3),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X19,X3),X20,X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_16]) ).

fof(c_0_814,plain,
    ! [X19,X20,X15,X1,X2,X3] :
      ( ~ class_Ring__and__Field_Opordered__ring(X3)
      | c_lessequals(X15,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,X2,X3),X19,X3),X20,X3),X3)
      | ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X19,X3),X15,X3),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X19,X3),X20,X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_17]) ).

fof(c_0_815,plain,
    ! [X17,X4,X5,X9,X10] :
      ( c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X10,X17,tc_nat),X5,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X9,X17,tc_nat),X4,tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(X5,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X9,X10,tc_nat),X17,tc_nat),X4,tc_nat),tc_nat)
      | ~ c_lessequals(X10,X9,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_18]) ).

fof(c_0_816,plain,
    ! [X17,X4,X5,X9,X10] :
      ( c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X10,X17,tc_nat),X5,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X9,X17,tc_nat),X4,tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X10,X9,tc_nat),X17,tc_nat),X5,tc_nat),X4,tc_nat)
      | ~ c_lessequals(X9,X10,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_19]) ).

fof(c_0_817,plain,
    ! [X7,X24,X8,X20,X25,X3] :
      ( ~ class_Ring__and__Field_Odvd(X3)
      | ~ class_Ring__and__Field_Ocomm__ring(X3)
      | c_Ring__and__Field_Odvd__class_Odvd(X20,c_HOL_Oplus__class_Oplus(X7,X24,X3),X3)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X20,c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X7,c_HOL_Otimes__class_Otimes(X8,X25,X3),X3),X24,X3),X3)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X20,X25,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_20]) ).

fof(c_0_818,plain,
    ! [X7,X24,X8,X20,X25,X3] :
      ( ~ class_Ring__and__Field_Odvd(X3)
      | ~ class_Ring__and__Field_Ocomm__ring(X3)
      | c_Ring__and__Field_Odvd__class_Odvd(X20,c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X7,c_HOL_Otimes__class_Otimes(X8,X25,X3),X3),X24,X3),X3)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X20,c_HOL_Oplus__class_Oplus(X7,X24,X3),X3)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X20,X25,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_21]) ).

fof(c_0_819,plain,
    ! [X17,X4,X9,X10] :
      ( ~ c_lessequals(X10,X9,tc_nat)
      | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X10,X17,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X9,X10,tc_nat),X17,tc_nat),X4,tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X9,X17,tc_nat),X4,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_22]) ).

fof(c_0_820,plain,
    ! [X17,X5,X9,X10] :
      ( ~ c_lessequals(X9,X10,tc_nat)
      | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X10,X17,tc_nat),X5,tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X9,X17,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X10,X9,tc_nat),X17,tc_nat),X5,tc_nat),tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_23]) ).

fof(c_0_821,plain,
    ! [X3] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X3),c_HOL_Ozero__class_Ozero(X3),X3),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X3),c_HOL_Ozero__class_Ozero(X3),X3),X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_24]) ).

fof(c_0_822,plain,
    ! [X19,X15,X1,X2,X3] :
      ( ~ class_Ring__and__Field_Oring(X3)
      | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X19,X3),X15,X3) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X19,X3),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X1,X3),X19,X3),X15,X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_25]) ).

fof(c_0_823,plain,
    ! [X19,X20,X1,X2,X3] :
      ( ~ class_Ring__and__Field_Oring(X3)
      | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X19,X3),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,X2,X3),X19,X3),X20,X3),X3) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X19,X3),X20,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_26]) ).

fof(c_0_824,plain,
    ! [X22,X23,X15,X1] :
      ( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,c_Divides_Odiv__class_Omod(X23,X15,tc_nat),tc_nat),X22,tc_nat),c_HOL_Otimes__class_Otimes(X1,X15,tc_nat),tc_nat)
      | ~ c_HOL_Oord__class_Oless(X22,X1,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X15,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_27]) ).

fof(c_0_825,plain,
    ! [X6,X7,X3] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
      | X7 = c_HOL_Ozero__class_Ozero(X3)
      | ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X7,X7,X3),c_HOL_Otimes__class_Otimes(X6,X6,X3),X3),c_HOL_Ozero__class_Ozero(X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_28]) ).

fof(c_0_826,plain,
    ! [X6,X7,X3] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
      | X6 = c_HOL_Ozero__class_Ozero(X3)
      | ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X7,X7,X3),c_HOL_Otimes__class_Otimes(X6,X6,X3),X3),c_HOL_Ozero__class_Ozero(X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_29]) ).

fof(c_0_827,plain,
    ! [X6,X7,X3] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X7,X7,X3),c_HOL_Otimes__class_Otimes(X6,X6,X3),X3),c_HOL_Ozero__class_Ozero(X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_30]) ).

fof(c_0_828,plain,
    ! [X17,X4,X5,X9,X10] :
      ( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X10,X17,tc_nat),X5,tc_nat) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X9,X17,tc_nat),X4,tc_nat)
      | ~ c_lessequals(X9,X10,tc_nat)
      | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X10,X9,tc_nat),X17,tc_nat),X5,tc_nat) = X4 ),
    inference(fof_simplification,[status(thm)],[c_0_31]) ).

fof(c_0_829,plain,
    ! [X17,X4,X5,X9,X10] :
      ( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X10,X17,tc_nat),X5,tc_nat) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X9,X17,tc_nat),X4,tc_nat)
      | ~ c_lessequals(X10,X9,tc_nat)
      | X5 = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X9,X10,tc_nat),X17,tc_nat),X4,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_32]) ).

fof(c_0_830,plain,
    ! [X19,X20,X15,X1,X2,X3] :
      ( ~ class_Ring__and__Field_Oring(X3)
      | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X19,X3),X15,X3) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X19,X3),X20,X3)
      | X15 = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,X2,X3),X19,X3),X20,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_33]) ).

fof(c_0_831,plain,
    ! [X19,X20,X15,X1,X2,X3] :
      ( ~ class_Ring__and__Field_Oring(X3)
      | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X19,X3),X15,X3) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X19,X3),X20,X3)
      | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X1,X3),X19,X3),X15,X3) = X20 ),
    inference(fof_simplification,[status(thm)],[c_0_34]) ).

fof(c_0_832,plain,
    ! [X19,X15,X1,X2,X3] :
      ( ~ class_Ring__and__Field_Osemiring(X3)
      | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X19,X3),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X19,X3),X15,X3),X3) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X2,X1,X3),X19,X3),X15,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_35]) ).

fof(c_0_833,plain,
    ! [X16,X6,X7,X31,X3] :
      ( ~ class_Ring__and__Field_Oidom(X3)
      | ~ class_Int_Onumber__ring(X3)
      | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X31,X6,X3),c_HOL_Otimes__class_Otimes(X7,X16,X3),X3) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X31,X16,X3),c_HOL_Otimes__class_Otimes(X7,X6,X3),X3)
      | X6 = X16
      | X31 = X7 ),
    inference(fof_simplification,[status(thm)],[c_0_36]) ).

fof(c_0_834,plain,
    ! [X20,X15,X1,X2,X3] :
      ( ~ class_Ring__and__Field_Oidom(X3)
      | ~ class_Int_Onumber__ring(X3)
      | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X15,X3),c_HOL_Otimes__class_Otimes(X1,X20,X3),X3) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X20,X3),c_HOL_Otimes__class_Otimes(X1,X15,X3),X3)
      | X15 = X20
      | X2 = X1 ),
    inference(fof_simplification,[status(thm)],[c_0_37]) ).

fof(c_0_835,axiom,
    ! [X17,X8,X9,X10] : c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X10,X17,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X9,X17,tc_nat),X8,tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X10,X9,tc_nat),X17,tc_nat),X8,tc_nat),
    c_0_38 ).

fof(c_0_836,axiom,
    ! [X16,X6,X7,X31] :
      ( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X31,X6,tc_nat),c_HOL_Otimes__class_Otimes(X7,X16,tc_nat),tc_nat) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X31,X16,tc_nat),c_HOL_Otimes__class_Otimes(X7,X6,tc_nat),tc_nat)
      | X6 = X16
      | X31 = X7 ),
    c_0_39 ).

fof(c_0_837,axiom,
    ! [X20,X15,X1,X2] :
      ( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X15,tc_nat),c_HOL_Otimes__class_Otimes(X1,X20,tc_nat),tc_nat) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X20,tc_nat),c_HOL_Otimes__class_Otimes(X1,X15,tc_nat),tc_nat)
      | X15 = X20
      | X2 = X1 ),
    c_0_40 ).

fof(c_0_838,plain,
    ! [X7,X22,X2,X3] :
      ( ~ class_Ring__and__Field_Oordered__idom(X3)
      | c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X7,X2,X3),X3),X22,X3)
      | ~ c_HOL_Oord__class_Oless(X7,c_HOL_Oplus__class_Oplus(X2,X22,X3),X3)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X2,X22,X3),X7,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_41]) ).

fof(c_0_839,plain,
    ! [X15,X1,X2,X3] :
      ( ~ class_Divides_Oring__div(X3)
      | c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X2,X1,X3),X15,X3) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(c_Divides_Odiv__class_Omod(X2,X15,X3),c_Divides_Odiv__class_Omod(X1,X15,X3),X3),X15,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_42]) ).

fof(c_0_840,plain,
    ! [X15,X1,X2,X3] :
      ( ~ class_Divides_Osemiring__div(X3)
      | c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X2,X1,X3),X15,X3) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(X2,X15,X3),c_Divides_Odiv__class_Omod(X1,X15,X3),X3),X15,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_43]) ).

fof(c_0_841,plain,
    ! [X15,X1,X2,X3] :
      ( ~ class_Divides_Osemiring__div(X3)
      | c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X2,X1,X3),X15,X3) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(X2,X15,X3),c_Divides_Odiv__class_Omod(X1,X15,X3),X3),X15,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_44]) ).

fof(c_0_842,plain,
    ! [X1,X2,X3] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X3)
      | c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(c_HOL_Oabs__class_Oabs(X2,X3),c_HOL_Oabs__class_Oabs(X1,X3),X3),X3),c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X2,X1,X3),X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_45]) ).

fof(c_0_843,axiom,
    ! [X4,X5,X8] : c_Divides_Odiv__class_Omod(c_Suc(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X8,X4,tc_nat),X5,tc_nat)),X4,tc_nat) = c_Divides_Odiv__class_Omod(c_Suc(X5),X4,tc_nat),
    c_0_46 ).

fof(c_0_844,plain,
    ! [X3] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
      | c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X3),c_HOL_Ozero__class_Ozero(X3),X3),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X3),c_HOL_Ozero__class_Ozero(X3),X3),X3),c_HOL_Ozero__class_Ozero(X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_47]) ).

fof(c_0_845,plain,
    ! [X15,X26,X1,X28,X2,X3] :
      ( ~ class_Divides_Oring__div(X3)
      | c_Divides_Odiv__class_Omod(X1,X15,X3) != c_Divides_Odiv__class_Omod(X26,X15,X3)
      | c_Divides_Odiv__class_Omod(X2,X15,X3) != c_Divides_Odiv__class_Omod(X28,X15,X3)
      | c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X2,X1,X3),X15,X3) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X28,X26,X3),X15,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_48]) ).

fof(c_0_846,plain,
    ! [X15,X26,X1,X28,X2,X3] :
      ( ~ class_Divides_Osemiring__div(X3)
      | c_Divides_Odiv__class_Omod(X1,X15,X3) != c_Divides_Odiv__class_Omod(X26,X15,X3)
      | c_Divides_Odiv__class_Omod(X2,X15,X3) != c_Divides_Odiv__class_Omod(X28,X15,X3)
      | c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X2,X1,X3),X15,X3) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X28,X26,X3),X15,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_49]) ).

fof(c_0_847,plain,
    ! [X15,X26,X1,X28,X2,X3] :
      ( ~ class_Divides_Osemiring__div(X3)
      | c_Divides_Odiv__class_Omod(X1,X15,X3) != c_Divides_Odiv__class_Omod(X26,X15,X3)
      | c_Divides_Odiv__class_Omod(X2,X15,X3) != c_Divides_Odiv__class_Omod(X28,X15,X3)
      | c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X2,X1,X3),X15,X3) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X28,X26,X3),X15,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_50]) ).

fof(c_0_848,plain,
    ! [X11,X12,X13,X14,X3] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
      | c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X14,X13,X3),c_HOL_Otimes__class_Otimes(X12,X11,X3),X3) = c_HOL_Otimes__class_Otimes(X12,c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X14,X13,X3),X11,X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_51]) ).

fof(c_0_849,plain,
    ! [X11,X12,X13,X14,X3] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
      | c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X14,X13,X3),c_HOL_Otimes__class_Otimes(X12,X11,X3),X3) = c_HOL_Otimes__class_Otimes(X14,c_HOL_Otimes__class_Otimes(X13,c_HOL_Otimes__class_Otimes(X12,X11,X3),X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_52]) ).

fof(c_0_850,plain,
    ! [X20,X15,X1,X2,X3] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X3)
      | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X15,X3),c_HOL_Otimes__class_Otimes(X1,X20,X3),X3)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X15,X3)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X2,X3)
      | ~ c_lessequals(X15,X20,X3)
      | ~ c_HOL_Oord__class_Oless(X2,X1,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_53]) ).

fof(c_0_851,plain,
    ! [X20,X15,X1,X2,X3] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X3)
      | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X15,X3),c_HOL_Otimes__class_Otimes(X1,X20,X3),X3)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X15,X3)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3)
      | ~ c_HOL_Oord__class_Oless(X15,X20,X3)
      | ~ c_lessequals(X2,X1,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_54]) ).

fof(c_0_852,plain,
    ! [X20,X15,X1,X2,X3] :
      ( ~ class_Ring__and__Field_Opordered__semiring(X3)
      | c_lessequals(c_HOL_Otimes__class_Otimes(X2,X15,X3),c_HOL_Otimes__class_Otimes(X1,X20,X3),X3)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X15,X3)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X2,X3)
      | ~ c_lessequals(X15,X20,X3)
      | ~ c_lessequals(X2,X1,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_55]) ).

fof(c_0_853,plain,
    ! [X20,X15,X1,X2,X3] :
      ( ~ class_Ring__and__Field_Opordered__semiring(X3)
      | c_lessequals(c_HOL_Otimes__class_Otimes(X2,X15,X3),c_HOL_Otimes__class_Otimes(X1,X20,X3),X3)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X15,X3)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X1,X3)
      | ~ c_lessequals(X15,X20,X3)
      | ~ c_lessequals(X2,X1,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_56]) ).

fof(c_0_854,plain,
    ! [X20,X15,X1,X2,X3] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X3)
      | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X15,X3),c_HOL_Otimes__class_Otimes(X1,X20,X3),X3)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X15,X3)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X2,X3)
      | ~ c_HOL_Oord__class_Oless(X15,X20,X3)
      | ~ c_HOL_Oord__class_Oless(X2,X1,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_57]) ).

fof(c_0_855,plain,
    ! [X20,X15,X1,X2,X3] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X3)
      | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X15,X3),c_HOL_Otimes__class_Otimes(X1,X20,X3),X3)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X15,X3)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X1,X3)
      | ~ c_HOL_Oord__class_Oless(X15,X20,X3)
      | ~ c_HOL_Oord__class_Oless(X2,X1,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_58]) ).

fof(c_0_856,plain,
    ! [X20,X15,X1,X2,X3] :
      ( ~ class_Ring__and__Field_Oordered__idom(X3)
      | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(X2,X3),c_HOL_Oabs__class_Oabs(X1,X3),X3),c_HOL_Otimes__class_Otimes(X15,X20,X3),X3)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(X1,X3),X20,X3)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(X2,X3),X15,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_59]) ).

fof(c_0_857,plain,
    ! [X7,X22,X2,X3] :
      ( ~ class_Ring__and__Field_Oordered__idom(X3)
      | c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X2,X22,X3),X7,X3)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X7,X2,X3),X3),X22,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_60]) ).

fof(c_0_858,plain,
    ! [X7,X22,X2,X3] :
      ( ~ class_Ring__and__Field_Oordered__idom(X3)
      | c_HOL_Oord__class_Oless(X7,c_HOL_Oplus__class_Oplus(X2,X22,X3),X3)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X7,X2,X3),X3),X22,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_61]) ).

fof(c_0_859,plain,
    ! [X4,X5,X8] :
      ( c_HOL_Oord__class_Oless(X5,X4,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X5,X8,tc_nat),c_HOL_Ominus__class_Ominus(X4,X8,tc_nat),tc_nat)
      | ~ c_lessequals(X8,X4,tc_nat)
      | ~ c_lessequals(X8,X5,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_62]) ).

fof(c_0_860,plain,
    ! [X4,X5,X8] :
      ( c_lessequals(X5,X4,tc_nat)
      | ~ c_lessequals(c_HOL_Ominus__class_Ominus(X5,X8,tc_nat),c_HOL_Ominus__class_Ominus(X4,X8,tc_nat),tc_nat)
      | ~ c_lessequals(X8,X4,tc_nat)
      | ~ c_lessequals(X8,X5,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_63]) ).

fof(c_0_861,plain,
    ! [X6,X7,X3] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X7,X7,X3),c_HOL_Otimes__class_Otimes(X6,X6,X3),X3),X3)
      | X7 = c_HOL_Ozero__class_Ozero(X3) ),
    inference(fof_simplification,[status(thm)],[c_0_64]) ).

fof(c_0_862,plain,
    ! [X6,X7,X3] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X7,X7,X3),c_HOL_Otimes__class_Otimes(X6,X6,X3),X3),X3)
      | X6 = c_HOL_Ozero__class_Ozero(X3) ),
    inference(fof_simplification,[status(thm)],[c_0_65]) ).

fof(c_0_863,plain,
    ! [X6,X7,X3] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
      | c_lessequals(c_HOL_Ozero__class_Ozero(X3),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X7,X7,X3),c_HOL_Otimes__class_Otimes(X6,X6,X3),X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_66]) ).

fof(c_0_864,axiom,
    ! [X6,X34,X18,X7,X4] :
      ( c_HOL_Oplus__class_Oplus(X7,c_HOL_Otimes__class_Otimes(X4,X18,tc_nat),tc_nat) != c_HOL_Oplus__class_Oplus(X6,c_HOL_Otimes__class_Otimes(X4,X34,tc_nat),tc_nat)
      | c_Divides_Odiv__class_Omod(X7,X4,tc_nat) = c_Divides_Odiv__class_Omod(X6,X4,tc_nat) ),
    c_0_67 ).

fof(c_0_865,plain,
    ! [X15,X1,X2,X3] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
      | c_HOL_Oord__class_Oless(X1,X2,X3)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X15,X2,X3),c_HOL_Otimes__class_Otimes(X15,X1,X3),X3)
      | ~ c_HOL_Oord__class_Oless(X15,c_HOL_Ozero__class_Ozero(X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_68]) ).

fof(c_0_866,plain,
    ! [X15,X1,X2,X3] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
      | c_HOL_Oord__class_Oless(X2,X1,X3)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X15,X2,X3),c_HOL_Otimes__class_Otimes(X15,X1,X3),X3)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X15,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_69]) ).

fof(c_0_867,plain,
    ! [X15,X1,X2,X3] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
      | c_lessequals(X1,X2,X3)
      | ~ c_lessequals(c_HOL_Otimes__class_Otimes(X15,X2,X3),c_HOL_Otimes__class_Otimes(X15,X1,X3),X3)
      | ~ c_HOL_Oord__class_Oless(X15,c_HOL_Ozero__class_Ozero(X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_70]) ).

fof(c_0_868,plain,
    ! [X15,X1,X2,X3] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
      | c_lessequals(X2,X1,X3)
      | ~ c_lessequals(c_HOL_Otimes__class_Otimes(X15,X2,X3),c_HOL_Otimes__class_Otimes(X15,X1,X3),X3)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X15,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_71]) ).

fof(c_0_869,plain,
    ! [X15,X1,X2,X3] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X3)
      | c_lessequals(X2,X1,X3)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X15,X3)
      | ~ c_lessequals(c_HOL_Otimes__class_Otimes(X15,X2,X3),c_HOL_Otimes__class_Otimes(X15,X1,X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_72]) ).

fof(c_0_870,plain,
    ! [X15,X1,X2,X3] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X3)
      | c_lessequals(X2,X1,X3)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X15,X3)
      | ~ c_lessequals(c_HOL_Otimes__class_Otimes(X2,X15,X3),c_HOL_Otimes__class_Otimes(X1,X15,X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_73]) ).

fof(c_0_871,plain,
    ! [X15,X1,X2,X3] :
      ( ~ class_Ring__and__Field_Oordered__semiring(X3)
      | c_HOL_Oord__class_Oless(X2,X1,X3)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X15,X3)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X15,X2,X3),c_HOL_Otimes__class_Otimes(X15,X1,X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_74]) ).

fof(c_0_872,plain,
    ! [X15,X1,X2,X3] :
      ( ~ class_Ring__and__Field_Oordered__semiring(X3)
      | c_HOL_Oord__class_Oless(X2,X1,X3)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X15,X3)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X15,X3),c_HOL_Otimes__class_Otimes(X1,X15,X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_75]) ).

fof(c_0_873,plain,
    ! [X15,X1,X2,X3] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X3)
      | c_HOL_Oord__class_Oless(X2,X1,X3)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X15,X3)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X15,X2,X3),c_HOL_Otimes__class_Otimes(X15,X1,X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_76]) ).

fof(c_0_874,plain,
    ! [X15,X1,X2,X3] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X3)
      | c_HOL_Oord__class_Oless(X2,X1,X3)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X15,X3)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X15,X3),c_HOL_Otimes__class_Otimes(X1,X15,X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_77]) ).

fof(c_0_875,plain,
    ! [X4,X5,X8] :
      ( c_Ring__and__Field_Odvd__class_Odvd(X5,X4,tc_nat)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X8,X5,tc_nat),c_HOL_Otimes__class_Otimes(X8,X4,tc_nat),tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X8,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_78]) ).

fof(c_0_876,plain,
    ! [X4,X5,X8] :
      ( c_Ring__and__Field_Odvd__class_Odvd(X5,X4,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X8,tc_nat)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X8,X5,tc_nat),c_HOL_Otimes__class_Otimes(X8,X4,tc_nat),tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_79]) ).

fof(c_0_877,plain,
    ! [X4,X5,X8] :
      ( c_HOL_Oord__class_Oless(X5,X4,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X8,X5,tc_nat),c_HOL_Otimes__class_Otimes(X8,X4,tc_nat),tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X8,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_80]) ).

fof(c_0_878,plain,
    ! [X4,X5,X8] :
      ( c_lessequals(X5,X4,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X8,tc_nat)
      | ~ c_lessequals(c_HOL_Otimes__class_Otimes(X5,X8,tc_nat),c_HOL_Otimes__class_Otimes(X4,X8,tc_nat),tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_81]) ).

fof(c_0_879,plain,
    ! [X4,X5,X8] :
      ( c_lessequals(X5,X4,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X8,tc_nat)
      | ~ c_lessequals(c_HOL_Otimes__class_Otimes(X8,X5,tc_nat),c_HOL_Otimes__class_Otimes(X8,X4,tc_nat),tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_82]) ).

fof(c_0_880,plain,
    ! [X4,X5,X8] :
      ( c_lessequals(X5,X4,tc_nat)
      | ~ c_lessequals(c_HOL_Otimes__class_Otimes(X8,X5,tc_nat),c_HOL_Otimes__class_Otimes(X8,X4,tc_nat),tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X8,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_83]) ).

fof(c_0_881,plain,
    ! [X15,X1,X2,X3] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
      | c_HOL_Oord__class_Oless(X15,c_HOL_Ozero__class_Ozero(X3),X3)
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X15,X3)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X15,X3),c_HOL_Otimes__class_Otimes(X1,X15,X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_84]) ).

fof(c_0_882,plain,
    ! [X15,X1,X2,X3] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
      | c_HOL_Oord__class_Oless(X15,c_HOL_Ozero__class_Ozero(X3),X3)
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X15,X3)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X15,X2,X3),c_HOL_Otimes__class_Otimes(X15,X1,X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_85]) ).

fof(c_0_883,plain,
    ! [X7,X20,X15,X3] :
      ( ~ class_Ring__and__Field_Oidom(X3)
      | ~ class_Int_Onumber__ring(X3)
      | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X7,X15,X3),c_HOL_Otimes__class_Otimes(X7,X20,X3),X3) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X7,X20,X3),c_HOL_Otimes__class_Otimes(X7,X15,X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_86]) ).

fof(c_0_884,plain,
    ! [X16,X6,X7,X3] :
      ( ~ class_Ring__and__Field_Oidom(X3)
      | ~ class_Int_Onumber__ring(X3)
      | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X7,X6,X3),c_HOL_Otimes__class_Otimes(X7,X16,X3),X3) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X7,X16,X3),c_HOL_Otimes__class_Otimes(X7,X6,X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_87]) ).

fof(c_0_885,plain,
    ! [X18] : ~ c_Parity_Oeven__odd__class_Oeven(c_Suc(c_HOL_Otimes__class_Otimes(c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),X18,tc_nat)),tc_nat),
    inference(fof_simplification,[status(thm)],[c_0_88]) ).

fof(c_0_886,plain,
    ! [X15,X1,X2,X3] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
      | c_HOL_Oord__class_Oless(X15,c_HOL_Ozero__class_Ozero(X3),X3)
      | c_HOL_Oord__class_Oless(X2,X1,X3)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X15,X3),c_HOL_Otimes__class_Otimes(X1,X15,X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_89]) ).

fof(c_0_887,plain,
    ! [X15,X1,X2,X3] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
      | c_HOL_Oord__class_Oless(X1,X2,X3)
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X15,X3)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X15,X3),c_HOL_Otimes__class_Otimes(X1,X15,X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_90]) ).

fof(c_0_888,plain,
    ! [X15,X1,X2,X3] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
      | c_HOL_Oord__class_Oless(X15,c_HOL_Ozero__class_Ozero(X3),X3)
      | c_HOL_Oord__class_Oless(X2,X1,X3)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X15,X2,X3),c_HOL_Otimes__class_Otimes(X15,X1,X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_91]) ).

fof(c_0_889,plain,
    ! [X15,X1,X2,X3] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
      | c_HOL_Oord__class_Oless(X1,X2,X3)
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X15,X3)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X15,X2,X3),c_HOL_Otimes__class_Otimes(X15,X1,X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_92]) ).

fof(c_0_890,plain,
    ! [X20,X15,X1,X2,X3] :
      ( ~ class_OrderedGroup_Oab__group__add(X3)
      | c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X2,X15,X3),c_HOL_Oplus__class_Oplus(X1,X20,X3),X3) = c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X2,X1,X3),c_HOL_Ominus__class_Ominus(X15,X20,X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_93]) ).

fof(c_0_891,plain,
    ! [X15,X1,X2,X3] :
      ( ~ class_Divides_Oring__div(X3)
      | c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X2,X1,X3),X15,X3) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(c_Divides_Odiv__class_Omod(X2,X15,X3),X1,X3),X15,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_94]) ).

fof(c_0_892,plain,
    ! [X15,X1,X2,X3] :
      ( ~ class_Divides_Oring__div(X3)
      | c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X2,X1,X3),X15,X3) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X2,c_Divides_Odiv__class_Omod(X1,X15,X3),X3),X15,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_95]) ).

fof(c_0_893,plain,
    ! [X15,X1,X2,X3] :
      ( ~ class_Divides_Osemiring__div(X3)
      | c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X2,X1,X3),X15,X3) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(X2,X15,X3),X1,X3),X15,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_96]) ).

fof(c_0_894,plain,
    ! [X15,X1,X2,X3] :
      ( ~ class_Divides_Osemiring__div(X3)
      | c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X2,X1,X3),X15,X3) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X2,c_Divides_Odiv__class_Omod(X1,X15,X3),X3),X15,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_97]) ).

fof(c_0_895,plain,
    ! [X15,X1,X2,X3] :
      ( ~ class_Divides_Osemiring__div(X3)
      | c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X2,X1,X3),X15,X3) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(X2,X15,X3),X1,X3),X15,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_98]) ).

fof(c_0_896,plain,
    ! [X15,X1,X2,X3] :
      ( ~ class_Divides_Osemiring__div(X3)
      | c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X2,X1,X3),X15,X3) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X2,c_Divides_Odiv__class_Omod(X1,X15,X3),X3),X15,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_99]) ).

fof(c_0_897,plain,
    ! [X20,X15,X1,X2,X3] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
      | c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X2,X1,X3),c_HOL_Oplus__class_Oplus(X15,X20,X3),X3) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X2,X15,X3),c_HOL_Oplus__class_Oplus(X1,X20,X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_100]) ).

fof(c_0_898,plain,
    ! [X15,X1,X2,X3] :
      ( ~ class_Divides_Osemiring__div(X3)
      | c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(X2,X15,X3),X1,X3),X15,X3) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X2,X1,X3),X15,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_101]) ).

fof(c_0_899,plain,
    ! [X15,X1,X2,X3] :
      ( ~ class_Divides_Osemiring__div(X3)
      | c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X2,c_Divides_Odiv__class_Omod(X1,X15,X3),X3),X15,X3) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X2,X1,X3),X15,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_102]) ).

fof(c_0_900,plain,
    ! [X15,X1,X2,X3] :
      ( ~ class_Divides_Osemiring__div(X3)
      | c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(X2,X15,X3),X1,X3),X15,X3) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X2,X1,X3),X15,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_103]) ).

fof(c_0_901,plain,
    ! [X11,X12,X13,X14,X3] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
      | c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X14,X13,X3),c_HOL_Otimes__class_Otimes(X12,X11,X3),X3) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X14,X12,X3),c_HOL_Otimes__class_Otimes(X13,X11,X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_104]) ).

fof(c_0_902,plain,
    ! [X15,X1,X2,X3] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
      | c_HOL_Oord__class_Oless(X1,X2,X3)
      | c_HOL_Oord__class_Oless(X2,X1,X3)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X15,X2,X3),c_HOL_Otimes__class_Otimes(X15,X1,X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_105]) ).

fof(c_0_903,plain,
    ! [X15,X1,X2,X3] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
      | c_HOL_Oord__class_Oless(X1,X2,X3)
      | c_HOL_Oord__class_Oless(X2,X1,X3)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X15,X3),c_HOL_Otimes__class_Otimes(X1,X15,X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_106]) ).

fof(c_0_904,plain,
    ! [X7,X22,X20,X15,X3] :
      ( ~ class_Ring__and__Field_Oidom(X3)
      | ~ class_Int_Onumber__ring(X3)
      | c_HOL_Oplus__class_Oplus(X7,c_HOL_Otimes__class_Otimes(X22,X15,X3),X3) != c_HOL_Oplus__class_Oplus(X7,c_HOL_Otimes__class_Otimes(X22,X20,X3),X3)
      | X15 = X20
      | X22 = c_HOL_Ozero__class_Ozero(X3) ),
    inference(fof_simplification,[status(thm)],[c_0_107]) ).

fof(c_0_905,axiom,
    ! [X7,X20,X15] : c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X7,X15,tc_nat),c_HOL_Otimes__class_Otimes(X7,X20,tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X7,X20,tc_nat),c_HOL_Otimes__class_Otimes(X7,X15,tc_nat),tc_nat),
    c_0_108 ).

fof(c_0_906,axiom,
    ! [X16,X6,X7] : c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X7,X6,tc_nat),c_HOL_Otimes__class_Otimes(X7,X16,tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X7,X16,tc_nat),c_HOL_Otimes__class_Otimes(X7,X6,tc_nat),tc_nat),
    c_0_109 ).

fof(c_0_907,plain,
    ! [X5,X8,X9] :
      ( c_HOL_Ominus__class_Ominus(c_Suc(c_HOL_Ominus__class_Ominus(X9,X8,tc_nat)),X5,tc_nat) = c_HOL_Ominus__class_Ominus(c_Suc(X9),c_HOL_Oplus__class_Oplus(X8,X5,tc_nat),tc_nat)
      | ~ c_lessequals(X8,X9,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_110]) ).

fof(c_0_908,plain,
    ! [X5,X8,X9] :
      ( c_HOL_Ominus__class_Ominus(X5,c_Suc(c_HOL_Ominus__class_Ominus(X9,X8,tc_nat)),tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X5,X8,tc_nat),c_Suc(X9),tc_nat)
      | ~ c_lessequals(X8,X9,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_111]) ).

fof(c_0_909,plain,
    ! [X4,X5,X8] :
      ( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X5,X8,tc_nat),c_HOL_Ominus__class_Ominus(X4,X8,tc_nat),tc_nat)
      | ~ c_HOL_Oord__class_Oless(X5,X4,tc_nat)
      | ~ c_lessequals(X8,X4,tc_nat)
      | ~ c_lessequals(X8,X5,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_112]) ).

fof(c_0_910,plain,
    ! [X4,X5,X8] :
      ( c_lessequals(c_HOL_Ominus__class_Ominus(X5,X8,tc_nat),c_HOL_Ominus__class_Ominus(X4,X8,tc_nat),tc_nat)
      | ~ c_lessequals(X5,X4,tc_nat)
      | ~ c_lessequals(X8,X4,tc_nat)
      | ~ c_lessequals(X8,X5,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_113]) ).

fof(c_0_911,plain,
    ! [X1,X2,X3] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X3)
      | c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X2,X1,X3),X3),c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(X2,X3),c_HOL_Oabs__class_Oabs(X1,X3),X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_114]) ).

fof(c_0_912,plain,
    ! [X1,X2,X3] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X3)
      | c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Oplus__class_Oplus(X2,X1,X3),X3),c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(X2,X3),c_HOL_Oabs__class_Oabs(X1,X3),X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_115]) ).

fof(c_0_913,plain,
    ! [X1,X2,X3] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X3)
      | c_lessequals(c_HOL_Ominus__class_Ominus(c_HOL_Oabs__class_Oabs(X2,X3),c_HOL_Oabs__class_Oabs(X1,X3),X3),c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X2,X1,X3),X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_116]) ).

fof(c_0_914,plain,
    ! [X1,X2,X3] :
      ( ~ class_Ring__and__Field_Olordered__ring(X3)
      | c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(X2,X1,X3),X3),c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(X2,X3),c_HOL_Oabs__class_Oabs(X1,X3),X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_117]) ).

fof(c_0_915,plain,
    ! [X20,X15,X1,X2,X3] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
      | c_lessequals(X2,c_HOL_Oplus__class_Oplus(X1,X20,X3),X3)
      | ~ c_lessequals(X15,X20,X3)
      | ~ c_lessequals(X2,c_HOL_Oplus__class_Oplus(X1,X15,X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_118]) ).

fof(c_0_916,plain,
    ! [X4,X5,X8] :
      ( c_lessequals(X5,X4,tc_nat)
      | ~ c_lessequals(c_HOL_Otimes__class_Otimes(c_Suc(X8),X5,tc_nat),c_HOL_Otimes__class_Otimes(c_Suc(X8),X4,tc_nat),tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_119]) ).

fof(c_0_917,plain,
    ! [X4,X5,X8] :
      ( c_HOL_Oord__class_Oless(X5,X4,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Suc(X8),X5,tc_nat),c_HOL_Otimes__class_Otimes(c_Suc(X8),X4,tc_nat),tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_120]) ).

fof(c_0_918,axiom,
    ! [X7,X22,X20,X15] :
      ( c_HOL_Oplus__class_Oplus(X7,c_HOL_Otimes__class_Otimes(X22,X15,tc_nat),tc_nat) != c_HOL_Oplus__class_Oplus(X7,c_HOL_Otimes__class_Otimes(X22,X20,tc_nat),tc_nat)
      | X15 = X20
      | X22 = c_HOL_Ozero__class_Ozero(tc_nat) ),
    c_0_121 ).

fof(c_0_919,plain,
    ! [X15,X1,X2,X3] :
      ( ~ class_Ring__and__Field_Oidom(X3)
      | c_Ring__and__Field_Odvd__class_Odvd(X2,X1,X3)
      | X15 = c_HOL_Ozero__class_Ozero(X3)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X15,X2,X3),c_HOL_Otimes__class_Otimes(X15,X1,X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_122]) ).

fof(c_0_920,plain,
    ! [X15,X1,X2,X3] :
      ( ~ class_Ring__and__Field_Oidom(X3)
      | c_Ring__and__Field_Odvd__class_Odvd(X2,X1,X3)
      | X15 = c_HOL_Ozero__class_Ozero(X3)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X2,X15,X3),c_HOL_Otimes__class_Otimes(X1,X15,X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_123]) ).

fof(c_0_921,plain,
    ! [X8,X9,X10] :
      ( c_lessequals(X10,c_HOL_Ominus__class_Ominus(X9,X8,tc_nat),tc_nat)
      | ~ c_lessequals(c_HOL_Oplus__class_Oplus(X10,X8,tc_nat),X9,tc_nat)
      | ~ c_lessequals(X8,X9,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_124]) ).

fof(c_0_922,plain,
    ! [X8,X9,X10] :
      ( c_lessequals(c_HOL_Oplus__class_Oplus(X10,X8,tc_nat),X9,tc_nat)
      | ~ c_lessequals(X10,c_HOL_Ominus__class_Ominus(X9,X8,tc_nat),tc_nat)
      | ~ c_lessequals(X8,X9,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_125]) ).

fof(c_0_923,plain,
    ! [X15,X1,X2,X3] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
      | c_HOL_Oord__class_Oless(X2,X1,X3)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X15,X2,X3),c_HOL_Oplus__class_Oplus(X15,X1,X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_126]) ).

fof(c_0_924,plain,
    ! [X15,X1,X2,X3] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
      | c_HOL_Oord__class_Oless(X2,X1,X3)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X2,X15,X3),c_HOL_Oplus__class_Oplus(X1,X15,X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_127]) ).

fof(c_0_925,plain,
    ! [X15,X1,X2,X3] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
      | c_lessequals(X2,X1,X3)
      | ~ c_lessequals(c_HOL_Oplus__class_Oplus(X2,X15,X3),c_HOL_Oplus__class_Oplus(X1,X15,X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_128]) ).

fof(c_0_926,plain,
    ! [X15,X1,X2,X3] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
      | c_lessequals(X2,X1,X3)
      | ~ c_lessequals(c_HOL_Oplus__class_Oplus(X15,X2,X3),c_HOL_Oplus__class_Oplus(X15,X1,X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_129]) ).

fof(c_0_927,plain,
    ! [X4,X5,X8] :
      ( c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X5,X8,tc_nat),c_HOL_Ominus__class_Ominus(X4,X8,tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(X5,X4,tc_nat)
      | ~ c_lessequals(X8,X4,tc_nat)
      | ~ c_lessequals(X8,X5,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_130]) ).

fof(c_0_928,plain,
    ! [X15,X1,X2,X3] :
      ( ~ class_OrderedGroup_Olordered__ab__group__add__abs(X3)
      | c_lessequals(X2,c_HOL_Oplus__class_Oplus(X15,c_HOL_Oabs__class_Oabs(X1,X3),X3),X3)
      | ~ c_lessequals(c_HOL_Oplus__class_Oplus(X2,X1,X3),X15,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_131]) ).

fof(c_0_929,plain,
    ! [X4,X5,X8] :
      ( c_Ring__and__Field_Odvd__class_Odvd(X8,X5,tc_nat)
      | ~ c_lessequals(X4,X5,tc_nat)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X8,X4,tc_nat)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X8,c_HOL_Ominus__class_Ominus(X5,X4,tc_nat),tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_132]) ).

fof(c_0_930,plain,
    ! [X4,X5,X8] :
      ( c_Ring__and__Field_Odvd__class_Odvd(X8,X4,tc_nat)
      | ~ c_lessequals(X4,X5,tc_nat)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X8,X5,tc_nat)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X8,c_HOL_Ominus__class_Ominus(X5,X4,tc_nat),tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_133]) ).

fof(c_0_931,plain,
    ! [X4,X5,X8] :
      ( c_Ring__and__Field_Odvd__class_Odvd(X5,X4,tc_nat)
      | X8 = c_HOL_Ozero__class_Ozero(tc_nat)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X8,X5,tc_nat),c_HOL_Otimes__class_Otimes(X8,X4,tc_nat),tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_134]) ).

fof(c_0_932,plain,
    ! [X4,X5,X8] :
      ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X8,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X5,X8,tc_nat),c_HOL_Otimes__class_Otimes(X4,X8,tc_nat),tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_135]) ).

fof(c_0_933,plain,
    ! [X4,X5,X8] :
      ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X8,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X8,X5,tc_nat),c_HOL_Otimes__class_Otimes(X8,X4,tc_nat),tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_136]) ).

fof(c_0_934,plain,
    ! [X4,X5,X8] :
      ( c_HOL_Oord__class_Oless(X5,X4,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X5,X8,tc_nat),c_HOL_Otimes__class_Otimes(X4,X8,tc_nat),tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_137]) ).

fof(c_0_935,plain,
    ! [X4,X5,X8] :
      ( c_HOL_Oord__class_Oless(X5,X4,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X8,X5,tc_nat),c_HOL_Otimes__class_Otimes(X8,X4,tc_nat),tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_138]) ).

fof(c_0_936,plain,
    ! [X4,X5,X8] :
      ( c_HOL_Oord__class_Oless(X5,X4,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X8,X5,tc_nat),c_HOL_Oplus__class_Oplus(X8,X4,tc_nat),tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_139]) ).

fof(c_0_937,plain,
    ! [X4,X5,X8] :
      ( c_lessequals(X5,X4,tc_nat)
      | ~ c_lessequals(c_HOL_Oplus__class_Oplus(X8,X5,tc_nat),c_HOL_Oplus__class_Oplus(X8,X4,tc_nat),tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_140]) ).

fof(c_0_938,plain,
    ! [X15,X1,X2,X3] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
      | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X15,X2,X3),c_HOL_Otimes__class_Otimes(X15,X1,X3),X3)
      | ~ c_HOL_Oord__class_Oless(X1,X2,X3)
      | ~ c_HOL_Oord__class_Oless(X15,c_HOL_Ozero__class_Ozero(X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_141]) ).

fof(c_0_939,plain,
    ! [X15,X1,X2,X3] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
      | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X15,X2,X3),c_HOL_Otimes__class_Otimes(X15,X1,X3),X3)
      | ~ c_HOL_Oord__class_Oless(X2,X1,X3)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X15,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_142]) ).

fof(c_0_940,plain,
    ! [X15,X1,X2,X3] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
      | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X15,X2,X3),c_HOL_Otimes__class_Otimes(X15,X1,X3),X3)
      | ~ c_HOL_Oord__class_Oless(X15,c_HOL_Ozero__class_Ozero(X3),X3)
      | ~ c_HOL_Oord__class_Oless(X1,X2,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_143]) ).

fof(c_0_941,plain,
    ! [X15,X1,X2,X3] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X3)
      | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X15,X2,X3),c_HOL_Otimes__class_Otimes(X15,X1,X3),X3)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X15,X3)
      | ~ c_HOL_Oord__class_Oless(X2,X1,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_144]) ).

fof(c_0_942,plain,
    ! [X15,X1,X2,X3] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
      | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X15,X2,X3),c_HOL_Otimes__class_Otimes(X15,X1,X3),X3)
      | ~ c_HOL_Oord__class_Oless(X2,X1,X3)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X15,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_145]) ).

fof(c_0_943,plain,
    ! [X15,X1,X2,X3] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
      | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X15,X2,X3),c_HOL_Otimes__class_Otimes(X15,X1,X3),X3)
      | ~ c_HOL_Oord__class_Oless(X1,X2,X3)
      | ~ c_HOL_Oord__class_Oless(X15,c_HOL_Ozero__class_Ozero(X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_146]) ).

fof(c_0_944,plain,
    ! [X15,X1,X2,X3] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
      | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X15,X3),c_HOL_Otimes__class_Otimes(X1,X15,X3),X3)
      | ~ c_HOL_Oord__class_Oless(X15,c_HOL_Ozero__class_Ozero(X3),X3)
      | ~ c_HOL_Oord__class_Oless(X1,X2,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_147]) ).

fof(c_0_945,plain,
    ! [X15,X1,X2,X3] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X3)
      | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X15,X3),c_HOL_Otimes__class_Otimes(X1,X15,X3),X3)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X15,X3)
      | ~ c_HOL_Oord__class_Oless(X2,X1,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_148]) ).

fof(c_0_946,plain,
    ! [X15,X1,X2,X3] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
      | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X15,X3),c_HOL_Otimes__class_Otimes(X1,X15,X3),X3)
      | ~ c_HOL_Oord__class_Oless(X2,X1,X3)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X15,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_149]) ).

fof(c_0_947,plain,
    ! [X15,X1,X2,X3] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
      | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X15,X3),c_HOL_Otimes__class_Otimes(X1,X15,X3),X3)
      | ~ c_HOL_Oord__class_Oless(X1,X2,X3)
      | ~ c_HOL_Oord__class_Oless(X15,c_HOL_Ozero__class_Ozero(X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_150]) ).

fof(c_0_948,plain,
    ! [X15,X1,X2,X3] :
      ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X3)
      | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X15,X2,X3),c_HOL_Otimes__class_Otimes(X15,X1,X3),X3)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X15,X3)
      | ~ c_HOL_Oord__class_Oless(X2,X1,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_151]) ).

fof(c_0_949,plain,
    ! [X15,X1,X2,X3] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
      | c_lessequals(c_HOL_Otimes__class_Otimes(X15,X2,X3),c_HOL_Otimes__class_Otimes(X15,X1,X3),X3)
      | ~ c_lessequals(X1,X2,X3)
      | ~ c_HOL_Oord__class_Oless(X15,c_HOL_Ozero__class_Ozero(X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_152]) ).

fof(c_0_950,plain,
    ! [X15,X1,X2,X3] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
      | c_lessequals(c_HOL_Otimes__class_Otimes(X15,X2,X3),c_HOL_Otimes__class_Otimes(X15,X1,X3),X3)
      | ~ c_lessequals(X2,X1,X3)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X15,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_153]) ).

fof(c_0_951,plain,
    ! [X15,X1,X2,X3] :
      ( ~ class_Ring__and__Field_Opordered__ring(X3)
      | c_lessequals(c_HOL_Otimes__class_Otimes(X2,X15,X3),c_HOL_Otimes__class_Otimes(X1,X15,X3),X3)
      | ~ c_lessequals(X15,c_HOL_Ozero__class_Ozero(X3),X3)
      | ~ c_lessequals(X1,X2,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_154]) ).

fof(c_0_952,plain,
    ! [X15,X1,X2,X3] :
      ( ~ class_Ring__and__Field_Opordered__ring(X3)
      | c_lessequals(c_HOL_Otimes__class_Otimes(X15,X2,X3),c_HOL_Otimes__class_Otimes(X15,X1,X3),X3)
      | ~ c_lessequals(X15,c_HOL_Ozero__class_Ozero(X3),X3)
      | ~ c_lessequals(X1,X2,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_155]) ).

fof(c_0_953,plain,
    ! [X15,X1,X2,X3] :
      ( ~ class_Ring__and__Field_Omult__mono(X3)
      | c_lessequals(c_HOL_Otimes__class_Otimes(X2,X15,X3),c_HOL_Otimes__class_Otimes(X1,X15,X3),X3)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X15,X3)
      | ~ c_lessequals(X2,X1,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_156]) ).

fof(c_0_954,plain,
    ! [X15,X1,X2,X3] :
      ( ~ class_Ring__and__Field_Omult__mono(X3)
      | c_lessequals(c_HOL_Otimes__class_Otimes(X15,X2,X3),c_HOL_Otimes__class_Otimes(X15,X1,X3),X3)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X15,X3)
      | ~ c_lessequals(X2,X1,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_157]) ).

fof(c_0_955,plain,
    ! [X15,X1,X2,X3] :
      ( ~ class_Ring__and__Field_Omult__mono1(X3)
      | c_lessequals(c_HOL_Otimes__class_Otimes(X15,X2,X3),c_HOL_Otimes__class_Otimes(X15,X1,X3),X3)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X15,X3)
      | ~ c_lessequals(X2,X1,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_158]) ).

fof(c_0_956,plain,
    ! [X4,X5,X8] :
      ( c_lessequals(X5,c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X4,X5,tc_nat),X8,tc_nat),tc_nat)
      | ~ c_lessequals(X8,X4,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_159]) ).

fof(c_0_957,plain,
    ! [X20,X15,X1,X2,X3] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
      | c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X2,X15,X3),c_HOL_Otimes__class_Otimes(X1,X20,X3),X3)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X15,X20,X3)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X1,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_160]) ).

fof(c_0_958,plain,
    ! [X20,X15,X1,X2,X3] :
      ( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X3)
      | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X2,X15,X3),c_HOL_Oplus__class_Oplus(X1,X20,X3),X3)
      | ~ c_HOL_Oord__class_Oless(X15,X20,X3)
      | ~ c_HOL_Oord__class_Oless(X2,X1,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_161]) ).

fof(c_0_959,plain,
    ! [X20,X15,X1,X2,X3] :
      ( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X3)
      | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X2,X15,X3),c_HOL_Oplus__class_Oplus(X1,X20,X3),X3)
      | ~ c_HOL_Oord__class_Oless(X15,X20,X3)
      | ~ c_lessequals(X2,X1,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_162]) ).

fof(c_0_960,plain,
    ! [X20,X15,X1,X2,X3] :
      ( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X3)
      | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X2,X15,X3),c_HOL_Oplus__class_Oplus(X1,X20,X3),X3)
      | ~ c_lessequals(X15,X20,X3)
      | ~ c_HOL_Oord__class_Oless(X2,X1,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_163]) ).

fof(c_0_961,plain,
    ! [X20,X15,X1,X2,X3] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X3)
      | c_lessequals(c_HOL_Oplus__class_Oplus(X2,X15,X3),c_HOL_Oplus__class_Oplus(X1,X20,X3),X3)
      | ~ c_lessequals(X15,X20,X3)
      | ~ c_lessequals(X2,X1,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_164]) ).

fof(c_0_962,plain,
    ! [X6,X7,X3] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
      | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X7,X7,X3),c_HOL_Otimes__class_Otimes(X6,X6,X3),X3) != c_HOL_Ozero__class_Ozero(X3)
      | X6 = c_HOL_Ozero__class_Ozero(X3) ),
    inference(fof_simplification,[status(thm)],[c_0_165]) ).

fof(c_0_963,plain,
    ! [X6,X7,X3] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
      | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X7,X7,X3),c_HOL_Otimes__class_Otimes(X6,X6,X3),X3) != c_HOL_Ozero__class_Ozero(X3)
      | X7 = c_HOL_Ozero__class_Ozero(X3) ),
    inference(fof_simplification,[status(thm)],[c_0_166]) ).

fof(c_0_964,plain,
    ! [X15,X1,X2,X3] :
      ( ~ class_Divides_Osemiring__div(X3)
      | c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X2,X15,X3),c_HOL_Otimes__class_Otimes(X1,X15,X3),X3) = c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(X2,X1,X3),X15,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_167]) ).

fof(c_0_965,plain,
    ! [X15,X1,X2,X3] :
      ( ~ class_Divides_Osemiring__div(X3)
      | c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X15,X2,X3),c_HOL_Otimes__class_Otimes(X15,X1,X3),X3) = c_HOL_Otimes__class_Otimes(X15,c_Divides_Odiv__class_Omod(X2,X1,X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_168]) ).

fof(c_0_966,plain,
    ! [X27,X6,X7,X3] :
      ( ~ class_RealVector_Oreal__normed__algebra(X3)
      | c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X7,X6,X3),X27,X3) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X7,X27,X3),c_HOL_Otimes__class_Otimes(X6,X27,X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_169]) ).

fof(c_0_967,plain,
    ! [X1,X28,X2,X3] :
      ( ~ class_RealVector_Oreal__normed__algebra(X3)
      | c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X28,X3),X1,X3) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X2,X1,X3),c_HOL_Otimes__class_Otimes(X28,X1,X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_170]) ).

fof(c_0_968,plain,
    ! [X26,X1,X2,X3] :
      ( ~ class_RealVector_Oreal__normed__algebra(X3)
      | c_HOL_Otimes__class_Otimes(X2,c_HOL_Ominus__class_Ominus(X1,X26,X3),X3) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X2,X1,X3),c_HOL_Otimes__class_Otimes(X2,X26,X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_171]) ).

fof(c_0_969,plain,
    ! [X6,X18,X7,X3] :
      ( ~ class_RealVector_Oreal__normed__algebra(X3)
      | c_HOL_Otimes__class_Otimes(X18,c_HOL_Ominus__class_Ominus(X7,X6,X3),X3) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X18,X7,X3),c_HOL_Otimes__class_Otimes(X18,X6,X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_172]) ).

fof(c_0_970,plain,
    ! [X16,X6,X7,X3] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
      | c_HOL_Ominus__class_Ominus(c_Orderings_Oord__class_Omin(X7,X6,X3),X16,X3) = c_Orderings_Oord__class_Omin(c_HOL_Ominus__class_Ominus(X7,X16,X3),c_HOL_Ominus__class_Ominus(X6,X16,X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_173]) ).

fof(c_0_971,plain,
    ! [X15,X1,X2,X3] :
      ( ~ class_Divides_Osemiring__div(X3)
      | c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X2,c_HOL_Otimes__class_Otimes(X15,X1,X3),X3),X1,X3) = c_Divides_Odiv__class_Omod(X2,X1,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_174]) ).

fof(c_0_972,plain,
    ! [X15,X1,X2,X3] :
      ( ~ class_Divides_Osemiring__div(X3)
      | c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X2,c_HOL_Otimes__class_Otimes(X1,X15,X3),X3),X1,X3) = c_Divides_Odiv__class_Omod(X2,X1,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_175]) ).

fof(c_0_973,plain,
    ! [X16,X6,X7,X3] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
      | c_HOL_Oplus__class_Oplus(c_Orderings_Oord__class_Omin(X7,X6,X3),X16,X3) = c_Orderings_Oord__class_Omin(c_HOL_Oplus__class_Oplus(X7,X16,X3),c_HOL_Oplus__class_Oplus(X6,X16,X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_176]) ).

fof(c_0_974,plain,
    ! [X5,X1,X2,X3] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
      | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X5,X3),c_HOL_Otimes__class_Otimes(X1,X5,X3),X3) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X2,X1,X3),X5,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_177]) ).

fof(c_0_975,plain,
    ! [X15,X1,X2,X3] :
      ( ~ class_Ring__and__Field_Ocomm__semiring(X3)
      | c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X2,X1,X3),X15,X3) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X15,X3),c_HOL_Otimes__class_Otimes(X1,X15,X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_178]) ).

fof(c_0_976,plain,
    ! [X16,X6,X7,X3] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
      | c_HOL_Otimes__class_Otimes(X7,c_HOL_Oplus__class_Oplus(X6,X16,X3),X3) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X7,X6,X3),c_HOL_Otimes__class_Otimes(X7,X16,X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_179]) ).

fof(c_0_977,plain,
    ! [X1,X28,X2,X3] :
      ( ~ class_RealVector_Oreal__normed__algebra(X3)
      | c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X2,X28,X3),X1,X3) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X1,X3),c_HOL_Otimes__class_Otimes(X28,X1,X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_180]) ).

fof(c_0_978,plain,
    ! [X27,X6,X7,X3] :
      ( ~ class_RealVector_Oreal__normed__algebra(X3)
      | c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X7,X6,X3),X27,X3) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X7,X27,X3),c_HOL_Otimes__class_Otimes(X6,X27,X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_181]) ).

fof(c_0_979,plain,
    ! [X26,X1,X2,X3] :
      ( ~ class_RealVector_Oreal__normed__algebra(X3)
      | c_HOL_Otimes__class_Otimes(X2,c_HOL_Oplus__class_Oplus(X1,X26,X3),X3) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X1,X3),c_HOL_Otimes__class_Otimes(X2,X26,X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_182]) ).

fof(c_0_980,plain,
    ! [X6,X18,X7,X3] :
      ( ~ class_RealVector_Oreal__normed__algebra(X3)
      | c_HOL_Otimes__class_Otimes(X18,c_HOL_Oplus__class_Oplus(X7,X6,X3),X3) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X18,X7,X3),c_HOL_Otimes__class_Otimes(X18,X6,X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_183]) ).

fof(c_0_981,plain,
    ! [X15,X1,X2,X3] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
      | c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X2,X1,X3),X15,X3) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X15,X3),c_HOL_Otimes__class_Otimes(X1,X15,X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_184]) ).

fof(c_0_982,plain,
    ! [X4,X5,X8] :
      ( c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X8,X5,tc_nat),c_HOL_Otimes__class_Otimes(X8,X4,tc_nat),tc_nat)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X5,X4,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X8,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_185]) ).

fof(c_0_983,plain,
    ! [X4,X5,X8] :
      ( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X5,X8,tc_nat),c_HOL_Otimes__class_Otimes(X4,X8,tc_nat),tc_nat)
      | ~ c_HOL_Oord__class_Oless(X5,X4,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X8,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_186]) ).

fof(c_0_984,plain,
    ! [X4,X5,X8] :
      ( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X8,X5,tc_nat),c_HOL_Otimes__class_Otimes(X8,X4,tc_nat),tc_nat)
      | ~ c_HOL_Oord__class_Oless(X5,X4,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X8,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_187]) ).

fof(c_0_985,plain,
    ! [X8,X9,X10] :
      ( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X8,X10,tc_nat),c_HOL_Otimes__class_Otimes(X8,X9,tc_nat),tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X8,tc_nat)
      | ~ c_HOL_Oord__class_Oless(X10,X9,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_188]) ).

fof(c_0_986,plain,
    ! [X8,X9,X10] :
      ( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X10,X8,tc_nat),c_HOL_Otimes__class_Otimes(X9,X8,tc_nat),tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X8,tc_nat)
      | ~ c_HOL_Oord__class_Oless(X10,X9,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_189]) ).

fof(c_0_987,plain,
    ! [X4,X5,X8] :
      ( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X8,X5,tc_nat),c_HOL_Otimes__class_Otimes(X8,X4,tc_nat),tc_nat)
      | ~ c_HOL_Oord__class_Oless(X5,X4,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X8,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_190]) ).

fof(c_0_988,plain,
    ! [X4,X5,X8] :
      ( c_lessequals(c_HOL_Otimes__class_Otimes(X8,X5,tc_nat),c_HOL_Otimes__class_Otimes(X8,X4,tc_nat),tc_nat)
      | ~ c_lessequals(X5,X4,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X8,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_191]) ).

fof(c_0_989,plain,
    ! [X4,X5,X29] :
      ( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X29,X4,tc_nat),c_HOL_Ominus__class_Ominus(X29,X5,tc_nat),tc_nat)
      | ~ c_HOL_Oord__class_Oless(X5,X29,tc_nat)
      | ~ c_HOL_Oord__class_Oless(X5,X4,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_192]) ).

fof(c_0_990,plain,
    ! [X15,X1,X2] :
      ( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X2,X15,tc_nat),c_HOL_Ominus__class_Ominus(X1,X15,tc_nat),tc_nat)
      | ~ c_lessequals(X15,X2,tc_nat)
      | ~ c_HOL_Oord__class_Oless(X2,X1,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_193]) ).

fof(c_0_991,plain,
    ! [X29,X8,X9,X10] :
      ( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X10,X8,tc_nat),c_HOL_Oplus__class_Oplus(X9,X29,tc_nat),tc_nat)
      | ~ c_HOL_Oord__class_Oless(X8,X29,tc_nat)
      | ~ c_HOL_Oord__class_Oless(X10,X9,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_194]) ).

fof(c_0_992,plain,
    ! [X29,X8,X9,X10] :
      ( c_lessequals(c_HOL_Oplus__class_Oplus(X10,X8,tc_nat),c_HOL_Oplus__class_Oplus(X9,X29,tc_nat),tc_nat)
      | ~ c_lessequals(X8,X29,tc_nat)
      | ~ c_lessequals(X10,X9,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_195]) ).

fof(c_0_993,plain,
    ! [X29,X8,X9,X10] :
      ( c_lessequals(c_HOL_Otimes__class_Otimes(X10,X8,tc_nat),c_HOL_Otimes__class_Otimes(X9,X29,tc_nat),tc_nat)
      | ~ c_lessequals(X8,X29,tc_nat)
      | ~ c_lessequals(X10,X9,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_196]) ).

fof(c_0_994,plain,
    ! [X1,X2,X3] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X3)
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X1,X3)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_HOL_Otimes__class_Otimes(X1,X2,X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_197]) ).

fof(c_0_995,plain,
    ! [X1,X2,X3] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X3)
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X1,X3)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_HOL_Otimes__class_Otimes(X2,X1,X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_198]) ).

fof(c_0_996,plain,
    ! [X1,X2,X3] :
      ( ~ class_Ring__and__Field_Opordered__ring__abs(X3)
      | c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(X2,X1,X3),X3) = c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(X2,X3),c_HOL_Oabs__class_Oabs(X1,X3),X3)
      | ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X3),X3)
      | ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_199]) ).

fof(c_0_997,plain,
    ! [X1,X2,X3] :
      ( ~ class_Ring__and__Field_Opordered__ring__abs(X3)
      | c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(X2,X1,X3),X3) = c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(X2,X3),c_HOL_Oabs__class_Oabs(X1,X3),X3)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X1,X3)
      | ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_200]) ).

fof(c_0_998,plain,
    ! [X1,X2,X3] :
      ( ~ class_Ring__and__Field_Opordered__ring__abs(X3)
      | c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(X2,X1,X3),X3) = c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(X2,X3),c_HOL_Oabs__class_Oabs(X1,X3),X3)
      | ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X3),X3)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X2,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_201]) ).

fof(c_0_999,plain,
    ! [X1,X2,X3] :
      ( ~ class_Ring__and__Field_Opordered__ring__abs(X3)
      | c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(X2,X1,X3),X3) = c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(X2,X3),c_HOL_Oabs__class_Oabs(X1,X3),X3)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X1,X3)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X2,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_202]) ).

fof(c_0_1000,axiom,
    ! [X4,X5,X8] : c_HOL_Otimes__class_Otimes(X8,c_HOL_Ominus__class_Ominus(X5,X4,tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X8,X5,tc_nat),c_HOL_Otimes__class_Otimes(X8,X4,tc_nat),tc_nat),
    c_0_203 ).

fof(c_0_1001,axiom,
    ! [X4,X5,X8] : c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X5,X4,tc_nat),X8,tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X5,X8,tc_nat),c_HOL_Otimes__class_Otimes(X4,X8,tc_nat),tc_nat),
    c_0_204 ).

fof(c_0_1002,axiom,
    ! [X4,X5,X10] : c_Orderings_Oord__class_Omin(c_HOL_Ominus__class_Ominus(X5,X10,tc_nat),c_HOL_Ominus__class_Ominus(X4,X10,tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(c_Orderings_Oord__class_Omin(X5,X4,tc_nat),X10,tc_nat),
    c_0_205 ).

fof(c_0_1003,axiom,
    ! [X4,X5,X8] : c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X8,X4,tc_nat),X5,tc_nat),X4,tc_nat) = c_Divides_Odiv__class_Omod(X5,X4,tc_nat),
    c_0_206 ).

fof(c_0_1004,axiom,
    ! [X4,X5,X8] : c_HOL_Otimes__class_Otimes(X8,c_Divides_Odiv__class_Omod(X5,X4,tc_nat),tc_nat) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X8,X5,tc_nat),c_HOL_Otimes__class_Otimes(X8,X4,tc_nat),tc_nat),
    c_0_207 ).

fof(c_0_1005,axiom,
    ! [X4,X5,X8] : c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(X5,X4,tc_nat),X8,tc_nat) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X5,X8,tc_nat),c_HOL_Otimes__class_Otimes(X4,X8,tc_nat),tc_nat),
    c_0_208 ).

fof(c_0_1006,axiom,
    ! [X4,X5,X8] : c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X5,X4,tc_nat),X8,tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X5,X8,tc_nat),c_HOL_Otimes__class_Otimes(X4,X8,tc_nat),tc_nat),
    c_0_209 ).

fof(c_0_1007,axiom,
    ! [X4,X5,X8] : c_HOL_Otimes__class_Otimes(X8,c_HOL_Oplus__class_Oplus(X5,X4,tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X8,X5,tc_nat),c_HOL_Otimes__class_Otimes(X8,X4,tc_nat),tc_nat),
    c_0_210 ).

fof(c_0_1008,plain,
    ! [X8,X10] :
      ( ~ c_lessequals(X10,c_HOL_Oplus__class_Oplus(X8,X10,tc_nat),tc_nat)
      | c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X8,X10,tc_nat),X10,tc_nat) = X8 ),
    inference(fof_simplification,[status(thm)],[c_0_211]) ).

fof(c_0_1009,plain,
    ! [X8,X9,X10] :
      ( c_HOL_Oord__class_Oless(X10,c_HOL_Ominus__class_Ominus(X9,X8,tc_nat),tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X10,X8,tc_nat),X9,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_212]) ).

fof(c_0_1010,plain,
    ! [X8,X9,X10] :
      ( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X10,X8,tc_nat),X9,tc_nat)
      | ~ c_HOL_Oord__class_Oless(X10,c_HOL_Ominus__class_Ominus(X9,X8,tc_nat),tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_213]) ).

fof(c_0_1011,plain,
    ! [X8,X9,X10] :
      ( c_lessequals(X9,c_HOL_Oplus__class_Oplus(X10,X8,tc_nat),tc_nat)
      | ~ c_lessequals(c_HOL_Ominus__class_Ominus(X9,X8,tc_nat),X10,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_214]) ).

fof(c_0_1012,plain,
    ! [X8,X9,X10] :
      ( c_lessequals(c_HOL_Ominus__class_Ominus(X9,X8,tc_nat),X10,tc_nat)
      | ~ c_lessequals(X9,c_HOL_Oplus__class_Oplus(X10,X8,tc_nat),tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_215]) ).

fof(c_0_1013,plain,
    ! [X4,X5,X8,X3] :
      ( ~ class_Divides_Osemiring__div(X3)
      | c_Ring__and__Field_Odvd__class_Odvd(X8,X5,X3)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X8,c_Divides_Odiv__class_Omod(X5,X4,X3),X3)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X8,X4,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_216]) ).

fof(c_0_1014,plain,
    ! [X4,X5,X8,X3] :
      ( ~ class_Divides_Osemiring__div(X3)
      | c_Ring__and__Field_Odvd__class_Odvd(X8,X5,X3)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X8,X4,X3)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X8,c_Divides_Odiv__class_Omod(X5,X4,X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_217]) ).

fof(c_0_1015,plain,
    ! [X16,X6,X7,X17,X3] :
      ( ~ class_OrderedGroup_Oab__group__add(X3)
      | c_HOL_Oplus__class_Oplus(X7,c_HOL_Oplus__class_Oplus(X6,X16,X3),X3) != c_HOL_Oplus__class_Oplus(X6,X17,X3)
      | c_HOL_Oplus__class_Oplus(X7,X16,X3) = X17 ),
    inference(fof_simplification,[status(thm)],[c_0_218]) ).

fof(c_0_1016,plain,
    ! [X8,X9,X10] :
      ( c_HOL_Oplus__class_Oplus(X10,c_HOL_Ominus__class_Ominus(X9,X8,tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X10,X9,tc_nat),X8,tc_nat)
      | ~ c_lessequals(X8,X9,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_219]) ).

fof(c_0_1017,plain,
    ! [X8,X9,X10] :
      ( c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X9,X8,tc_nat),X10,tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X9,X10,tc_nat),X8,tc_nat)
      | ~ c_lessequals(X8,X9,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_220]) ).

fof(c_0_1018,plain,
    ! [X8,X9,X10] :
      ( c_HOL_Ominus__class_Ominus(X10,c_HOL_Ominus__class_Ominus(X9,X8,tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X10,X8,tc_nat),X9,tc_nat)
      | ~ c_lessequals(X8,X9,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_221]) ).

fof(c_0_1019,plain,
    ! [X8,X9,X10] :
      ( c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X10,X9,tc_nat),X8,tc_nat) = c_HOL_Oplus__class_Oplus(X10,c_HOL_Ominus__class_Ominus(X9,X8,tc_nat),tc_nat)
      | ~ c_lessequals(X8,X9,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_222]) ).

fof(c_0_1020,plain,
    ! [X8,X9,X10] :
      ( c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X9,X10,tc_nat),X8,tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X9,X8,tc_nat),X10,tc_nat)
      | ~ c_lessequals(X8,X9,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_223]) ).

fof(c_0_1021,plain,
    ! [X1,X2,X3] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
      | c_lessequals(X1,c_HOL_Ozero__class_Ozero(X3),X3)
      | c_lessequals(c_HOL_Ozero__class_Ozero(X3),X1,X3)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),c_HOL_Otimes__class_Otimes(X2,X1,X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_224]) ).

fof(c_0_1022,plain,
    ! [X1,X2,X3] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
      | c_lessequals(X2,c_HOL_Ozero__class_Ozero(X3),X3)
      | c_lessequals(c_HOL_Ozero__class_Ozero(X3),X1,X3)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),c_HOL_Otimes__class_Otimes(X2,X1,X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_225]) ).

fof(c_0_1023,plain,
    ! [X1,X2,X3] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
      | c_lessequals(X1,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),c_HOL_Otimes__class_Otimes(X2,X1,X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_226]) ).

fof(c_0_1024,plain,
    ! [X1,X2,X3] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
      | c_lessequals(X2,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),c_HOL_Otimes__class_Otimes(X2,X1,X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_227]) ).

fof(c_0_1025,plain,
    ! [X1,X2,X3] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
      | 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(X2,X1,X3),c_HOL_Ozero__class_Ozero(X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_228]) ).

fof(c_0_1026,plain,
    ! [X1,X2,X3] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
      | 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(X2,X1,X3),c_HOL_Ozero__class_Ozero(X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_229]) ).

fof(c_0_1027,plain,
    ! [X1,X2,X3] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
      | 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(X2,X1,X3),c_HOL_Ozero__class_Ozero(X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_230]) ).

fof(c_0_1028,plain,
    ! [X1,X2,X3] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
      | 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(X2,X1,X3),c_HOL_Ozero__class_Ozero(X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_231]) ).

fof(c_0_1029,plain,
    ! [X4,X5] :
      ( c_lessequals(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Otimes__class_Otimes(X5,X4,tc_nat),tc_nat)
      | ~ 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)),X5,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_232]) ).

fof(c_0_1030,plain,
    ! [X4,X5] :
      ( c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Otimes__class_Otimes(X5,X4,tc_nat),tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X5,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X4,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_233]) ).

fof(c_0_1031,plain,
    ! [X16,X6,X7,X3] :
      ( ~ class_Orderings_Olinorder(X3)
      | c_HOL_Oord__class_Oless(X6,X16,X3)
      | c_HOL_Oord__class_Oless(X7,X16,X3)
      | ~ c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omin(X7,X6,X3),X16,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_234]) ).

fof(c_0_1032,plain,
    ! [X16,X6,X7,X3] :
      ( ~ class_Orderings_Olinorder(X3)
      | c_lessequals(X6,X16,X3)
      | c_lessequals(X7,X16,X3)
      | ~ c_lessequals(c_Orderings_Oord__class_Omin(X7,X6,X3),X16,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_235]) ).

fof(c_0_1033,plain,
    ! [X4,X5,X8] :
      ( c_lessequals(c_HOL_Otimes__class_Otimes(c_Suc(X8),X5,tc_nat),c_HOL_Otimes__class_Otimes(c_Suc(X8),X4,tc_nat),tc_nat)
      | ~ c_lessequals(X5,X4,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_236]) ).

fof(c_0_1034,plain,
    ! [X4,X5,X8] :
      ( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Suc(X8),X5,tc_nat),c_HOL_Otimes__class_Otimes(c_Suc(X8),X4,tc_nat),tc_nat)
      | ~ c_HOL_Oord__class_Oless(X5,X4,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_237]) ).

fof(c_0_1035,plain,
    ! [X1,X2,X3] :
      ( ~ class_OrderedGroup_Opordered__comm__monoid__add(X3)
      | c_lessequals(c_HOL_Oplus__class_Oplus(X2,X1,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(fof_simplification,[status(thm)],[c_0_238]) ).

fof(c_0_1036,plain,
    ! [X1,X2,X3] :
      ( ~ class_OrderedGroup_Opordered__comm__monoid__add(X3)
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_HOL_Oplus__class_Oplus(X2,X1,X3),X3)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X1,X3)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_239]) ).

fof(c_0_1037,plain,
    ! [X1,X2,X3] :
      ( ~ class_OrderedGroup_Opordered__comm__monoid__add(X3)
      | c_lessequals(c_HOL_Ozero__class_Ozero(X3),c_HOL_Oplus__class_Oplus(X2,X1,X3),X3)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X1,X3)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X2,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_240]) ).

fof(c_0_1038,plain,
    ! [X1,X2,X3] :
      ( ~ class_OrderedGroup_Opordered__comm__monoid__add(X3)
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_HOL_Oplus__class_Oplus(X2,X1,X3),X3)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X1,X3)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_241]) ).

fof(c_0_1039,plain,
    ! [X1,X2,X3] :
      ( ~ class_OrderedGroup_Opordered__comm__monoid__add(X3)
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_HOL_Oplus__class_Oplus(X2,X1,X3),X3)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X1,X3)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X2,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_242]) ).

fof(c_0_1040,plain,
    ! [X1,X2,X3] :
      ( ~ class_Ring__and__Field_Opordered__cancel__semiring(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),X2,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_243]) ).

fof(c_0_1041,plain,
    ! [X1,X2,X3] :
      ( ~ class_Ring__and__Field_Opordered__cancel__semiring(X3)
      | c_lessequals(c_HOL_Otimes__class_Otimes(X2,X1,X3),c_HOL_Ozero__class_Ozero(X3),X3)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X1,X3)
      | ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_244]) ).

fof(c_0_1042,plain,
    ! [X1,X2,X3] :
      ( ~ class_Ring__and__Field_Opordered__cancel__semiring(X3)
      | c_lessequals(c_HOL_Otimes__class_Otimes(X2,X1,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),X2,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_245]) ).

fof(c_0_1043,plain,
    ! [X1,X2,X3] :
      ( ~ class_Ring__and__Field_Opordered__cancel__semiring(X3)
      | c_lessequals(c_HOL_Otimes__class_Otimes(X2,X1,X3),c_HOL_Ozero__class_Ozero(X3),X3)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X1,X3)
      | ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_246]) ).

fof(c_0_1044,plain,
    ! [X1,X2,X3] :
      ( ~ class_Ring__and__Field_Opordered__cancel__semiring(X3)
      | c_lessequals(c_HOL_Otimes__class_Otimes(X2,X1,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),X2,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_247]) ).

fof(c_0_1045,plain,
    ! [X1,X2,X3] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
      | c_lessequals(c_HOL_Otimes__class_Otimes(X2,X1,X3),c_HOL_Ozero__class_Ozero(X3),X3)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X1,X3)
      | ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_248]) ).

fof(c_0_1046,plain,
    ! [X1,X2,X3] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
      | c_lessequals(c_HOL_Otimes__class_Otimes(X2,X1,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),X2,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_249]) ).

fof(c_0_1047,plain,
    ! [X1,X2,X3] :
      ( ~ class_OrderedGroup_Opordered__comm__monoid__add(X3)
      | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X2,X1,X3),c_HOL_Ozero__class_Ozero(X3),X3)
      | ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X3),X3)
      | ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_250]) ).

fof(c_0_1048,plain,
    ! [X1,X2,X3] :
      ( ~ class_Ring__and__Field_Opordered__cancel__semiring(X3)
      | c_lessequals(c_HOL_Ozero__class_Ozero(X3),c_HOL_Otimes__class_Otimes(X2,X1,X3),X3)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X1,X3)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X2,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_251]) ).

fof(c_0_1049,plain,
    ! [X1,X2,X3] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
      | c_lessequals(c_HOL_Ozero__class_Ozero(X3),c_HOL_Otimes__class_Otimes(X2,X1,X3),X3)
      | ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X3),X3)
      | ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_252]) ).

fof(c_0_1050,plain,
    ! [X1,X2,X3] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
      | c_lessequals(c_HOL_Ozero__class_Ozero(X3),c_HOL_Otimes__class_Otimes(X2,X1,X3),X3)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X1,X3)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X2,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_253]) ).

fof(c_0_1051,plain,
    ! [X1,X2,X3] :
      ( ~ class_Ring__and__Field_Opordered__ring(X3)
      | c_lessequals(c_HOL_Ozero__class_Ozero(X3),c_HOL_Otimes__class_Otimes(X2,X1,X3),X3)
      | ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X3),X3)
      | ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_254]) ).

fof(c_0_1052,plain,
    ! [X1,X2,X3] :
      ( ~ class_Ring__and__Field_Opordered__ring(X3)
      | c_lessequals(c_HOL_Ozero__class_Ozero(X3),c_HOL_Otimes__class_Otimes(X2,X1,X3),X3)
      | ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X3),X3)
      | ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_255]) ).

fof(c_0_1053,plain,
    ! [X1,X2,X3] :
      ( ~ class_Ring__and__Field_Opordered__ring(X3)
      | c_lessequals(c_HOL_Ozero__class_Ozero(X3),c_HOL_Otimes__class_Otimes(X2,X1,X3),X3)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X1,X3)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X2,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_256]) ).

fof(c_0_1054,plain,
    ! [X1,X2,X3] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_HOL_Otimes__class_Otimes(X2,X1,X3),X3)
      | ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X3),X3)
      | ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_257]) ).

fof(c_0_1055,plain,
    ! [X1,X2,X3] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X3)
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_HOL_Otimes__class_Otimes(X2,X1,X3),X3)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X1,X3)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_258]) ).

fof(c_0_1056,plain,
    ! [X1,X2,X3] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X3)
      | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Ozero__class_Ozero(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),X2,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_259]) ).

fof(c_0_1057,plain,
    ! [X1,X2,X3] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X3)
      | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X1,X3),c_HOL_Ozero__class_Ozero(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),X2,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_260]) ).

fof(c_0_1058,plain,
    ! [X1,X2,X3] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X3)
      | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X1,X3),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(X2,c_HOL_Ozero__class_Ozero(X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_261]) ).

fof(c_0_1059,plain,
    ! [X1,X2,X3] :
      ( ~ class_OrderedGroup_Opordered__comm__monoid__add(X3)
      | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X2,X1,X3),c_HOL_Ozero__class_Ozero(X3),X3)
      | ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X3),X3)
      | ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_262]) ).

fof(c_0_1060,plain,
    ! [X1,X2,X3] :
      ( ~ class_OrderedGroup_Opordered__comm__monoid__add(X3)
      | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X2,X1,X3),c_HOL_Ozero__class_Ozero(X3),X3)
      | ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X3),X3)
      | ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_263]) ).

fof(c_0_1061,plain,
    ! [X4,X5] :
      ( 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),X5,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oplus__class_Oplus(X5,X4,tc_nat),tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_264]) ).

fof(c_0_1062,axiom,
    ! [X5] : c_lessequals(X5,c_HOL_Otimes__class_Otimes(X5,c_HOL_Otimes__class_Otimes(X5,X5,tc_nat),tc_nat),tc_nat),
    c_0_265 ).

fof(c_0_1063,plain,
    ! [X4,X5] :
      ( c_HOL_Oord__class_Oless(X4,c_HOL_Otimes__class_Otimes(X5,X4,tc_nat),tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X5,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X4,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_266]) ).

fof(c_0_1064,plain,
    ! [X4,X5] :
      ( c_HOL_Oord__class_Oless(X4,c_HOL_Otimes__class_Otimes(X4,X5,tc_nat),tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X5,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X4,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_267]) ).

fof(c_0_1065,plain,
    ! [X15,X1,X2,X3] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
      | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X15,X2,X3),c_HOL_Oplus__class_Oplus(X15,X1,X3),X3)
      | ~ c_HOL_Oord__class_Oless(X2,X1,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_268]) ).

fof(c_0_1066,plain,
    ! [X15,X1,X2,X3] :
      ( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X3)
      | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X15,X2,X3),c_HOL_Oplus__class_Oplus(X15,X1,X3),X3)
      | ~ c_HOL_Oord__class_Oless(X2,X1,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_269]) ).

fof(c_0_1067,plain,
    ! [X15,X1,X2,X3] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
      | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X2,X15,X3),c_HOL_Oplus__class_Oplus(X1,X15,X3),X3)
      | ~ c_HOL_Oord__class_Oless(X2,X1,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_270]) ).

fof(c_0_1068,plain,
    ! [X15,X1,X2,X3] :
      ( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X3)
      | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X2,X15,X3),c_HOL_Oplus__class_Oplus(X1,X15,X3),X3)
      | ~ c_HOL_Oord__class_Oless(X2,X1,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_271]) ).

fof(c_0_1069,plain,
    ! [X15,X1,X2,X3] :
      ( ~ class_Ring__and__Field_Oidom(X3)
      | c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X2,X15,X3),c_HOL_Otimes__class_Otimes(X1,X15,X3),X3)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X1,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_272]) ).

fof(c_0_1070,plain,
    ! [X15,X1,X2,X3] :
      ( ~ class_Ring__and__Field_Oidom(X3)
      | c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X15,X2,X3),c_HOL_Otimes__class_Otimes(X15,X1,X3),X3)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X1,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_273]) ).

fof(c_0_1071,plain,
    ! [X15,X1,X2,X3] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
      | c_lessequals(c_HOL_Oplus__class_Oplus(X2,X15,X3),c_HOL_Oplus__class_Oplus(X1,X15,X3),X3)
      | ~ c_lessequals(X2,X1,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_274]) ).

fof(c_0_1072,plain,
    ! [X15,X1,X2,X3] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
      | c_lessequals(c_HOL_Oplus__class_Oplus(X15,X2,X3),c_HOL_Oplus__class_Oplus(X15,X1,X3),X3)
      | ~ c_lessequals(X2,X1,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_275]) ).

fof(c_0_1073,plain,
    ! [X15,X1,X2,X3] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X3)
      | c_lessequals(c_HOL_Oplus__class_Oplus(X2,X15,X3),c_HOL_Oplus__class_Oplus(X1,X15,X3),X3)
      | ~ c_lessequals(X2,X1,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_276]) ).

fof(c_0_1074,plain,
    ! [X15,X1,X2,X3] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X3)
      | c_lessequals(c_HOL_Oplus__class_Oplus(X15,X2,X3),c_HOL_Oplus__class_Oplus(X15,X1,X3),X3)
      | ~ c_lessequals(X2,X1,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_277]) ).

fof(c_0_1075,plain,
    ! [X16,X6,X7] :
      ( ~ c_Ring__and__Field_Odvd__class_Odvd(X16,X7,tc_nat)
      | c_Ring__and__Field_Odvd__class_Odvd(X16,X6,tc_nat)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X6,X16,tc_nat)
      | c_Ring__and__Field_Odvd__class_Odvd(X6,X7,tc_nat)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X7,X6,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_278]) ).

fof(c_0_1076,plain,
    ! [X15,X1,X2,X3] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
      | ~ class_OrderedGroup_Ocomm__monoid__add(X3)
      | c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(X2,X15,X3),X3)
      | ~ c_lessequals(X1,X15,X3)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_279]) ).

fof(c_0_1077,plain,
    ! [X15,X1,X2,X3] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
      | ~ class_OrderedGroup_Ocomm__monoid__add(X3)
      | c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(X2,X15,X3),X3)
      | ~ c_HOL_Oord__class_Oless(X1,X15,X3)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X2,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_280]) ).

fof(c_0_1078,plain,
    ! [X15,X1,X2,X3] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
      | ~ class_OrderedGroup_Ocomm__monoid__add(X3)
      | c_lessequals(X1,c_HOL_Oplus__class_Oplus(X2,X15,X3),X3)
      | ~ c_lessequals(X1,X15,X3)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X2,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_281]) ).

fof(c_0_1079,plain,
    ! [X15,X1,X2,X3] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
      | ~ class_OrderedGroup_Ocomm__monoid__add(X3)
      | c_lessequals(X1,c_HOL_Oplus__class_Oplus(X2,X15,X3),X3)
      | ~ c_lessequals(X1,X2,X3)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X15,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_282]) ).

fof(c_0_1080,plain,
    ! [X15,X1,X2,X3] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X3)
      | c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(X2,X15,X3),X3)
      | ~ c_HOL_Oord__class_Oless(X1,X15,X3)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_283]) ).

fof(c_0_1081,plain,
    ! [X4,X5,X29] :
      ( c_lessequals(c_HOL_Ominus__class_Ominus(X29,X4,tc_nat),c_HOL_Ominus__class_Ominus(X29,X5,tc_nat),tc_nat)
      | ~ c_lessequals(X5,X4,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_284]) ).

fof(c_0_1082,plain,
    ! [X4,X5,X29] :
      ( c_lessequals(c_HOL_Ominus__class_Ominus(X5,X29,tc_nat),c_HOL_Ominus__class_Ominus(X4,X29,tc_nat),tc_nat)
      | ~ c_lessequals(X5,X4,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_285]) ).

fof(c_0_1083,plain,
    ! [X8,X9,X10] :
      ( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X10,X8,tc_nat),c_HOL_Oplus__class_Oplus(X9,X8,tc_nat),tc_nat)
      | ~ c_HOL_Oord__class_Oless(X10,X9,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_286]) ).

fof(c_0_1084,plain,
    ! [X4,X5,X8] :
      ( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X8,X5,tc_nat),c_HOL_Oplus__class_Oplus(X8,X4,tc_nat),tc_nat)
      | ~ c_HOL_Oord__class_Oless(X5,X4,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_287]) ).

fof(c_0_1085,plain,
    ! [X4,X5,X8] :
      ( c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X8,X5,tc_nat),c_HOL_Otimes__class_Otimes(X8,X4,tc_nat),tc_nat)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X5,X4,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_288]) ).

fof(c_0_1086,plain,
    ! [X8,X9,X10] :
      ( c_lessequals(c_HOL_Otimes__class_Otimes(X10,X8,tc_nat),c_HOL_Otimes__class_Otimes(X9,X8,tc_nat),tc_nat)
      | ~ c_lessequals(X10,X9,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_289]) ).

fof(c_0_1087,plain,
    ! [X8,X9,X10] :
      ( c_lessequals(c_HOL_Otimes__class_Otimes(X8,X10,tc_nat),c_HOL_Otimes__class_Otimes(X8,X9,tc_nat),tc_nat)
      | ~ c_lessequals(X10,X9,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_290]) ).

fof(c_0_1088,plain,
    ! [X4,X5,X8] :
      ( c_lessequals(c_HOL_Otimes__class_Otimes(X8,X5,tc_nat),c_HOL_Otimes__class_Otimes(X8,X4,tc_nat),tc_nat)
      | ~ c_lessequals(X5,X4,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_291]) ).

fof(c_0_1089,plain,
    ! [X4,X5,X8] :
      ( c_lessequals(c_HOL_Otimes__class_Otimes(X5,X8,tc_nat),c_HOL_Otimes__class_Otimes(X4,X8,tc_nat),tc_nat)
      | ~ c_lessequals(X5,X4,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_292]) ).

fof(c_0_1090,plain,
    ! [X8,X9,X10] :
      ( c_lessequals(c_HOL_Oplus__class_Oplus(X10,X8,tc_nat),c_HOL_Oplus__class_Oplus(X9,X8,tc_nat),tc_nat)
      | ~ c_lessequals(X10,X9,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_293]) ).

fof(c_0_1091,plain,
    ! [X4,X5,X8] :
      ( c_lessequals(c_HOL_Oplus__class_Oplus(X8,X5,tc_nat),c_HOL_Oplus__class_Oplus(X8,X4,tc_nat),tc_nat)
      | ~ c_lessequals(X5,X4,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_294]) ).

fof(c_0_1092,plain,
    ! [X16,X6,X7,X3] :
      ( ~ class_Ring__and__Field_Ocomm__ring__1(X3)
      | c_Ring__and__Field_Odvd__class_Odvd(X7,c_HOL_Ominus__class_Ominus(X6,X16,X3),X3)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X7,X16,X3)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X7,X6,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_295]) ).

fof(c_0_1093,plain,
    ! [X16,X6,X7,X3] :
      ( ~ class_Orderings_Olinorder(X3)
      | c_HOL_Oord__class_Oless(X16,c_Orderings_Oord__class_Omin(X7,X6,X3),X3)
      | ~ c_HOL_Oord__class_Oless(X16,X6,X3)
      | ~ c_HOL_Oord__class_Oless(X16,X7,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_296]) ).

fof(c_0_1094,plain,
    ! [X15,X1,X2,X3] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
      | c_Ring__and__Field_Odvd__class_Odvd(X2,c_HOL_Oplus__class_Oplus(X1,X15,X3),X3)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X15,X3)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X1,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_297]) ).

fof(c_0_1095,plain,
    ! [X7,X1,X2,X3] :
      ( ~ class_Orderings_Olinorder(X3)
      | c_lessequals(X7,c_Orderings_Oord__class_Omin(X2,X1,X3),X3)
      | ~ c_lessequals(X7,X1,X3)
      | ~ c_lessequals(X7,X2,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_298]) ).

fof(c_0_1096,plain,
    ! [X16,X6,X7,X3] :
      ( ~ class_Orderings_Olinorder(X3)
      | c_lessequals(X7,c_Orderings_Oord__class_Omin(X6,X16,X3),X3)
      | ~ c_lessequals(X7,X16,X3)
      | ~ c_lessequals(X7,X6,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_299]) ).

fof(c_0_1097,plain,
    ! [X16,X6,X7,X3] :
      ( ~ class_Orderings_Olinorder(X3)
      | c_lessequals(X7,c_Orderings_Oord__class_Omin(X6,X16,X3),X3)
      | ~ c_lessequals(X7,X16,X3)
      | ~ c_lessequals(X7,X6,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_300]) ).

fof(c_0_1098,plain,
    ! [X4,X5,X8,X3] :
      ( ~ class_Divides_Osemiring__div(X3)
      | c_Ring__and__Field_Odvd__class_Odvd(X8,c_Divides_Odiv__class_Omod(X5,X4,X3),X3)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X8,X4,X3)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X8,X5,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_301]) ).

fof(c_0_1099,plain,
    ! [X4,X5,X8,X3] :
      ( ~ class_Divides_Osemiring__div(X3)
      | c_Ring__and__Field_Odvd__class_Odvd(X8,c_Divides_Odiv__class_Omod(X5,X4,X3),X3)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X8,X5,X3)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X8,X4,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_302]) ).

fof(c_0_1100,plain,
    ! [X1,X2,X3] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X3)
      | c_HOL_Oabs__class_Oabs(c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(X2,X3),c_HOL_Oabs__class_Oabs(X1,X3),X3),X3) = c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(X2,X3),c_HOL_Oabs__class_Oabs(X1,X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_303]) ).

fof(c_0_1101,plain,
    ! [X4,X5] :
      ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Otimes__class_Otimes(X5,X4,tc_nat),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),X5,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_304]) ).

fof(c_0_1102,plain,
    ! [X4,X5,X8] :
      ( c_HOL_Ominus__class_Ominus(X5,X8,tc_nat) != c_HOL_Ominus__class_Ominus(X4,X8,tc_nat)
      | ~ c_lessequals(X8,X4,tc_nat)
      | ~ c_lessequals(X8,X5,tc_nat)
      | X5 = X4 ),
    inference(fof_simplification,[status(thm)],[c_0_305]) ).

fof(c_0_1103,plain,
    ! [X4,X5] :
      ( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X5,X4,tc_nat),X5,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X5,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_306]) ).

fof(c_0_1104,plain,
    ! [X2,X3] :
      ( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
      | c_lessequals(X2,c_HOL_Ozero__class_Ozero(X3),X3)
      | ~ c_lessequals(c_HOL_Oplus__class_Oplus(X2,X2,X3),c_HOL_Ozero__class_Ozero(X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_307]) ).

fof(c_0_1105,plain,
    ! [X2,X3] :
      ( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
      | c_lessequals(c_HOL_Ozero__class_Ozero(X3),X2,X3)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),c_HOL_Oplus__class_Oplus(X2,X2,X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_308]) ).

fof(c_0_1106,plain,
    ! [X2,X3] :
      ( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_HOL_Oplus__class_Oplus(X2,X2,X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_309]) ).

fof(c_0_1107,plain,
    ! [X2,X3] :
      ( ~ class_Ring__and__Field_Oordered__idom(X3)
      | c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X3),X3)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X2,X2,X3),c_HOL_Ozero__class_Ozero(X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_310]) ).

fof(c_0_1108,plain,
    ! [X2,X3] :
      ( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
      | c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X3),X3)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X2,X2,X3),c_HOL_Ozero__class_Ozero(X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_311]) ).

fof(c_0_1109,axiom,
    ! [X4,X5,X8] : c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(c_Suc(X5),X4,tc_nat),c_Suc(X8),tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X5,X4,tc_nat),X8,tc_nat),
    c_0_312 ).

fof(c_0_1110,plain,
    ! [X4,X5] :
      ( c_lessequals(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X5,tc_nat)
      | ~ c_lessequals(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Otimes__class_Otimes(X5,X4,tc_nat),tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_313]) ).

fof(c_0_1111,plain,
    ! [X4,X5] :
      ( 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(X5,X4,tc_nat),tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_314]) ).

fof(c_0_1112,plain,
    ! [X16,X6,X7,X3] :
      ( ~ class_Orderings_Olinorder(X3)
      | c_Orderings_Oord__class_Omin(X7,c_Orderings_Oord__class_Omin(X6,X16,X3),X3) = c_Orderings_Oord__class_Omin(X6,c_Orderings_Oord__class_Omin(X7,X16,X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_315]) ).

fof(c_0_1113,plain,
    ! [X16,X6,X7,X3] :
      ( ~ class_Orderings_Olinorder(X3)
      | c_Orderings_Oord__class_Omin(c_Orderings_Oord__class_Omin(X7,X6,X3),X16,X3) = c_Orderings_Oord__class_Omin(X7,c_Orderings_Oord__class_Omin(X6,X16,X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_316]) ).

fof(c_0_1114,plain,
    ! [X15,X1,X2,X3] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
      | c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X2,X1,X3),X15,X3) = c_HOL_Oplus__class_Oplus(X2,c_HOL_Oplus__class_Oplus(X1,X15,X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_317]) ).

fof(c_0_1115,plain,
    ! [X20,X15,X2,X3] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
      | c_HOL_Oplus__class_Oplus(X2,c_HOL_Oplus__class_Oplus(X15,X20,X3),X3) = c_HOL_Oplus__class_Oplus(X15,c_HOL_Oplus__class_Oplus(X2,X20,X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_318]) ).

fof(c_0_1116,plain,
    ! [X15,X1,X2,X3] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
      | c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X2,X1,X3),X15,X3) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X2,X15,X3),X1,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_319]) ).

fof(c_0_1117,plain,
    ! [X20,X15,X2,X3] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
      | c_HOL_Oplus__class_Oplus(X2,c_HOL_Oplus__class_Oplus(X15,X20,X3),X3) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X2,X15,X3),X20,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_320]) ).

fof(c_0_1118,plain,
    ! [X15,X1,X2,X3] :
      ( ~ class_OrderedGroup_Oab__semigroup__add(X3)
      | c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X2,X1,X3),X15,X3) = c_HOL_Oplus__class_Oplus(X2,c_HOL_Oplus__class_Oplus(X1,X15,X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_321]) ).

fof(c_0_1119,plain,
    ! [X16,X6,X7,X3] :
      ( ~ class_OrderedGroup_Oab__group__add(X3)
      | c_HOL_Oplus__class_Oplus(X7,c_HOL_Oplus__class_Oplus(X6,X16,X3),X3) = c_HOL_Oplus__class_Oplus(X6,c_HOL_Oplus__class_Oplus(X7,X16,X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_322]) ).

fof(c_0_1120,plain,
    ! [X16,X6,X7,X3] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
      | c_HOL_Oplus__class_Oplus(X7,c_HOL_Oplus__class_Oplus(X6,X16,X3),X3) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X7,X6,X3),X16,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_323]) ).

fof(c_0_1121,plain,
    ! [X16,X6,X7,X3] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
      | c_HOL_Otimes__class_Otimes(X7,c_HOL_Otimes__class_Otimes(X6,X16,X3),X3) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X7,X6,X3),X16,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_324]) ).

fof(c_0_1122,plain,
    ! [X11,X12,X14,X3] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
      | c_HOL_Otimes__class_Otimes(X14,c_HOL_Otimes__class_Otimes(X12,X11,X3),X3) = c_HOL_Otimes__class_Otimes(X12,c_HOL_Otimes__class_Otimes(X14,X11,X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_325]) ).

fof(c_0_1123,plain,
    ! [X11,X12,X14,X3] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
      | c_HOL_Otimes__class_Otimes(X14,c_HOL_Otimes__class_Otimes(X12,X11,X3),X3) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X14,X12,X3),X11,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_326]) ).

fof(c_0_1124,plain,
    ! [X12,X13,X14,X3] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
      | c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X14,X13,X3),X12,X3) = c_HOL_Otimes__class_Otimes(X14,c_HOL_Otimes__class_Otimes(X13,X12,X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_327]) ).

fof(c_0_1125,plain,
    ! [X12,X13,X14,X3] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
      | c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X14,X13,X3),X12,X3) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X14,X12,X3),X13,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_328]) ).

fof(c_0_1126,plain,
    ! [X15,X1,X2,X3] :
      ( ~ class_OrderedGroup_Oab__semigroup__mult(X3)
      | c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X2,X1,X3),X15,X3) = c_HOL_Otimes__class_Otimes(X2,c_HOL_Otimes__class_Otimes(X1,X15,X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_329]) ).

fof(c_0_1127,plain,
    ! [X15,X1,X2,X3] :
      ( ~ class_OrderedGroup_Ocomm__monoid__add(X3)
      | c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X2,X1,X3),X15,X3) = c_HOL_Oplus__class_Oplus(X2,c_HOL_Oplus__class_Oplus(X1,X15,X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_330]) ).

fof(c_0_1128,plain,
    ! [X15,X1,X2,X3] :
      ( ~ class_OrderedGroup_Ocomm__monoid__add(X3)
      | c_HOL_Oplus__class_Oplus(X2,c_HOL_Oplus__class_Oplus(X1,X15,X3),X3) = c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X2,X15,X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_331]) ).

fof(c_0_1129,plain,
    ! [X3] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
      | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X3),c_HOL_Ozero__class_Ozero(X3),X3),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X3),c_HOL_Ozero__class_Ozero(X3),X3),X3) = c_HOL_Ozero__class_Ozero(X3) ),
    inference(fof_simplification,[status(thm)],[c_0_332]) ).

fof(c_0_1130,plain,
    ! [X16,X6,X7] :
      ( c_Ring__and__Field_Odvd__class_Odvd(X7,X16,tc_nat)
      | c_Ring__and__Field_Odvd__class_Odvd(X16,X6,tc_nat)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X6,X16,tc_nat)
      | c_Ring__and__Field_Odvd__class_Odvd(X6,X7,tc_nat)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X7,X6,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_333]) ).

fof(c_0_1131,plain,
    ! [X1,X2,X3] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
      | c_HOL_Oord__class_Oless(X2,X1,X3)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X2,X1,X3),c_HOL_Ozero__class_Ozero(X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_334]) ).

fof(c_0_1132,plain,
    ! [X1,X2,X3] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
      | c_lessequals(X2,X1,X3)
      | ~ c_lessequals(c_HOL_Ominus__class_Ominus(X2,X1,X3),c_HOL_Ozero__class_Ozero(X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_335]) ).

fof(c_0_1133,axiom,
    ! [X4,X5] : c_Divides_Odiv__class_Omod(c_Suc(X5),X4,tc_nat) = c_Divides_Odiv__class_Omod(c_Suc(c_Divides_Odiv__class_Omod(X5,X4,tc_nat)),X4,tc_nat),
    c_0_336 ).

fof(c_0_1134,plain,
    ! [X4,X5,X8] :
      ( c_Ring__and__Field_Odvd__class_Odvd(X8,c_HOL_Ominus__class_Ominus(X5,X4,tc_nat),tc_nat)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X8,X4,tc_nat)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X8,X5,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_337]) ).

fof(c_0_1135,plain,
    ! [X32,X6,X33,X7,X3] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
      | c_HOL_Ominus__class_Ominus(X7,X6,X3) != c_HOL_Ominus__class_Ominus(X33,X32,X3)
      | c_HOL_Oord__class_Oless(X7,X6,X3)
      | ~ c_HOL_Oord__class_Oless(X33,X32,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_338]) ).

fof(c_0_1136,plain,
    ! [X32,X6,X33,X7,X3] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
      | c_HOL_Ominus__class_Ominus(X7,X6,X3) != c_HOL_Ominus__class_Ominus(X33,X32,X3)
      | c_HOL_Oord__class_Oless(X33,X32,X3)
      | ~ c_HOL_Oord__class_Oless(X7,X6,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_339]) ).

fof(c_0_1137,plain,
    ! [X32,X6,X33,X7,X3] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
      | c_HOL_Ominus__class_Ominus(X7,X6,X3) != c_HOL_Ominus__class_Ominus(X33,X32,X3)
      | c_lessequals(X6,X7,X3)
      | ~ c_lessequals(X32,X33,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_340]) ).

fof(c_0_1138,plain,
    ! [X32,X6,X33,X7,X3] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
      | c_HOL_Ominus__class_Ominus(X7,X6,X3) != c_HOL_Ominus__class_Ominus(X33,X32,X3)
      | c_lessequals(X32,X33,X3)
      | ~ c_lessequals(X6,X7,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_341]) ).

fof(c_0_1139,axiom,
    ! [X4,X5,X8] :
      ( c_lessequals(c_HOL_Otimes__class_Otimes(X5,X8,tc_nat),c_HOL_Otimes__class_Otimes(X4,X8,tc_nat),tc_nat)
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X8,tc_nat) ),
    c_0_342 ).

fof(c_0_1140,axiom,
    ! [X4,X5,X8] :
      ( c_lessequals(c_HOL_Otimes__class_Otimes(X8,X5,tc_nat),c_HOL_Otimes__class_Otimes(X8,X4,tc_nat),tc_nat)
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X8,tc_nat) ),
    c_0_343 ).

fof(c_0_1141,plain,
    ! [X16,X6,X7,X3] :
      ( ~ class_Orderings_Olinorder(X3)
      | c_HOL_Oord__class_Oless(X16,X7,X3)
      | ~ c_HOL_Oord__class_Oless(X16,c_Orderings_Oord__class_Omin(X7,X6,X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_344]) ).

fof(c_0_1142,plain,
    ! [X16,X6,X7,X3] :
      ( ~ class_Orderings_Olinorder(X3)
      | c_HOL_Oord__class_Oless(X16,X6,X3)
      | ~ c_HOL_Oord__class_Oless(X16,c_Orderings_Oord__class_Omin(X7,X6,X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_345]) ).

fof(c_0_1143,plain,
    ! [X16,X6,X7,X3] :
      ( ~ class_Orderings_Olinorder(X3)
      | c_lessequals(X7,X16,X3)
      | ~ c_lessequals(X7,c_Orderings_Oord__class_Omin(X6,X16,X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_346]) ).

fof(c_0_1144,plain,
    ! [X16,X6,X7,X3] :
      ( ~ class_Orderings_Olinorder(X3)
      | c_lessequals(X7,X6,X3)
      | ~ c_lessequals(X7,c_Orderings_Oord__class_Omin(X6,X16,X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_347]) ).

fof(c_0_1145,plain,
    ! [X7,X1,X2,X3] :
      ( ~ class_Orderings_Olinorder(X3)
      | c_lessequals(X7,X1,X3)
      | ~ c_lessequals(X7,c_Orderings_Oord__class_Omin(X2,X1,X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_348]) ).

fof(c_0_1146,plain,
    ! [X7,X1,X2,X3] :
      ( ~ class_Orderings_Olinorder(X3)
      | c_lessequals(X7,X2,X3)
      | ~ c_lessequals(X7,c_Orderings_Oord__class_Omin(X2,X1,X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_349]) ).

fof(c_0_1147,plain,
    ! [X15,X1,X2,X3] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
      | c_Ring__and__Field_Odvd__class_Odvd(X1,X15,X3)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X2,X1,X3),X15,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_350]) ).

fof(c_0_1148,plain,
    ! [X15,X1,X2,X3] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
      | c_Ring__and__Field_Odvd__class_Odvd(X2,X15,X3)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X2,X1,X3),X15,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_351]) ).

fof(c_0_1149,plain,
    ! [X4,X5,X3] :
      ( ~ class_Ring__and__Field_Oring__1(X3)
      | c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Ominus__class_Ominus(X5,X4,tc_nat),X3) = c_HOL_Ominus__class_Ominus(c_Nat_Osemiring__1__class_Oof__nat(X5,X3),c_Nat_Osemiring__1__class_Oof__nat(X4,X3),X3)
      | ~ c_lessequals(X4,X5,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_352]) ).

fof(c_0_1150,axiom,
    ! [X8,X9,X10] : c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X10,X9,tc_nat),X8,tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X10,X8,tc_nat),X9,tc_nat),
    c_0_353 ).

fof(c_0_1151,axiom,
    ! [X8,X9,X10] : c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X10,X9,tc_nat),X8,tc_nat) = c_HOL_Ominus__class_Ominus(X10,c_HOL_Oplus__class_Oplus(X9,X8,tc_nat),tc_nat),
    c_0_354 ).

fof(c_0_1152,axiom,
    ! [X4,X5,X8] : c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X5,X8,tc_nat),c_HOL_Oplus__class_Oplus(X4,X8,tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(X5,X4,tc_nat),
    c_0_355 ).

fof(c_0_1153,axiom,
    ! [X4,X5,X8] : c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X8,X5,tc_nat),c_HOL_Oplus__class_Oplus(X8,X4,tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(X5,X4,tc_nat),
    c_0_356 ).

fof(c_0_1154,axiom,
    ! [X16,X6,X7] : c_HOL_Oplus__class_Oplus(X7,c_HOL_Oplus__class_Oplus(X6,X16,tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(X6,c_HOL_Oplus__class_Oplus(X7,X16,tc_nat),tc_nat),
    c_0_357 ).

fof(c_0_1155,axiom,
    ! [X4,X5,X8] : c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X5,X4,tc_nat),X8,tc_nat) = c_HOL_Oplus__class_Oplus(X5,c_HOL_Oplus__class_Oplus(X4,X8,tc_nat),tc_nat),
    c_0_358 ).

fof(c_0_1156,axiom,
    ! [X4,X5,X8] : c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X5,X4,tc_nat),X8,tc_nat) = c_HOL_Otimes__class_Otimes(X5,c_HOL_Otimes__class_Otimes(X4,X8,tc_nat),tc_nat),
    c_0_359 ).

fof(c_0_1157,plain,
    ! [X15,X1,X2,X3] :
      ( ~ class_Divides_Osemiring__div(X3)
      | c_Divides_Odiv__class_Omod(c_Divides_Odiv__class_Omod(X2,X1,X3),X15,X3) = c_Divides_Odiv__class_Omod(X2,X15,X3)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X15,X1,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_360]) ).

fof(c_0_1158,plain,
    ! [X4,X5] :
      ( 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(X5,X4,tc_nat),tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_361]) ).

fof(c_0_1159,plain,
    ! [X4,X5] :
      ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X5,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Otimes__class_Otimes(X5,X4,tc_nat),tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_362]) ).

fof(c_0_1160,plain,
    ! [X4,X5] :
      ( c_HOL_Oord__class_Oless(X5,X4,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ominus__class_Ominus(X4,X5,tc_nat),tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_363]) ).

fof(c_0_1161,plain,
    ! [X16,X6,X7] :
      ( ~ c_Ring__and__Field_Odvd__class_Odvd(X16,X7,tc_nat)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X6,X16,tc_nat)
      | c_Ring__and__Field_Odvd__class_Odvd(X6,X7,tc_nat)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X7,X6,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_364]) ).

fof(c_0_1162,plain,
    ! [X16,X6,X7] :
      ( ~ c_Ring__and__Field_Odvd__class_Odvd(X16,X7,tc_nat)
      | c_Ring__and__Field_Odvd__class_Odvd(X16,X6,tc_nat)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X6,X16,tc_nat)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X7,X6,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_365]) ).

fof(c_0_1163,plain,
    ! [X6,X7,X3] :
      ( ~ class_Ring__and__Field_Oordered__idom(X3)
      | c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(X6,X3),X7,X3) = c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(X6,X7,X3),X3)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X7,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_366]) ).

fof(c_0_1164,plain,
    ! [X4,X5,X29,X8] :
      ( c_HOL_Oplus__class_Oplus(X5,X29,tc_nat) != c_HOL_Oplus__class_Oplus(X8,X4,tc_nat)
      | ~ c_HOL_Oord__class_Oless(X8,X29,tc_nat)
      | c_HOL_Oord__class_Oless(X5,X4,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_367]) ).

fof(c_0_1165,plain,
    ! [X8,X9,X10] :
      ( c_HOL_Oord__class_Oless(X10,X8,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X10,X9,tc_nat),X8,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_368]) ).

fof(c_0_1166,plain,
    ! [X4,X8] :
      ( c_Ring__and__Field_Odvd__class_Odvd(X8,X4,tc_nat)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X8,c_HOL_Oplus__class_Oplus(X4,X8,tc_nat),tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_369]) ).

fof(c_0_1167,plain,
    ! [X4,X5,X8] :
      ( c_lessequals(X8,X4,tc_nat)
      | ~ c_lessequals(c_HOL_Oplus__class_Oplus(X5,X8,tc_nat),X4,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_370]) ).

fof(c_0_1168,plain,
    ! [X4,X5,X8] :
      ( c_lessequals(X5,X4,tc_nat)
      | ~ c_lessequals(c_HOL_Oplus__class_Oplus(X5,X8,tc_nat),X4,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_371]) ).

fof(c_0_1169,plain,
    ! [X1,X2,X3] :
      ( ~ class_Ring__and__Field_Oidom(X3)
      | c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X2,c_HOL_Ozero__class_Ozero(X3),X3),c_HOL_Otimes__class_Otimes(X1,c_HOL_Ozero__class_Ozero(X3),X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_372]) ).

fof(c_0_1170,plain,
    ! [X1,X2,X3] :
      ( ~ class_Ring__and__Field_Oidom(X3)
      | c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X3),X2,X3),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X3),X1,X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_373]) ).

fof(c_0_1171,plain,
    ! [X6,X7,X3] :
      ( ~ class_OrderedGroup_Opordered__comm__monoid__add(X3)
      | c_HOL_Oplus__class_Oplus(X7,X6,X3) != c_HOL_Ozero__class_Ozero(X3)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X6,X3)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X7,X3)
      | X7 = c_HOL_Ozero__class_Ozero(X3) ),
    inference(fof_simplification,[status(thm)],[c_0_374]) ).

fof(c_0_1172,plain,
    ! [X6,X7,X3] :
      ( ~ class_OrderedGroup_Opordered__comm__monoid__add(X3)
      | c_HOL_Oplus__class_Oplus(X7,X6,X3) != c_HOL_Ozero__class_Ozero(X3)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X6,X3)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X7,X3)
      | X6 = c_HOL_Ozero__class_Ozero(X3) ),
    inference(fof_simplification,[status(thm)],[c_0_375]) ).

fof(c_0_1173,plain,
    ! [X4,X5] :
      ( c_Divides_Odiv__class_Omod(X5,X4,tc_nat) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X5,X4,tc_nat),X4,tc_nat)
      | ~ c_lessequals(X4,X5,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_376]) ).

fof(c_0_1174,plain,
    ! [X3] :
      ( ~ class_OrderedGroup_Opordered__comm__monoid__add(X3)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),c_HOL_Ozero__class_Ozero(X3),X3)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),c_HOL_Ozero__class_Ozero(X3),X3)
      | c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X3),c_HOL_Ozero__class_Ozero(X3),X3) = c_HOL_Ozero__class_Ozero(X3) ),
    inference(fof_simplification,[status(thm)],[c_0_377]) ).

fof(c_0_1175,axiom,
    ! [X4,X5] :
      ( c_Divides_Odiv__class_Omod(c_Suc(X5),X4,tc_nat) = c_Suc(c_Divides_Odiv__class_Omod(X5,X4,tc_nat))
      | c_Suc(c_Divides_Odiv__class_Omod(X5,X4,tc_nat)) = X4 ),
    c_0_378 ).

fof(c_0_1176,plain,
    ! [X16,X6,X7] :
      ( c_Ring__and__Field_Odvd__class_Odvd(X7,X16,tc_nat)
      | c_Ring__and__Field_Odvd__class_Odvd(X16,X6,tc_nat)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X6,X16,tc_nat)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X7,X6,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_379]) ).

fof(c_0_1177,plain,
    ! [X16,X6,X7] :
      ( c_Ring__and__Field_Odvd__class_Odvd(X7,X16,tc_nat)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X6,X16,tc_nat)
      | c_Ring__and__Field_Odvd__class_Odvd(X6,X7,tc_nat)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X7,X6,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_380]) ).

fof(c_0_1178,axiom,
    ! [X4,X5] : c_Ring__and__Field_Odvd__class_Odvd(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),X4,tc_nat),tc_nat),
    c_0_381 ).

fof(c_0_1179,plain,
    ! [X2,X3] :
      ( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
      | c_lessequals(c_HOL_Oplus__class_Oplus(X2,X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
      | ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_382]) ).

fof(c_0_1180,plain,
    ! [X2,X3] :
      ( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
      | c_lessequals(c_HOL_Ozero__class_Ozero(X3),c_HOL_Oplus__class_Oplus(X2,X2,X3),X3)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X2,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_383]) ).

fof(c_0_1181,plain,
    ! [X2,X3] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X2,X3),c_HOL_Ozero__class_Ozero(X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_384]) ).

fof(c_0_1182,plain,
    ! [X2,X3] :
      ( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_HOL_Oplus__class_Oplus(X2,X2,X3),X3)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_385]) ).

fof(c_0_1183,plain,
    ! [X2,X3] :
      ( ~ class_Ring__and__Field_Oordered__idom(X3)
      | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X2,X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
      | ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_386]) ).

fof(c_0_1184,plain,
    ! [X2,X3] :
      ( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
      | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X2,X2,X3),c_HOL_Ozero__class_Ozero(X3),X3)
      | ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_387]) ).

fof(c_0_1185,plain,
    ! [X6,X7] :
      ( ~ c_Parity_Oeven__odd__class_Oeven(X6,tc_nat)
      | c_Parity_Oeven__odd__class_Oeven(X7,tc_nat)
      | c_HOL_Oord__class_Oless(X7,X6,tc_nat)
      | ~ c_Parity_Oeven__odd__class_Oeven(c_HOL_Ominus__class_Ominus(X7,X6,tc_nat),tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_388]) ).

fof(c_0_1186,plain,
    ! [X6,X7] :
      ( ~ c_Parity_Oeven__odd__class_Oeven(X7,tc_nat)
      | c_Parity_Oeven__odd__class_Oeven(X6,tc_nat)
      | c_HOL_Oord__class_Oless(X7,X6,tc_nat)
      | ~ c_Parity_Oeven__odd__class_Oeven(c_HOL_Ominus__class_Ominus(X7,X6,tc_nat),tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_389]) ).

fof(c_0_1187,axiom,
    ! [X7,X5] : c_HOL_Oord__class_Oless(X5,c_Suc(c_HOL_Oplus__class_Oplus(X5,X7,tc_nat)),tc_nat),
    c_0_390 ).

fof(c_0_1188,axiom,
    ! [X5,X10] : c_HOL_Oord__class_Oless(X10,c_Suc(c_HOL_Oplus__class_Oplus(X5,X10,tc_nat)),tc_nat),
    c_0_391 ).

fof(c_0_1189,axiom,
    ! [X5,X10] : c_HOL_Oord__class_Oless(X10,c_Suc(c_HOL_Oplus__class_Oplus(X10,X5,tc_nat)),tc_nat),
    c_0_392 ).

fof(c_0_1190,axiom,
    ! [X4,X5] :
      ( c_Divides_Odiv__class_Omod(X5,X4,tc_nat) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X5,X4,tc_nat),X4,tc_nat)
      | c_HOL_Oord__class_Oless(X5,X4,tc_nat) ),
    c_0_393 ).

fof(c_0_1191,plain,
    ! [X1,X2,X3] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
      | c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X2,X1,X3),c_HOL_Ozero__class_Ozero(X3),X3)
      | ~ c_HOL_Oord__class_Oless(X2,X1,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_394]) ).

fof(c_0_1192,plain,
    ! [X1,X2,X3] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
      | c_lessequals(c_HOL_Ominus__class_Ominus(X2,X1,X3),c_HOL_Ozero__class_Ozero(X3),X3)
      | ~ c_lessequals(X2,X1,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_395]) ).

fof(c_0_1193,plain,
    ! [X4,X10] :
      ( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X4,c_Suc(X10),tc_nat),X4,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_396]) ).

fof(c_0_1194,plain,
    ! [X4,X5,X8] :
      ( c_HOL_Otimes__class_Otimes(X8,X5,tc_nat) != c_HOL_Otimes__class_Otimes(X8,X4,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X8,tc_nat)
      | X5 = X4 ),
    inference(fof_simplification,[status(thm)],[c_0_397]) ).

fof(c_0_1195,plain,
    ! [X4,X5] :
      ( ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X5,tc_nat)
      | ~ c_HOL_Oord__class_Oless(X5,X4,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X5,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_398]) ).

fof(c_0_1196,plain,
    ! [X7,X1,X2,X3] :
      ( ~ class_Orderings_Olinorder(X3)
      | c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omin(X2,X1,X3),X7,X3)
      | ~ c_HOL_Oord__class_Oless(X2,X7,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_399]) ).

fof(c_0_1197,plain,
    ! [X7,X1,X2,X3] :
      ( ~ class_Orderings_Olinorder(X3)
      | c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omin(X2,X1,X3),X7,X3)
      | ~ c_HOL_Oord__class_Oless(X1,X7,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_400]) ).

fof(c_0_1198,plain,
    ! [X16,X6,X7,X3] :
      ( ~ class_Orderings_Olinorder(X3)
      | c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omin(X7,X6,X3),X16,X3)
      | ~ c_HOL_Oord__class_Oless(X7,X16,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_401]) ).

fof(c_0_1199,plain,
    ! [X16,X6,X7,X3] :
      ( ~ class_Orderings_Olinorder(X3)
      | c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omin(X7,X6,X3),X16,X3)
      | ~ c_HOL_Oord__class_Oless(X6,X16,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_402]) ).

fof(c_0_1200,plain,
    ! [X16,X6,X7,X3] :
      ( ~ class_Orderings_Olinorder(X3)
      | c_lessequals(c_Orderings_Oord__class_Omin(X7,X6,X3),X16,X3)
      | ~ c_lessequals(X6,X16,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_403]) ).

fof(c_0_1201,plain,
    ! [X16,X6,X7,X3] :
      ( ~ class_Orderings_Olinorder(X3)
      | c_lessequals(c_Orderings_Oord__class_Omin(X7,X6,X3),X16,X3)
      | ~ c_lessequals(X7,X16,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_404]) ).

fof(c_0_1202,plain,
    ! [X7,X1,X2,X3] :
      ( ~ class_Orderings_Olinorder(X3)
      | c_lessequals(c_Orderings_Oord__class_Omin(X2,X1,X3),X7,X3)
      | ~ c_lessequals(X1,X7,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_405]) ).

fof(c_0_1203,plain,
    ! [X7,X1,X2,X3] :
      ( ~ class_Orderings_Olinorder(X3)
      | c_lessequals(c_Orderings_Oord__class_Omin(X2,X1,X3),X7,X3)
      | ~ c_lessequals(X2,X7,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_406]) ).

fof(c_0_1204,plain,
    ! [X15,X1,X2,X3] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
      | c_Ring__and__Field_Odvd__class_Odvd(X2,c_HOL_Otimes__class_Otimes(X1,X15,X3),X3)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X1,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_407]) ).

fof(c_0_1205,plain,
    ! [X15,X1,X2,X3] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
      | c_Ring__and__Field_Odvd__class_Odvd(X2,c_HOL_Otimes__class_Otimes(X1,X15,X3),X3)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X15,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_408]) ).

fof(c_0_1206,plain,
    ! [X4,X5] :
      ( c_HOL_Ominus__class_Ominus(c_Suc(X5),X4,tc_nat) = c_Suc(c_HOL_Ominus__class_Ominus(X5,X4,tc_nat))
      | ~ c_lessequals(X4,X5,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_409]) ).

fof(c_0_1207,plain,
    ! [X1,X2,X3] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X3)
      | c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X2,X1,X3),X3) = c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X1,X2,X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_410]) ).

fof(c_0_1208,plain,
    ! [X4,X5] :
      ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oplus__class_Oplus(X5,X4,tc_nat),tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X5,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_411]) ).

fof(c_0_1209,plain,
    ! [X4,X5] :
      ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oplus__class_Oplus(X5,X4,tc_nat),tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_412]) ).

fof(c_0_1210,plain,
    ! [X9,X10] : ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X9,X10,tc_nat),X10,tc_nat),
    inference(fof_simplification,[status(thm)],[c_0_413]) ).

fof(c_0_1211,plain,
    ! [X9,X10] : ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X10,X9,tc_nat),X10,tc_nat),
    inference(fof_simplification,[status(thm)],[c_0_414]) ).

fof(c_0_1212,plain,
    ! [X4,X5] :
      ( c_HOL_Oord__class_Oless(c_Divides_Odiv__class_Omod(X5,X4,tc_nat),X4,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_415]) ).

fof(c_0_1213,plain,
    ! [X4,X5] :
      ( c_lessequals(c_Divides_Odiv__class_Omod(X5,X4,tc_nat),X4,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_416]) ).

fof(c_0_1214,plain,
    ! [X4,X5] :
      ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ominus__class_Ominus(X4,X5,tc_nat),tc_nat)
      | ~ c_HOL_Oord__class_Oless(X5,X4,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_417]) ).

fof(c_0_1215,plain,
    ! [X4,X10] :
      ( c_HOL_Ominus__class_Ominus(X4,c_HOL_Ominus__class_Ominus(X4,X10,tc_nat),tc_nat) = X10
      | ~ c_lessequals(X10,X4,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_418]) ).

fof(c_0_1216,plain,
    ! [X9,X10] :
      ( ~ c_lessequals(X10,X9,tc_nat)
      | X9 = c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X9,X10,tc_nat),X10,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_419]) ).

fof(c_0_1217,plain,
    ! [X4,X5] :
      ( c_HOL_Oplus__class_Oplus(X4,c_HOL_Ominus__class_Ominus(X5,X4,tc_nat),tc_nat) = X5
      | ~ c_lessequals(X4,X5,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_420]) ).

fof(c_0_1218,plain,
    ! [X4,X5] :
      ( c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X5,X4,tc_nat),X4,tc_nat) = X5
      | ~ c_lessequals(X4,X5,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_421]) ).

fof(c_0_1219,plain,
    ! [X4,X8,X9] :
      ( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X9,X4,tc_nat),X8,tc_nat)
      | ~ c_HOL_Oord__class_Oless(X9,X8,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_422]) ).

fof(c_0_1220,plain,
    ! [X5,X9,X10] :
      ( c_HOL_Oord__class_Oless(X10,c_HOL_Oplus__class_Oplus(X5,X9,tc_nat),tc_nat)
      | ~ c_HOL_Oord__class_Oless(X10,X9,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_423]) ).

fof(c_0_1221,plain,
    ! [X5,X9,X10] :
      ( c_HOL_Oord__class_Oless(X10,c_HOL_Oplus__class_Oplus(X9,X5,tc_nat),tc_nat)
      | ~ c_HOL_Oord__class_Oless(X10,X9,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_424]) ).

fof(c_0_1222,plain,
    ! [X16,X6,X7] :
      ( c_HOL_Oord__class_Oless(X7,c_HOL_Oplus__class_Oplus(X6,X16,tc_nat),tc_nat)
      | ~ c_HOL_Oord__class_Oless(X7,X16,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_425]) ).

fof(c_0_1223,plain,
    ! [X16,X6,X7] :
      ( c_HOL_Oord__class_Oless(X7,c_HOL_Oplus__class_Oplus(X6,X16,tc_nat),tc_nat)
      | ~ c_HOL_Oord__class_Oless(X7,X6,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_426]) ).

fof(c_0_1224,plain,
    ! [X4,X8] :
      ( c_Ring__and__Field_Odvd__class_Odvd(X8,c_HOL_Oplus__class_Oplus(X4,X8,tc_nat),tc_nat)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X8,X4,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_427]) ).

fof(c_0_1225,plain,
    ! [X5,X9,X10] :
      ( c_lessequals(X10,c_HOL_Oplus__class_Oplus(X5,X9,tc_nat),tc_nat)
      | ~ c_lessequals(X10,X9,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_428]) ).

fof(c_0_1226,plain,
    ! [X5,X9,X10] :
      ( c_lessequals(X10,c_HOL_Oplus__class_Oplus(X9,X5,tc_nat),tc_nat)
      | ~ c_lessequals(X10,X9,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_429]) ).

fof(c_0_1227,plain,
    ! [X16,X6,X7] :
      ( c_lessequals(X7,c_HOL_Oplus__class_Oplus(X6,X16,tc_nat),tc_nat)
      | ~ c_lessequals(X7,X16,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_430]) ).

fof(c_0_1228,plain,
    ! [X16,X6,X7] :
      ( c_lessequals(X7,c_HOL_Oplus__class_Oplus(X6,X16,tc_nat),tc_nat)
      | ~ c_lessequals(X7,X6,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_431]) ).

fof(c_0_1229,plain,
    ! [X16,X6,X7,X3] :
      ( ~ class_Orderings_Opreorder(X3)
      | c_HOL_Oord__class_Oless(X7,X16,X3)
      | ~ c_HOL_Oord__class_Oless(X6,X16,X3)
      | ~ c_HOL_Oord__class_Oless(X7,X6,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_432]) ).

fof(c_0_1230,plain,
    ! [X16,X6,X7,X3] :
      ( ~ class_Orderings_Oorder(X3)
      | c_HOL_Oord__class_Oless(X16,X7,X3)
      | ~ c_HOL_Oord__class_Oless(X16,X6,X3)
      | ~ c_HOL_Oord__class_Oless(X6,X7,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_433]) ).

fof(c_0_1231,plain,
    ! [X16,X6,X7,X3] :
      ( ~ class_Orderings_Oorder(X3)
      | c_lessequals(X16,X7,X3)
      | ~ c_lessequals(X16,X6,X3)
      | ~ c_lessequals(X6,X7,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_434]) ).

fof(c_0_1232,plain,
    ! [X16,X6,X7,X3] :
      ( ~ class_Orderings_Opreorder(X3)
      | c_lessequals(X7,X16,X3)
      | ~ c_lessequals(X6,X16,X3)
      | ~ c_lessequals(X7,X6,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_435]) ).

fof(c_0_1233,plain,
    ! [X16,X6,X7,X3] :
      ( ~ class_Orderings_Opreorder(X3)
      | c_HOL_Oord__class_Oless(X7,X16,X3)
      | ~ c_HOL_Oord__class_Oless(X6,X16,X3)
      | ~ c_lessequals(X7,X6,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_436]) ).

fof(c_0_1234,plain,
    ! [X16,X6,X7,X3] :
      ( ~ class_Orderings_Opreorder(X3)
      | c_HOL_Oord__class_Oless(X7,X16,X3)
      | ~ c_lessequals(X6,X16,X3)
      | ~ c_HOL_Oord__class_Oless(X7,X6,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_437]) ).

fof(c_0_1235,plain,
    ! [X16,X6,X7,X3] :
      ( ~ class_Orderings_Oorder(X3)
      | c_HOL_Oord__class_Oless(X16,X7,X3)
      | ~ c_HOL_Oord__class_Oless(X16,X6,X3)
      | ~ c_lessequals(X6,X7,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_438]) ).

fof(c_0_1236,plain,
    ! [X16,X6,X7,X3] :
      ( ~ class_Orderings_Oorder(X3)
      | c_HOL_Oord__class_Oless(X16,X7,X3)
      | ~ c_lessequals(X16,X6,X3)
      | ~ c_HOL_Oord__class_Oless(X6,X7,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_439]) ).

fof(c_0_1237,plain,
    ! [X15,X1,X2,X3] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
      | c_Ring__and__Field_Odvd__class_Odvd(X2,X15,X3)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X15,X3)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X1,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_440]) ).

fof(c_0_1238,plain,
    ! [X1,X2,X3] :
      ( ~ class_Ring__and__Field_Oordered__idom(X3)
      | c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(X2,X1,X3),X3) = c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(X2,X3),c_HOL_Oabs__class_Oabs(X1,X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_441]) ).

fof(c_0_1239,axiom,
    ! [X4,X5] :
      ( c_Suc(c_Divides_Odiv__class_Omod(X5,X4,tc_nat)) != X4
      | c_Divides_Odiv__class_Omod(c_Suc(X5),X4,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat) ),
    c_0_442 ).

fof(c_0_1240,plain,
    ! [X4,X5,X3] :
      ( ~ class_Ring__and__Field_Osemiring__1(X3)
      | c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Otimes__class_Otimes(X5,X4,tc_nat),X3) = c_HOL_Otimes__class_Otimes(c_Nat_Osemiring__1__class_Oof__nat(X5,X3),c_Nat_Osemiring__1__class_Oof__nat(X4,X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_443]) ).

fof(c_0_1241,plain,
    ! [X4,X5,X3] :
      ( ~ class_Ring__and__Field_Osemiring__1(X3)
      | c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Oplus__class_Oplus(X5,X4,tc_nat),X3) = c_HOL_Oplus__class_Oplus(c_Nat_Osemiring__1__class_Oof__nat(X5,X3),c_Nat_Osemiring__1__class_Oof__nat(X4,X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_444]) ).

fof(c_0_1242,plain,
    ! [X4,X5] :
      ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X5,tc_nat)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X5,X4,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_445]) ).

fof(c_0_1243,plain,
    ! [X4,X5,X3] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X3)
      | c_HOL_Oord__class_Oless(X5,X4,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X5,X3),c_Nat_Osemiring__1__class_Oof__nat(X4,X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_446]) ).

fof(c_0_1244,plain,
    ! [X4,X5,X3] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X3)
      | c_lessequals(X5,X4,tc_nat)
      | ~ c_lessequals(c_Nat_Osemiring__1__class_Oof__nat(X5,X3),c_Nat_Osemiring__1__class_Oof__nat(X4,X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_447]) ).

fof(c_0_1245,plain,
    ! [X8,X9,X10] :
      ( c_HOL_Oord__class_Oless(c_Suc(X10),X8,tc_nat)
      | ~ c_HOL_Oord__class_Oless(X9,X8,tc_nat)
      | ~ c_HOL_Oord__class_Oless(X10,X9,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_448]) ).

fof(c_0_1246,plain,
    ! [X4,X8] :
      ( c_lessequals(X8,X4,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X8,X4,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_449]) ).

fof(c_0_1247,plain,
    ! [X1,X2,X3] :
      ( ~ class_Divides_Osemiring__div(X3)
      | c_Divides_Odiv__class_Omod(c_Divides_Odiv__class_Omod(X2,X1,X3),X1,X3) = c_Divides_Odiv__class_Omod(X2,X1,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_450]) ).

fof(c_0_1248,plain,
    ! [X6,X7,X3] :
      ( ~ class_Orderings_Olinorder(X3)
      | c_Orderings_Oord__class_Omin(X7,c_Orderings_Oord__class_Omin(X7,X6,X3),X3) = c_Orderings_Oord__class_Omin(X7,X6,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_451]) ).

fof(c_0_1249,plain,
    ! [X1,X2,X3] :
      ( ~ class_Divides_Osemiring__div(X3)
      | c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X2,X1,X3),X1,X3) = c_Divides_Odiv__class_Omod(X2,X1,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_452]) ).

fof(c_0_1250,plain,
    ! [X1,X2,X3] :
      ( ~ 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(fof_simplification,[status(thm)],[c_0_453]) ).

fof(c_0_1251,plain,
    ! [X6,X7,X3] :
      ( ~ class_OrderedGroup_Oab__semigroup__idem__mult(X3)
      | c_HOL_Otimes__class_Otimes(X7,c_HOL_Otimes__class_Otimes(X7,X6,X3),X3) = c_HOL_Otimes__class_Otimes(X7,X6,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_454]) ).

fof(c_0_1252,plain,
    ! [X4] :
      ( c_Suc(c_HOL_Ominus__class_Ominus(X4,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat)) = X4
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_455]) ).

fof(c_0_1253,plain,
    ! [X8,X9,X10] :
      ( c_lessequals(X10,X8,tc_nat)
      | ~ c_lessequals(X9,X8,tc_nat)
      | ~ c_lessequals(X10,X9,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_456]) ).

fof(c_0_1254,plain,
    ! [X16,X6,X7] :
      ( c_Ring__and__Field_Odvd__class_Odvd(X7,X16,tc_nat)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X6,X16,tc_nat)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X7,X6,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_457]) ).

fof(c_0_1255,plain,
    ! [X4,X5] :
      ( ~ c_Parity_Oeven__odd__class_Oeven(c_HOL_Oplus__class_Oplus(X5,X4,tc_nat),tc_nat)
      | ~ c_Parity_Oeven__odd__class_Oeven(X4,tc_nat)
      | c_Parity_Oeven__odd__class_Oeven(X5,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_458]) ).

fof(c_0_1256,plain,
    ! [X4,X5] :
      ( ~ c_Parity_Oeven__odd__class_Oeven(c_HOL_Oplus__class_Oplus(X5,X4,tc_nat),tc_nat)
      | c_Parity_Oeven__odd__class_Oeven(X4,tc_nat)
      | ~ c_Parity_Oeven__odd__class_Oeven(X5,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_459]) ).

fof(c_0_1257,plain,
    ! [X4,X5] :
      ( c_Parity_Oeven__odd__class_Oeven(X4,tc_nat)
      | ~ c_Parity_Oeven__odd__class_Oeven(X5,tc_nat)
      | ~ c_Parity_Oeven__odd__class_Oeven(c_HOL_Oplus__class_Oplus(X5,X4,tc_nat),tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_460]) ).

fof(c_0_1258,plain,
    ! [X4,X5] :
      ( c_Parity_Oeven__odd__class_Oeven(X5,tc_nat)
      | ~ c_Parity_Oeven__odd__class_Oeven(X4,tc_nat)
      | ~ c_Parity_Oeven__odd__class_Oeven(c_HOL_Oplus__class_Oplus(X5,X4,tc_nat),tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_461]) ).

fof(c_0_1259,plain,
    ! [X6,X7] :
      ( ~ c_Parity_Oeven__odd__class_Oeven(X6,tc_nat)
      | c_Parity_Oeven__odd__class_Oeven(X7,tc_nat)
      | ~ c_Parity_Oeven__odd__class_Oeven(c_HOL_Oplus__class_Oplus(X7,X6,tc_nat),tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_462]) ).

fof(c_0_1260,plain,
    ! [X6,X7] :
      ( ~ c_Parity_Oeven__odd__class_Oeven(X7,tc_nat)
      | c_Parity_Oeven__odd__class_Oeven(X6,tc_nat)
      | ~ c_Parity_Oeven__odd__class_Oeven(c_HOL_Oplus__class_Oplus(X7,X6,tc_nat),tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_463]) ).

fof(c_0_1261,axiom,
    ! [X4,X5] : c_HOL_Otimes__class_Otimes(X5,c_Suc(X4),tc_nat) = c_HOL_Oplus__class_Oplus(X5,c_HOL_Otimes__class_Otimes(X5,X4,tc_nat),tc_nat),
    c_0_464 ).

fof(c_0_1262,axiom,
    ! [X4,X5] : c_HOL_Otimes__class_Otimes(c_Suc(X5),X4,tc_nat) = c_HOL_Oplus__class_Oplus(X4,c_HOL_Otimes__class_Otimes(X5,X4,tc_nat),tc_nat),
    c_0_465 ).

fof(c_0_1263,axiom,
    ! [X4,X5] :
      ( c_HOL_Oplus__class_Oplus(X4,c_HOL_Ominus__class_Ominus(X5,X4,tc_nat),tc_nat) = X5
      | c_HOL_Oord__class_Oless(X5,X4,tc_nat) ),
    c_0_466 ).

fof(c_0_1264,plain,
    ! [X6,X7] :
      ( c_Parity_Oeven__odd__class_Oeven(X6,tc_nat)
      | c_Parity_Oeven__odd__class_Oeven(X7,tc_nat)
      | ~ c_Parity_Oeven__odd__class_Oeven(c_HOL_Otimes__class_Otimes(X7,X6,tc_nat),tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_467]) ).

fof(c_0_1265,plain,
    ! [X6,X7,X3] :
      ( ~ class_Orderings_Opreorder(X3)
      | c_HOL_Oord__class_Oless(X7,X6,X3)
      | c_lessequals(X6,X7,X3)
      | ~ c_lessequals(X7,X6,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_468]) ).

fof(c_0_1266,plain,
    ! [X6,X7] :
      ( c_Parity_Oeven__odd__class_Oeven(c_HOL_Ominus__class_Ominus(X7,X6,tc_nat),tc_nat)
      | ~ c_HOL_Oord__class_Oless(X7,X6,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_469]) ).

fof(c_0_1267,plain,
    ! [X4,X3] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X3)
      | 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(X3),c_Nat_Osemiring__1__class_Oof__nat(X4,X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_470]) ).

fof(c_0_1268,plain,
    ! [X4,X5,X3] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X3)
      | c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X5,X3),c_Nat_Osemiring__1__class_Oof__nat(X4,X3),X3)
      | ~ c_HOL_Oord__class_Oless(X5,X4,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_471]) ).

fof(c_0_1269,plain,
    ! [X4,X5,X3] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X3)
      | c_lessequals(c_Nat_Osemiring__1__class_Oof__nat(X5,X3),c_Nat_Osemiring__1__class_Oof__nat(X4,X3),X3)
      | ~ c_lessequals(X5,X4,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_472]) ).

fof(c_0_1270,plain,
    ! [X5,X8,X3] :
      ( ~ class_Ring__and__Field_Oordered__idom(X3)
      | c_Ring__and__Field_Odvd__class_Odvd(X5,X8,X3)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X5,c_HOL_Oabs__class_Oabs(X8,X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_473]) ).

fof(c_0_1271,plain,
    ! [X5,X8,X3] :
      ( ~ class_Ring__and__Field_Oordered__idom(X3)
      | c_Ring__and__Field_Odvd__class_Odvd(X5,X8,X3)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oabs__class_Oabs(X5,X3),X8,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_474]) ).

fof(c_0_1272,plain,
    ! [X1,X2,X3] :
      ( ~ class_Ring__and__Field_Oordered__idom(X3)
      | c_HOL_Oord__class_Oless(X2,X1,X3)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(X2,X3),X1,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_475]) ).

fof(c_0_1273,plain,
    ! [X1,X2,X3] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X3)
      | c_lessequals(X2,X1,X3)
      | ~ c_lessequals(c_HOL_Oabs__class_Oabs(X2,X3),X1,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_476]) ).

fof(c_0_1274,plain,
    ! [X16,X6,X7,X3] :
      ( ~ class_Ring__and__Field_Oidom(X3)
      | ~ class_Int_Onumber__ring(X3)
      | c_HOL_Oplus__class_Oplus(X7,X6,X3) != c_HOL_Oplus__class_Oplus(X7,X16,X3)
      | X6 = X16 ),
    inference(fof_simplification,[status(thm)],[c_0_477]) ).

fof(c_0_1275,axiom,
    ! [X4,X5,X8] :
      ( c_HOL_Otimes__class_Otimes(c_Suc(X8),X5,tc_nat) != c_HOL_Otimes__class_Otimes(c_Suc(X8),X4,tc_nat)
      | X5 = X4 ),
    c_0_478 ).

fof(c_0_1276,plain,
    ! [X4,X3] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X3)
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_Nat_Osemiring__1__class_Oof__nat(X4,X3),X3)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_479]) ).

fof(c_0_1277,plain,
    ! [X6,X7,X3] :
      ( ~ class_Orderings_Oorder(X3)
      | X7 = X6
      | ~ c_lessequals(X7,X6,X3)
      | ~ c_lessequals(X6,X7,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_480]) ).

fof(c_0_1278,plain,
    ! [X6,X7,X3] :
      ( ~ class_Orderings_Oorder(X3)
      | X7 = X6
      | ~ c_lessequals(X6,X7,X3)
      | ~ c_lessequals(X7,X6,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_481]) ).

fof(c_0_1279,plain,
    ! [X6,X7,X3] :
      ( ~ class_Orderings_Oorder(X3)
      | X7 = X6
      | ~ c_lessequals(X6,X7,X3)
      | ~ c_lessequals(X7,X6,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_482]) ).

fof(c_0_1280,plain,
    ! [X6,X18,X7,X3] :
      ( ~ class_OrderedGroup_Oab__group__add(X3)
      | c_HOL_Ominus__class_Ominus(X18,X6,X3) != c_HOL_Ominus__class_Ominus(X7,X7,X3)
      | X18 = X6 ),
    inference(fof_simplification,[status(thm)],[c_0_483]) ).

fof(c_0_1281,plain,
    ! [X32,X33,X7,X3] :
      ( ~ class_OrderedGroup_Oab__group__add(X3)
      | c_HOL_Ominus__class_Ominus(X7,X7,X3) != c_HOL_Ominus__class_Ominus(X33,X32,X3)
      | X33 = X32 ),
    inference(fof_simplification,[status(thm)],[c_0_484]) ).

fof(c_0_1282,plain,
    ! [X15,X1,X2,X3] :
      ( ~ class_OrderedGroup_Ocancel__semigroup__add(X3)
      | c_HOL_Oplus__class_Oplus(X1,X2,X3) != c_HOL_Oplus__class_Oplus(X15,X2,X3)
      | X1 = X15 ),
    inference(fof_simplification,[status(thm)],[c_0_485]) ).

fof(c_0_1283,plain,
    ! [X15,X1,X2,X3] :
      ( ~ class_OrderedGroup_Ocancel__semigroup__add(X3)
      | c_HOL_Oplus__class_Oplus(X2,X1,X3) != c_HOL_Oplus__class_Oplus(X2,X15,X3)
      | X1 = X15 ),
    inference(fof_simplification,[status(thm)],[c_0_486]) ).

fof(c_0_1284,plain,
    ! [X15,X1,X2,X3] :
      ( ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X3)
      | c_HOL_Oplus__class_Oplus(X2,X1,X3) != c_HOL_Oplus__class_Oplus(X2,X15,X3)
      | X1 = X15 ),
    inference(fof_simplification,[status(thm)],[c_0_487]) ).

fof(c_0_1285,plain,
    ! [X6,X7,X3] :
      ( ~ class_Orderings_Opreorder(X3)
      | ~ c_HOL_Oord__class_Oless(X6,X7,X3)
      | ~ c_HOL_Oord__class_Oless(X7,X6,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_488]) ).

fof(c_0_1286,plain,
    ! [X1,X2,X3] :
      ( ~ class_Orderings_Opreorder(X3)
      | ~ c_HOL_Oord__class_Oless(X1,X2,X3)
      | ~ c_HOL_Oord__class_Oless(X2,X1,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_489]) ).

fof(c_0_1287,plain,
    ! [X6,X7,X3] :
      ( ~ class_Orderings_Olinorder(X3)
      | ~ c_HOL_Oord__class_Oless(X7,X6,X3)
      | ~ c_HOL_Oord__class_Oless(X6,X7,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_490]) ).

fof(c_0_1288,plain,
    ! [X1,X2,X3] :
      ( ~ class_Orderings_Oorder(X3)
      | ~ c_HOL_Oord__class_Oless(X2,X1,X3)
      | ~ c_HOL_Oord__class_Oless(X1,X2,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_491]) ).

fof(c_0_1289,plain,
    ! [X6,X7,X3] :
      ( ~ class_Orderings_Olinorder(X3)
      | ~ c_lessequals(X7,X6,X3)
      | ~ c_HOL_Oord__class_Oless(X6,X7,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_492]) ).

fof(c_0_1290,plain,
    ! [X6,X7,X3] :
      ( ~ class_Orderings_Olinorder(X3)
      | ~ c_HOL_Oord__class_Oless(X7,X6,X3)
      | ~ c_lessequals(X6,X7,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_493]) ).

fof(c_0_1291,plain,
    ! [X7,X3] :
      ( ~ class_Orderings_Olinorder(X3)
      | ~ c_lessequals(X7,X7,X3)
      | ~ c_HOL_Oord__class_Oless(X7,X7,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_494]) ).

fof(c_0_1292,plain,
    ! [X6,X7,X3] :
      ( ~ class_Orderings_Opreorder(X3)
      | ~ c_lessequals(X6,X7,X3)
      | ~ c_HOL_Oord__class_Oless(X7,X6,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_495]) ).

fof(c_0_1293,plain,
    ! [X4,X5] :
      ( X4 = X5
      | ~ c_HOL_Oord__class_Oless(X4,c_Suc(X5),tc_nat)
      | ~ c_lessequals(X5,X4,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_496]) ).

fof(c_0_1294,axiom,
    ! [X18] : c_Parity_Oeven__odd__class_Oeven(c_HOL_Otimes__class_Otimes(c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),X18,tc_nat),tc_nat),
    c_0_497 ).

fof(c_0_1295,plain,
    ! [X4,X5] :
      ( ~ c_HOL_Oord__class_Oless(X5,X4,tc_nat)
      | ~ c_HOL_Oord__class_Oless(X4,c_Suc(X5),tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_498]) ).

fof(c_0_1296,plain,
    ! [X4,X5] :
      ( ~ c_lessequals(X5,X4,tc_nat)
      | ~ c_lessequals(c_Suc(X4),X5,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_499]) ).

fof(c_0_1297,axiom,
    ! [X4,X5] :
      ( c_HOL_Ominus__class_Ominus(X4,X5,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)
      | c_HOL_Ominus__class_Ominus(X5,X4,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)
      | X5 = X4 ),
    c_0_500 ).

fof(c_0_1298,plain,
    ! [X2,X3] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
      | c_lessequals(c_HOL_Ozero__class_Ozero(X3),c_HOL_Otimes__class_Otimes(X2,X2,X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_501]) ).

fof(c_0_1299,plain,
    ! [X5,X8,X3] :
      ( ~ class_Ring__and__Field_Oordered__idom(X3)
      | c_Ring__and__Field_Odvd__class_Odvd(X5,c_HOL_Oabs__class_Oabs(X8,X3),X3)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X5,X8,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_502]) ).

fof(c_0_1300,plain,
    ! [X5,X8,X3] :
      ( ~ class_Ring__and__Field_Oordered__idom(X3)
      | c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oabs__class_Oabs(X5,X3),X8,X3)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X5,X8,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_503]) ).

fof(c_0_1301,axiom,
    ! [X4,X5] : c_Orderings_Oord__class_Omin(c_Suc(X5),c_Suc(X4),tc_nat) = c_Suc(c_Orderings_Oord__class_Omin(X5,X4,tc_nat)),
    c_0_504 ).

fof(c_0_1302,plain,
    ! [X1,X2,X3] :
      ( ~ class_Divides_Osemiring__div(X3)
      | c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X2,X1,X3),X1,X3) = c_HOL_Ozero__class_Ozero(X3) ),
    inference(fof_simplification,[status(thm)],[c_0_505]) ).

fof(c_0_1303,plain,
    ! [X1,X2,X3] :
      ( ~ 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(fof_simplification,[status(thm)],[c_0_506]) ).

fof(c_0_1304,axiom,
    ! [X4,X5,X8] :
      ( c_HOL_Otimes__class_Otimes(X8,X5,tc_nat) != c_HOL_Otimes__class_Otimes(X8,X4,tc_nat)
      | X5 = X4
      | X8 = c_HOL_Ozero__class_Ozero(tc_nat) ),
    c_0_507 ).

fof(c_0_1305,axiom,
    ! [X4,X5,X8] :
      ( c_HOL_Otimes__class_Otimes(X8,X5,tc_nat) != c_HOL_Otimes__class_Otimes(X8,X4,tc_nat)
      | X8 = c_HOL_Ozero__class_Ozero(tc_nat)
      | X5 = X4 ),
    c_0_508 ).

fof(c_0_1306,axiom,
    ! [X4,X5,X8] :
      ( c_HOL_Otimes__class_Otimes(X5,X8,tc_nat) != c_HOL_Otimes__class_Otimes(X4,X8,tc_nat)
      | X8 = c_HOL_Ozero__class_Ozero(tc_nat)
      | X5 = X4 ),
    c_0_509 ).

fof(c_0_1307,plain,
    ! [X6,X7] :
      ( X7 = X6
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X6,X7,tc_nat)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X7,X6,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_510]) ).

fof(c_0_1308,plain,
    ! [X4,X5] :
      ( X5 = X4
      | ~ c_lessequals(X4,X5,tc_nat)
      | ~ c_lessequals(X5,X4,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_511]) ).

fof(c_0_1309,plain,
    ! [X6,X7] :
      ( X7 = X6
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X6,X7,tc_nat)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X7,X6,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_512]) ).

fof(c_0_1310,plain,
    ! [X6,X7] :
      ( ~ c_Ring__and__Field_Odvd__class_Odvd(X6,X7,tc_nat)
      | X7 = X6
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X7,X6,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_513]) ).

fof(c_0_1311,plain,
    ! [X4,X5] :
      ( X5 = X4
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X5,tc_nat)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X5,X4,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_514]) ).

fof(c_0_1312,plain,
    ! [X6,X7] :
      ( X7 = X6
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X7,X6,tc_nat)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X6,X7,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_515]) ).

fof(c_0_1313,plain,
    ! [X1,X2] :
      ( ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
      | X2 = X1
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X1,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_516]) ).

fof(c_0_1314,plain,
    ! [X1,X2] :
      ( ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X1,tc_nat)
      | X2 = X1 ),
    inference(fof_simplification,[status(thm)],[c_0_517]) ).

fof(c_0_1315,plain,
    ! [X1,X2,X3] :
      ( ~ class_OrderedGroup_Ogroup__add(X3)
      | c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X2,X1,X3),X1,X3) = X2 ),
    inference(fof_simplification,[status(thm)],[c_0_518]) ).

fof(c_0_1316,plain,
    ! [X1,X2,X3] :
      ( ~ class_OrderedGroup_Ogroup__add(X3)
      | c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X2,X1,X3),X1,X3) = X2 ),
    inference(fof_simplification,[status(thm)],[c_0_519]) ).

fof(c_0_1317,axiom,
    ! [X16,X6,X7] :
      ( c_HOL_Oplus__class_Oplus(X7,X6,tc_nat) != c_HOL_Oplus__class_Oplus(X7,X16,tc_nat)
      | X6 = X16 ),
    c_0_520 ).

fof(c_0_1318,axiom,
    ! [X4,X5,X8] :
      ( c_HOL_Oplus__class_Oplus(X8,X5,tc_nat) != c_HOL_Oplus__class_Oplus(X8,X4,tc_nat)
      | X5 = X4 ),
    c_0_521 ).

fof(c_0_1319,axiom,
    ! [X4,X5,X8] :
      ( c_HOL_Oplus__class_Oplus(X5,X8,tc_nat) != c_HOL_Oplus__class_Oplus(X4,X8,tc_nat)
      | X5 = X4 ),
    c_0_522 ).

fof(c_0_1320,plain,
    ! [X8,X1,X3] :
      ( ~ class_Ring__and__Field_Odvd(X3)
      | c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Otimes__class_Otimes(X1,X8,X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_523]) ).

fof(c_0_1321,plain,
    ! [X1,X2,X3] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
      | c_Ring__and__Field_Odvd__class_Odvd(X2,c_HOL_Otimes__class_Otimes(X2,X1,X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_524]) ).

fof(c_0_1322,plain,
    ! [X1,X2,X3] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
      | c_Ring__and__Field_Odvd__class_Odvd(X2,c_HOL_Otimes__class_Otimes(X1,X2,X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_525]) ).

fof(c_0_1323,plain,
    ! [X6,X7,X3] :
      ( ~ class_Orderings_Olinorder(X3)
      | c_lessequals(c_Orderings_Oord__class_Omin(X7,X6,X3),X7,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_526]) ).

fof(c_0_1324,plain,
    ! [X6,X7,X3] :
      ( ~ class_Orderings_Olinorder(X3)
      | c_lessequals(c_Orderings_Oord__class_Omin(X7,X6,X3),X6,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_527]) ).

fof(c_0_1325,plain,
    ! [X2,X3] :
      ( ~ class_Ring__and__Field_Oordered__idom(X3)
      | c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(X2,X3),c_HOL_Oabs__class_Oabs(X2,X3),X3) = c_HOL_Otimes__class_Otimes(X2,X2,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_528]) ).

fof(c_0_1326,axiom,
    ! [X4,X5] : c_HOL_Oplus__class_Oplus(X5,c_Suc(X4),tc_nat) = c_Suc(c_HOL_Oplus__class_Oplus(X5,X4,tc_nat)),
    c_0_529 ).

fof(c_0_1327,axiom,
    ! [X4,X5] : c_HOL_Oplus__class_Oplus(c_Suc(X5),X4,tc_nat) = c_Suc(c_HOL_Oplus__class_Oplus(X5,X4,tc_nat)),
    c_0_530 ).

fof(c_0_1328,axiom,
    ! [X4,X5] : c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X5,X4,tc_nat),c_Suc(X5),tc_nat),
    c_0_531 ).

fof(c_0_1329,plain,
    ! [X3] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X3)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_HOL_Oabs__class_Oabs(c_HOL_Ozero__class_Ozero(X3),X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_532]) ).

fof(c_0_1330,plain,
    ! [X7] :
      ( c_Divides_Odiv__class_Omod(X7,c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
      | ~ c_Parity_Oeven__odd__class_Oeven(X7,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_533]) ).

fof(c_0_1331,axiom,
    ! [X7,X20] : c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X20,X7,tc_nat),X20,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
    c_0_534 ).

fof(c_0_1332,axiom,
    ! [X4,X5] : c_HOL_Ominus__class_Ominus(X4,c_HOL_Oplus__class_Oplus(X4,X5,tc_nat),tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
    c_0_535 ).

fof(c_0_1333,axiom,
    ! [X4,X5] : c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X5,X4,tc_nat),X4,tc_nat) = X5,
    c_0_536 ).

fof(c_0_1334,axiom,
    ! [X4,X5] : c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X4,X5,tc_nat),X4,tc_nat) = X5,
    c_0_537 ).

fof(c_0_1335,plain,
    ! [X6,X7] :
      ( c_Parity_Oeven__odd__class_Oeven(c_HOL_Ominus__class_Ominus(X7,X6,tc_nat),tc_nat)
      | ~ c_Parity_Oeven__odd__class_Oeven(X6,tc_nat)
      | ~ c_Parity_Oeven__odd__class_Oeven(X7,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_538]) ).

fof(c_0_1336,plain,
    ! [X4,X5] :
      ( ~ c_Parity_Oeven__odd__class_Oeven(X4,tc_nat)
      | ~ c_Parity_Oeven__odd__class_Oeven(X5,tc_nat)
      | c_Parity_Oeven__odd__class_Oeven(c_HOL_Oplus__class_Oplus(X5,X4,tc_nat),tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_539]) ).

fof(c_0_1337,plain,
    ! [X4,X5] :
      ( c_Parity_Oeven__odd__class_Oeven(c_HOL_Oplus__class_Oplus(X5,X4,tc_nat),tc_nat)
      | ~ c_Parity_Oeven__odd__class_Oeven(X4,tc_nat)
      | ~ c_Parity_Oeven__odd__class_Oeven(X5,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_540]) ).

fof(c_0_1338,plain,
    ! [X6,X7] :
      ( c_Parity_Oeven__odd__class_Oeven(c_HOL_Oplus__class_Oplus(X7,X6,tc_nat),tc_nat)
      | ~ c_Parity_Oeven__odd__class_Oeven(X6,tc_nat)
      | ~ c_Parity_Oeven__odd__class_Oeven(X7,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_541]) ).

fof(c_0_1339,axiom,
    ! [X4,X5] : c_lessequals(c_HOL_Ominus__class_Ominus(X5,X4,tc_nat),X5,tc_nat),
    c_0_542 ).

fof(c_0_1340,axiom,
    ! [X4,X5] : c_lessequals(X4,c_HOL_Oplus__class_Oplus(X4,X5,tc_nat),tc_nat),
    c_0_543 ).

fof(c_0_1341,axiom,
    ! [X4,X5] : c_lessequals(X4,c_HOL_Oplus__class_Oplus(X5,X4,tc_nat),tc_nat),
    c_0_544 ).

fof(c_0_1342,axiom,
    ! [X7,X5] : c_lessequals(X5,c_HOL_Oplus__class_Oplus(X5,X7,tc_nat),tc_nat),
    c_0_545 ).

fof(c_0_1343,axiom,
    ! [X7,X8] : c_lessequals(X8,c_HOL_Oplus__class_Oplus(X8,X7,tc_nat),tc_nat),
    c_0_546 ).

fof(c_0_1344,axiom,
    ! [X5] : c_lessequals(X5,c_HOL_Otimes__class_Otimes(X5,X5,tc_nat),tc_nat),
    c_0_547 ).

fof(c_0_1345,axiom,
    ! [X4,X5] : c_lessequals(c_Divides_Odiv__class_Omod(X5,X4,tc_nat),X5,tc_nat),
    c_0_548 ).

fof(c_0_1346,plain,
    ! [X4,X5] :
      ( c_HOL_Oord__class_Oless(X5,X4,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_Suc(X5),c_Suc(X4),tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_549]) ).

fof(c_0_1347,plain,
    ! [X4,X5] :
      ( c_lessequals(X4,X5,tc_nat)
      | ~ c_lessequals(c_Suc(X4),c_Suc(X5),tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_550]) ).

fof(c_0_1348,plain,
    ! [X1,X2,X3] :
      ( ~ class_Divides_Osemiring__div(X3)
      | c_Divides_Odiv__class_Omod(X1,X2,X3) != c_HOL_Ozero__class_Ozero(X3)
      | c_Ring__and__Field_Odvd__class_Odvd(X2,X1,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_551]) ).

fof(c_0_1349,plain,
    ! [X1,X2,X3] :
      ( ~ class_Divides_Osemiring__div(X3)
      | c_Divides_Odiv__class_Omod(X1,X2,X3) = c_HOL_Ozero__class_Ozero(X3)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X1,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_552]) ).

fof(c_0_1350,plain,
    ! [X4,X5] :
      ( X5 = c_Suc(X4)
      | c_lessequals(X5,X4,tc_nat)
      | ~ c_lessequals(X5,c_Suc(X4),tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_553]) ).

fof(c_0_1351,plain,
    ! [X6,X7,X3] :
      ( ~ class_Orderings_Oorder(X3)
      | c_HOL_Oord__class_Oless(X7,X6,X3)
      | X7 = X6
      | ~ c_lessequals(X7,X6,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_554]) ).

fof(c_0_1352,plain,
    ! [X6,X7,X3] :
      ( ~ class_Orderings_Oorder(X3)
      | X7 = X6
      | c_HOL_Oord__class_Oless(X7,X6,X3)
      | ~ c_lessequals(X7,X6,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_555]) ).

fof(c_0_1353,plain,
    ! [X1,X2,X3] :
      ( ~ class_Orderings_Oorder(X3)
      | c_HOL_Oord__class_Oless(X2,X1,X3)
      | X2 = X1
      | ~ c_lessequals(X2,X1,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_556]) ).

fof(c_0_1354,plain,
    ! [X1,X2,X3] :
      ( ~ class_Orderings_Oorder(X3)
      | c_HOL_Oord__class_Oless(X2,X1,X3)
      | ~ c_lessequals(X2,X1,X3)
      | X2 = X1 ),
    inference(fof_simplification,[status(thm)],[c_0_557]) ).

fof(c_0_1355,plain,
    ! [X6,X7,X3] :
      ( ~ class_Orderings_Olinorder(X3)
      | X7 = X6
      | ~ c_lessequals(X7,X6,X3)
      | c_HOL_Oord__class_Oless(X7,X6,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_558]) ).

fof(c_0_1356,plain,
    ! [X6,X7,X3] :
      ( ~ class_Orderings_Olinorder(X3)
      | X7 = X6
      | c_HOL_Oord__class_Oless(X7,X6,X3)
      | ~ c_lessequals(X7,X6,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_559]) ).

fof(c_0_1357,plain,
    ! [X1,X2,X3] :
      ( ~ class_Orderings_Oorder(X3)
      | c_HOL_Oord__class_Oless(X1,X2,X3)
      | ~ c_lessequals(X1,X2,X3)
      | X2 = X1 ),
    inference(fof_simplification,[status(thm)],[c_0_560]) ).

fof(c_0_1358,plain,
    ! [X1,X2,X3] :
      ( ~ class_Orderings_Oorder(X3)
      | c_HOL_Oord__class_Oless(X1,X2,X3)
      | X2 = X1
      | ~ c_lessequals(X1,X2,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_561]) ).

fof(c_0_1359,plain,
    ! [X6,X7,X3] :
      ( ~ class_Orderings_Olinorder(X3)
      | c_Orderings_Oord__class_Omin(X7,X6,X3) != X7
      | c_lessequals(X7,X6,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_562]) ).

fof(c_0_1360,plain,
    ! [X7,X4] :
      ( c_HOL_Oord__class_Oless(c_Suc(X7),c_Suc(X4),tc_nat)
      | ~ c_HOL_Oord__class_Oless(X7,X4,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_563]) ).

fof(c_0_1361,plain,
    ! [X4,X5] :
      ( c_HOL_Oord__class_Oless(c_Suc(X5),c_Suc(X4),tc_nat)
      | ~ c_HOL_Oord__class_Oless(X5,X4,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_564]) ).

fof(c_0_1362,plain,
    ! [X4,X5] :
      ( c_lessequals(c_Suc(X4),c_Suc(X5),tc_nat)
      | ~ c_lessequals(X4,X5,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_565]) ).

fof(c_0_1363,plain,
    ! [X4,X5] :
      ( X4 = X5
      | ~ c_HOL_Oord__class_Oless(X4,c_Suc(X5),tc_nat)
      | c_HOL_Oord__class_Oless(X4,X5,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_566]) ).

fof(c_0_1364,plain,
    ! [X4,X5] :
      ( X5 = X4
      | ~ c_HOL_Oord__class_Oless(X4,c_Suc(X5),tc_nat)
      | c_HOL_Oord__class_Oless(X4,X5,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_567]) ).

fof(c_0_1365,plain,
    ! [X4,X5] :
      ( X5 = X4
      | c_HOL_Oord__class_Oless(X5,X4,tc_nat)
      | ~ c_HOL_Oord__class_Oless(X5,c_Suc(X4),tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_568]) ).

fof(c_0_1366,plain,
    ! [X6,X7,X3] :
      ( ~ class_Orderings_Olinorder(X3)
      | c_Orderings_Oord__class_Omin(X7,X6,X3) = X6
      | ~ c_lessequals(X6,X7,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_569]) ).

fof(c_0_1367,plain,
    ! [X6,X7,X3] :
      ( ~ class_Orderings_Olinorder(X3)
      | c_Orderings_Oord__class_Omin(X7,X6,X3) = X7
      | ~ c_lessequals(X7,X6,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_570]) ).

fof(c_0_1368,plain,
    ! [X2,X3] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X3)
      | X2 = c_HOL_Ozero__class_Ozero(X3)
      | ~ c_lessequals(c_HOL_Oabs__class_Oabs(X2,X3),c_HOL_Ozero__class_Ozero(X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_571]) ).

fof(c_0_1369,plain,
    ! [X4,X5] :
      ( c_HOL_Oord__class_Oless(c_Suc(X5),X4,tc_nat)
      | c_Suc(X5) = X4
      | ~ c_HOL_Oord__class_Oless(X5,X4,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_572]) ).

fof(c_0_1370,plain,
    ! [X6,X7,X3] :
      ( ~ class_Orderings_Oorder(X3)
      | c_lessequals(X7,X6,X3)
      | ~ c_HOL_Oord__class_Oless(X7,X6,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_573]) ).

fof(c_0_1371,plain,
    ! [X6,X7,X3] :
      ( ~ class_Orderings_Opreorder(X3)
      | c_lessequals(X7,X6,X3)
      | ~ c_HOL_Oord__class_Oless(X7,X6,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_574]) ).

fof(c_0_1372,axiom,
    ! [X7] :
      ( c_Divides_Odiv__class_Omod(X7,c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)
      | c_Parity_Oeven__odd__class_Oeven(X7,tc_nat) ),
    c_0_575 ).

fof(c_0_1373,plain,
    ! [X4,X5] :
      ( c_HOL_Oord__class_Oless(X5,X4,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_Suc(X5),X4,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_576]) ).

fof(c_0_1374,plain,
    ! [X4,X5] :
      ( c_lessequals(X5,X4,tc_nat)
      | ~ c_lessequals(c_Suc(X5),X4,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_577]) ).

fof(c_0_1375,plain,
    ! [X4,X5] :
      ( c_lessequals(X5,X4,tc_nat)
      | ~ c_HOL_Oord__class_Oless(X5,c_Suc(X4),tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_578]) ).

fof(c_0_1376,plain,
    ! [X4,X5] :
      ( c_HOL_Oord__class_Oless(X4,X5,tc_nat)
      | ~ c_lessequals(c_Suc(X4),X5,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_579]) ).

fof(c_0_1377,plain,
    ! [X4,X5] :
      ( c_HOL_Oord__class_Oless(X5,X4,tc_nat)
      | ~ c_lessequals(c_Suc(X5),X4,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_580]) ).

fof(c_0_1378,plain,
    ! [X7] :
      ( X7 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
      | X7 = c_HOL_Ozero__class_Ozero(tc_nat)
      | ~ c_HOL_Oord__class_Oless(X7,c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_581]) ).

fof(c_0_1379,plain,
    ! [X2,X3] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X3)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(X2,X3),c_HOL_Ozero__class_Ozero(X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_582]) ).

fof(c_0_1380,plain,
    ! [X5,X3] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X3)
      | ~ c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X5,X3),c_HOL_Ozero__class_Ozero(X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_583]) ).

fof(c_0_1381,plain,
    ! [X4,X5] :
      ( c_HOL_Oord__class_Oless(X5,c_Suc(X4),tc_nat)
      | ~ c_HOL_Oord__class_Oless(X5,X4,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_584]) ).

fof(c_0_1382,plain,
    ! [X4,X5] :
      ( c_lessequals(X5,c_Suc(X4),tc_nat)
      | ~ c_lessequals(X5,X4,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_585]) ).

fof(c_0_1383,plain,
    ! [X7] :
      ( ~ c_lessequals(X7,X7,tc_nat)
      | c_HOL_Oord__class_Oless(X7,c_Suc(X7),tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_586]) ).

fof(c_0_1384,plain,
    ! [X4,X5] :
      ( c_HOL_Oord__class_Oless(X5,c_Suc(X4),tc_nat)
      | ~ c_lessequals(X5,X4,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_587]) ).

fof(c_0_1385,plain,
    ! [X4,X5] :
      ( c_lessequals(c_Suc(X4),X5,tc_nat)
      | ~ c_HOL_Oord__class_Oless(X4,X5,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_588]) ).

fof(c_0_1386,plain,
    ! [X4,X5] :
      ( c_lessequals(c_Suc(X5),X4,tc_nat)
      | ~ c_HOL_Oord__class_Oless(X5,X4,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_589]) ).

fof(c_0_1387,axiom,
    ! [X6,X7] :
      ( c_Parity_Oeven__odd__class_Oeven(c_HOL_Ominus__class_Ominus(X7,X6,tc_nat),tc_nat)
      | c_Parity_Oeven__odd__class_Oeven(X6,tc_nat)
      | c_Parity_Oeven__odd__class_Oeven(X7,tc_nat) ),
    c_0_590 ).

fof(c_0_1388,axiom,
    ! [X4,X5] :
      ( c_Parity_Oeven__odd__class_Oeven(X5,tc_nat)
      | c_Parity_Oeven__odd__class_Oeven(X4,tc_nat)
      | c_Parity_Oeven__odd__class_Oeven(c_HOL_Oplus__class_Oplus(X5,X4,tc_nat),tc_nat) ),
    c_0_591 ).

fof(c_0_1389,axiom,
    ! [X4,X5] :
      ( c_Parity_Oeven__odd__class_Oeven(c_HOL_Oplus__class_Oplus(X5,X4,tc_nat),tc_nat)
      | c_Parity_Oeven__odd__class_Oeven(X4,tc_nat)
      | c_Parity_Oeven__odd__class_Oeven(X5,tc_nat) ),
    c_0_592 ).

fof(c_0_1390,axiom,
    ! [X6,X7] :
      ( c_Parity_Oeven__odd__class_Oeven(c_HOL_Oplus__class_Oplus(X7,X6,tc_nat),tc_nat)
      | c_Parity_Oeven__odd__class_Oeven(X6,tc_nat)
      | c_Parity_Oeven__odd__class_Oeven(X7,tc_nat) ),
    c_0_593 ).

fof(c_0_1391,axiom,
    ! [X4,X5] :
      ( c_HOL_Ominus__class_Ominus(X5,X4,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)
      | c_lessequals(X5,X4,tc_nat) ),
    c_0_594 ).

fof(c_0_1392,plain,
    ! [X4,X5] :
      ( c_HOL_Oord__class_Oless(X5,X4,tc_nat)
      | X5 = X4
      | ~ c_lessequals(X5,X4,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_595]) ).

fof(c_0_1393,plain,
    ! [X4,X5] :
      ( X5 = X4
      | c_HOL_Oord__class_Oless(X5,X4,tc_nat)
      | ~ c_lessequals(X5,X4,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_596]) ).

fof(c_0_1394,plain,
    ! [X4,X5] :
      ( c_HOL_Oord__class_Oless(X5,X4,tc_nat)
      | X5 = X4
      | ~ c_lessequals(X5,X4,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_597]) ).

fof(c_0_1395,plain,
    ! [X4,X5] :
      ( c_HOL_Ominus__class_Ominus(X5,X4,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat)
      | ~ c_lessequals(X5,X4,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_598]) ).

fof(c_0_1396,plain,
    ! [X4,X5] :
      ( c_Divides_Odiv__class_Omod(X5,X4,tc_nat) = X5
      | ~ c_HOL_Oord__class_Oless(X5,X4,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_599]) ).

fof(c_0_1397,plain,
    ! [X4,X5] :
      ( c_lessequals(X5,X4,tc_nat)
      | ~ c_HOL_Oord__class_Oless(X5,X4,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_600]) ).

fof(c_0_1398,plain,
    ! [X6,X7] :
      ( c_lessequals(X7,X6,tc_nat)
      | ~ c_HOL_Oord__class_Oless(X7,X6,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_601]) ).

fof(c_0_1399,plain,
    ! [X6,X7] :
      ( c_Parity_Oeven__odd__class_Oeven(c_HOL_Otimes__class_Otimes(X7,X6,tc_nat),tc_nat)
      | ~ c_Parity_Oeven__odd__class_Oeven(X7,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_602]) ).

fof(c_0_1400,plain,
    ! [X6,X7] :
      ( c_Parity_Oeven__odd__class_Oeven(c_HOL_Otimes__class_Otimes(X7,X6,tc_nat),tc_nat)
      | ~ c_Parity_Oeven__odd__class_Oeven(X6,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_603]) ).

fof(c_0_1401,plain,
    ! [X6,X7,X3] :
      ( ~ class_Orderings_Olinorder(X3)
      | c_HOL_Oord__class_Oless(X6,X7,X3)
      | c_HOL_Oord__class_Oless(X7,X6,X3)
      | X7 = X6 ),
    inference(fof_simplification,[status(thm)],[c_0_604]) ).

fof(c_0_1402,plain,
    ! [X6,X7,X3] :
      ( ~ class_Orderings_Olinorder(X3)
      | c_HOL_Oord__class_Oless(X6,X7,X3)
      | X7 = X6
      | c_HOL_Oord__class_Oless(X7,X6,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_605]) ).

fof(c_0_1403,plain,
    ! [X6,X7,X3] :
      ( ~ class_Orderings_Olinorder(X3)
      | X7 = X6
      | c_HOL_Oord__class_Oless(X7,X6,X3)
      | c_HOL_Oord__class_Oless(X6,X7,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_606]) ).

fof(c_0_1404,plain,
    ! [X6,X7,X3] :
      ( ~ class_Orderings_Olinorder(X3)
      | X7 = X6
      | c_HOL_Oord__class_Oless(X6,X7,X3)
      | c_HOL_Oord__class_Oless(X7,X6,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_607]) ).

fof(c_0_1405,plain,
    ! [X6,X7,X3] :
      ( ~ class_Ring__and__Field_Oordered__idom(X3)
      | c_HOL_Oord__class_Oless(X6,X7,X3)
      | c_HOL_Oord__class_Oless(X7,X6,X3)
      | X7 = X6 ),
    inference(fof_simplification,[status(thm)],[c_0_608]) ).

fof(c_0_1406,plain,
    ! [X2,X3] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X3)
      | c_HOL_Oabs__class_Oabs(X2,X3) = X2
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X2,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_609]) ).

fof(c_0_1407,plain,
    ! [X2,X3] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X3)
      | c_HOL_Oabs__class_Oabs(X2,X3) = X2
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X2,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_610]) ).

fof(c_0_1408,axiom,
    ! [X4,X5] : c_HOL_Ominus__class_Ominus(c_Suc(X5),c_Suc(X4),tc_nat) = c_HOL_Ominus__class_Ominus(X5,X4,tc_nat),
    c_0_611 ).

fof(c_0_1409,axiom,
    ! [X4,X5] : c_HOL_Oplus__class_Oplus(c_Suc(X5),X4,tc_nat) = c_HOL_Oplus__class_Oplus(X5,c_Suc(X4),tc_nat),
    c_0_612 ).

fof(c_0_1410,plain,
    ! [X6,X7,X3] :
      ( ~ class_Orderings_Olinorder(X3)
      | c_lessequals(X6,X7,X3)
      | c_lessequals(X7,X6,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_613]) ).

fof(c_0_1411,plain,
    ! [X6,X7,X3] :
      ( ~ class_Orderings_Olinorder(X3)
      | c_HOL_Oord__class_Oless(X6,X7,X3)
      | c_lessequals(X7,X6,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_614]) ).

fof(c_0_1412,plain,
    ! [X6,X7,X3] :
      ( ~ class_Orderings_Olinorder(X3)
      | c_lessequals(X6,X7,X3)
      | c_HOL_Oord__class_Oless(X7,X6,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_615]) ).

fof(c_0_1413,plain,
    ! [X7,X3] :
      ( ~ class_Orderings_Olinorder(X3)
      | c_HOL_Oord__class_Oless(X7,X7,X3)
      | c_lessequals(X7,X7,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_616]) ).

fof(c_0_1414,plain,
    ! [X6,X7,X3] :
      ( ~ class_Orderings_Olinorder(X3)
      | c_HOL_Oord__class_Oless(X7,X6,X3)
      | c_lessequals(X6,X7,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_617]) ).

fof(c_0_1415,plain,
    ! [X1,X2,X3] :
      ( ~ class_OrderedGroup_Ocomm__monoid__add(X3)
      | c_HOL_Oplus__class_Oplus(X2,X1,X3) = c_HOL_Oplus__class_Oplus(X1,X2,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_618]) ).

fof(c_0_1416,plain,
    ! [X6,X7,X3] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
      | c_HOL_Oplus__class_Oplus(X7,X6,X3) = c_HOL_Oplus__class_Oplus(X6,X7,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_619]) ).

fof(c_0_1417,plain,
    ! [X15,X2,X3] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
      | c_HOL_Oplus__class_Oplus(X2,X15,X3) = c_HOL_Oplus__class_Oplus(X15,X2,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_620]) ).

fof(c_0_1418,plain,
    ! [X6,X7,X3] :
      ( ~ class_Orderings_Olinorder(X3)
      | c_Orderings_Oord__class_Omin(X7,X6,X3) = c_Orderings_Oord__class_Omin(X6,X7,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_621]) ).

fof(c_0_1419,plain,
    ! [X1,X2,X3] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
      | c_HOL_Otimes__class_Otimes(X2,X1,X3) = c_HOL_Otimes__class_Otimes(X1,X2,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_622]) ).

fof(c_0_1420,plain,
    ! [X6,X7,X3] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
      | c_HOL_Otimes__class_Otimes(X7,X6,X3) = c_HOL_Otimes__class_Otimes(X6,X7,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_623]) ).

fof(c_0_1421,axiom,
    ! [X7] :
      ( c_HOL_Oord__class_Oless(X7,X7,tc_nat)
      | c_HOL_Oord__class_Oless(X7,c_Suc(X7),tc_nat) ),
    c_0_624 ).

fof(c_0_1422,axiom,
    ! [X4,X5] :
      ( c_HOL_Oord__class_Oless(X4,c_Suc(X5),tc_nat)
      | c_HOL_Oord__class_Oless(X5,X4,tc_nat) ),
    c_0_625 ).

fof(c_0_1423,axiom,
    ! [X4,X5] :
      ( c_lessequals(c_Suc(X4),X5,tc_nat)
      | c_lessequals(X5,X4,tc_nat) ),
    c_0_626 ).

fof(c_0_1424,axiom,
    ! [X4,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),X4,tc_nat),
    c_0_627 ).

fof(c_0_1425,axiom,
    ! [X4,X5] : c_HOL_Otimes__class_Otimes(X5,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = c_HOL_Otimes__class_Otimes(X4,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
    c_0_628 ).

fof(c_0_1426,axiom,
    ! [X4,X5] :
      ( c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != c_HOL_Oplus__class_Oplus(X5,X4,tc_nat)
      | X4 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
      | X5 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
    c_0_629 ).

fof(c_0_1427,plain,
    ! [X5] :
      ( X5 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X5,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_630]) ).

fof(c_0_1428,axiom,
    ! [X4,X5] :
      ( c_HOL_Oplus__class_Oplus(X5,X4,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
      | X4 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
      | X5 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
    c_0_631 ).

fof(c_0_1429,plain,
    ! [X1,X2,X3] :
      ( ~ class_Ring__and__Field_Ono__zero__divisors(X3)
      | c_HOL_Otimes__class_Otimes(X2,X1,X3) != c_HOL_Ozero__class_Ozero(X3)
      | X2 = c_HOL_Ozero__class_Ozero(X3)
      | X1 = c_HOL_Ozero__class_Ozero(X3) ),
    inference(fof_simplification,[status(thm)],[c_0_632]) ).

fof(c_0_1430,plain,
    ! [X1,X2,X3] :
      ( ~ class_Ring__and__Field_Ono__zero__divisors(X3)
      | c_HOL_Otimes__class_Otimes(X2,X1,X3) != c_HOL_Ozero__class_Ozero(X3)
      | X1 = c_HOL_Ozero__class_Ozero(X3)
      | X2 = c_HOL_Ozero__class_Ozero(X3) ),
    inference(fof_simplification,[status(thm)],[c_0_633]) ).

fof(c_0_1431,plain,
    ! [X1,X2,X3] :
      ( ~ class_Ring__and__Field_Oring__no__zero__divisors(X3)
      | c_HOL_Otimes__class_Otimes(X2,X1,X3) != c_HOL_Ozero__class_Ozero(X3)
      | X1 = c_HOL_Ozero__class_Ozero(X3)
      | X2 = c_HOL_Ozero__class_Ozero(X3) ),
    inference(fof_simplification,[status(thm)],[c_0_634]) ).

fof(c_0_1432,axiom,
    ! [X6,X7] :
      ( c_HOL_Oord__class_Oless(X6,X7,tc_nat)
      | c_HOL_Oord__class_Oless(X7,X6,tc_nat)
      | X7 = X6 ),
    c_0_635 ).

fof(c_0_1433,axiom,
    ! [X4,X5] :
      ( c_HOL_Oord__class_Oless(X4,X5,tc_nat)
      | c_HOL_Oord__class_Oless(X5,X4,tc_nat)
      | X5 = X4 ),
    c_0_636 ).

fof(c_0_1434,plain,
    ! [X6,X7,X3] :
      ( ~ class_Ring__and__Field_Oidom(X3)
      | ~ class_Int_Onumber__ring(X3)
      | c_HOL_Ominus__class_Ominus(X7,X6,X3) != c_HOL_Ozero__class_Ozero(X3)
      | X7 = X6 ),
    inference(fof_simplification,[status(thm)],[c_0_637]) ).

fof(c_0_1435,plain,
    ! [X2,X3] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
      | X2 = c_HOL_Ozero__class_Ozero(X3)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ozero__class_Ozero(X3),X2,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_638]) ).

fof(c_0_1436,plain,
    ! [X7,X2,X3] :
      ( ~ class_Ring__and__Field_Oidom(X3)
      | ~ class_Int_Onumber__ring(X3)
      | X7 != c_HOL_Oplus__class_Oplus(X7,X2,X3)
      | X2 = c_HOL_Ozero__class_Ozero(X3) ),
    inference(fof_simplification,[status(thm)],[c_0_639]) ).

fof(c_0_1437,axiom,
    ! [X4,X5] :
      ( c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != c_HOL_Oplus__class_Oplus(X5,X4,tc_nat)
      | X5 = c_HOL_Ozero__class_Ozero(tc_nat)
      | X5 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
    c_0_640 ).

fof(c_0_1438,axiom,
    ! [X4,X5] :
      ( c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != c_HOL_Oplus__class_Oplus(X5,X4,tc_nat)
      | X4 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
      | X4 = c_HOL_Ozero__class_Ozero(tc_nat) ),
    c_0_641 ).

fof(c_0_1439,axiom,
    ! [X4,X5] :
      ( c_HOL_Oplus__class_Oplus(X5,X4,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
      | X4 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
      | X4 = c_HOL_Ozero__class_Ozero(tc_nat) ),
    c_0_642 ).

fof(c_0_1440,axiom,
    ! [X4,X5] :
      ( c_HOL_Oplus__class_Oplus(X5,X4,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
      | X5 = c_HOL_Ozero__class_Ozero(tc_nat)
      | X5 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
    c_0_643 ).

fof(c_0_1441,plain,
    ! [X4] :
      ( X4 = c_HOL_Ozero__class_Ozero(tc_nat)
      | ~ c_HOL_Oord__class_Oless(X4,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_644]) ).

fof(c_0_1442,axiom,
    ! [X4,X5] :
      ( c_lessequals(X4,X5,tc_nat)
      | c_lessequals(X5,X4,tc_nat) ),
    c_0_645 ).

fof(c_0_1443,plain,
    ! [X7] :
      ( c_Divides_Odiv__class_Omod(X7,c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat)
      | ~ c_Parity_Oeven__odd__class_Oeven(X7,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_646]) ).

fof(c_0_1444,plain,
    ! [X29,X8,X3] :
      ( ~ class_Ring__and__Field_Oordered__idom(X3)
      | c_HOL_Oabs__class_Oabs(X29,X3) != c_HOL_Oabs__class_Oabs(X8,X3)
      | c_Ring__and__Field_Odvd__class_Odvd(X29,X8,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_647]) ).

fof(c_0_1445,plain,
    ! [X3] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X3)
      | c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Ozero__class_Ozero(X3),X3),c_HOL_Ozero__class_Ozero(X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_648]) ).

fof(c_0_1446,axiom,
    ! [X4,X5] : c_HOL_Oplus__class_Oplus(X5,X4,tc_nat) = c_HOL_Oplus__class_Oplus(X4,X5,tc_nat),
    c_0_649 ).

fof(c_0_1447,axiom,
    ! [X4,X5] : c_HOL_Otimes__class_Otimes(X5,X4,tc_nat) = c_HOL_Otimes__class_Otimes(X4,X5,tc_nat),
    c_0_650 ).

fof(c_0_1448,plain,
    ! [X2,X3] :
      ( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
      | c_HOL_Oplus__class_Oplus(X2,X2,X3) != c_HOL_Ozero__class_Ozero(X3)
      | X2 = c_HOL_Ozero__class_Ozero(X3) ),
    inference(fof_simplification,[status(thm)],[c_0_651]) ).

fof(c_0_1449,axiom,
    ! [X7] :
      ( c_Divides_Odiv__class_Omod(X7,c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),tc_nat) = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
      | c_Parity_Oeven__odd__class_Oeven(X7,tc_nat) ),
    c_0_652 ).

fof(c_0_1450,axiom,
    ! [X4,X5] :
      ( c_HOL_Otimes__class_Otimes(X5,X4,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
      | X4 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
    c_0_653 ).

fof(c_0_1451,axiom,
    ! [X4,X5] :
      ( c_HOL_Otimes__class_Otimes(X5,X4,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
      | X5 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
    c_0_654 ).

fof(c_0_1452,axiom,
    ! [X4,X5] :
      ( c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != c_HOL_Oplus__class_Oplus(X5,X4,tc_nat)
      | X5 = c_HOL_Ozero__class_Ozero(tc_nat)
      | X4 = c_HOL_Ozero__class_Ozero(tc_nat) ),
    c_0_655 ).

fof(c_0_1453,axiom,
    ! [X4,X5] :
      ( c_HOL_Oplus__class_Oplus(X5,X4,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
      | X5 = c_HOL_Ozero__class_Ozero(tc_nat)
      | X4 = c_HOL_Ozero__class_Ozero(tc_nat) ),
    c_0_656 ).

fof(c_0_1454,plain,
    ! [X1,X2,X3] :
      ( ~ class_OrderedGroup_Ogroup__add(X3)
      | c_HOL_Ominus__class_Ominus(X2,X1,X3) != c_HOL_Ozero__class_Ozero(X3)
      | X2 = X1 ),
    inference(fof_simplification,[status(thm)],[c_0_657]) ).

fof(c_0_1455,plain,
    ! [X1,X2,X3] :
      ( ~ class_OrderedGroup_Oab__group__add(X3)
      | c_HOL_Ominus__class_Ominus(X2,X1,X3) != c_HOL_Ozero__class_Ozero(X3)
      | X2 = X1 ),
    inference(fof_simplification,[status(thm)],[c_0_658]) ).

fof(c_0_1456,plain,
    ! [X2,X3] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X3)
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_HOL_Oabs__class_Oabs(X2,X3),X3)
      | X2 = c_HOL_Ozero__class_Ozero(X3) ),
    inference(fof_simplification,[status(thm)],[c_0_659]) ).

fof(c_0_1457,axiom,
    ! [X4,X5] :
      ( c_HOL_Otimes__class_Otimes(X5,X4,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)
      | X4 = c_HOL_Ozero__class_Ozero(tc_nat)
      | X5 = c_HOL_Ozero__class_Ozero(tc_nat) ),
    c_0_660 ).

fof(c_0_1458,plain,
    ! [X2,X3] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X3)
      | c_lessequals(c_HOL_Ozero__class_Ozero(X3),c_HOL_Oabs__class_Oabs(X2,X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_661]) ).

fof(c_0_1459,plain,
    ! [X4,X3] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X3)
      | c_lessequals(c_HOL_Ozero__class_Ozero(X3),c_Nat_Osemiring__1__class_Oof__nat(X4,X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_662]) ).

fof(c_0_1460,plain,
    ! [X5,X3] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X3)
      | c_lessequals(c_HOL_Ozero__class_Ozero(X3),c_Nat_Osemiring__1__class_Oof__nat(X5,X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_663]) ).

fof(c_0_1461,plain,
    ! [X7,X3] :
      ( ~ class_Orderings_Oorder(X3)
      | ~ c_HOL_Oord__class_Oless(X7,X7,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_664]) ).

fof(c_0_1462,plain,
    ! [X7,X3] :
      ( ~ class_Orderings_Olinorder(X3)
      | ~ c_HOL_Oord__class_Oless(X7,X7,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_665]) ).

fof(c_0_1463,plain,
    ! [X7,X3] :
      ( ~ class_Orderings_Opreorder(X3)
      | ~ c_HOL_Oord__class_Oless(X7,X7,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_666]) ).

fof(c_0_1464,plain,
    ! [X4] : ~ c_lessequals(c_Suc(X4),X4,tc_nat),
    inference(fof_simplification,[status(thm)],[c_0_667]) ).

fof(c_0_1465,plain,
    ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
    inference(fof_simplification,[status(thm)],[c_0_668]) ).

fof(c_0_1466,plain,
    ! [X4] :
      ( X4 = c_HOL_Ozero__class_Ozero(tc_nat)
      | ~ c_lessequals(X4,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_669]) ).

fof(c_0_1467,axiom,
    ! [X4,X5] :
      ( c_HOL_Oplus__class_Oplus(X5,X4,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)
      | X4 = c_HOL_Ozero__class_Ozero(tc_nat) ),
    c_0_670 ).

fof(c_0_1468,axiom,
    ! [X4,X5] :
      ( c_HOL_Oplus__class_Oplus(X5,X4,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)
      | X5 = c_HOL_Ozero__class_Ozero(tc_nat) ),
    c_0_671 ).

fof(c_0_1469,plain,
    ! [X2,X3] :
      ( ~ class_Orderings_Olinorder(X3)
      | ~ class_OrderedGroup_Olordered__ab__group__add__abs(X3)
      | c_HOL_Oabs__class_Oabs(X2,X3) = X2
      | c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_672]) ).

fof(c_0_1470,axiom,
    ! [X4,X5] :
      ( c_HOL_Oplus__class_Oplus(X5,X4,tc_nat) != X5
      | X4 = c_HOL_Ozero__class_Ozero(tc_nat) ),
    c_0_673 ).

fof(c_0_1471,axiom,
    ! [X7,X2] :
      ( X7 != c_HOL_Oplus__class_Oplus(X7,X2,tc_nat)
      | X2 = c_HOL_Ozero__class_Ozero(tc_nat) ),
    c_0_674 ).

fof(c_0_1472,plain,
    ! [X5] : ~ c_HOL_Oord__class_Oless(X5,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
    inference(fof_simplification,[status(thm)],[c_0_675]) ).

fof(c_0_1473,plain,
    ! [X4] : ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
    inference(fof_simplification,[status(thm)],[c_0_676]) ).

fof(c_0_1474,plain,
    ! [X2,X3] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X3)
      | c_lessequals(X2,c_HOL_Oabs__class_Oabs(X2,X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_677]) ).

fof(c_0_1475,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)),
    c_0_678 ).

fof(c_0_1476,plain,
    ! [X4] : ~ c_HOL_Oord__class_Oless(X4,X4,tc_nat),
    inference(fof_simplification,[status(thm)],[c_0_679]) ).

fof(c_0_1477,plain,
    ! [X7] : ~ c_HOL_Oord__class_Oless(X7,X7,tc_nat),
    inference(fof_simplification,[status(thm)],[c_0_680]) ).

fof(c_0_1478,plain,
    ! [X2,X3] :
      ( ~ class_Ring__and__Field_Oabs__if(X3)
      | c_HOL_Oabs__class_Oabs(X2,X3) = X2
      | c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_681]) ).

fof(c_0_1479,plain,
    ! [X3] :
      ( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
      | c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X3),c_HOL_Ozero__class_Ozero(X3),X3) = c_HOL_Ozero__class_Ozero(X3) ),
    inference(fof_simplification,[status(thm)],[c_0_682]) ).

fof(c_0_1480,axiom,
    c_Ring__and__Field_Odvd__class_Odvd(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),
    c_0_683 ).

fof(c_0_1481,plain,
    ! [X7,X3] :
      ( ~ class_Ring__and__Field_Oidom(X3)
      | ~ class_Int_Onumber__ring(X3)
      | X7 = c_HOL_Oplus__class_Oplus(X7,c_HOL_Ozero__class_Ozero(X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_684]) ).

fof(c_0_1482,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)),
    c_0_685 ).

fof(c_0_1483,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),
    c_0_686 ).

fof(c_0_1484,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),
    c_0_687 ).

fof(c_0_1485,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)),
    c_0_688 ).

fof(c_0_1486,plain,
    ! [X7,X3] :
      ( ~ class_Ring__and__Field_Oidom(X3)
      | ~ class_Int_Onumber__ring(X3)
      | c_HOL_Ominus__class_Ominus(X7,X7,X3) = c_HOL_Ozero__class_Ozero(X3) ),
    inference(fof_simplification,[status(thm)],[c_0_689]) ).

fof(c_0_1487,plain,
    ! [X2,X3] :
      ( ~ class_Ring__and__Field_Oring__no__zero__divisors(X3)
      | c_HOL_Otimes__class_Otimes(X2,c_HOL_Ozero__class_Ozero(X3),X3) = c_HOL_Ozero__class_Ozero(X3) ),
    inference(fof_simplification,[status(thm)],[c_0_690]) ).

fof(c_0_1488,plain,
    ! [X1,X3] :
      ( ~ class_Ring__and__Field_Oring__no__zero__divisors(X3)
      | c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X3),X1,X3) = c_HOL_Ozero__class_Ozero(X3) ),
    inference(fof_simplification,[status(thm)],[c_0_691]) ).

fof(c_0_1489,plain,
    ! [X2,X3] :
      ( ~ class_Ring__and__Field_Omult__zero(X3)
      | c_HOL_Otimes__class_Otimes(X2,c_HOL_Ozero__class_Ozero(X3),X3) = c_HOL_Ozero__class_Ozero(X3) ),
    inference(fof_simplification,[status(thm)],[c_0_692]) ).

fof(c_0_1490,plain,
    ! [X2,X3] :
      ( ~ class_Ring__and__Field_Omult__zero(X3)
      | c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X3),X2,X3) = c_HOL_Ozero__class_Ozero(X3) ),
    inference(fof_simplification,[status(thm)],[c_0_693]) ).

fof(c_0_1491,plain,
    ! [X7,X3] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
      | c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X3),X7,X3) = c_HOL_Ozero__class_Ozero(X3) ),
    inference(fof_simplification,[status(thm)],[c_0_694]) ).

fof(c_0_1492,plain,
    ! [X7,X3] :
      ( ~ class_RealVector_Oreal__normed__algebra(X3)
      | c_HOL_Otimes__class_Otimes(X7,c_HOL_Ozero__class_Ozero(X3),X3) = c_HOL_Ozero__class_Ozero(X3) ),
    inference(fof_simplification,[status(thm)],[c_0_695]) ).

fof(c_0_1493,plain,
    ! [X2,X3] :
      ( ~ class_RealVector_Oreal__normed__algebra(X3)
      | c_HOL_Otimes__class_Otimes(X2,c_HOL_Ozero__class_Ozero(X3),X3) = c_HOL_Ozero__class_Ozero(X3) ),
    inference(fof_simplification,[status(thm)],[c_0_696]) ).

fof(c_0_1494,plain,
    ! [X1,X3] :
      ( ~ class_RealVector_Oreal__normed__algebra(X3)
      | c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X3),X1,X3) = c_HOL_Ozero__class_Ozero(X3) ),
    inference(fof_simplification,[status(thm)],[c_0_697]) ).

fof(c_0_1495,plain,
    ! [X6,X3] :
      ( ~ class_RealVector_Oreal__normed__algebra(X3)
      | c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X3),X6,X3) = c_HOL_Ozero__class_Ozero(X3) ),
    inference(fof_simplification,[status(thm)],[c_0_698]) ).

fof(c_0_1496,plain,
    ! [X2,X3] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
      | c_HOL_Otimes__class_Otimes(X2,c_HOL_Ozero__class_Ozero(X3),X3) = c_HOL_Ozero__class_Ozero(X3) ),
    inference(fof_simplification,[status(thm)],[c_0_699]) ).

fof(c_0_1497,plain,
    ! [X2,X3] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
      | c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X3),X2,X3) = c_HOL_Ozero__class_Ozero(X3) ),
    inference(fof_simplification,[status(thm)],[c_0_700]) ).

fof(c_0_1498,plain,
    ! [X2,X3] :
      ( ~ class_Divides_Osemiring__div(X3)
      | c_Divides_Odiv__class_Omod(c_HOL_Ozero__class_Ozero(X3),X2,X3) = c_HOL_Ozero__class_Ozero(X3) ),
    inference(fof_simplification,[status(thm)],[c_0_701]) ).

fof(c_0_1499,axiom,
    ! [X4] :
      ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat)
      | c_Parity_Oeven__odd__class_Oeven(X4,tc_nat) ),
    c_0_702 ).

fof(c_0_1500,plain,
    ! [X2,X3] :
      ( ~ class_OrderedGroup_Ogroup__add(X3)
      | c_HOL_Ominus__class_Ominus(X2,c_HOL_Ozero__class_Ozero(X3),X3) = X2 ),
    inference(fof_simplification,[status(thm)],[c_0_703]) ).

fof(c_0_1501,plain,
    ! [X2,X3] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
      | c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X3),X2,X3) = X2 ),
    inference(fof_simplification,[status(thm)],[c_0_704]) ).

fof(c_0_1502,plain,
    ! [X2,X3] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
      | c_HOL_Oplus__class_Oplus(X2,c_HOL_Ozero__class_Ozero(X3),X3) = X2 ),
    inference(fof_simplification,[status(thm)],[c_0_705]) ).

fof(c_0_1503,plain,
    ! [X2,X3] :
      ( ~ class_OrderedGroup_Ocomm__monoid__add(X3)
      | c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X3),X2,X3) = X2 ),
    inference(fof_simplification,[status(thm)],[c_0_706]) ).

fof(c_0_1504,plain,
    ! [X7,X3] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
      | c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X3),X7,X3) = X7 ),
    inference(fof_simplification,[status(thm)],[c_0_707]) ).

fof(c_0_1505,plain,
    ! [X2,X3] :
      ( ~ class_OrderedGroup_Ocomm__monoid__add(X3)
      | c_HOL_Oplus__class_Oplus(X2,c_HOL_Ozero__class_Ozero(X3),X3) = X2 ),
    inference(fof_simplification,[status(thm)],[c_0_708]) ).

fof(c_0_1506,plain,
    ! [X2,X3] :
      ( ~ class_OrderedGroup_Omonoid__add(X3)
      | c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X3),X2,X3) = X2 ),
    inference(fof_simplification,[status(thm)],[c_0_709]) ).

fof(c_0_1507,plain,
    ! [X2,X3] :
      ( ~ class_OrderedGroup_Omonoid__add(X3)
      | c_HOL_Oplus__class_Oplus(X2,c_HOL_Ozero__class_Ozero(X3),X3) = X2 ),
    inference(fof_simplification,[status(thm)],[c_0_710]) ).

fof(c_0_1508,plain,
    ! [X2,X3] :
      ( ~ class_Divides_Osemiring__div(X3)
      | c_Divides_Odiv__class_Omod(X2,c_HOL_Ozero__class_Ozero(X3),X3) = X2 ),
    inference(fof_simplification,[status(thm)],[c_0_711]) ).

fof(c_0_1509,axiom,
    c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),
    c_0_712 ).

fof(c_0_1510,plain,
    ! [X2,X3] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
      | c_Ring__and__Field_Odvd__class_Odvd(X2,c_HOL_Ozero__class_Ozero(X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_713]) ).

fof(c_0_1511,axiom,
    ! [X5] : c_Divides_Odiv__class_Omod(X5,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
    c_0_714 ).

fof(c_0_1512,plain,
    ! [X2,X3] :
      ( ~ class_OrderedGroup_Ogroup__add(X3)
      | c_HOL_Ominus__class_Ominus(X2,X2,X3) = c_HOL_Ozero__class_Ozero(X3) ),
    inference(fof_simplification,[status(thm)],[c_0_715]) ).

fof(c_0_1513,plain,
    ! [X7,X3] :
      ( ~ class_OrderedGroup_Ogroup__add(X3)
      | c_HOL_Ominus__class_Ominus(X7,X7,X3) = c_HOL_Ozero__class_Ozero(X3) ),
    inference(fof_simplification,[status(thm)],[c_0_716]) ).

fof(c_0_1514,plain,
    ! [X7,X3] :
      ( ~ class_OrderedGroup_Oab__group__add(X3)
      | c_HOL_Ominus__class_Ominus(X7,X7,X3) = c_HOL_Ozero__class_Ozero(X3) ),
    inference(fof_simplification,[status(thm)],[c_0_717]) ).

fof(c_0_1515,plain,
    ! [X2,X3] :
      ( ~ class_Divides_Osemiring__div(X3)
      | c_Divides_Odiv__class_Omod(X2,X2,X3) = c_HOL_Ozero__class_Ozero(X3) ),
    inference(fof_simplification,[status(thm)],[c_0_718]) ).

fof(c_0_1516,axiom,
    ! [X4] : c_lessequals(c_Suc(X4),c_Suc(X4),tc_nat),
    c_0_719 ).

fof(c_0_1517,axiom,
    ! [X8] : c_Ring__and__Field_Odvd__class_Odvd(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X8,tc_nat),
    c_0_720 ).

fof(c_0_1518,plain,
    ! [X7,X3] :
      ( ~ class_OrderedGroup_Oab__semigroup__idem__mult(X3)
      | c_HOL_Otimes__class_Otimes(X7,X7,X3) = X7 ),
    inference(fof_simplification,[status(thm)],[c_0_721]) ).

fof(c_0_1519,plain,
    ! [X7,X3] :
      ( ~ class_Orderings_Olinorder(X3)
      | c_Orderings_Oord__class_Omin(X7,X7,X3) = X7 ),
    inference(fof_simplification,[status(thm)],[c_0_722]) ).

fof(c_0_1520,axiom,
    ! [X4] : c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(X4),tc_nat),
    c_0_723 ).

fof(c_0_1521,axiom,
    ! [X7] : c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(X7),tc_nat),
    c_0_724 ).

fof(c_0_1522,plain,
    ! [X7,X3] :
      ( ~ class_Orderings_Oorder(X3)
      | c_lessequals(X7,X7,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_725]) ).

fof(c_0_1523,plain,
    ! [X7,X3] :
      ( ~ class_Orderings_Opreorder(X3)
      | c_lessequals(X7,X7,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_726]) ).

fof(c_0_1524,plain,
    ! [X2,X3] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
      | c_Ring__and__Field_Odvd__class_Odvd(X2,X2,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_727]) ).

fof(c_0_1525,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),
    c_0_728 ).

fof(c_0_1526,plain,
    ! [X2,X3] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X3)
      | c_HOL_Oabs__class_Oabs(c_HOL_Oabs__class_Oabs(X2,X3),X3) = c_HOL_Oabs__class_Oabs(X2,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_729]) ).

fof(c_0_1527,plain,
    ! [X4,X3] :
      ( ~ class_Ring__and__Field_Oordered__idom(X3)
      | c_HOL_Oabs__class_Oabs(c_Nat_Osemiring__1__class_Oof__nat(X4,X3),X3) = c_Nat_Osemiring__1__class_Oof__nat(X4,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_730]) ).

fof(c_0_1528,axiom,
    ! [X4] :
      ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat)
      | X4 = c_HOL_Ozero__class_Ozero(tc_nat) ),
    c_0_731 ).

fof(c_0_1529,axiom,
    ! [X7] : c_HOL_Oord__class_Oless(X7,c_Suc(X7),tc_nat),
    c_0_732 ).

fof(c_0_1530,axiom,
    ! [X4] : c_HOL_Oord__class_Oless(X4,c_Suc(X4),tc_nat),
    c_0_733 ).

fof(c_0_1531,axiom,
    c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
    c_0_734 ).

fof(c_0_1532,axiom,
    ! [X4] : c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
    c_0_735 ).

fof(c_0_1533,axiom,
    ! [X4] : c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
    c_0_736 ).

fof(c_0_1534,axiom,
    ! [X5] : c_HOL_Otimes__class_Otimes(X5,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
    c_0_737 ).

fof(c_0_1535,axiom,
    ! [X4] : c_Orderings_Oord__class_Omin(X4,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
    c_0_738 ).

fof(c_0_1536,axiom,
    ! [X4] : c_Orderings_Oord__class_Omin(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
    c_0_739 ).

fof(c_0_1537,axiom,
    ! [X5] : c_HOL_Ominus__class_Ominus(X5,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = X5,
    c_0_740 ).

fof(c_0_1538,axiom,
    ! [X4] : c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat) = X4,
    c_0_741 ).

fof(c_0_1539,axiom,
    ! [X5] : c_HOL_Oplus__class_Oplus(X5,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = X5,
    c_0_742 ).

fof(c_0_1540,axiom,
    ! [X7] : X7 = c_HOL_Oplus__class_Oplus(X7,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
    c_0_743 ).

fof(c_0_1541,axiom,
    ! [X7] : c_Ring__and__Field_Odvd__class_Odvd(X7,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
    c_0_744 ).

fof(c_0_1542,axiom,
    ! [X4] : c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat),
    c_0_745 ).

fof(c_0_1543,axiom,
    ! [X5] : c_HOL_Ominus__class_Ominus(X5,X5,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
    c_0_746 ).

fof(c_0_1544,plain,
    ! [X4,X5,X3] :
      ( ~ class_Nat_Osemiring__char__0(X3)
      | c_Nat_Osemiring__1__class_Oof__nat(X5,X3) != c_Nat_Osemiring__1__class_Oof__nat(X4,X3)
      | X5 = X4 ),
    inference(fof_simplification,[status(thm)],[c_0_747]) ).

fof(c_0_1545,axiom,
    ! [X4] : c_lessequals(X4,X4,tc_nat),
    c_0_748 ).

fof(c_0_1546,axiom,
    ! [X7] : c_lessequals(X7,X7,tc_nat),
    c_0_749 ).

fof(c_0_1547,axiom,
    ! [X7] : c_Ring__and__Field_Odvd__class_Odvd(X7,X7,tc_nat),
    c_0_750 ).

fof(c_0_1548,axiom,
    c_HOL_Oord__class_Oless(v_i,v_n,tc_nat),
    c_0_751 ).

fof(c_0_1549,axiom,
    c_HOL_Oord__class_Oless(v_i,v_n,tc_nat),
    c_0_752 ).

fof(c_0_1550,plain,
    ! [X7] :
      ( ~ c_Parity_Oeven__odd__class_Oeven(X7,tc_nat)
      | ~ c_Parity_Oeven__odd__class_Oeven(c_Suc(X7),tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_753]) ).

fof(c_0_1551,plain,
    ! [X2,X3] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X3)
      | c_HOL_Oabs__class_Oabs(X2,X3) != c_HOL_Ozero__class_Ozero(X3)
      | X2 = c_HOL_Ozero__class_Ozero(X3) ),
    inference(fof_simplification,[status(thm)],[c_0_754]) ).

fof(c_0_1552,axiom,
    ! [X7] :
      ( c_Parity_Oeven__odd__class_Oeven(c_Suc(X7),tc_nat)
      | c_Parity_Oeven__odd__class_Oeven(X7,tc_nat) ),
    c_0_755 ).

fof(c_0_1553,plain,
    ! [X3] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X3)
      | c_HOL_Oabs__class_Oabs(c_HOL_Ozero__class_Ozero(X3),X3) = c_HOL_Ozero__class_Ozero(X3) ),
    inference(fof_simplification,[status(thm)],[c_0_756]) ).

fof(c_0_1554,plain,
    ! [X3] :
      ( ~ class_Ring__and__Field_Osemiring__1(X3)
      | c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Ozero__class_Ozero(tc_nat),X3) = c_HOL_Ozero__class_Ozero(X3) ),
    inference(fof_simplification,[status(thm)],[c_0_757]) ).

fof(c_0_1555,axiom,
    c_Parity_Oeven__odd__class_Oeven(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
    c_0_758 ).

fof(c_0_1556,axiom,
    ! [X6,X7] :
      ( c_Suc(X7) != c_Suc(X6)
      | X7 = X6 ),
    c_0_759 ).

fof(c_0_1557,axiom,
    ! [X21,X30] :
      ( c_Suc(X30) != c_Suc(X21)
      | X30 = X21 ),
    c_0_760 ).

fof(c_0_1558,axiom,
    ! [X21] : c_Suc(X21) != c_HOL_Ozero__class_Ozero(tc_nat),
    c_0_761 ).

fof(c_0_1559,axiom,
    ! [X5] : c_Suc(X5) != c_HOL_Ozero__class_Ozero(tc_nat),
    c_0_762 ).

fof(c_0_1560,axiom,
    ! [X5] : c_HOL_Ozero__class_Ozero(tc_nat) != c_Suc(X5),
    c_0_763 ).

fof(c_0_1561,axiom,
    ! [X21] : c_HOL_Ozero__class_Ozero(tc_nat) != c_Suc(X21),
    c_0_764 ).

fof(c_0_1562,axiom,
    ! [X4] : c_Suc(X4) != X4,
    c_0_765 ).

fof(c_0_1563,axiom,
    ! [X4] : X4 != c_Suc(X4),
    c_0_766 ).

fof(c_0_1564,axiom,
    class_Orderings_Oorder(tc_nat),
    c_0_767 ).

fof(c_0_1565,axiom,
    class_Orderings_Olinorder(tc_nat),
    c_0_768 ).

fof(c_0_1566,axiom,
    class_Orderings_Opreorder(tc_nat),
    c_0_769 ).

fof(c_0_1567,axiom,
    class_Ring__and__Field_Odvd(tc_nat),
    c_0_770 ).

fof(c_0_1568,axiom,
    class_Nat_Osemiring__char__0(tc_nat),
    c_0_771 ).

fof(c_0_1569,axiom,
    class_Divides_Osemiring__div(tc_nat),
    c_0_772 ).

fof(c_0_1570,axiom,
    class_OrderedGroup_Omonoid__add(tc_nat),
    c_0_773 ).

fof(c_0_1571,axiom,
    class_Ring__and__Field_Osemiring(tc_nat),
    c_0_774 ).

fof(c_0_1572,axiom,
    class_Ring__and__Field_Omult__mono(tc_nat),
    c_0_775 ).

fof(c_0_1573,axiom,
    class_Ring__and__Field_Omult__zero(tc_nat),
    c_0_776 ).

fof(c_0_1574,axiom,
    class_Ring__and__Field_Omult__mono1(tc_nat),
    c_0_777 ).

fof(c_0_1575,axiom,
    class_Ring__and__Field_Osemiring__1(tc_nat),
    c_0_778 ).

fof(c_0_1576,axiom,
    class_OrderedGroup_Ocomm__monoid__add(tc_nat),
    c_0_779 ).

fof(c_0_1577,axiom,
    class_Ring__and__Field_Ocomm__semiring(tc_nat),
    c_0_780 ).

fof(c_0_1578,axiom,
    class_OrderedGroup_Oab__semigroup__add(tc_nat),
    c_0_781 ).

fof(c_0_1579,axiom,
    class_OrderedGroup_Oab__semigroup__mult(tc_nat),
    c_0_782 ).

fof(c_0_1580,axiom,
    class_Ring__and__Field_Ocomm__semiring__1(tc_nat),
    c_0_783 ).

fof(c_0_1581,axiom,
    class_Ring__and__Field_Oordered__semidom(tc_nat),
    c_0_784 ).

fof(c_0_1582,axiom,
    class_Ring__and__Field_Ono__zero__divisors(tc_nat),
    c_0_785 ).

fof(c_0_1583,axiom,
    class_Ring__and__Field_Oordered__semiring(tc_nat),
    c_0_786 ).

fof(c_0_1584,axiom,
    class_Ring__and__Field_Opordered__semiring(tc_nat),
    c_0_787 ).

fof(c_0_1585,axiom,
    class_OrderedGroup_Ocancel__semigroup__add(tc_nat),
    c_0_788 ).

fof(c_0_1586,axiom,
    class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat),
    c_0_789 ).

fof(c_0_1587,axiom,
    class_OrderedGroup_Opordered__comm__monoid__add(tc_nat),
    c_0_790 ).

fof(c_0_1588,axiom,
    class_OrderedGroup_Opordered__ab__semigroup__add(tc_nat),
    c_0_791 ).

fof(c_0_1589,axiom,
    class_Ring__and__Field_Oordered__semiring__strict(tc_nat),
    c_0_792 ).

fof(c_0_1590,axiom,
    class_Ring__and__Field_Opordered__cancel__semiring(tc_nat),
    c_0_793 ).

fof(c_0_1591,axiom,
    class_Ring__and__Field_Oordered__comm__semiring__strict(tc_nat),
    c_0_794 ).

fof(c_0_1592,axiom,
    class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat),
    c_0_795 ).

fof(c_0_1593,axiom,
    class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat),
    c_0_796 ).

fof(c_0_1594,plain,
    ! [X8,X9,X10,X11,X12] :
      ( ~ class_RealVector_Oreal__normed__algebra(X12)
      | c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X9,X8,X12),c_HOL_Otimes__class_Otimes(X11,X10,X12),X12) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X9,X11,X12),c_HOL_Ominus__class_Ominus(X8,X10,X12),X12),c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X9,X11,X12),X10,X12),X12),c_HOL_Otimes__class_Otimes(X11,c_HOL_Ominus__class_Ominus(X8,X10,X12),X12),X12) ),
    inference(variable_rename,[status(thm)],[c_0_797]) ).

fof(c_0_1595,plain,
    ! [X21,X22,X23,X24,X25] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X25)
      | c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X24,X23,X25),c_HOL_Oplus__class_Oplus(X22,X21,X25),X25),X25),c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X24,X22,X25),X25),c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X23,X21,X25),X25),X25),X25) ),
    inference(variable_rename,[status(thm)],[c_0_798]) ).

fof(c_0_1596,plain,
    ! [X18,X19,X20,X21,X22] :
      ( c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X22,X18,tc_nat),X20,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X21,X18,tc_nat),X19,tc_nat),tc_nat)
      | ~ c_lessequals(X20,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X21,X22,tc_nat),X18,tc_nat),X19,tc_nat),tc_nat)
      | ~ c_lessequals(X22,X21,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_799]) ).

fof(c_0_1597,plain,
    ! [X18,X19,X20,X21,X22] :
      ( c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X22,X18,tc_nat),X20,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X21,X18,tc_nat),X19,tc_nat),tc_nat)
      | ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X22,X21,tc_nat),X18,tc_nat),X20,tc_nat),X19,tc_nat)
      | ~ c_lessequals(X21,X22,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_800]) ).

fof(c_0_1598,plain,
    ! [X18,X19,X20,X21,X22] :
      ( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X22,X18,tc_nat),X20,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X21,X18,tc_nat),X19,tc_nat),tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X22,X21,tc_nat),X18,tc_nat),X20,tc_nat),X19,tc_nat)
      | ~ c_lessequals(X21,X22,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_801]) ).

fof(c_0_1599,plain,
    ! [X18,X19,X20,X21,X22] :
      ( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X22,X18,tc_nat),X20,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X21,X18,tc_nat),X19,tc_nat),tc_nat)
      | ~ c_HOL_Oord__class_Oless(X20,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X21,X22,tc_nat),X18,tc_nat),X19,tc_nat),tc_nat)
      | ~ c_lessequals(X22,X21,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_802]) ).

fof(c_0_1600,plain,
    ! [X21,X22,X23,X24,X25,X26] :
      ( ~ class_Ring__and__Field_Opordered__ring(X26)
      | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X25,X21,X26),X23,X26),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X24,X21,X26),X22,X26),X26)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X25,X24,X26),X21,X26),X23,X26),X22,X26) ),
    inference(variable_rename,[status(thm)],[c_0_803]) ).

fof(c_0_1601,plain,
    ! [X21,X22,X23,X24,X25,X26] :
      ( ~ class_Ring__and__Field_Opordered__ring(X26)
      | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X25,X21,X26),X23,X26),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X24,X21,X26),X22,X26),X26)
      | ~ c_HOL_Oord__class_Oless(X23,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X24,X25,X26),X21,X26),X22,X26),X26) ),
    inference(variable_rename,[status(thm)],[c_0_804]) ).

fof(c_0_1602,plain,
    ! [X21,X22,X23,X24,X25,X26] :
      ( ~ class_Ring__and__Field_Opordered__ring(X26)
      | c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X25,X21,X26),X23,X26),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X24,X21,X26),X22,X26),X26)
      | ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X25,X24,X26),X21,X26),X23,X26),X22,X26) ),
    inference(variable_rename,[status(thm)],[c_0_805]) ).

fof(c_0_1603,plain,
    ! [X21,X22,X23,X24,X25,X26] :
      ( ~ class_Ring__and__Field_Opordered__ring(X26)
      | c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X25,X21,X26),X23,X26),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X24,X21,X26),X22,X26),X26)
      | ~ c_lessequals(X23,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X24,X25,X26),X21,X26),X22,X26),X26) ),
    inference(variable_rename,[status(thm)],[c_0_806]) ).

fof(c_0_1604,plain,
    ! [X18,X19,X20,X21,X22] :
      ( c_lessequals(X20,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X21,X22,tc_nat),X18,tc_nat),X19,tc_nat),tc_nat)
      | ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X22,X18,tc_nat),X20,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X21,X18,tc_nat),X19,tc_nat),tc_nat)
      | ~ c_lessequals(X22,X21,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_807]) ).

fof(c_0_1605,plain,
    ! [X18,X19,X20,X21,X22] :
      ( c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X22,X21,tc_nat),X18,tc_nat),X20,tc_nat),X19,tc_nat)
      | ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X22,X18,tc_nat),X20,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X21,X18,tc_nat),X19,tc_nat),tc_nat)
      | ~ c_lessequals(X21,X22,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_808]) ).

fof(c_0_1606,plain,
    ! [X18,X19,X20,X21,X22] :
      ( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X22,X21,tc_nat),X18,tc_nat),X20,tc_nat),X19,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X22,X18,tc_nat),X20,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X21,X18,tc_nat),X19,tc_nat),tc_nat)
      | ~ c_lessequals(X21,X22,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_809]) ).

fof(c_0_1607,plain,
    ! [X18,X19,X20,X21,X22] :
      ( c_HOL_Oord__class_Oless(X20,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X21,X22,tc_nat),X18,tc_nat),X19,tc_nat),tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X22,X18,tc_nat),X20,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X21,X18,tc_nat),X19,tc_nat),tc_nat)
      | ~ c_lessequals(X22,X21,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_810]) ).

fof(c_0_1608,plain,
    ! [X21,X22,X23,X24,X25,X26] :
      ( ~ class_Ring__and__Field_Opordered__ring(X26)
      | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X25,X24,X26),X21,X26),X23,X26),X22,X26)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X25,X21,X26),X23,X26),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X24,X21,X26),X22,X26),X26) ),
    inference(variable_rename,[status(thm)],[c_0_811]) ).

fof(c_0_1609,plain,
    ! [X21,X22,X23,X24,X25,X26] :
      ( ~ class_Ring__and__Field_Opordered__ring(X26)
      | c_HOL_Oord__class_Oless(X23,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X24,X25,X26),X21,X26),X22,X26),X26)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X25,X21,X26),X23,X26),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X24,X21,X26),X22,X26),X26) ),
    inference(variable_rename,[status(thm)],[c_0_812]) ).

fof(c_0_1610,plain,
    ! [X21,X22,X23,X24,X25,X26] :
      ( ~ class_Ring__and__Field_Opordered__ring(X26)
      | c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X25,X24,X26),X21,X26),X23,X26),X22,X26)
      | ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X25,X21,X26),X23,X26),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X24,X21,X26),X22,X26),X26) ),
    inference(variable_rename,[status(thm)],[c_0_813]) ).

fof(c_0_1611,plain,
    ! [X21,X22,X23,X24,X25,X26] :
      ( ~ class_Ring__and__Field_Opordered__ring(X26)
      | c_lessequals(X23,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X24,X25,X26),X21,X26),X22,X26),X26)
      | ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X25,X21,X26),X23,X26),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X24,X21,X26),X22,X26),X26) ),
    inference(variable_rename,[status(thm)],[c_0_814]) ).

fof(c_0_1612,plain,
    ! [X18,X19,X20,X21,X22] :
      ( c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X22,X18,tc_nat),X20,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X21,X18,tc_nat),X19,tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(X20,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X21,X22,tc_nat),X18,tc_nat),X19,tc_nat),tc_nat)
      | ~ c_lessequals(X22,X21,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_815]) ).

fof(c_0_1613,plain,
    ! [X18,X19,X20,X21,X22] :
      ( c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X22,X18,tc_nat),X20,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X21,X18,tc_nat),X19,tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X22,X21,tc_nat),X18,tc_nat),X20,tc_nat),X19,tc_nat)
      | ~ c_lessequals(X21,X22,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_816]) ).

fof(c_0_1614,plain,
    ! [X26,X27,X28,X29,X30,X31] :
      ( ~ class_Ring__and__Field_Odvd(X31)
      | ~ class_Ring__and__Field_Ocomm__ring(X31)
      | c_Ring__and__Field_Odvd__class_Odvd(X29,c_HOL_Oplus__class_Oplus(X26,X27,X31),X31)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X29,c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X26,c_HOL_Otimes__class_Otimes(X28,X30,X31),X31),X27,X31),X31)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X29,X30,X31) ),
    inference(variable_rename,[status(thm)],[c_0_817]) ).

fof(c_0_1615,plain,
    ! [X26,X27,X28,X29,X30,X31] :
      ( ~ class_Ring__and__Field_Odvd(X31)
      | ~ class_Ring__and__Field_Ocomm__ring(X31)
      | c_Ring__and__Field_Odvd__class_Odvd(X29,c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X26,c_HOL_Otimes__class_Otimes(X28,X30,X31),X31),X27,X31),X31)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X29,c_HOL_Oplus__class_Oplus(X26,X27,X31),X31)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X29,X30,X31) ),
    inference(variable_rename,[status(thm)],[c_0_818]) ).

fof(c_0_1616,plain,
    ! [X18,X19,X20,X21] :
      ( ~ c_lessequals(X21,X20,tc_nat)
      | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X21,X18,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X20,X21,tc_nat),X18,tc_nat),X19,tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X20,X18,tc_nat),X19,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_819]) ).

fof(c_0_1617,plain,
    ! [X18,X19,X20,X21] :
      ( ~ c_lessequals(X20,X21,tc_nat)
      | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X21,X18,tc_nat),X19,tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X20,X18,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X21,X20,tc_nat),X18,tc_nat),X19,tc_nat),tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_820]) ).

fof(c_0_1618,plain,
    ! [X4] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X4)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X4),c_HOL_Ozero__class_Ozero(X4),X4),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X4),c_HOL_Ozero__class_Ozero(X4),X4),X4),X4) ),
    inference(variable_rename,[status(thm)],[c_0_821]) ).

fof(c_0_1619,plain,
    ! [X20,X21,X22,X23,X24] :
      ( ~ class_Ring__and__Field_Oring(X24)
      | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X23,X20,X24),X21,X24) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X22,X20,X24),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X23,X22,X24),X20,X24),X21,X24),X24) ),
    inference(variable_rename,[status(thm)],[c_0_822]) ).

fof(c_0_1620,plain,
    ! [X21,X22,X23,X24,X25] :
      ( ~ class_Ring__and__Field_Oring(X25)
      | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X24,X21,X25),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X23,X24,X25),X21,X25),X22,X25),X25) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X23,X21,X25),X22,X25) ),
    inference(variable_rename,[status(thm)],[c_0_823]) ).

fof(c_0_1621,plain,
    ! [X24,X25,X26,X27] :
      ( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X27,c_Divides_Odiv__class_Omod(X25,X26,tc_nat),tc_nat),X24,tc_nat),c_HOL_Otimes__class_Otimes(X27,X26,tc_nat),tc_nat)
      | ~ c_HOL_Oord__class_Oless(X24,X27,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X26,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_824]) ).

fof(c_0_1622,plain,
    ! [X8,X9,X10] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X10)
      | X9 = c_HOL_Ozero__class_Ozero(X10)
      | ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X9,X9,X10),c_HOL_Otimes__class_Otimes(X8,X8,X10),X10),c_HOL_Ozero__class_Ozero(X10),X10) ),
    inference(variable_rename,[status(thm)],[c_0_825]) ).

fof(c_0_1623,plain,
    ! [X8,X9,X10] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X10)
      | X8 = c_HOL_Ozero__class_Ozero(X10)
      | ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X9,X9,X10),c_HOL_Otimes__class_Otimes(X8,X8,X10),X10),c_HOL_Ozero__class_Ozero(X10),X10) ),
    inference(variable_rename,[status(thm)],[c_0_826]) ).

fof(c_0_1624,plain,
    ! [X8,X9,X10] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X10)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X9,X9,X10),c_HOL_Otimes__class_Otimes(X8,X8,X10),X10),c_HOL_Ozero__class_Ozero(X10),X10) ),
    inference(variable_rename,[status(thm)],[c_0_827]) ).

fof(c_0_1625,plain,
    ! [X18,X19,X20,X21,X22] :
      ( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X22,X18,tc_nat),X20,tc_nat) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X21,X18,tc_nat),X19,tc_nat)
      | ~ c_lessequals(X21,X22,tc_nat)
      | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X22,X21,tc_nat),X18,tc_nat),X20,tc_nat) = X19 ),
    inference(variable_rename,[status(thm)],[c_0_828]) ).

fof(c_0_1626,plain,
    ! [X18,X19,X20,X21,X22] :
      ( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X22,X18,tc_nat),X20,tc_nat) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X21,X18,tc_nat),X19,tc_nat)
      | ~ c_lessequals(X22,X21,tc_nat)
      | X20 = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X21,X22,tc_nat),X18,tc_nat),X19,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_829]) ).

fof(c_0_1627,plain,
    ! [X21,X22,X23,X24,X25,X26] :
      ( ~ class_Ring__and__Field_Oring(X26)
      | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X25,X21,X26),X23,X26) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X24,X21,X26),X22,X26)
      | X23 = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X24,X25,X26),X21,X26),X22,X26) ),
    inference(variable_rename,[status(thm)],[c_0_830]) ).

fof(c_0_1628,plain,
    ! [X21,X22,X23,X24,X25,X26] :
      ( ~ class_Ring__and__Field_Oring(X26)
      | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X25,X21,X26),X23,X26) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X24,X21,X26),X22,X26)
      | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X25,X24,X26),X21,X26),X23,X26) = X22 ),
    inference(variable_rename,[status(thm)],[c_0_831]) ).

fof(c_0_1629,plain,
    ! [X20,X21,X22,X23,X24] :
      ( ~ class_Ring__and__Field_Osemiring(X24)
      | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X23,X20,X24),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X22,X20,X24),X21,X24),X24) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X23,X22,X24),X20,X24),X21,X24) ),
    inference(variable_rename,[status(thm)],[c_0_832]) ).

fof(c_0_1630,plain,
    ! [X32,X33,X34,X35,X36] :
      ( ~ class_Ring__and__Field_Oidom(X36)
      | ~ class_Int_Onumber__ring(X36)
      | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X35,X33,X36),c_HOL_Otimes__class_Otimes(X34,X32,X36),X36) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X35,X32,X36),c_HOL_Otimes__class_Otimes(X34,X33,X36),X36)
      | X33 = X32
      | X35 = X34 ),
    inference(variable_rename,[status(thm)],[c_0_833]) ).

fof(c_0_1631,plain,
    ! [X21,X22,X23,X24,X25] :
      ( ~ class_Ring__and__Field_Oidom(X25)
      | ~ class_Int_Onumber__ring(X25)
      | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X24,X22,X25),c_HOL_Otimes__class_Otimes(X23,X21,X25),X25) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X24,X21,X25),c_HOL_Otimes__class_Otimes(X23,X22,X25),X25)
      | X22 = X21
      | X24 = X23 ),
    inference(variable_rename,[status(thm)],[c_0_834]) ).

fof(c_0_1632,plain,
    ! [X18,X19,X20,X21] : c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X21,X18,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X20,X18,tc_nat),X19,tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X21,X20,tc_nat),X18,tc_nat),X19,tc_nat),
    inference(variable_rename,[status(thm)],[c_0_835]) ).

fof(c_0_1633,plain,
    ! [X32,X33,X34,X35] :
      ( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X35,X33,tc_nat),c_HOL_Otimes__class_Otimes(X34,X32,tc_nat),tc_nat) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X35,X32,tc_nat),c_HOL_Otimes__class_Otimes(X34,X33,tc_nat),tc_nat)
      | X33 = X32
      | X35 = X34 ),
    inference(variable_rename,[status(thm)],[c_0_836]) ).

fof(c_0_1634,plain,
    ! [X21,X22,X23,X24] :
      ( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X24,X22,tc_nat),c_HOL_Otimes__class_Otimes(X23,X21,tc_nat),tc_nat) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X24,X21,tc_nat),c_HOL_Otimes__class_Otimes(X23,X22,tc_nat),tc_nat)
      | X22 = X21
      | X24 = X23 ),
    inference(variable_rename,[status(thm)],[c_0_837]) ).

fof(c_0_1635,plain,
    ! [X23,X24,X25,X26] :
      ( ~ class_Ring__and__Field_Oordered__idom(X26)
      | c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X23,X25,X26),X26),X24,X26)
      | ~ c_HOL_Oord__class_Oless(X23,c_HOL_Oplus__class_Oplus(X25,X24,X26),X26)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X25,X24,X26),X23,X26) ),
    inference(variable_rename,[status(thm)],[c_0_838]) ).

fof(c_0_1636,plain,
    ! [X16,X17,X18,X19] :
      ( ~ class_Divides_Oring__div(X19)
      | c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X18,X17,X19),X16,X19) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(c_Divides_Odiv__class_Omod(X18,X16,X19),c_Divides_Odiv__class_Omod(X17,X16,X19),X19),X16,X19) ),
    inference(variable_rename,[status(thm)],[c_0_839]) ).

fof(c_0_1637,plain,
    ! [X16,X17,X18,X19] :
      ( ~ class_Divides_Osemiring__div(X19)
      | c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X18,X17,X19),X16,X19) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(X18,X16,X19),c_Divides_Odiv__class_Omod(X17,X16,X19),X19),X16,X19) ),
    inference(variable_rename,[status(thm)],[c_0_840]) ).

fof(c_0_1638,plain,
    ! [X16,X17,X18,X19] :
      ( ~ class_Divides_Osemiring__div(X19)
      | c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X18,X17,X19),X16,X19) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(X18,X16,X19),c_Divides_Odiv__class_Omod(X17,X16,X19),X19),X16,X19) ),
    inference(variable_rename,[status(thm)],[c_0_841]) ).

fof(c_0_1639,plain,
    ! [X4,X5,X6] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X6)
      | c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(c_HOL_Oabs__class_Oabs(X5,X6),c_HOL_Oabs__class_Oabs(X4,X6),X6),X6),c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X5,X4,X6),X6),X6) ),
    inference(variable_rename,[status(thm)],[c_0_842]) ).

fof(c_0_1640,plain,
    ! [X9,X10,X11] : c_Divides_Odiv__class_Omod(c_Suc(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X11,X9,tc_nat),X10,tc_nat)),X9,tc_nat) = c_Divides_Odiv__class_Omod(c_Suc(X10),X9,tc_nat),
    inference(variable_rename,[status(thm)],[c_0_843]) ).

fof(c_0_1641,plain,
    ! [X4] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X4)
      | c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X4),c_HOL_Ozero__class_Ozero(X4),X4),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X4),c_HOL_Ozero__class_Ozero(X4),X4),X4),c_HOL_Ozero__class_Ozero(X4),X4) ),
    inference(variable_rename,[status(thm)],[c_0_844]) ).

fof(c_0_1642,plain,
    ! [X29,X30,X31,X32,X33,X34] :
      ( ~ class_Divides_Oring__div(X34)
      | c_Divides_Odiv__class_Omod(X31,X29,X34) != c_Divides_Odiv__class_Omod(X30,X29,X34)
      | c_Divides_Odiv__class_Omod(X33,X29,X34) != c_Divides_Odiv__class_Omod(X32,X29,X34)
      | c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X33,X31,X34),X29,X34) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X32,X30,X34),X29,X34) ),
    inference(variable_rename,[status(thm)],[c_0_845]) ).

fof(c_0_1643,plain,
    ! [X29,X30,X31,X32,X33,X34] :
      ( ~ class_Divides_Osemiring__div(X34)
      | c_Divides_Odiv__class_Omod(X31,X29,X34) != c_Divides_Odiv__class_Omod(X30,X29,X34)
      | c_Divides_Odiv__class_Omod(X33,X29,X34) != c_Divides_Odiv__class_Omod(X32,X29,X34)
      | c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X33,X31,X34),X29,X34) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X32,X30,X34),X29,X34) ),
    inference(variable_rename,[status(thm)],[c_0_846]) ).

fof(c_0_1644,plain,
    ! [X29,X30,X31,X32,X33,X34] :
      ( ~ class_Divides_Osemiring__div(X34)
      | c_Divides_Odiv__class_Omod(X31,X29,X34) != c_Divides_Odiv__class_Omod(X30,X29,X34)
      | c_Divides_Odiv__class_Omod(X33,X29,X34) != c_Divides_Odiv__class_Omod(X32,X29,X34)
      | c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X33,X31,X34),X29,X34) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X32,X30,X34),X29,X34) ),
    inference(variable_rename,[status(thm)],[c_0_847]) ).

fof(c_0_1645,plain,
    ! [X15,X16,X17,X18,X19] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X19)
      | c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X18,X17,X19),c_HOL_Otimes__class_Otimes(X16,X15,X19),X19) = c_HOL_Otimes__class_Otimes(X16,c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X18,X17,X19),X15,X19),X19) ),
    inference(variable_rename,[status(thm)],[c_0_848]) ).

fof(c_0_1646,plain,
    ! [X15,X16,X17,X18,X19] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X19)
      | c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X18,X17,X19),c_HOL_Otimes__class_Otimes(X16,X15,X19),X19) = c_HOL_Otimes__class_Otimes(X18,c_HOL_Otimes__class_Otimes(X17,c_HOL_Otimes__class_Otimes(X16,X15,X19),X19),X19) ),
    inference(variable_rename,[status(thm)],[c_0_849]) ).

fof(c_0_1647,plain,
    ! [X21,X22,X23,X24,X25] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X25)
      | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X24,X22,X25),c_HOL_Otimes__class_Otimes(X23,X21,X25),X25)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X25),X22,X25)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X25),X24,X25)
      | ~ c_lessequals(X22,X21,X25)
      | ~ c_HOL_Oord__class_Oless(X24,X23,X25) ),
    inference(variable_rename,[status(thm)],[c_0_850]) ).

fof(c_0_1648,plain,
    ! [X21,X22,X23,X24,X25] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X25)
      | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X24,X22,X25),c_HOL_Otimes__class_Otimes(X23,X21,X25),X25)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X25),X22,X25)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X25),X24,X25)
      | ~ c_HOL_Oord__class_Oless(X22,X21,X25)
      | ~ c_lessequals(X24,X23,X25) ),
    inference(variable_rename,[status(thm)],[c_0_851]) ).

fof(c_0_1649,plain,
    ! [X21,X22,X23,X24,X25] :
      ( ~ class_Ring__and__Field_Opordered__semiring(X25)
      | c_lessequals(c_HOL_Otimes__class_Otimes(X24,X22,X25),c_HOL_Otimes__class_Otimes(X23,X21,X25),X25)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X25),X22,X25)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X25),X24,X25)
      | ~ c_lessequals(X22,X21,X25)
      | ~ c_lessequals(X24,X23,X25) ),
    inference(variable_rename,[status(thm)],[c_0_852]) ).

fof(c_0_1650,plain,
    ! [X21,X22,X23,X24,X25] :
      ( ~ class_Ring__and__Field_Opordered__semiring(X25)
      | c_lessequals(c_HOL_Otimes__class_Otimes(X24,X22,X25),c_HOL_Otimes__class_Otimes(X23,X21,X25),X25)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X25),X22,X25)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X25),X23,X25)
      | ~ c_lessequals(X22,X21,X25)
      | ~ c_lessequals(X24,X23,X25) ),
    inference(variable_rename,[status(thm)],[c_0_853]) ).

fof(c_0_1651,plain,
    ! [X21,X22,X23,X24,X25] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X25)
      | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X24,X22,X25),c_HOL_Otimes__class_Otimes(X23,X21,X25),X25)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X25),X22,X25)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X25),X24,X25)
      | ~ c_HOL_Oord__class_Oless(X22,X21,X25)
      | ~ c_HOL_Oord__class_Oless(X24,X23,X25) ),
    inference(variable_rename,[status(thm)],[c_0_854]) ).

fof(c_0_1652,plain,
    ! [X21,X22,X23,X24,X25] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X25)
      | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X24,X22,X25),c_HOL_Otimes__class_Otimes(X23,X21,X25),X25)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X25),X22,X25)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X25),X23,X25)
      | ~ c_HOL_Oord__class_Oless(X22,X21,X25)
      | ~ c_HOL_Oord__class_Oless(X24,X23,X25) ),
    inference(variable_rename,[status(thm)],[c_0_855]) ).

fof(c_0_1653,plain,
    ! [X21,X22,X23,X24,X25] :
      ( ~ class_Ring__and__Field_Oordered__idom(X25)
      | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(X24,X25),c_HOL_Oabs__class_Oabs(X23,X25),X25),c_HOL_Otimes__class_Otimes(X22,X21,X25),X25)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(X23,X25),X21,X25)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(X24,X25),X22,X25) ),
    inference(variable_rename,[status(thm)],[c_0_856]) ).

fof(c_0_1654,plain,
    ! [X23,X24,X25,X26] :
      ( ~ class_Ring__and__Field_Oordered__idom(X26)
      | c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X25,X24,X26),X23,X26)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X23,X25,X26),X26),X24,X26) ),
    inference(variable_rename,[status(thm)],[c_0_857]) ).

fof(c_0_1655,plain,
    ! [X23,X24,X25,X26] :
      ( ~ class_Ring__and__Field_Oordered__idom(X26)
      | c_HOL_Oord__class_Oless(X23,c_HOL_Oplus__class_Oplus(X25,X24,X26),X26)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X23,X25,X26),X26),X24,X26) ),
    inference(variable_rename,[status(thm)],[c_0_858]) ).

fof(c_0_1656,plain,
    ! [X9,X10,X11] :
      ( c_HOL_Oord__class_Oless(X10,X9,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X10,X11,tc_nat),c_HOL_Ominus__class_Ominus(X9,X11,tc_nat),tc_nat)
      | ~ c_lessequals(X11,X9,tc_nat)
      | ~ c_lessequals(X11,X10,tc_nat) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_859])])]) ).

fof(c_0_1657,plain,
    ! [X9,X10,X11] :
      ( c_lessequals(X10,X9,tc_nat)
      | ~ c_lessequals(c_HOL_Ominus__class_Ominus(X10,X11,tc_nat),c_HOL_Ominus__class_Ominus(X9,X11,tc_nat),tc_nat)
      | ~ c_lessequals(X11,X9,tc_nat)
      | ~ c_lessequals(X11,X10,tc_nat) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_860])])]) ).

fof(c_0_1658,plain,
    ! [X8,X9,X10] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X10)
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X10),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X9,X9,X10),c_HOL_Otimes__class_Otimes(X8,X8,X10),X10),X10)
      | X9 = c_HOL_Ozero__class_Ozero(X10) ),
    inference(variable_rename,[status(thm)],[c_0_861]) ).

fof(c_0_1659,plain,
    ! [X8,X9,X10] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X10)
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X10),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X9,X9,X10),c_HOL_Otimes__class_Otimes(X8,X8,X10),X10),X10)
      | X8 = c_HOL_Ozero__class_Ozero(X10) ),
    inference(variable_rename,[status(thm)],[c_0_862]) ).

fof(c_0_1660,plain,
    ! [X8,X9,X10] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X10)
      | c_lessequals(c_HOL_Ozero__class_Ozero(X10),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X9,X9,X10),c_HOL_Otimes__class_Otimes(X8,X8,X10),X10),X10) ),
    inference(variable_rename,[status(thm)],[c_0_863]) ).

fof(c_0_1661,plain,
    ! [X35,X36,X37,X38,X39] :
      ( c_HOL_Oplus__class_Oplus(X38,c_HOL_Otimes__class_Otimes(X39,X37,tc_nat),tc_nat) != c_HOL_Oplus__class_Oplus(X35,c_HOL_Otimes__class_Otimes(X39,X36,tc_nat),tc_nat)
      | c_Divides_Odiv__class_Omod(X38,X39,tc_nat) = c_Divides_Odiv__class_Omod(X35,X39,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_864]) ).

fof(c_0_1662,plain,
    ! [X16,X17,X18,X19] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X19)
      | c_HOL_Oord__class_Oless(X17,X18,X19)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X16,X18,X19),c_HOL_Otimes__class_Otimes(X16,X17,X19),X19)
      | ~ c_HOL_Oord__class_Oless(X16,c_HOL_Ozero__class_Ozero(X19),X19) ),
    inference(variable_rename,[status(thm)],[c_0_865]) ).

fof(c_0_1663,plain,
    ! [X16,X17,X18,X19] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X19)
      | c_HOL_Oord__class_Oless(X18,X17,X19)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X16,X18,X19),c_HOL_Otimes__class_Otimes(X16,X17,X19),X19)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X19),X16,X19) ),
    inference(variable_rename,[status(thm)],[c_0_866]) ).

fof(c_0_1664,plain,
    ! [X16,X17,X18,X19] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X19)
      | c_lessequals(X17,X18,X19)
      | ~ c_lessequals(c_HOL_Otimes__class_Otimes(X16,X18,X19),c_HOL_Otimes__class_Otimes(X16,X17,X19),X19)
      | ~ c_HOL_Oord__class_Oless(X16,c_HOL_Ozero__class_Ozero(X19),X19) ),
    inference(variable_rename,[status(thm)],[c_0_867]) ).

fof(c_0_1665,plain,
    ! [X16,X17,X18,X19] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X19)
      | c_lessequals(X18,X17,X19)
      | ~ c_lessequals(c_HOL_Otimes__class_Otimes(X16,X18,X19),c_HOL_Otimes__class_Otimes(X16,X17,X19),X19)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X19),X16,X19) ),
    inference(variable_rename,[status(thm)],[c_0_868]) ).

fof(c_0_1666,plain,
    ! [X16,X17,X18,X19] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X19)
      | c_lessequals(X18,X17,X19)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X19),X16,X19)
      | ~ c_lessequals(c_HOL_Otimes__class_Otimes(X16,X18,X19),c_HOL_Otimes__class_Otimes(X16,X17,X19),X19) ),
    inference(variable_rename,[status(thm)],[c_0_869]) ).

fof(c_0_1667,plain,
    ! [X16,X17,X18,X19] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X19)
      | c_lessequals(X18,X17,X19)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X19),X16,X19)
      | ~ c_lessequals(c_HOL_Otimes__class_Otimes(X18,X16,X19),c_HOL_Otimes__class_Otimes(X17,X16,X19),X19) ),
    inference(variable_rename,[status(thm)],[c_0_870]) ).

fof(c_0_1668,plain,
    ! [X16,X17,X18,X19] :
      ( ~ class_Ring__and__Field_Oordered__semiring(X19)
      | c_HOL_Oord__class_Oless(X18,X17,X19)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X19),X16,X19)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X16,X18,X19),c_HOL_Otimes__class_Otimes(X16,X17,X19),X19) ),
    inference(variable_rename,[status(thm)],[c_0_871]) ).

fof(c_0_1669,plain,
    ! [X16,X17,X18,X19] :
      ( ~ class_Ring__and__Field_Oordered__semiring(X19)
      | c_HOL_Oord__class_Oless(X18,X17,X19)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X19),X16,X19)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X18,X16,X19),c_HOL_Otimes__class_Otimes(X17,X16,X19),X19) ),
    inference(variable_rename,[status(thm)],[c_0_872]) ).

fof(c_0_1670,plain,
    ! [X16,X17,X18,X19] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X19)
      | c_HOL_Oord__class_Oless(X18,X17,X19)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X19),X16,X19)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X16,X18,X19),c_HOL_Otimes__class_Otimes(X16,X17,X19),X19) ),
    inference(variable_rename,[status(thm)],[c_0_873]) ).

fof(c_0_1671,plain,
    ! [X16,X17,X18,X19] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X19)
      | c_HOL_Oord__class_Oless(X18,X17,X19)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X19),X16,X19)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X18,X16,X19),c_HOL_Otimes__class_Otimes(X17,X16,X19),X19) ),
    inference(variable_rename,[status(thm)],[c_0_874]) ).

fof(c_0_1672,plain,
    ! [X9,X10,X11] :
      ( c_Ring__and__Field_Odvd__class_Odvd(X10,X9,tc_nat)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X11,X10,tc_nat),c_HOL_Otimes__class_Otimes(X11,X9,tc_nat),tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X11,tc_nat) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_875])])]) ).

fof(c_0_1673,plain,
    ! [X9,X10,X11] :
      ( c_Ring__and__Field_Odvd__class_Odvd(X10,X9,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X11,tc_nat)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X11,X10,tc_nat),c_HOL_Otimes__class_Otimes(X11,X9,tc_nat),tc_nat) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_876])])]) ).

fof(c_0_1674,plain,
    ! [X9,X10,X11] :
      ( c_HOL_Oord__class_Oless(X10,X9,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X11,X10,tc_nat),c_HOL_Otimes__class_Otimes(X11,X9,tc_nat),tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X11,tc_nat) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_877])])]) ).

fof(c_0_1675,plain,
    ! [X9,X10,X11] :
      ( c_lessequals(X10,X9,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X11,tc_nat)
      | ~ c_lessequals(c_HOL_Otimes__class_Otimes(X10,X11,tc_nat),c_HOL_Otimes__class_Otimes(X9,X11,tc_nat),tc_nat) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_878])])]) ).

fof(c_0_1676,plain,
    ! [X9,X10,X11] :
      ( c_lessequals(X10,X9,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X11,tc_nat)
      | ~ c_lessequals(c_HOL_Otimes__class_Otimes(X11,X10,tc_nat),c_HOL_Otimes__class_Otimes(X11,X9,tc_nat),tc_nat) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_879])])]) ).

fof(c_0_1677,plain,
    ! [X9,X10,X11] :
      ( c_lessequals(X10,X9,tc_nat)
      | ~ c_lessequals(c_HOL_Otimes__class_Otimes(X11,X10,tc_nat),c_HOL_Otimes__class_Otimes(X11,X9,tc_nat),tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X11,tc_nat) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_880])])]) ).

fof(c_0_1678,plain,
    ! [X16,X17,X18,X19] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X19)
      | c_HOL_Oord__class_Oless(X16,c_HOL_Ozero__class_Ozero(X19),X19)
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X19),X16,X19)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X18,X16,X19),c_HOL_Otimes__class_Otimes(X17,X16,X19),X19) ),
    inference(variable_rename,[status(thm)],[c_0_881]) ).

fof(c_0_1679,plain,
    ! [X16,X17,X18,X19] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X19)
      | c_HOL_Oord__class_Oless(X16,c_HOL_Ozero__class_Ozero(X19),X19)
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X19),X16,X19)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X16,X18,X19),c_HOL_Otimes__class_Otimes(X16,X17,X19),X19) ),
    inference(variable_rename,[status(thm)],[c_0_882]) ).

fof(c_0_1680,plain,
    ! [X21,X22,X23,X24] :
      ( ~ class_Ring__and__Field_Oidom(X24)
      | ~ class_Int_Onumber__ring(X24)
      | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X21,X23,X24),c_HOL_Otimes__class_Otimes(X21,X22,X24),X24) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X21,X22,X24),c_HOL_Otimes__class_Otimes(X21,X23,X24),X24) ),
    inference(variable_rename,[status(thm)],[c_0_883]) ).

fof(c_0_1681,plain,
    ! [X17,X18,X19,X20] :
      ( ~ class_Ring__and__Field_Oidom(X20)
      | ~ class_Int_Onumber__ring(X20)
      | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X19,X18,X20),c_HOL_Otimes__class_Otimes(X19,X17,X20),X20) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X19,X17,X20),c_HOL_Otimes__class_Otimes(X19,X18,X20),X20) ),
    inference(variable_rename,[status(thm)],[c_0_884]) ).

fof(c_0_1682,plain,
    ! [X19] : ~ c_Parity_Oeven__odd__class_Oeven(c_Suc(c_HOL_Otimes__class_Otimes(c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),X19,tc_nat)),tc_nat),
    inference(variable_rename,[status(thm)],[c_0_885]) ).

fof(c_0_1683,plain,
    ! [X16,X17,X18,X19] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X19)
      | c_HOL_Oord__class_Oless(X16,c_HOL_Ozero__class_Ozero(X19),X19)
      | c_HOL_Oord__class_Oless(X18,X17,X19)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X18,X16,X19),c_HOL_Otimes__class_Otimes(X17,X16,X19),X19) ),
    inference(variable_rename,[status(thm)],[c_0_886]) ).

fof(c_0_1684,plain,
    ! [X16,X17,X18,X19] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X19)
      | c_HOL_Oord__class_Oless(X17,X18,X19)
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X19),X16,X19)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X18,X16,X19),c_HOL_Otimes__class_Otimes(X17,X16,X19),X19) ),
    inference(variable_rename,[status(thm)],[c_0_887]) ).

fof(c_0_1685,plain,
    ! [X16,X17,X18,X19] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X19)
      | c_HOL_Oord__class_Oless(X16,c_HOL_Ozero__class_Ozero(X19),X19)
      | c_HOL_Oord__class_Oless(X18,X17,X19)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X16,X18,X19),c_HOL_Otimes__class_Otimes(X16,X17,X19),X19) ),
    inference(variable_rename,[status(thm)],[c_0_888]) ).

fof(c_0_1686,plain,
    ! [X16,X17,X18,X19] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X19)
      | c_HOL_Oord__class_Oless(X17,X18,X19)
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X19),X16,X19)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X16,X18,X19),c_HOL_Otimes__class_Otimes(X16,X17,X19),X19) ),
    inference(variable_rename,[status(thm)],[c_0_889]) ).

fof(c_0_1687,plain,
    ! [X21,X22,X23,X24,X25] :
      ( ~ class_OrderedGroup_Oab__group__add(X25)
      | c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X24,X22,X25),c_HOL_Oplus__class_Oplus(X23,X21,X25),X25) = c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X24,X23,X25),c_HOL_Ominus__class_Ominus(X22,X21,X25),X25) ),
    inference(variable_rename,[status(thm)],[c_0_890]) ).

fof(c_0_1688,plain,
    ! [X16,X17,X18,X19] :
      ( ~ class_Divides_Oring__div(X19)
      | c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X18,X17,X19),X16,X19) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(c_Divides_Odiv__class_Omod(X18,X16,X19),X17,X19),X16,X19) ),
    inference(variable_rename,[status(thm)],[c_0_891]) ).

fof(c_0_1689,plain,
    ! [X16,X17,X18,X19] :
      ( ~ class_Divides_Oring__div(X19)
      | c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X18,X17,X19),X16,X19) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X18,c_Divides_Odiv__class_Omod(X17,X16,X19),X19),X16,X19) ),
    inference(variable_rename,[status(thm)],[c_0_892]) ).

fof(c_0_1690,plain,
    ! [X16,X17,X18,X19] :
      ( ~ class_Divides_Osemiring__div(X19)
      | c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X18,X17,X19),X16,X19) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(X18,X16,X19),X17,X19),X16,X19) ),
    inference(variable_rename,[status(thm)],[c_0_893]) ).

fof(c_0_1691,plain,
    ! [X16,X17,X18,X19] :
      ( ~ class_Divides_Osemiring__div(X19)
      | c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X18,X17,X19),X16,X19) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X18,c_Divides_Odiv__class_Omod(X17,X16,X19),X19),X16,X19) ),
    inference(variable_rename,[status(thm)],[c_0_894]) ).

fof(c_0_1692,plain,
    ! [X16,X17,X18,X19] :
      ( ~ class_Divides_Osemiring__div(X19)
      | c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X18,X17,X19),X16,X19) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(X18,X16,X19),X17,X19),X16,X19) ),
    inference(variable_rename,[status(thm)],[c_0_895]) ).

fof(c_0_1693,plain,
    ! [X16,X17,X18,X19] :
      ( ~ class_Divides_Osemiring__div(X19)
      | c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X18,X17,X19),X16,X19) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X18,c_Divides_Odiv__class_Omod(X17,X16,X19),X19),X16,X19) ),
    inference(variable_rename,[status(thm)],[c_0_896]) ).

fof(c_0_1694,plain,
    ! [X21,X22,X23,X24,X25] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X25)
      | c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X24,X23,X25),c_HOL_Oplus__class_Oplus(X22,X21,X25),X25) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X24,X22,X25),c_HOL_Oplus__class_Oplus(X23,X21,X25),X25) ),
    inference(variable_rename,[status(thm)],[c_0_897]) ).

fof(c_0_1695,plain,
    ! [X16,X17,X18,X19] :
      ( ~ class_Divides_Osemiring__div(X19)
      | c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(X18,X16,X19),X17,X19),X16,X19) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X18,X17,X19),X16,X19) ),
    inference(variable_rename,[status(thm)],[c_0_898]) ).

fof(c_0_1696,plain,
    ! [X16,X17,X18,X19] :
      ( ~ class_Divides_Osemiring__div(X19)
      | c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X18,c_Divides_Odiv__class_Omod(X17,X16,X19),X19),X16,X19) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X18,X17,X19),X16,X19) ),
    inference(variable_rename,[status(thm)],[c_0_899]) ).

fof(c_0_1697,plain,
    ! [X16,X17,X18,X19] :
      ( ~ class_Divides_Osemiring__div(X19)
      | c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(X18,X16,X19),X17,X19),X16,X19) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X18,X17,X19),X16,X19) ),
    inference(variable_rename,[status(thm)],[c_0_900]) ).

fof(c_0_1698,plain,
    ! [X15,X16,X17,X18,X19] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X19)
      | c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X18,X17,X19),c_HOL_Otimes__class_Otimes(X16,X15,X19),X19) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X18,X16,X19),c_HOL_Otimes__class_Otimes(X17,X15,X19),X19) ),
    inference(variable_rename,[status(thm)],[c_0_901]) ).

fof(c_0_1699,plain,
    ! [X16,X17,X18,X19] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X19)
      | c_HOL_Oord__class_Oless(X17,X18,X19)
      | c_HOL_Oord__class_Oless(X18,X17,X19)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X16,X18,X19),c_HOL_Otimes__class_Otimes(X16,X17,X19),X19) ),
    inference(variable_rename,[status(thm)],[c_0_902]) ).

fof(c_0_1700,plain,
    ! [X16,X17,X18,X19] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X19)
      | c_HOL_Oord__class_Oless(X17,X18,X19)
      | c_HOL_Oord__class_Oless(X18,X17,X19)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X18,X16,X19),c_HOL_Otimes__class_Otimes(X17,X16,X19),X19) ),
    inference(variable_rename,[status(thm)],[c_0_903]) ).

fof(c_0_1701,plain,
    ! [X23,X24,X25,X26,X27] :
      ( ~ class_Ring__and__Field_Oidom(X27)
      | ~ class_Int_Onumber__ring(X27)
      | c_HOL_Oplus__class_Oplus(X23,c_HOL_Otimes__class_Otimes(X24,X26,X27),X27) != c_HOL_Oplus__class_Oplus(X23,c_HOL_Otimes__class_Otimes(X24,X25,X27),X27)
      | X26 = X25
      | X24 = c_HOL_Ozero__class_Ozero(X27) ),
    inference(variable_rename,[status(thm)],[c_0_904]) ).

fof(c_0_1702,plain,
    ! [X21,X22,X23] : c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X21,X23,tc_nat),c_HOL_Otimes__class_Otimes(X21,X22,tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X21,X22,tc_nat),c_HOL_Otimes__class_Otimes(X21,X23,tc_nat),tc_nat),
    inference(variable_rename,[status(thm)],[c_0_905]) ).

fof(c_0_1703,plain,
    ! [X17,X18,X19] : c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X19,X18,tc_nat),c_HOL_Otimes__class_Otimes(X19,X17,tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X19,X17,tc_nat),c_HOL_Otimes__class_Otimes(X19,X18,tc_nat),tc_nat),
    inference(variable_rename,[status(thm)],[c_0_906]) ).

fof(c_0_1704,plain,
    ! [X10,X11,X12] :
      ( c_HOL_Ominus__class_Ominus(c_Suc(c_HOL_Ominus__class_Ominus(X12,X11,tc_nat)),X10,tc_nat) = c_HOL_Ominus__class_Ominus(c_Suc(X12),c_HOL_Oplus__class_Oplus(X11,X10,tc_nat),tc_nat)
      | ~ c_lessequals(X11,X12,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_907]) ).

fof(c_0_1705,plain,
    ! [X10,X11,X12] :
      ( c_HOL_Ominus__class_Ominus(X10,c_Suc(c_HOL_Ominus__class_Ominus(X12,X11,tc_nat)),tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X10,X11,tc_nat),c_Suc(X12),tc_nat)
      | ~ c_lessequals(X11,X12,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_908]) ).

fof(c_0_1706,plain,
    ! [X9,X10,X11] :
      ( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X10,X11,tc_nat),c_HOL_Ominus__class_Ominus(X9,X11,tc_nat),tc_nat)
      | ~ c_HOL_Oord__class_Oless(X10,X9,tc_nat)
      | ~ c_lessequals(X11,X9,tc_nat)
      | ~ c_lessequals(X11,X10,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_909]) ).

fof(c_0_1707,plain,
    ! [X9,X10,X11] :
      ( c_lessequals(c_HOL_Ominus__class_Ominus(X10,X11,tc_nat),c_HOL_Ominus__class_Ominus(X9,X11,tc_nat),tc_nat)
      | ~ c_lessequals(X10,X9,tc_nat)
      | ~ c_lessequals(X11,X9,tc_nat)
      | ~ c_lessequals(X11,X10,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_910]) ).

fof(c_0_1708,plain,
    ! [X4,X5,X6] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X6)
      | c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X5,X4,X6),X6),c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(X5,X6),c_HOL_Oabs__class_Oabs(X4,X6),X6),X6) ),
    inference(variable_rename,[status(thm)],[c_0_911]) ).

fof(c_0_1709,plain,
    ! [X4,X5,X6] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X6)
      | c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Oplus__class_Oplus(X5,X4,X6),X6),c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(X5,X6),c_HOL_Oabs__class_Oabs(X4,X6),X6),X6) ),
    inference(variable_rename,[status(thm)],[c_0_912]) ).

fof(c_0_1710,plain,
    ! [X4,X5,X6] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X6)
      | c_lessequals(c_HOL_Ominus__class_Ominus(c_HOL_Oabs__class_Oabs(X5,X6),c_HOL_Oabs__class_Oabs(X4,X6),X6),c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X5,X4,X6),X6),X6) ),
    inference(variable_rename,[status(thm)],[c_0_913]) ).

fof(c_0_1711,plain,
    ! [X4,X5,X6] :
      ( ~ class_Ring__and__Field_Olordered__ring(X6)
      | c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(X5,X4,X6),X6),c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(X5,X6),c_HOL_Oabs__class_Oabs(X4,X6),X6),X6) ),
    inference(variable_rename,[status(thm)],[c_0_914]) ).

fof(c_0_1712,plain,
    ! [X21,X22,X23,X24,X25] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add(X25)
      | c_lessequals(X24,c_HOL_Oplus__class_Oplus(X23,X21,X25),X25)
      | ~ c_lessequals(X22,X21,X25)
      | ~ c_lessequals(X24,c_HOL_Oplus__class_Oplus(X23,X22,X25),X25) ),
    inference(variable_rename,[status(thm)],[c_0_915]) ).

fof(c_0_1713,plain,
    ! [X9,X10,X11] :
      ( c_lessequals(X10,X9,tc_nat)
      | ~ c_lessequals(c_HOL_Otimes__class_Otimes(c_Suc(X11),X10,tc_nat),c_HOL_Otimes__class_Otimes(c_Suc(X11),X9,tc_nat),tc_nat) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_916])])]) ).

fof(c_0_1714,plain,
    ! [X9,X10,X11] :
      ( c_HOL_Oord__class_Oless(X10,X9,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Suc(X11),X10,tc_nat),c_HOL_Otimes__class_Otimes(c_Suc(X11),X9,tc_nat),tc_nat) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_917])])]) ).

fof(c_0_1715,plain,
    ! [X23,X24,X25,X26] :
      ( c_HOL_Oplus__class_Oplus(X23,c_HOL_Otimes__class_Otimes(X24,X26,tc_nat),tc_nat) != c_HOL_Oplus__class_Oplus(X23,c_HOL_Otimes__class_Otimes(X24,X25,tc_nat),tc_nat)
      | X26 = X25
      | X24 = c_HOL_Ozero__class_Ozero(tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_918]) ).

fof(c_0_1716,plain,
    ! [X16,X17,X18,X19] :
      ( ~ class_Ring__and__Field_Oidom(X19)
      | c_Ring__and__Field_Odvd__class_Odvd(X18,X17,X19)
      | X16 = c_HOL_Ozero__class_Ozero(X19)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X16,X18,X19),c_HOL_Otimes__class_Otimes(X16,X17,X19),X19) ),
    inference(variable_rename,[status(thm)],[c_0_919]) ).

fof(c_0_1717,plain,
    ! [X16,X17,X18,X19] :
      ( ~ class_Ring__and__Field_Oidom(X19)
      | c_Ring__and__Field_Odvd__class_Odvd(X18,X17,X19)
      | X16 = c_HOL_Ozero__class_Ozero(X19)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X18,X16,X19),c_HOL_Otimes__class_Otimes(X17,X16,X19),X19) ),
    inference(variable_rename,[status(thm)],[c_0_920]) ).

fof(c_0_1718,plain,
    ! [X11,X12,X13] :
      ( c_lessequals(X13,c_HOL_Ominus__class_Ominus(X12,X11,tc_nat),tc_nat)
      | ~ c_lessequals(c_HOL_Oplus__class_Oplus(X13,X11,tc_nat),X12,tc_nat)
      | ~ c_lessequals(X11,X12,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_921]) ).

fof(c_0_1719,plain,
    ! [X11,X12,X13] :
      ( c_lessequals(c_HOL_Oplus__class_Oplus(X13,X11,tc_nat),X12,tc_nat)
      | ~ c_lessequals(X13,c_HOL_Ominus__class_Ominus(X12,X11,tc_nat),tc_nat)
      | ~ c_lessequals(X11,X12,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_922]) ).

fof(c_0_1720,plain,
    ! [X16,X17,X18,X19] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X19)
      | c_HOL_Oord__class_Oless(X18,X17,X19)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X16,X18,X19),c_HOL_Oplus__class_Oplus(X16,X17,X19),X19) ),
    inference(variable_rename,[status(thm)],[c_0_923]) ).

fof(c_0_1721,plain,
    ! [X16,X17,X18,X19] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X19)
      | c_HOL_Oord__class_Oless(X18,X17,X19)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X18,X16,X19),c_HOL_Oplus__class_Oplus(X17,X16,X19),X19) ),
    inference(variable_rename,[status(thm)],[c_0_924]) ).

fof(c_0_1722,plain,
    ! [X16,X17,X18,X19] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X19)
      | c_lessequals(X18,X17,X19)
      | ~ c_lessequals(c_HOL_Oplus__class_Oplus(X18,X16,X19),c_HOL_Oplus__class_Oplus(X17,X16,X19),X19) ),
    inference(variable_rename,[status(thm)],[c_0_925]) ).

fof(c_0_1723,plain,
    ! [X16,X17,X18,X19] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X19)
      | c_lessequals(X18,X17,X19)
      | ~ c_lessequals(c_HOL_Oplus__class_Oplus(X16,X18,X19),c_HOL_Oplus__class_Oplus(X16,X17,X19),X19) ),
    inference(variable_rename,[status(thm)],[c_0_926]) ).

fof(c_0_1724,plain,
    ! [X9,X10,X11] :
      ( c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X10,X11,tc_nat),c_HOL_Ominus__class_Ominus(X9,X11,tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(X10,X9,tc_nat)
      | ~ c_lessequals(X11,X9,tc_nat)
      | ~ c_lessequals(X11,X10,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_927]) ).

fof(c_0_1725,plain,
    ! [X16,X17,X18,X19] :
      ( ~ class_OrderedGroup_Olordered__ab__group__add__abs(X19)
      | c_lessequals(X18,c_HOL_Oplus__class_Oplus(X16,c_HOL_Oabs__class_Oabs(X17,X19),X19),X19)
      | ~ c_lessequals(c_HOL_Oplus__class_Oplus(X18,X17,X19),X16,X19) ),
    inference(variable_rename,[status(thm)],[c_0_928]) ).

fof(c_0_1726,plain,
    ! [X9,X10,X11] :
      ( c_Ring__and__Field_Odvd__class_Odvd(X11,X10,tc_nat)
      | ~ c_lessequals(X9,X10,tc_nat)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X11,X9,tc_nat)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X11,c_HOL_Ominus__class_Ominus(X10,X9,tc_nat),tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_929]) ).

fof(c_0_1727,plain,
    ! [X9,X10,X11] :
      ( c_Ring__and__Field_Odvd__class_Odvd(X11,X9,tc_nat)
      | ~ c_lessequals(X9,X10,tc_nat)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X11,X10,tc_nat)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X11,c_HOL_Ominus__class_Ominus(X10,X9,tc_nat),tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_930]) ).

fof(c_0_1728,plain,
    ! [X9,X10,X11] :
      ( c_Ring__and__Field_Odvd__class_Odvd(X10,X9,tc_nat)
      | X11 = c_HOL_Ozero__class_Ozero(tc_nat)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X11,X10,tc_nat),c_HOL_Otimes__class_Otimes(X11,X9,tc_nat),tc_nat) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_931])])]) ).

fof(c_0_1729,plain,
    ! [X9,X10,X11] :
      ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X11,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X10,X11,tc_nat),c_HOL_Otimes__class_Otimes(X9,X11,tc_nat),tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_932]) ).

fof(c_0_1730,plain,
    ! [X9,X10,X11] :
      ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X11,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X11,X10,tc_nat),c_HOL_Otimes__class_Otimes(X11,X9,tc_nat),tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_933]) ).

fof(c_0_1731,plain,
    ! [X9,X10,X11] :
      ( c_HOL_Oord__class_Oless(X10,X9,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X10,X11,tc_nat),c_HOL_Otimes__class_Otimes(X9,X11,tc_nat),tc_nat) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_934])])]) ).

fof(c_0_1732,plain,
    ! [X9,X10,X11] :
      ( c_HOL_Oord__class_Oless(X10,X9,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X11,X10,tc_nat),c_HOL_Otimes__class_Otimes(X11,X9,tc_nat),tc_nat) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_935])])]) ).

fof(c_0_1733,plain,
    ! [X9,X10,X11] :
      ( c_HOL_Oord__class_Oless(X10,X9,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X11,X10,tc_nat),c_HOL_Oplus__class_Oplus(X11,X9,tc_nat),tc_nat) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_936])])]) ).

fof(c_0_1734,plain,
    ! [X9,X10,X11] :
      ( c_lessequals(X10,X9,tc_nat)
      | ~ c_lessequals(c_HOL_Oplus__class_Oplus(X11,X10,tc_nat),c_HOL_Oplus__class_Oplus(X11,X9,tc_nat),tc_nat) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_937])])]) ).

fof(c_0_1735,plain,
    ! [X16,X17,X18,X19] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X19)
      | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X16,X18,X19),c_HOL_Otimes__class_Otimes(X16,X17,X19),X19)
      | ~ c_HOL_Oord__class_Oless(X17,X18,X19)
      | ~ c_HOL_Oord__class_Oless(X16,c_HOL_Ozero__class_Ozero(X19),X19) ),
    inference(variable_rename,[status(thm)],[c_0_938]) ).

fof(c_0_1736,plain,
    ! [X16,X17,X18,X19] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X19)
      | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X16,X18,X19),c_HOL_Otimes__class_Otimes(X16,X17,X19),X19)
      | ~ c_HOL_Oord__class_Oless(X18,X17,X19)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X19),X16,X19) ),
    inference(variable_rename,[status(thm)],[c_0_939]) ).

fof(c_0_1737,plain,
    ! [X16,X17,X18,X19] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X19)
      | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X16,X18,X19),c_HOL_Otimes__class_Otimes(X16,X17,X19),X19)
      | ~ c_HOL_Oord__class_Oless(X16,c_HOL_Ozero__class_Ozero(X19),X19)
      | ~ c_HOL_Oord__class_Oless(X17,X18,X19) ),
    inference(variable_rename,[status(thm)],[c_0_940]) ).

fof(c_0_1738,plain,
    ! [X16,X17,X18,X19] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X19)
      | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X16,X18,X19),c_HOL_Otimes__class_Otimes(X16,X17,X19),X19)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X19),X16,X19)
      | ~ c_HOL_Oord__class_Oless(X18,X17,X19) ),
    inference(variable_rename,[status(thm)],[c_0_941]) ).

fof(c_0_1739,plain,
    ! [X16,X17,X18,X19] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X19)
      | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X16,X18,X19),c_HOL_Otimes__class_Otimes(X16,X17,X19),X19)
      | ~ c_HOL_Oord__class_Oless(X18,X17,X19)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X19),X16,X19) ),
    inference(variable_rename,[status(thm)],[c_0_942]) ).

fof(c_0_1740,plain,
    ! [X16,X17,X18,X19] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X19)
      | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X16,X18,X19),c_HOL_Otimes__class_Otimes(X16,X17,X19),X19)
      | ~ c_HOL_Oord__class_Oless(X17,X18,X19)
      | ~ c_HOL_Oord__class_Oless(X16,c_HOL_Ozero__class_Ozero(X19),X19) ),
    inference(variable_rename,[status(thm)],[c_0_943]) ).

fof(c_0_1741,plain,
    ! [X16,X17,X18,X19] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X19)
      | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X18,X16,X19),c_HOL_Otimes__class_Otimes(X17,X16,X19),X19)
      | ~ c_HOL_Oord__class_Oless(X16,c_HOL_Ozero__class_Ozero(X19),X19)
      | ~ c_HOL_Oord__class_Oless(X17,X18,X19) ),
    inference(variable_rename,[status(thm)],[c_0_944]) ).

fof(c_0_1742,plain,
    ! [X16,X17,X18,X19] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X19)
      | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X18,X16,X19),c_HOL_Otimes__class_Otimes(X17,X16,X19),X19)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X19),X16,X19)
      | ~ c_HOL_Oord__class_Oless(X18,X17,X19) ),
    inference(variable_rename,[status(thm)],[c_0_945]) ).

fof(c_0_1743,plain,
    ! [X16,X17,X18,X19] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X19)
      | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X18,X16,X19),c_HOL_Otimes__class_Otimes(X17,X16,X19),X19)
      | ~ c_HOL_Oord__class_Oless(X18,X17,X19)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X19),X16,X19) ),
    inference(variable_rename,[status(thm)],[c_0_946]) ).

fof(c_0_1744,plain,
    ! [X16,X17,X18,X19] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X19)
      | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X18,X16,X19),c_HOL_Otimes__class_Otimes(X17,X16,X19),X19)
      | ~ c_HOL_Oord__class_Oless(X17,X18,X19)
      | ~ c_HOL_Oord__class_Oless(X16,c_HOL_Ozero__class_Ozero(X19),X19) ),
    inference(variable_rename,[status(thm)],[c_0_947]) ).

fof(c_0_1745,plain,
    ! [X16,X17,X18,X19] :
      ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X19)
      | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X16,X18,X19),c_HOL_Otimes__class_Otimes(X16,X17,X19),X19)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X19),X16,X19)
      | ~ c_HOL_Oord__class_Oless(X18,X17,X19) ),
    inference(variable_rename,[status(thm)],[c_0_948]) ).

fof(c_0_1746,plain,
    ! [X16,X17,X18,X19] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X19)
      | c_lessequals(c_HOL_Otimes__class_Otimes(X16,X18,X19),c_HOL_Otimes__class_Otimes(X16,X17,X19),X19)
      | ~ c_lessequals(X17,X18,X19)
      | ~ c_HOL_Oord__class_Oless(X16,c_HOL_Ozero__class_Ozero(X19),X19) ),
    inference(variable_rename,[status(thm)],[c_0_949]) ).

fof(c_0_1747,plain,
    ! [X16,X17,X18,X19] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X19)
      | c_lessequals(c_HOL_Otimes__class_Otimes(X16,X18,X19),c_HOL_Otimes__class_Otimes(X16,X17,X19),X19)
      | ~ c_lessequals(X18,X17,X19)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X19),X16,X19) ),
    inference(variable_rename,[status(thm)],[c_0_950]) ).

fof(c_0_1748,plain,
    ! [X16,X17,X18,X19] :
      ( ~ class_Ring__and__Field_Opordered__ring(X19)
      | c_lessequals(c_HOL_Otimes__class_Otimes(X18,X16,X19),c_HOL_Otimes__class_Otimes(X17,X16,X19),X19)
      | ~ c_lessequals(X16,c_HOL_Ozero__class_Ozero(X19),X19)
      | ~ c_lessequals(X17,X18,X19) ),
    inference(variable_rename,[status(thm)],[c_0_951]) ).

fof(c_0_1749,plain,
    ! [X16,X17,X18,X19] :
      ( ~ class_Ring__and__Field_Opordered__ring(X19)
      | c_lessequals(c_HOL_Otimes__class_Otimes(X16,X18,X19),c_HOL_Otimes__class_Otimes(X16,X17,X19),X19)
      | ~ c_lessequals(X16,c_HOL_Ozero__class_Ozero(X19),X19)
      | ~ c_lessequals(X17,X18,X19) ),
    inference(variable_rename,[status(thm)],[c_0_952]) ).

fof(c_0_1750,plain,
    ! [X16,X17,X18,X19] :
      ( ~ class_Ring__and__Field_Omult__mono(X19)
      | c_lessequals(c_HOL_Otimes__class_Otimes(X18,X16,X19),c_HOL_Otimes__class_Otimes(X17,X16,X19),X19)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X19),X16,X19)
      | ~ c_lessequals(X18,X17,X19) ),
    inference(variable_rename,[status(thm)],[c_0_953]) ).

fof(c_0_1751,plain,
    ! [X16,X17,X18,X19] :
      ( ~ class_Ring__and__Field_Omult__mono(X19)
      | c_lessequals(c_HOL_Otimes__class_Otimes(X16,X18,X19),c_HOL_Otimes__class_Otimes(X16,X17,X19),X19)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X19),X16,X19)
      | ~ c_lessequals(X18,X17,X19) ),
    inference(variable_rename,[status(thm)],[c_0_954]) ).

fof(c_0_1752,plain,
    ! [X16,X17,X18,X19] :
      ( ~ class_Ring__and__Field_Omult__mono1(X19)
      | c_lessequals(c_HOL_Otimes__class_Otimes(X16,X18,X19),c_HOL_Otimes__class_Otimes(X16,X17,X19),X19)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X19),X16,X19)
      | ~ c_lessequals(X18,X17,X19) ),
    inference(variable_rename,[status(thm)],[c_0_955]) ).

fof(c_0_1753,plain,
    ! [X9,X10,X11] :
      ( c_lessequals(X10,c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X9,X10,tc_nat),X11,tc_nat),tc_nat)
      | ~ c_lessequals(X11,X9,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_956]) ).

fof(c_0_1754,plain,
    ! [X21,X22,X23,X24,X25] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X25)
      | c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X24,X22,X25),c_HOL_Otimes__class_Otimes(X23,X21,X25),X25)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X22,X21,X25)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X24,X23,X25) ),
    inference(variable_rename,[status(thm)],[c_0_957]) ).

fof(c_0_1755,plain,
    ! [X21,X22,X23,X24,X25] :
      ( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X25)
      | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X24,X22,X25),c_HOL_Oplus__class_Oplus(X23,X21,X25),X25)
      | ~ c_HOL_Oord__class_Oless(X22,X21,X25)
      | ~ c_HOL_Oord__class_Oless(X24,X23,X25) ),
    inference(variable_rename,[status(thm)],[c_0_958]) ).

fof(c_0_1756,plain,
    ! [X21,X22,X23,X24,X25] :
      ( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X25)
      | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X24,X22,X25),c_HOL_Oplus__class_Oplus(X23,X21,X25),X25)
      | ~ c_HOL_Oord__class_Oless(X22,X21,X25)
      | ~ c_lessequals(X24,X23,X25) ),
    inference(variable_rename,[status(thm)],[c_0_959]) ).

fof(c_0_1757,plain,
    ! [X21,X22,X23,X24,X25] :
      ( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X25)
      | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X24,X22,X25),c_HOL_Oplus__class_Oplus(X23,X21,X25),X25)
      | ~ c_lessequals(X22,X21,X25)
      | ~ c_HOL_Oord__class_Oless(X24,X23,X25) ),
    inference(variable_rename,[status(thm)],[c_0_960]) ).

fof(c_0_1758,plain,
    ! [X21,X22,X23,X24,X25] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X25)
      | c_lessequals(c_HOL_Oplus__class_Oplus(X24,X22,X25),c_HOL_Oplus__class_Oplus(X23,X21,X25),X25)
      | ~ c_lessequals(X22,X21,X25)
      | ~ c_lessequals(X24,X23,X25) ),
    inference(variable_rename,[status(thm)],[c_0_961]) ).

fof(c_0_1759,plain,
    ! [X8,X9,X10] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X10)
      | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X9,X9,X10),c_HOL_Otimes__class_Otimes(X8,X8,X10),X10) != c_HOL_Ozero__class_Ozero(X10)
      | X8 = c_HOL_Ozero__class_Ozero(X10) ),
    inference(variable_rename,[status(thm)],[c_0_962]) ).

fof(c_0_1760,plain,
    ! [X8,X9,X10] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X10)
      | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X9,X9,X10),c_HOL_Otimes__class_Otimes(X8,X8,X10),X10) != c_HOL_Ozero__class_Ozero(X10)
      | X9 = c_HOL_Ozero__class_Ozero(X10) ),
    inference(variable_rename,[status(thm)],[c_0_963]) ).

fof(c_0_1761,plain,
    ! [X16,X17,X18,X19] :
      ( ~ class_Divides_Osemiring__div(X19)
      | c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X18,X16,X19),c_HOL_Otimes__class_Otimes(X17,X16,X19),X19) = c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(X18,X17,X19),X16,X19) ),
    inference(variable_rename,[status(thm)],[c_0_964]) ).

fof(c_0_1762,plain,
    ! [X16,X17,X18,X19] :
      ( ~ class_Divides_Osemiring__div(X19)
      | c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X16,X18,X19),c_HOL_Otimes__class_Otimes(X16,X17,X19),X19) = c_HOL_Otimes__class_Otimes(X16,c_Divides_Odiv__class_Omod(X18,X17,X19),X19) ),
    inference(variable_rename,[status(thm)],[c_0_965]) ).

fof(c_0_1763,plain,
    ! [X28,X29,X30,X31] :
      ( ~ class_RealVector_Oreal__normed__algebra(X31)
      | c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X30,X29,X31),X28,X31) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X30,X28,X31),c_HOL_Otimes__class_Otimes(X29,X28,X31),X31) ),
    inference(variable_rename,[status(thm)],[c_0_966]) ).

fof(c_0_1764,plain,
    ! [X29,X30,X31,X32] :
      ( ~ class_RealVector_Oreal__normed__algebra(X32)
      | c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X31,X30,X32),X29,X32) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X31,X29,X32),c_HOL_Otimes__class_Otimes(X30,X29,X32),X32) ),
    inference(variable_rename,[status(thm)],[c_0_967]) ).

fof(c_0_1765,plain,
    ! [X27,X28,X29,X30] :
      ( ~ class_RealVector_Oreal__normed__algebra(X30)
      | c_HOL_Otimes__class_Otimes(X29,c_HOL_Ominus__class_Ominus(X28,X27,X30),X30) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X29,X28,X30),c_HOL_Otimes__class_Otimes(X29,X27,X30),X30) ),
    inference(variable_rename,[status(thm)],[c_0_968]) ).

fof(c_0_1766,plain,
    ! [X19,X20,X21,X22] :
      ( ~ class_RealVector_Oreal__normed__algebra(X22)
      | c_HOL_Otimes__class_Otimes(X20,c_HOL_Ominus__class_Ominus(X21,X19,X22),X22) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X20,X21,X22),c_HOL_Otimes__class_Otimes(X20,X19,X22),X22) ),
    inference(variable_rename,[status(thm)],[c_0_969]) ).

fof(c_0_1767,plain,
    ! [X17,X18,X19,X20] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add(X20)
      | c_HOL_Ominus__class_Ominus(c_Orderings_Oord__class_Omin(X19,X18,X20),X17,X20) = c_Orderings_Oord__class_Omin(c_HOL_Ominus__class_Ominus(X19,X17,X20),c_HOL_Ominus__class_Ominus(X18,X17,X20),X20) ),
    inference(variable_rename,[status(thm)],[c_0_970]) ).

fof(c_0_1768,plain,
    ! [X16,X17,X18,X19] :
      ( ~ class_Divides_Osemiring__div(X19)
      | c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X18,c_HOL_Otimes__class_Otimes(X16,X17,X19),X19),X17,X19) = c_Divides_Odiv__class_Omod(X18,X17,X19) ),
    inference(variable_rename,[status(thm)],[c_0_971]) ).

fof(c_0_1769,plain,
    ! [X16,X17,X18,X19] :
      ( ~ class_Divides_Osemiring__div(X19)
      | c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X18,c_HOL_Otimes__class_Otimes(X17,X16,X19),X19),X17,X19) = c_Divides_Odiv__class_Omod(X18,X17,X19) ),
    inference(variable_rename,[status(thm)],[c_0_972]) ).

fof(c_0_1770,plain,
    ! [X17,X18,X19,X20] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X20)
      | c_HOL_Oplus__class_Oplus(c_Orderings_Oord__class_Omin(X19,X18,X20),X17,X20) = c_Orderings_Oord__class_Omin(c_HOL_Oplus__class_Oplus(X19,X17,X20),c_HOL_Oplus__class_Oplus(X18,X17,X20),X20) ),
    inference(variable_rename,[status(thm)],[c_0_973]) ).

fof(c_0_1771,plain,
    ! [X6,X7,X8,X9] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X9)
      | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X8,X6,X9),c_HOL_Otimes__class_Otimes(X7,X6,X9),X9) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X8,X7,X9),X6,X9) ),
    inference(variable_rename,[status(thm)],[c_0_974]) ).

fof(c_0_1772,plain,
    ! [X16,X17,X18,X19] :
      ( ~ class_Ring__and__Field_Ocomm__semiring(X19)
      | c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X18,X17,X19),X16,X19) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X18,X16,X19),c_HOL_Otimes__class_Otimes(X17,X16,X19),X19) ),
    inference(variable_rename,[status(thm)],[c_0_975]) ).

fof(c_0_1773,plain,
    ! [X17,X18,X19,X20] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X20)
      | c_HOL_Otimes__class_Otimes(X19,c_HOL_Oplus__class_Oplus(X18,X17,X20),X20) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X19,X18,X20),c_HOL_Otimes__class_Otimes(X19,X17,X20),X20) ),
    inference(variable_rename,[status(thm)],[c_0_976]) ).

fof(c_0_1774,plain,
    ! [X29,X30,X31,X32] :
      ( ~ class_RealVector_Oreal__normed__algebra(X32)
      | c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X31,X30,X32),X29,X32) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X31,X29,X32),c_HOL_Otimes__class_Otimes(X30,X29,X32),X32) ),
    inference(variable_rename,[status(thm)],[c_0_977]) ).

fof(c_0_1775,plain,
    ! [X28,X29,X30,X31] :
      ( ~ class_RealVector_Oreal__normed__algebra(X31)
      | c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X30,X29,X31),X28,X31) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X30,X28,X31),c_HOL_Otimes__class_Otimes(X29,X28,X31),X31) ),
    inference(variable_rename,[status(thm)],[c_0_978]) ).

fof(c_0_1776,plain,
    ! [X27,X28,X29,X30] :
      ( ~ class_RealVector_Oreal__normed__algebra(X30)
      | c_HOL_Otimes__class_Otimes(X29,c_HOL_Oplus__class_Oplus(X28,X27,X30),X30) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X29,X28,X30),c_HOL_Otimes__class_Otimes(X29,X27,X30),X30) ),
    inference(variable_rename,[status(thm)],[c_0_979]) ).

fof(c_0_1777,plain,
    ! [X19,X20,X21,X22] :
      ( ~ class_RealVector_Oreal__normed__algebra(X22)
      | c_HOL_Otimes__class_Otimes(X20,c_HOL_Oplus__class_Oplus(X21,X19,X22),X22) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X20,X21,X22),c_HOL_Otimes__class_Otimes(X20,X19,X22),X22) ),
    inference(variable_rename,[status(thm)],[c_0_980]) ).

fof(c_0_1778,plain,
    ! [X16,X17,X18,X19] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X19)
      | c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X18,X17,X19),X16,X19) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X18,X16,X19),c_HOL_Otimes__class_Otimes(X17,X16,X19),X19) ),
    inference(variable_rename,[status(thm)],[c_0_981]) ).

fof(c_0_1779,plain,
    ! [X9,X10,X11] :
      ( c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X11,X10,tc_nat),c_HOL_Otimes__class_Otimes(X11,X9,tc_nat),tc_nat)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X10,X9,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X11,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_982]) ).

fof(c_0_1780,plain,
    ! [X9,X10,X11] :
      ( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X10,X11,tc_nat),c_HOL_Otimes__class_Otimes(X9,X11,tc_nat),tc_nat)
      | ~ c_HOL_Oord__class_Oless(X10,X9,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X11,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_983]) ).

fof(c_0_1781,plain,
    ! [X9,X10,X11] :
      ( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X11,X10,tc_nat),c_HOL_Otimes__class_Otimes(X11,X9,tc_nat),tc_nat)
      | ~ c_HOL_Oord__class_Oless(X10,X9,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X11,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_984]) ).

fof(c_0_1782,plain,
    ! [X11,X12,X13] :
      ( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X11,X13,tc_nat),c_HOL_Otimes__class_Otimes(X11,X12,tc_nat),tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X11,tc_nat)
      | ~ c_HOL_Oord__class_Oless(X13,X12,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_985]) ).

fof(c_0_1783,plain,
    ! [X11,X12,X13] :
      ( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X13,X11,tc_nat),c_HOL_Otimes__class_Otimes(X12,X11,tc_nat),tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X11,tc_nat)
      | ~ c_HOL_Oord__class_Oless(X13,X12,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_986]) ).

fof(c_0_1784,plain,
    ! [X9,X10,X11] :
      ( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X11,X10,tc_nat),c_HOL_Otimes__class_Otimes(X11,X9,tc_nat),tc_nat)
      | ~ c_HOL_Oord__class_Oless(X10,X9,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X11,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_987]) ).

fof(c_0_1785,plain,
    ! [X9,X10,X11] :
      ( c_lessequals(c_HOL_Otimes__class_Otimes(X11,X10,tc_nat),c_HOL_Otimes__class_Otimes(X11,X9,tc_nat),tc_nat)
      | ~ c_lessequals(X10,X9,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X11,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_988]) ).

fof(c_0_1786,plain,
    ! [X30,X31,X32] :
      ( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X32,X30,tc_nat),c_HOL_Ominus__class_Ominus(X32,X31,tc_nat),tc_nat)
      | ~ c_HOL_Oord__class_Oless(X31,X32,tc_nat)
      | ~ c_HOL_Oord__class_Oless(X31,X30,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_989]) ).

fof(c_0_1787,plain,
    ! [X16,X17,X18] :
      ( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X18,X16,tc_nat),c_HOL_Ominus__class_Ominus(X17,X16,tc_nat),tc_nat)
      | ~ c_lessequals(X16,X18,tc_nat)
      | ~ c_HOL_Oord__class_Oless(X18,X17,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_990]) ).

fof(c_0_1788,plain,
    ! [X30,X31,X32,X33] :
      ( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X33,X31,tc_nat),c_HOL_Oplus__class_Oplus(X32,X30,tc_nat),tc_nat)
      | ~ c_HOL_Oord__class_Oless(X31,X30,tc_nat)
      | ~ c_HOL_Oord__class_Oless(X33,X32,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_991]) ).

fof(c_0_1789,plain,
    ! [X30,X31,X32,X33] :
      ( c_lessequals(c_HOL_Oplus__class_Oplus(X33,X31,tc_nat),c_HOL_Oplus__class_Oplus(X32,X30,tc_nat),tc_nat)
      | ~ c_lessequals(X31,X30,tc_nat)
      | ~ c_lessequals(X33,X32,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_992]) ).

fof(c_0_1790,plain,
    ! [X30,X31,X32,X33] :
      ( c_lessequals(c_HOL_Otimes__class_Otimes(X33,X31,tc_nat),c_HOL_Otimes__class_Otimes(X32,X30,tc_nat),tc_nat)
      | ~ c_lessequals(X31,X30,tc_nat)
      | ~ c_lessequals(X33,X32,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_993]) ).

fof(c_0_1791,plain,
    ! [X4,X5,X6] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X6)
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X6),X4,X6)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X6),X5,X6)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X6),c_HOL_Otimes__class_Otimes(X4,X5,X6),X6) ),
    inference(variable_rename,[status(thm)],[c_0_994]) ).

fof(c_0_1792,plain,
    ! [X4,X5,X6] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X6)
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X6),X4,X6)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X6),X5,X6)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X6),c_HOL_Otimes__class_Otimes(X5,X4,X6),X6) ),
    inference(variable_rename,[status(thm)],[c_0_995]) ).

fof(c_0_1793,plain,
    ! [X4,X5,X6] :
      ( ~ class_Ring__and__Field_Opordered__ring__abs(X6)
      | c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(X5,X4,X6),X6) = c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(X5,X6),c_HOL_Oabs__class_Oabs(X4,X6),X6)
      | ~ c_lessequals(X4,c_HOL_Ozero__class_Ozero(X6),X6)
      | ~ c_lessequals(X5,c_HOL_Ozero__class_Ozero(X6),X6) ),
    inference(variable_rename,[status(thm)],[c_0_996]) ).

fof(c_0_1794,plain,
    ! [X4,X5,X6] :
      ( ~ class_Ring__and__Field_Opordered__ring__abs(X6)
      | c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(X5,X4,X6),X6) = c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(X5,X6),c_HOL_Oabs__class_Oabs(X4,X6),X6)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X6),X4,X6)
      | ~ c_lessequals(X5,c_HOL_Ozero__class_Ozero(X6),X6) ),
    inference(variable_rename,[status(thm)],[c_0_997]) ).

fof(c_0_1795,plain,
    ! [X4,X5,X6] :
      ( ~ class_Ring__and__Field_Opordered__ring__abs(X6)
      | c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(X5,X4,X6),X6) = c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(X5,X6),c_HOL_Oabs__class_Oabs(X4,X6),X6)
      | ~ c_lessequals(X4,c_HOL_Ozero__class_Ozero(X6),X6)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X6),X5,X6) ),
    inference(variable_rename,[status(thm)],[c_0_998]) ).

fof(c_0_1796,plain,
    ! [X4,X5,X6] :
      ( ~ class_Ring__and__Field_Opordered__ring__abs(X6)
      | c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(X5,X4,X6),X6) = c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(X5,X6),c_HOL_Oabs__class_Oabs(X4,X6),X6)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X6),X4,X6)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X6),X5,X6) ),
    inference(variable_rename,[status(thm)],[c_0_999]) ).

fof(c_0_1797,plain,
    ! [X9,X10,X11] : c_HOL_Otimes__class_Otimes(X11,c_HOL_Ominus__class_Ominus(X10,X9,tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X11,X10,tc_nat),c_HOL_Otimes__class_Otimes(X11,X9,tc_nat),tc_nat),
    inference(variable_rename,[status(thm)],[c_0_1000]) ).

fof(c_0_1798,plain,
    ! [X9,X10,X11] : c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X10,X9,tc_nat),X11,tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X10,X11,tc_nat),c_HOL_Otimes__class_Otimes(X9,X11,tc_nat),tc_nat),
    inference(variable_rename,[status(thm)],[c_0_1001]) ).

fof(c_0_1799,plain,
    ! [X11,X12,X13] : c_Orderings_Oord__class_Omin(c_HOL_Ominus__class_Ominus(X12,X13,tc_nat),c_HOL_Ominus__class_Ominus(X11,X13,tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(c_Orderings_Oord__class_Omin(X12,X11,tc_nat),X13,tc_nat),
    inference(variable_rename,[status(thm)],[c_0_1002]) ).

fof(c_0_1800,plain,
    ! [X9,X10,X11] : c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X11,X9,tc_nat),X10,tc_nat),X9,tc_nat) = c_Divides_Odiv__class_Omod(X10,X9,tc_nat),
    inference(variable_rename,[status(thm)],[c_0_1003]) ).

fof(c_0_1801,plain,
    ! [X9,X10,X11] : c_HOL_Otimes__class_Otimes(X11,c_Divides_Odiv__class_Omod(X10,X9,tc_nat),tc_nat) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X11,X10,tc_nat),c_HOL_Otimes__class_Otimes(X11,X9,tc_nat),tc_nat),
    inference(variable_rename,[status(thm)],[c_0_1004]) ).

fof(c_0_1802,plain,
    ! [X9,X10,X11] : c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(X10,X9,tc_nat),X11,tc_nat) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X10,X11,tc_nat),c_HOL_Otimes__class_Otimes(X9,X11,tc_nat),tc_nat),
    inference(variable_rename,[status(thm)],[c_0_1005]) ).

fof(c_0_1803,plain,
    ! [X9,X10,X11] : c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X10,X9,tc_nat),X11,tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X10,X11,tc_nat),c_HOL_Otimes__class_Otimes(X9,X11,tc_nat),tc_nat),
    inference(variable_rename,[status(thm)],[c_0_1006]) ).

fof(c_0_1804,plain,
    ! [X9,X10,X11] : c_HOL_Otimes__class_Otimes(X11,c_HOL_Oplus__class_Oplus(X10,X9,tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X11,X10,tc_nat),c_HOL_Otimes__class_Otimes(X11,X9,tc_nat),tc_nat),
    inference(variable_rename,[status(thm)],[c_0_1007]) ).

fof(c_0_1805,plain,
    ! [X11,X12] :
      ( ~ c_lessequals(X12,c_HOL_Oplus__class_Oplus(X11,X12,tc_nat),tc_nat)
      | c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X11,X12,tc_nat),X12,tc_nat) = X11 ),
    inference(variable_rename,[status(thm)],[c_0_1008]) ).

fof(c_0_1806,plain,
    ! [X11,X12,X13] :
      ( c_HOL_Oord__class_Oless(X13,c_HOL_Ominus__class_Ominus(X12,X11,tc_nat),tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X13,X11,tc_nat),X12,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_1009]) ).

fof(c_0_1807,plain,
    ! [X11,X12,X13] :
      ( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X13,X11,tc_nat),X12,tc_nat)
      | ~ c_HOL_Oord__class_Oless(X13,c_HOL_Ominus__class_Ominus(X12,X11,tc_nat),tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_1010]) ).

fof(c_0_1808,plain,
    ! [X11,X12,X13] :
      ( c_lessequals(X12,c_HOL_Oplus__class_Oplus(X13,X11,tc_nat),tc_nat)
      | ~ c_lessequals(c_HOL_Ominus__class_Ominus(X12,X11,tc_nat),X13,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_1011]) ).

fof(c_0_1809,plain,
    ! [X11,X12,X13] :
      ( c_lessequals(c_HOL_Ominus__class_Ominus(X12,X11,tc_nat),X13,tc_nat)
      | ~ c_lessequals(X12,c_HOL_Oplus__class_Oplus(X13,X11,tc_nat),tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_1012]) ).

fof(c_0_1810,plain,
    ! [X9,X10,X11,X12] :
      ( ~ class_Divides_Osemiring__div(X12)
      | c_Ring__and__Field_Odvd__class_Odvd(X11,X10,X12)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X11,c_Divides_Odiv__class_Omod(X10,X9,X12),X12)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X11,X9,X12) ),
    inference(variable_rename,[status(thm)],[c_0_1013]) ).

fof(c_0_1811,plain,
    ! [X9,X10,X11,X12] :
      ( ~ class_Divides_Osemiring__div(X12)
      | c_Ring__and__Field_Odvd__class_Odvd(X11,X10,X12)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X11,X9,X12)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X11,c_Divides_Odiv__class_Omod(X10,X9,X12),X12) ),
    inference(variable_rename,[status(thm)],[c_0_1014]) ).

fof(c_0_1812,plain,
    ! [X18,X19,X20,X21,X22] :
      ( ~ class_OrderedGroup_Oab__group__add(X22)
      | c_HOL_Oplus__class_Oplus(X20,c_HOL_Oplus__class_Oplus(X19,X18,X22),X22) != c_HOL_Oplus__class_Oplus(X19,X21,X22)
      | c_HOL_Oplus__class_Oplus(X20,X18,X22) = X21 ),
    inference(variable_rename,[status(thm)],[c_0_1015]) ).

fof(c_0_1813,plain,
    ! [X11,X12,X13] :
      ( c_HOL_Oplus__class_Oplus(X13,c_HOL_Ominus__class_Ominus(X12,X11,tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X13,X12,tc_nat),X11,tc_nat)
      | ~ c_lessequals(X11,X12,tc_nat) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1016])])]) ).

fof(c_0_1814,plain,
    ! [X11,X12,X13] :
      ( c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X12,X11,tc_nat),X13,tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X12,X13,tc_nat),X11,tc_nat)
      | ~ c_lessequals(X11,X12,tc_nat) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1017])])]) ).

fof(c_0_1815,plain,
    ! [X11,X12,X13] :
      ( c_HOL_Ominus__class_Ominus(X13,c_HOL_Ominus__class_Ominus(X12,X11,tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X13,X11,tc_nat),X12,tc_nat)
      | ~ c_lessequals(X11,X12,tc_nat) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1018])])]) ).

fof(c_0_1816,plain,
    ! [X11,X12,X13] :
      ( c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X13,X12,tc_nat),X11,tc_nat) = c_HOL_Oplus__class_Oplus(X13,c_HOL_Ominus__class_Ominus(X12,X11,tc_nat),tc_nat)
      | ~ c_lessequals(X11,X12,tc_nat) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1019])])]) ).

fof(c_0_1817,plain,
    ! [X11,X12,X13] :
      ( c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X12,X13,tc_nat),X11,tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X12,X11,tc_nat),X13,tc_nat)
      | ~ c_lessequals(X11,X12,tc_nat) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1020])])]) ).

fof(c_0_1818,plain,
    ! [X4,X5,X6] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X6)
      | c_lessequals(X4,c_HOL_Ozero__class_Ozero(X6),X6)
      | c_lessequals(c_HOL_Ozero__class_Ozero(X6),X4,X6)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X6),c_HOL_Otimes__class_Otimes(X5,X4,X6),X6) ),
    inference(variable_rename,[status(thm)],[c_0_1021]) ).

fof(c_0_1819,plain,
    ! [X4,X5,X6] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X6)
      | c_lessequals(X5,c_HOL_Ozero__class_Ozero(X6),X6)
      | c_lessequals(c_HOL_Ozero__class_Ozero(X6),X4,X6)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X6),c_HOL_Otimes__class_Otimes(X5,X4,X6),X6) ),
    inference(variable_rename,[status(thm)],[c_0_1022]) ).

fof(c_0_1820,plain,
    ! [X4,X5,X6] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X6)
      | c_lessequals(X4,c_HOL_Ozero__class_Ozero(X6),X6)
      | c_lessequals(c_HOL_Ozero__class_Ozero(X6),X5,X6)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X6),c_HOL_Otimes__class_Otimes(X5,X4,X6),X6) ),
    inference(variable_rename,[status(thm)],[c_0_1023]) ).

fof(c_0_1821,plain,
    ! [X4,X5,X6] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X6)
      | c_lessequals(X5,c_HOL_Ozero__class_Ozero(X6),X6)
      | c_lessequals(c_HOL_Ozero__class_Ozero(X6),X5,X6)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X6),c_HOL_Otimes__class_Otimes(X5,X4,X6),X6) ),
    inference(variable_rename,[status(thm)],[c_0_1024]) ).

fof(c_0_1822,plain,
    ! [X4,X5,X6] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X6)
      | c_lessequals(c_HOL_Ozero__class_Ozero(X6),X4,X6)
      | c_lessequals(X4,c_HOL_Ozero__class_Ozero(X6),X6)
      | ~ c_lessequals(c_HOL_Otimes__class_Otimes(X5,X4,X6),c_HOL_Ozero__class_Ozero(X6),X6) ),
    inference(variable_rename,[status(thm)],[c_0_1025]) ).

fof(c_0_1823,plain,
    ! [X4,X5,X6] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X6)
      | c_lessequals(X5,c_HOL_Ozero__class_Ozero(X6),X6)
      | c_lessequals(X4,c_HOL_Ozero__class_Ozero(X6),X6)
      | ~ c_lessequals(c_HOL_Otimes__class_Otimes(X5,X4,X6),c_HOL_Ozero__class_Ozero(X6),X6) ),
    inference(variable_rename,[status(thm)],[c_0_1026]) ).

fof(c_0_1824,plain,
    ! [X4,X5,X6] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X6)
      | c_lessequals(c_HOL_Ozero__class_Ozero(X6),X4,X6)
      | c_lessequals(c_HOL_Ozero__class_Ozero(X6),X5,X6)
      | ~ c_lessequals(c_HOL_Otimes__class_Otimes(X5,X4,X6),c_HOL_Ozero__class_Ozero(X6),X6) ),
    inference(variable_rename,[status(thm)],[c_0_1027]) ).

fof(c_0_1825,plain,
    ! [X4,X5,X6] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X6)
      | c_lessequals(X5,c_HOL_Ozero__class_Ozero(X6),X6)
      | c_lessequals(c_HOL_Ozero__class_Ozero(X6),X5,X6)
      | ~ c_lessequals(c_HOL_Otimes__class_Otimes(X5,X4,X6),c_HOL_Ozero__class_Ozero(X6),X6) ),
    inference(variable_rename,[status(thm)],[c_0_1028]) ).

fof(c_0_1826,plain,
    ! [X6,X7] :
      ( c_lessequals(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Otimes__class_Otimes(X7,X6,tc_nat),tc_nat)
      | ~ c_lessequals(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X6,tc_nat)
      | ~ c_lessequals(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X7,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_1029]) ).

fof(c_0_1827,plain,
    ! [X6,X7] :
      ( c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Otimes__class_Otimes(X7,X6,tc_nat),tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X7,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X6,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_1030]) ).

fof(c_0_1828,plain,
    ! [X17,X18,X19,X20] :
      ( ~ class_Orderings_Olinorder(X20)
      | c_HOL_Oord__class_Oless(X18,X17,X20)
      | c_HOL_Oord__class_Oless(X19,X17,X20)
      | ~ c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omin(X19,X18,X20),X17,X20) ),
    inference(variable_rename,[status(thm)],[c_0_1031]) ).

fof(c_0_1829,plain,
    ! [X17,X18,X19,X20] :
      ( ~ class_Orderings_Olinorder(X20)
      | c_lessequals(X18,X17,X20)
      | c_lessequals(X19,X17,X20)
      | ~ c_lessequals(c_Orderings_Oord__class_Omin(X19,X18,X20),X17,X20) ),
    inference(variable_rename,[status(thm)],[c_0_1032]) ).

fof(c_0_1830,plain,
    ! [X9,X10,X11] :
      ( c_lessequals(c_HOL_Otimes__class_Otimes(c_Suc(X11),X10,tc_nat),c_HOL_Otimes__class_Otimes(c_Suc(X11),X9,tc_nat),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_1033])])]) ).

fof(c_0_1831,plain,
    ! [X9,X10,X11] :
      ( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Suc(X11),X10,tc_nat),c_HOL_Otimes__class_Otimes(c_Suc(X11),X9,tc_nat),tc_nat)
      | ~ c_HOL_Oord__class_Oless(X10,X9,tc_nat) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1034])])]) ).

fof(c_0_1832,plain,
    ! [X4,X5,X6] :
      ( ~ class_OrderedGroup_Opordered__comm__monoid__add(X6)
      | c_lessequals(c_HOL_Oplus__class_Oplus(X5,X4,X6),c_HOL_Ozero__class_Ozero(X6),X6)
      | ~ c_lessequals(X4,c_HOL_Ozero__class_Ozero(X6),X6)
      | ~ c_lessequals(X5,c_HOL_Ozero__class_Ozero(X6),X6) ),
    inference(variable_rename,[status(thm)],[c_0_1035]) ).

fof(c_0_1833,plain,
    ! [X4,X5,X6] :
      ( ~ class_OrderedGroup_Opordered__comm__monoid__add(X6)
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X6),c_HOL_Oplus__class_Oplus(X5,X4,X6),X6)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X6),X4,X6)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X6),X5,X6) ),
    inference(variable_rename,[status(thm)],[c_0_1036]) ).

fof(c_0_1834,plain,
    ! [X4,X5,X6] :
      ( ~ class_OrderedGroup_Opordered__comm__monoid__add(X6)
      | c_lessequals(c_HOL_Ozero__class_Ozero(X6),c_HOL_Oplus__class_Oplus(X5,X4,X6),X6)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X6),X4,X6)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X6),X5,X6) ),
    inference(variable_rename,[status(thm)],[c_0_1037]) ).

fof(c_0_1835,plain,
    ! [X4,X5,X6] :
      ( ~ class_OrderedGroup_Opordered__comm__monoid__add(X6)
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X6),c_HOL_Oplus__class_Oplus(X5,X4,X6),X6)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X6),X4,X6)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X6),X5,X6) ),
    inference(variable_rename,[status(thm)],[c_0_1038]) ).

fof(c_0_1836,plain,
    ! [X4,X5,X6] :
      ( ~ class_OrderedGroup_Opordered__comm__monoid__add(X6)
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X6),c_HOL_Oplus__class_Oplus(X5,X4,X6),X6)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X6),X4,X6)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X6),X5,X6) ),
    inference(variable_rename,[status(thm)],[c_0_1039]) ).

fof(c_0_1837,plain,
    ! [X4,X5,X6] :
      ( ~ class_Ring__and__Field_Opordered__cancel__semiring(X6)
      | c_lessequals(c_HOL_Otimes__class_Otimes(X4,X5,X6),c_HOL_Ozero__class_Ozero(X6),X6)
      | ~ c_lessequals(X4,c_HOL_Ozero__class_Ozero(X6),X6)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X6),X5,X6) ),
    inference(variable_rename,[status(thm)],[c_0_1040]) ).

fof(c_0_1838,plain,
    ! [X4,X5,X6] :
      ( ~ class_Ring__and__Field_Opordered__cancel__semiring(X6)
      | c_lessequals(c_HOL_Otimes__class_Otimes(X5,X4,X6),c_HOL_Ozero__class_Ozero(X6),X6)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X6),X4,X6)
      | ~ c_lessequals(X5,c_HOL_Ozero__class_Ozero(X6),X6) ),
    inference(variable_rename,[status(thm)],[c_0_1041]) ).

fof(c_0_1839,plain,
    ! [X4,X5,X6] :
      ( ~ class_Ring__and__Field_Opordered__cancel__semiring(X6)
      | c_lessequals(c_HOL_Otimes__class_Otimes(X5,X4,X6),c_HOL_Ozero__class_Ozero(X6),X6)
      | ~ c_lessequals(X4,c_HOL_Ozero__class_Ozero(X6),X6)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X6),X5,X6) ),
    inference(variable_rename,[status(thm)],[c_0_1042]) ).

fof(c_0_1840,plain,
    ! [X4,X5,X6] :
      ( ~ class_Ring__and__Field_Opordered__cancel__semiring(X6)
      | c_lessequals(c_HOL_Otimes__class_Otimes(X5,X4,X6),c_HOL_Ozero__class_Ozero(X6),X6)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X6),X4,X6)
      | ~ c_lessequals(X5,c_HOL_Ozero__class_Ozero(X6),X6) ),
    inference(variable_rename,[status(thm)],[c_0_1043]) ).

fof(c_0_1841,plain,
    ! [X4,X5,X6] :
      ( ~ class_Ring__and__Field_Opordered__cancel__semiring(X6)
      | c_lessequals(c_HOL_Otimes__class_Otimes(X5,X4,X6),c_HOL_Ozero__class_Ozero(X6),X6)
      | ~ c_lessequals(X4,c_HOL_Ozero__class_Ozero(X6),X6)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X6),X5,X6) ),
    inference(variable_rename,[status(thm)],[c_0_1044]) ).

fof(c_0_1842,plain,
    ! [X4,X5,X6] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X6)
      | c_lessequals(c_HOL_Otimes__class_Otimes(X5,X4,X6),c_HOL_Ozero__class_Ozero(X6),X6)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X6),X4,X6)
      | ~ c_lessequals(X5,c_HOL_Ozero__class_Ozero(X6),X6) ),
    inference(variable_rename,[status(thm)],[c_0_1045]) ).

fof(c_0_1843,plain,
    ! [X4,X5,X6] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X6)
      | c_lessequals(c_HOL_Otimes__class_Otimes(X5,X4,X6),c_HOL_Ozero__class_Ozero(X6),X6)
      | ~ c_lessequals(X4,c_HOL_Ozero__class_Ozero(X6),X6)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X6),X5,X6) ),
    inference(variable_rename,[status(thm)],[c_0_1046]) ).

fof(c_0_1844,plain,
    ! [X4,X5,X6] :
      ( ~ class_OrderedGroup_Opordered__comm__monoid__add(X6)
      | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X5,X4,X6),c_HOL_Ozero__class_Ozero(X6),X6)
      | ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X6),X6)
      | ~ c_HOL_Oord__class_Oless(X5,c_HOL_Ozero__class_Ozero(X6),X6) ),
    inference(variable_rename,[status(thm)],[c_0_1047]) ).

fof(c_0_1845,plain,
    ! [X4,X5,X6] :
      ( ~ class_Ring__and__Field_Opordered__cancel__semiring(X6)
      | c_lessequals(c_HOL_Ozero__class_Ozero(X6),c_HOL_Otimes__class_Otimes(X5,X4,X6),X6)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X6),X4,X6)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X6),X5,X6) ),
    inference(variable_rename,[status(thm)],[c_0_1048]) ).

fof(c_0_1846,plain,
    ! [X4,X5,X6] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X6)
      | c_lessequals(c_HOL_Ozero__class_Ozero(X6),c_HOL_Otimes__class_Otimes(X5,X4,X6),X6)
      | ~ c_lessequals(X4,c_HOL_Ozero__class_Ozero(X6),X6)
      | ~ c_lessequals(X5,c_HOL_Ozero__class_Ozero(X6),X6) ),
    inference(variable_rename,[status(thm)],[c_0_1049]) ).

fof(c_0_1847,plain,
    ! [X4,X5,X6] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X6)
      | c_lessequals(c_HOL_Ozero__class_Ozero(X6),c_HOL_Otimes__class_Otimes(X5,X4,X6),X6)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X6),X4,X6)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X6),X5,X6) ),
    inference(variable_rename,[status(thm)],[c_0_1050]) ).

fof(c_0_1848,plain,
    ! [X4,X5,X6] :
      ( ~ class_Ring__and__Field_Opordered__ring(X6)
      | c_lessequals(c_HOL_Ozero__class_Ozero(X6),c_HOL_Otimes__class_Otimes(X5,X4,X6),X6)
      | ~ c_lessequals(X4,c_HOL_Ozero__class_Ozero(X6),X6)
      | ~ c_lessequals(X5,c_HOL_Ozero__class_Ozero(X6),X6) ),
    inference(variable_rename,[status(thm)],[c_0_1051]) ).

fof(c_0_1849,plain,
    ! [X4,X5,X6] :
      ( ~ class_Ring__and__Field_Opordered__ring(X6)
      | c_lessequals(c_HOL_Ozero__class_Ozero(X6),c_HOL_Otimes__class_Otimes(X5,X4,X6),X6)
      | ~ c_lessequals(X4,c_HOL_Ozero__class_Ozero(X6),X6)
      | ~ c_lessequals(X5,c_HOL_Ozero__class_Ozero(X6),X6) ),
    inference(variable_rename,[status(thm)],[c_0_1052]) ).

fof(c_0_1850,plain,
    ! [X4,X5,X6] :
      ( ~ class_Ring__and__Field_Opordered__ring(X6)
      | c_lessequals(c_HOL_Ozero__class_Ozero(X6),c_HOL_Otimes__class_Otimes(X5,X4,X6),X6)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X6),X4,X6)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X6),X5,X6) ),
    inference(variable_rename,[status(thm)],[c_0_1053]) ).

fof(c_0_1851,plain,
    ! [X4,X5,X6] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X6)
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X6),c_HOL_Otimes__class_Otimes(X5,X4,X6),X6)
      | ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X6),X6)
      | ~ c_HOL_Oord__class_Oless(X5,c_HOL_Ozero__class_Ozero(X6),X6) ),
    inference(variable_rename,[status(thm)],[c_0_1054]) ).

fof(c_0_1852,plain,
    ! [X4,X5,X6] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X6)
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X6),c_HOL_Otimes__class_Otimes(X5,X4,X6),X6)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X6),X4,X6)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X6),X5,X6) ),
    inference(variable_rename,[status(thm)],[c_0_1055]) ).

fof(c_0_1853,plain,
    ! [X4,X5,X6] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X6)
      | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X4,X5,X6),c_HOL_Ozero__class_Ozero(X6),X6)
      | ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X6),X6)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X6),X5,X6) ),
    inference(variable_rename,[status(thm)],[c_0_1056]) ).

fof(c_0_1854,plain,
    ! [X4,X5,X6] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X6)
      | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X5,X4,X6),c_HOL_Ozero__class_Ozero(X6),X6)
      | ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X6),X6)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X6),X5,X6) ),
    inference(variable_rename,[status(thm)],[c_0_1057]) ).

fof(c_0_1855,plain,
    ! [X4,X5,X6] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X6)
      | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X5,X4,X6),c_HOL_Ozero__class_Ozero(X6),X6)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X6),X4,X6)
      | ~ c_HOL_Oord__class_Oless(X5,c_HOL_Ozero__class_Ozero(X6),X6) ),
    inference(variable_rename,[status(thm)],[c_0_1058]) ).

fof(c_0_1856,plain,
    ! [X4,X5,X6] :
      ( ~ class_OrderedGroup_Opordered__comm__monoid__add(X6)
      | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X5,X4,X6),c_HOL_Ozero__class_Ozero(X6),X6)
      | ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X6),X6)
      | ~ c_lessequals(X5,c_HOL_Ozero__class_Ozero(X6),X6) ),
    inference(variable_rename,[status(thm)],[c_0_1059]) ).

fof(c_0_1857,plain,
    ! [X4,X5,X6] :
      ( ~ class_OrderedGroup_Opordered__comm__monoid__add(X6)
      | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X5,X4,X6),c_HOL_Ozero__class_Ozero(X6),X6)
      | ~ c_lessequals(X4,c_HOL_Ozero__class_Ozero(X6),X6)
      | ~ c_HOL_Oord__class_Oless(X5,c_HOL_Ozero__class_Ozero(X6),X6) ),
    inference(variable_rename,[status(thm)],[c_0_1060]) ).

fof(c_0_1858,plain,
    ! [X6,X7] :
      ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X6,tc_nat)
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X7,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oplus__class_Oplus(X7,X6,tc_nat),tc_nat) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1061])])]) ).

fof(c_0_1859,plain,
    ! [X6] : c_lessequals(X6,c_HOL_Otimes__class_Otimes(X6,c_HOL_Otimes__class_Otimes(X6,X6,tc_nat),tc_nat),tc_nat),
    inference(variable_rename,[status(thm)],[c_0_1062]) ).

fof(c_0_1860,plain,
    ! [X6,X7] :
      ( c_HOL_Oord__class_Oless(X6,c_HOL_Otimes__class_Otimes(X7,X6,tc_nat),tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X7,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X6,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_1063]) ).

fof(c_0_1861,plain,
    ! [X6,X7] :
      ( c_HOL_Oord__class_Oless(X6,c_HOL_Otimes__class_Otimes(X6,X7,tc_nat),tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X7,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X6,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_1064]) ).

fof(c_0_1862,plain,
    ! [X16,X17,X18,X19] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X19)
      | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X16,X18,X19),c_HOL_Oplus__class_Oplus(X16,X17,X19),X19)
      | ~ c_HOL_Oord__class_Oless(X18,X17,X19) ),
    inference(variable_rename,[status(thm)],[c_0_1065]) ).

fof(c_0_1863,plain,
    ! [X16,X17,X18,X19] :
      ( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X19)
      | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X16,X18,X19),c_HOL_Oplus__class_Oplus(X16,X17,X19),X19)
      | ~ c_HOL_Oord__class_Oless(X18,X17,X19) ),
    inference(variable_rename,[status(thm)],[c_0_1066]) ).

fof(c_0_1864,plain,
    ! [X16,X17,X18,X19] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X19)
      | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X18,X16,X19),c_HOL_Oplus__class_Oplus(X17,X16,X19),X19)
      | ~ c_HOL_Oord__class_Oless(X18,X17,X19) ),
    inference(variable_rename,[status(thm)],[c_0_1067]) ).

fof(c_0_1865,plain,
    ! [X16,X17,X18,X19] :
      ( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X19)
      | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X18,X16,X19),c_HOL_Oplus__class_Oplus(X17,X16,X19),X19)
      | ~ c_HOL_Oord__class_Oless(X18,X17,X19) ),
    inference(variable_rename,[status(thm)],[c_0_1068]) ).

fof(c_0_1866,plain,
    ! [X16,X17,X18,X19] :
      ( ~ class_Ring__and__Field_Oidom(X19)
      | c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X18,X16,X19),c_HOL_Otimes__class_Otimes(X17,X16,X19),X19)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X18,X17,X19) ),
    inference(variable_rename,[status(thm)],[c_0_1069]) ).

fof(c_0_1867,plain,
    ! [X16,X17,X18,X19] :
      ( ~ class_Ring__and__Field_Oidom(X19)
      | c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X16,X18,X19),c_HOL_Otimes__class_Otimes(X16,X17,X19),X19)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X18,X17,X19) ),
    inference(variable_rename,[status(thm)],[c_0_1070]) ).

fof(c_0_1868,plain,
    ! [X16,X17,X18,X19] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X19)
      | c_lessequals(c_HOL_Oplus__class_Oplus(X18,X16,X19),c_HOL_Oplus__class_Oplus(X17,X16,X19),X19)
      | ~ c_lessequals(X18,X17,X19) ),
    inference(variable_rename,[status(thm)],[c_0_1071]) ).

fof(c_0_1869,plain,
    ! [X16,X17,X18,X19] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X19)
      | c_lessequals(c_HOL_Oplus__class_Oplus(X16,X18,X19),c_HOL_Oplus__class_Oplus(X16,X17,X19),X19)
      | ~ c_lessequals(X18,X17,X19) ),
    inference(variable_rename,[status(thm)],[c_0_1072]) ).

fof(c_0_1870,plain,
    ! [X16,X17,X18,X19] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X19)
      | c_lessequals(c_HOL_Oplus__class_Oplus(X18,X16,X19),c_HOL_Oplus__class_Oplus(X17,X16,X19),X19)
      | ~ c_lessequals(X18,X17,X19) ),
    inference(variable_rename,[status(thm)],[c_0_1073]) ).

fof(c_0_1871,plain,
    ! [X16,X17,X18,X19] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X19)
      | c_lessequals(c_HOL_Oplus__class_Oplus(X16,X18,X19),c_HOL_Oplus__class_Oplus(X16,X17,X19),X19)
      | ~ c_lessequals(X18,X17,X19) ),
    inference(variable_rename,[status(thm)],[c_0_1074]) ).

fof(c_0_1872,plain,
    ! [X17,X18,X19] :
      ( ~ c_Ring__and__Field_Odvd__class_Odvd(X17,X19,tc_nat)
      | c_Ring__and__Field_Odvd__class_Odvd(X17,X18,tc_nat)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X18,X17,tc_nat)
      | c_Ring__and__Field_Odvd__class_Odvd(X18,X19,tc_nat)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X19,X18,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_1075]) ).

fof(c_0_1873,plain,
    ! [X16,X17,X18,X19] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X19)
      | ~ class_OrderedGroup_Ocomm__monoid__add(X19)
      | c_HOL_Oord__class_Oless(X17,c_HOL_Oplus__class_Oplus(X18,X16,X19),X19)
      | ~ c_lessequals(X17,X16,X19)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X19),X18,X19) ),
    inference(variable_rename,[status(thm)],[c_0_1076]) ).

fof(c_0_1874,plain,
    ! [X16,X17,X18,X19] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X19)
      | ~ class_OrderedGroup_Ocomm__monoid__add(X19)
      | c_HOL_Oord__class_Oless(X17,c_HOL_Oplus__class_Oplus(X18,X16,X19),X19)
      | ~ c_HOL_Oord__class_Oless(X17,X16,X19)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X19),X18,X19) ),
    inference(variable_rename,[status(thm)],[c_0_1077]) ).

fof(c_0_1875,plain,
    ! [X16,X17,X18,X19] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X19)
      | ~ class_OrderedGroup_Ocomm__monoid__add(X19)
      | c_lessequals(X17,c_HOL_Oplus__class_Oplus(X18,X16,X19),X19)
      | ~ c_lessequals(X17,X16,X19)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X19),X18,X19) ),
    inference(variable_rename,[status(thm)],[c_0_1078]) ).

fof(c_0_1876,plain,
    ! [X16,X17,X18,X19] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X19)
      | ~ class_OrderedGroup_Ocomm__monoid__add(X19)
      | c_lessequals(X17,c_HOL_Oplus__class_Oplus(X18,X16,X19),X19)
      | ~ c_lessequals(X17,X18,X19)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X19),X16,X19) ),
    inference(variable_rename,[status(thm)],[c_0_1079]) ).

fof(c_0_1877,plain,
    ! [X16,X17,X18,X19] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X19)
      | c_HOL_Oord__class_Oless(X17,c_HOL_Oplus__class_Oplus(X18,X16,X19),X19)
      | ~ c_HOL_Oord__class_Oless(X17,X16,X19)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X19),X18,X19) ),
    inference(variable_rename,[status(thm)],[c_0_1080]) ).

fof(c_0_1878,plain,
    ! [X30,X31,X32] :
      ( c_lessequals(c_HOL_Ominus__class_Ominus(X32,X30,tc_nat),c_HOL_Ominus__class_Ominus(X32,X31,tc_nat),tc_nat)
      | ~ c_lessequals(X31,X30,tc_nat) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1081])])]) ).

fof(c_0_1879,plain,
    ! [X30,X31,X32] :
      ( c_lessequals(c_HOL_Ominus__class_Ominus(X31,X32,tc_nat),c_HOL_Ominus__class_Ominus(X30,X32,tc_nat),tc_nat)
      | ~ c_lessequals(X31,X30,tc_nat) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1082])])]) ).

fof(c_0_1880,plain,
    ! [X11,X12,X13] :
      ( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X13,X11,tc_nat),c_HOL_Oplus__class_Oplus(X12,X11,tc_nat),tc_nat)
      | ~ c_HOL_Oord__class_Oless(X13,X12,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_1083]) ).

fof(c_0_1881,plain,
    ! [X9,X10,X11] :
      ( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X11,X10,tc_nat),c_HOL_Oplus__class_Oplus(X11,X9,tc_nat),tc_nat)
      | ~ c_HOL_Oord__class_Oless(X10,X9,tc_nat) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1084])])]) ).

fof(c_0_1882,plain,
    ! [X9,X10,X11] :
      ( c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X11,X10,tc_nat),c_HOL_Otimes__class_Otimes(X11,X9,tc_nat),tc_nat)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X10,X9,tc_nat) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1085])])]) ).

fof(c_0_1883,plain,
    ! [X11,X12,X13] :
      ( c_lessequals(c_HOL_Otimes__class_Otimes(X13,X11,tc_nat),c_HOL_Otimes__class_Otimes(X12,X11,tc_nat),tc_nat)
      | ~ c_lessequals(X13,X12,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_1086]) ).

fof(c_0_1884,plain,
    ! [X11,X12,X13] :
      ( c_lessequals(c_HOL_Otimes__class_Otimes(X11,X13,tc_nat),c_HOL_Otimes__class_Otimes(X11,X12,tc_nat),tc_nat)
      | ~ c_lessequals(X13,X12,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_1087]) ).

fof(c_0_1885,plain,
    ! [X9,X10,X11] :
      ( c_lessequals(c_HOL_Otimes__class_Otimes(X11,X10,tc_nat),c_HOL_Otimes__class_Otimes(X11,X9,tc_nat),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_1088])])]) ).

fof(c_0_1886,plain,
    ! [X9,X10,X11] :
      ( c_lessequals(c_HOL_Otimes__class_Otimes(X10,X11,tc_nat),c_HOL_Otimes__class_Otimes(X9,X11,tc_nat),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_1089])])]) ).

fof(c_0_1887,plain,
    ! [X11,X12,X13] :
      ( c_lessequals(c_HOL_Oplus__class_Oplus(X13,X11,tc_nat),c_HOL_Oplus__class_Oplus(X12,X11,tc_nat),tc_nat)
      | ~ c_lessequals(X13,X12,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_1090]) ).

fof(c_0_1888,plain,
    ! [X9,X10,X11] :
      ( c_lessequals(c_HOL_Oplus__class_Oplus(X11,X10,tc_nat),c_HOL_Oplus__class_Oplus(X11,X9,tc_nat),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_1091])])]) ).

fof(c_0_1889,plain,
    ! [X17,X18,X19,X20] :
      ( ~ class_Ring__and__Field_Ocomm__ring__1(X20)
      | c_Ring__and__Field_Odvd__class_Odvd(X19,c_HOL_Ominus__class_Ominus(X18,X17,X20),X20)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X19,X17,X20)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X19,X18,X20) ),
    inference(variable_rename,[status(thm)],[c_0_1092]) ).

fof(c_0_1890,plain,
    ! [X17,X18,X19,X20] :
      ( ~ class_Orderings_Olinorder(X20)
      | c_HOL_Oord__class_Oless(X17,c_Orderings_Oord__class_Omin(X19,X18,X20),X20)
      | ~ c_HOL_Oord__class_Oless(X17,X18,X20)
      | ~ c_HOL_Oord__class_Oless(X17,X19,X20) ),
    inference(variable_rename,[status(thm)],[c_0_1093]) ).

fof(c_0_1891,plain,
    ! [X16,X17,X18,X19] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X19)
      | c_Ring__and__Field_Odvd__class_Odvd(X18,c_HOL_Oplus__class_Oplus(X17,X16,X19),X19)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X18,X16,X19)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X18,X17,X19) ),
    inference(variable_rename,[status(thm)],[c_0_1094]) ).

fof(c_0_1892,plain,
    ! [X8,X9,X10,X11] :
      ( ~ class_Orderings_Olinorder(X11)
      | c_lessequals(X8,c_Orderings_Oord__class_Omin(X10,X9,X11),X11)
      | ~ c_lessequals(X8,X9,X11)
      | ~ c_lessequals(X8,X10,X11) ),
    inference(variable_rename,[status(thm)],[c_0_1095]) ).

fof(c_0_1893,plain,
    ! [X17,X18,X19,X20] :
      ( ~ class_Orderings_Olinorder(X20)
      | c_lessequals(X19,c_Orderings_Oord__class_Omin(X18,X17,X20),X20)
      | ~ c_lessequals(X19,X17,X20)
      | ~ c_lessequals(X19,X18,X20) ),
    inference(variable_rename,[status(thm)],[c_0_1096]) ).

fof(c_0_1894,plain,
    ! [X17,X18,X19,X20] :
      ( ~ class_Orderings_Olinorder(X20)
      | c_lessequals(X19,c_Orderings_Oord__class_Omin(X18,X17,X20),X20)
      | ~ c_lessequals(X19,X17,X20)
      | ~ c_lessequals(X19,X18,X20) ),
    inference(variable_rename,[status(thm)],[c_0_1097]) ).

fof(c_0_1895,plain,
    ! [X9,X10,X11,X12] :
      ( ~ class_Divides_Osemiring__div(X12)
      | c_Ring__and__Field_Odvd__class_Odvd(X11,c_Divides_Odiv__class_Omod(X10,X9,X12),X12)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X11,X9,X12)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X11,X10,X12) ),
    inference(variable_rename,[status(thm)],[c_0_1098]) ).

fof(c_0_1896,plain,
    ! [X9,X10,X11,X12] :
      ( ~ class_Divides_Osemiring__div(X12)
      | c_Ring__and__Field_Odvd__class_Odvd(X11,c_Divides_Odiv__class_Omod(X10,X9,X12),X12)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X11,X10,X12)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X11,X9,X12) ),
    inference(variable_rename,[status(thm)],[c_0_1099]) ).

fof(c_0_1897,plain,
    ! [X4,X5,X6] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X6)
      | c_HOL_Oabs__class_Oabs(c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(X5,X6),c_HOL_Oabs__class_Oabs(X4,X6),X6),X6) = c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(X5,X6),c_HOL_Oabs__class_Oabs(X4,X6),X6) ),
    inference(variable_rename,[status(thm)],[c_0_1100]) ).

fof(c_0_1898,plain,
    ! [X6,X7] :
      ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Otimes__class_Otimes(X7,X6,tc_nat),tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X6,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X7,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_1101]) ).

fof(c_0_1899,plain,
    ! [X9,X10,X11] :
      ( c_HOL_Ominus__class_Ominus(X10,X11,tc_nat) != c_HOL_Ominus__class_Ominus(X9,X11,tc_nat)
      | ~ c_lessequals(X11,X9,tc_nat)
      | ~ c_lessequals(X11,X10,tc_nat)
      | X10 = X9 ),
    inference(variable_rename,[status(thm)],[c_0_1102]) ).

fof(c_0_1900,plain,
    ! [X6,X7] :
      ( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X7,X6,tc_nat),X7,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X7,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X6,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_1103]) ).

fof(c_0_1901,plain,
    ! [X4,X5] :
      ( ~ class_OrderedGroup_Olordered__ab__group__add(X5)
      | c_lessequals(X4,c_HOL_Ozero__class_Ozero(X5),X5)
      | ~ c_lessequals(c_HOL_Oplus__class_Oplus(X4,X4,X5),c_HOL_Ozero__class_Ozero(X5),X5) ),
    inference(variable_rename,[status(thm)],[c_0_1104]) ).

fof(c_0_1902,plain,
    ! [X4,X5] :
      ( ~ class_OrderedGroup_Olordered__ab__group__add(X5)
      | c_lessequals(c_HOL_Ozero__class_Ozero(X5),X4,X5)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X5),c_HOL_Oplus__class_Oplus(X4,X4,X5),X5) ),
    inference(variable_rename,[status(thm)],[c_0_1105]) ).

fof(c_0_1903,plain,
    ! [X4,X5] :
      ( ~ class_OrderedGroup_Olordered__ab__group__add(X5)
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),X4,X5)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),c_HOL_Oplus__class_Oplus(X4,X4,X5),X5) ),
    inference(variable_rename,[status(thm)],[c_0_1106]) ).

fof(c_0_1904,plain,
    ! [X4,X5] :
      ( ~ class_Ring__and__Field_Oordered__idom(X5)
      | c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X5),X5)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X4,X4,X5),c_HOL_Ozero__class_Ozero(X5),X5) ),
    inference(variable_rename,[status(thm)],[c_0_1107]) ).

fof(c_0_1905,plain,
    ! [X4,X5] :
      ( ~ class_OrderedGroup_Olordered__ab__group__add(X5)
      | c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X5),X5)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X4,X4,X5),c_HOL_Ozero__class_Ozero(X5),X5) ),
    inference(variable_rename,[status(thm)],[c_0_1108]) ).

fof(c_0_1906,plain,
    ! [X9,X10,X11] : c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(c_Suc(X10),X9,tc_nat),c_Suc(X11),tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X10,X9,tc_nat),X11,tc_nat),
    inference(variable_rename,[status(thm)],[c_0_1109]) ).

fof(c_0_1907,plain,
    ! [X6,X7] :
      ( c_lessequals(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X7,tc_nat)
      | ~ c_lessequals(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Otimes__class_Otimes(X7,X6,tc_nat),tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_1110]) ).

fof(c_0_1908,plain,
    ! [X6,X7] :
      ( c_lessequals(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X6,tc_nat)
      | ~ c_lessequals(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Otimes__class_Otimes(X7,X6,tc_nat),tc_nat) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1111])])]) ).

fof(c_0_1909,plain,
    ! [X17,X18,X19,X20] :
      ( ~ class_Orderings_Olinorder(X20)
      | c_Orderings_Oord__class_Omin(X19,c_Orderings_Oord__class_Omin(X18,X17,X20),X20) = c_Orderings_Oord__class_Omin(X18,c_Orderings_Oord__class_Omin(X19,X17,X20),X20) ),
    inference(variable_rename,[status(thm)],[c_0_1112]) ).

fof(c_0_1910,plain,
    ! [X17,X18,X19,X20] :
      ( ~ class_Orderings_Olinorder(X20)
      | c_Orderings_Oord__class_Omin(c_Orderings_Oord__class_Omin(X19,X18,X20),X17,X20) = c_Orderings_Oord__class_Omin(X19,c_Orderings_Oord__class_Omin(X18,X17,X20),X20) ),
    inference(variable_rename,[status(thm)],[c_0_1113]) ).

fof(c_0_1911,plain,
    ! [X16,X17,X18,X19] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X19)
      | c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X18,X17,X19),X16,X19) = c_HOL_Oplus__class_Oplus(X18,c_HOL_Oplus__class_Oplus(X17,X16,X19),X19) ),
    inference(variable_rename,[status(thm)],[c_0_1114]) ).

fof(c_0_1912,plain,
    ! [X21,X22,X23,X24] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(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_1115]) ).

fof(c_0_1913,plain,
    ! [X16,X17,X18,X19] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X19)
      | c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X18,X17,X19),X16,X19) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X18,X16,X19),X17,X19) ),
    inference(variable_rename,[status(thm)],[c_0_1116]) ).

fof(c_0_1914,plain,
    ! [X21,X22,X23,X24] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X24)
      | c_HOL_Oplus__class_Oplus(X23,c_HOL_Oplus__class_Oplus(X22,X21,X24),X24) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X23,X22,X24),X21,X24) ),
    inference(variable_rename,[status(thm)],[c_0_1117]) ).

fof(c_0_1915,plain,
    ! [X16,X17,X18,X19] :
      ( ~ class_OrderedGroup_Oab__semigroup__add(X19)
      | c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X18,X17,X19),X16,X19) = c_HOL_Oplus__class_Oplus(X18,c_HOL_Oplus__class_Oplus(X17,X16,X19),X19) ),
    inference(variable_rename,[status(thm)],[c_0_1118]) ).

fof(c_0_1916,plain,
    ! [X17,X18,X19,X20] :
      ( ~ class_OrderedGroup_Oab__group__add(X20)
      | c_HOL_Oplus__class_Oplus(X19,c_HOL_Oplus__class_Oplus(X18,X17,X20),X20) = c_HOL_Oplus__class_Oplus(X18,c_HOL_Oplus__class_Oplus(X19,X17,X20),X20) ),
    inference(variable_rename,[status(thm)],[c_0_1119]) ).

fof(c_0_1917,plain,
    ! [X17,X18,X19,X20] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X20)
      | c_HOL_Oplus__class_Oplus(X19,c_HOL_Oplus__class_Oplus(X18,X17,X20),X20) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X19,X18,X20),X17,X20) ),
    inference(variable_rename,[status(thm)],[c_0_1120]) ).

fof(c_0_1918,plain,
    ! [X17,X18,X19,X20] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X20)
      | c_HOL_Otimes__class_Otimes(X19,c_HOL_Otimes__class_Otimes(X18,X17,X20),X20) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X19,X18,X20),X17,X20) ),
    inference(variable_rename,[status(thm)],[c_0_1121]) ).

fof(c_0_1919,plain,
    ! [X15,X16,X17,X18] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X18)
      | c_HOL_Otimes__class_Otimes(X17,c_HOL_Otimes__class_Otimes(X16,X15,X18),X18) = c_HOL_Otimes__class_Otimes(X16,c_HOL_Otimes__class_Otimes(X17,X15,X18),X18) ),
    inference(variable_rename,[status(thm)],[c_0_1122]) ).

fof(c_0_1920,plain,
    ! [X15,X16,X17,X18] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X18)
      | c_HOL_Otimes__class_Otimes(X17,c_HOL_Otimes__class_Otimes(X16,X15,X18),X18) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X17,X16,X18),X15,X18) ),
    inference(variable_rename,[status(thm)],[c_0_1123]) ).

fof(c_0_1921,plain,
    ! [X15,X16,X17,X18] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X18)
      | c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X17,X16,X18),X15,X18) = c_HOL_Otimes__class_Otimes(X17,c_HOL_Otimes__class_Otimes(X16,X15,X18),X18) ),
    inference(variable_rename,[status(thm)],[c_0_1124]) ).

fof(c_0_1922,plain,
    ! [X15,X16,X17,X18] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X18)
      | c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X17,X16,X18),X15,X18) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X17,X15,X18),X16,X18) ),
    inference(variable_rename,[status(thm)],[c_0_1125]) ).

fof(c_0_1923,plain,
    ! [X16,X17,X18,X19] :
      ( ~ class_OrderedGroup_Oab__semigroup__mult(X19)
      | c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X18,X17,X19),X16,X19) = c_HOL_Otimes__class_Otimes(X18,c_HOL_Otimes__class_Otimes(X17,X16,X19),X19) ),
    inference(variable_rename,[status(thm)],[c_0_1126]) ).

fof(c_0_1924,plain,
    ! [X16,X17,X18,X19] :
      ( ~ class_OrderedGroup_Ocomm__monoid__add(X19)
      | c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X18,X17,X19),X16,X19) = c_HOL_Oplus__class_Oplus(X18,c_HOL_Oplus__class_Oplus(X17,X16,X19),X19) ),
    inference(variable_rename,[status(thm)],[c_0_1127]) ).

fof(c_0_1925,plain,
    ! [X16,X17,X18,X19] :
      ( ~ class_OrderedGroup_Ocomm__monoid__add(X19)
      | c_HOL_Oplus__class_Oplus(X18,c_HOL_Oplus__class_Oplus(X17,X16,X19),X19) = c_HOL_Oplus__class_Oplus(X17,c_HOL_Oplus__class_Oplus(X18,X16,X19),X19) ),
    inference(variable_rename,[status(thm)],[c_0_1128]) ).

fof(c_0_1926,plain,
    ! [X4] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X4)
      | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X4),c_HOL_Ozero__class_Ozero(X4),X4),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X4),c_HOL_Ozero__class_Ozero(X4),X4),X4) = c_HOL_Ozero__class_Ozero(X4) ),
    inference(variable_rename,[status(thm)],[c_0_1129]) ).

fof(c_0_1927,plain,
    ! [X17,X18,X19] :
      ( c_Ring__and__Field_Odvd__class_Odvd(X19,X17,tc_nat)
      | c_Ring__and__Field_Odvd__class_Odvd(X17,X18,tc_nat)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X18,X17,tc_nat)
      | c_Ring__and__Field_Odvd__class_Odvd(X18,X19,tc_nat)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X19,X18,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_1130]) ).

fof(c_0_1928,plain,
    ! [X4,X5,X6] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add(X6)
      | c_HOL_Oord__class_Oless(X5,X4,X6)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X5,X4,X6),c_HOL_Ozero__class_Ozero(X6),X6) ),
    inference(variable_rename,[status(thm)],[c_0_1131]) ).

fof(c_0_1929,plain,
    ! [X4,X5,X6] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add(X6)
      | c_lessequals(X5,X4,X6)
      | ~ c_lessequals(c_HOL_Ominus__class_Ominus(X5,X4,X6),c_HOL_Ozero__class_Ozero(X6),X6) ),
    inference(variable_rename,[status(thm)],[c_0_1132]) ).

fof(c_0_1930,plain,
    ! [X6,X7] : c_Divides_Odiv__class_Omod(c_Suc(X7),X6,tc_nat) = c_Divides_Odiv__class_Omod(c_Suc(c_Divides_Odiv__class_Omod(X7,X6,tc_nat)),X6,tc_nat),
    inference(variable_rename,[status(thm)],[c_0_1133]) ).

fof(c_0_1931,plain,
    ! [X9,X10,X11] :
      ( c_Ring__and__Field_Odvd__class_Odvd(X11,c_HOL_Ominus__class_Ominus(X10,X9,tc_nat),tc_nat)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X11,X9,tc_nat)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X11,X10,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_1134]) ).

fof(c_0_1932,plain,
    ! [X34,X35,X36,X37,X38] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add(X38)
      | c_HOL_Ominus__class_Ominus(X37,X35,X38) != c_HOL_Ominus__class_Ominus(X36,X34,X38)
      | c_HOL_Oord__class_Oless(X37,X35,X38)
      | ~ c_HOL_Oord__class_Oless(X36,X34,X38) ),
    inference(variable_rename,[status(thm)],[c_0_1135]) ).

fof(c_0_1933,plain,
    ! [X34,X35,X36,X37,X38] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add(X38)
      | c_HOL_Ominus__class_Ominus(X37,X35,X38) != c_HOL_Ominus__class_Ominus(X36,X34,X38)
      | c_HOL_Oord__class_Oless(X36,X34,X38)
      | ~ c_HOL_Oord__class_Oless(X37,X35,X38) ),
    inference(variable_rename,[status(thm)],[c_0_1136]) ).

fof(c_0_1934,plain,
    ! [X34,X35,X36,X37,X38] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add(X38)
      | c_HOL_Ominus__class_Ominus(X37,X35,X38) != c_HOL_Ominus__class_Ominus(X36,X34,X38)
      | c_lessequals(X35,X37,X38)
      | ~ c_lessequals(X34,X36,X38) ),
    inference(variable_rename,[status(thm)],[c_0_1137]) ).

fof(c_0_1935,plain,
    ! [X34,X35,X36,X37,X38] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add(X38)
      | c_HOL_Ominus__class_Ominus(X37,X35,X38) != c_HOL_Ominus__class_Ominus(X36,X34,X38)
      | c_lessequals(X34,X36,X38)
      | ~ c_lessequals(X35,X37,X38) ),
    inference(variable_rename,[status(thm)],[c_0_1138]) ).

fof(c_0_1936,plain,
    ! [X9,X10,X11] :
      ( c_lessequals(c_HOL_Otimes__class_Otimes(X10,X11,tc_nat),c_HOL_Otimes__class_Otimes(X9,X11,tc_nat),tc_nat)
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X11,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_1139]) ).

fof(c_0_1937,plain,
    ! [X9,X10,X11] :
      ( c_lessequals(c_HOL_Otimes__class_Otimes(X11,X10,tc_nat),c_HOL_Otimes__class_Otimes(X11,X9,tc_nat),tc_nat)
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X11,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_1140]) ).

fof(c_0_1938,plain,
    ! [X17,X18,X19,X20] :
      ( ~ class_Orderings_Olinorder(X20)
      | c_HOL_Oord__class_Oless(X17,X19,X20)
      | ~ c_HOL_Oord__class_Oless(X17,c_Orderings_Oord__class_Omin(X19,X18,X20),X20) ),
    inference(variable_rename,[status(thm)],[c_0_1141]) ).

fof(c_0_1939,plain,
    ! [X17,X18,X19,X20] :
      ( ~ class_Orderings_Olinorder(X20)
      | c_HOL_Oord__class_Oless(X17,X18,X20)
      | ~ c_HOL_Oord__class_Oless(X17,c_Orderings_Oord__class_Omin(X19,X18,X20),X20) ),
    inference(variable_rename,[status(thm)],[c_0_1142]) ).

fof(c_0_1940,plain,
    ! [X17,X18,X19,X20] :
      ( ~ class_Orderings_Olinorder(X20)
      | c_lessequals(X19,X17,X20)
      | ~ c_lessequals(X19,c_Orderings_Oord__class_Omin(X18,X17,X20),X20) ),
    inference(variable_rename,[status(thm)],[c_0_1143]) ).

fof(c_0_1941,plain,
    ! [X17,X18,X19,X20] :
      ( ~ class_Orderings_Olinorder(X20)
      | c_lessequals(X19,X18,X20)
      | ~ c_lessequals(X19,c_Orderings_Oord__class_Omin(X18,X17,X20),X20) ),
    inference(variable_rename,[status(thm)],[c_0_1144]) ).

fof(c_0_1942,plain,
    ! [X8,X9,X10,X11] :
      ( ~ class_Orderings_Olinorder(X11)
      | c_lessequals(X8,X9,X11)
      | ~ c_lessequals(X8,c_Orderings_Oord__class_Omin(X10,X9,X11),X11) ),
    inference(variable_rename,[status(thm)],[c_0_1145]) ).

fof(c_0_1943,plain,
    ! [X8,X9,X10,X11] :
      ( ~ class_Orderings_Olinorder(X11)
      | c_lessequals(X8,X10,X11)
      | ~ c_lessequals(X8,c_Orderings_Oord__class_Omin(X10,X9,X11),X11) ),
    inference(variable_rename,[status(thm)],[c_0_1146]) ).

fof(c_0_1944,plain,
    ! [X16,X17,X18,X19] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X19)
      | c_Ring__and__Field_Odvd__class_Odvd(X17,X16,X19)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X18,X17,X19),X16,X19) ),
    inference(variable_rename,[status(thm)],[c_0_1147]) ).

fof(c_0_1945,plain,
    ! [X16,X17,X18,X19] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X19)
      | c_Ring__and__Field_Odvd__class_Odvd(X18,X16,X19)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X18,X17,X19),X16,X19) ),
    inference(variable_rename,[status(thm)],[c_0_1148]) ).

fof(c_0_1946,plain,
    ! [X6,X7,X8] :
      ( ~ class_Ring__and__Field_Oring__1(X8)
      | c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Ominus__class_Ominus(X7,X6,tc_nat),X8) = c_HOL_Ominus__class_Ominus(c_Nat_Osemiring__1__class_Oof__nat(X7,X8),c_Nat_Osemiring__1__class_Oof__nat(X6,X8),X8)
      | ~ c_lessequals(X6,X7,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_1149]) ).

fof(c_0_1947,plain,
    ! [X11,X12,X13] : c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X13,X12,tc_nat),X11,tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X13,X11,tc_nat),X12,tc_nat),
    inference(variable_rename,[status(thm)],[c_0_1150]) ).

fof(c_0_1948,plain,
    ! [X11,X12,X13] : c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X13,X12,tc_nat),X11,tc_nat) = c_HOL_Ominus__class_Ominus(X13,c_HOL_Oplus__class_Oplus(X12,X11,tc_nat),tc_nat),
    inference(variable_rename,[status(thm)],[c_0_1151]) ).

fof(c_0_1949,plain,
    ! [X9,X10,X11] : c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X10,X11,tc_nat),c_HOL_Oplus__class_Oplus(X9,X11,tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(X10,X9,tc_nat),
    inference(variable_rename,[status(thm)],[c_0_1152]) ).

fof(c_0_1950,plain,
    ! [X9,X10,X11] : c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X11,X10,tc_nat),c_HOL_Oplus__class_Oplus(X11,X9,tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(X10,X9,tc_nat),
    inference(variable_rename,[status(thm)],[c_0_1153]) ).

fof(c_0_1951,plain,
    ! [X17,X18,X19] : c_HOL_Oplus__class_Oplus(X19,c_HOL_Oplus__class_Oplus(X18,X17,tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(X18,c_HOL_Oplus__class_Oplus(X19,X17,tc_nat),tc_nat),
    inference(variable_rename,[status(thm)],[c_0_1154]) ).

fof(c_0_1952,plain,
    ! [X9,X10,X11] : c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X10,X9,tc_nat),X11,tc_nat) = c_HOL_Oplus__class_Oplus(X10,c_HOL_Oplus__class_Oplus(X9,X11,tc_nat),tc_nat),
    inference(variable_rename,[status(thm)],[c_0_1155]) ).

fof(c_0_1953,plain,
    ! [X9,X10,X11] : c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X10,X9,tc_nat),X11,tc_nat) = c_HOL_Otimes__class_Otimes(X10,c_HOL_Otimes__class_Otimes(X9,X11,tc_nat),tc_nat),
    inference(variable_rename,[status(thm)],[c_0_1156]) ).

fof(c_0_1954,plain,
    ! [X16,X17,X18,X19] :
      ( ~ class_Divides_Osemiring__div(X19)
      | c_Divides_Odiv__class_Omod(c_Divides_Odiv__class_Omod(X18,X17,X19),X16,X19) = c_Divides_Odiv__class_Omod(X18,X16,X19)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X16,X17,X19) ),
    inference(variable_rename,[status(thm)],[c_0_1157]) ).

fof(c_0_1955,plain,
    ! [X6,X7] :
      ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X6,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Otimes__class_Otimes(X7,X6,tc_nat),tc_nat) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1158])])]) ).

fof(c_0_1956,plain,
    ! [X6,X7] :
      ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X7,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Otimes__class_Otimes(X7,X6,tc_nat),tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_1159]) ).

fof(c_0_1957,plain,
    ! [X6,X7] :
      ( c_HOL_Oord__class_Oless(X7,X6,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ominus__class_Ominus(X6,X7,tc_nat),tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_1160]) ).

fof(c_0_1958,plain,
    ! [X17,X18,X19] :
      ( ~ c_Ring__and__Field_Odvd__class_Odvd(X17,X19,tc_nat)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X18,X17,tc_nat)
      | c_Ring__and__Field_Odvd__class_Odvd(X18,X19,tc_nat)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X19,X18,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_1161]) ).

fof(c_0_1959,plain,
    ! [X17,X18,X19] :
      ( ~ c_Ring__and__Field_Odvd__class_Odvd(X17,X19,tc_nat)
      | c_Ring__and__Field_Odvd__class_Odvd(X17,X18,tc_nat)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X18,X17,tc_nat)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X19,X18,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_1162]) ).

fof(c_0_1960,plain,
    ! [X8,X9,X10] :
      ( ~ class_Ring__and__Field_Oordered__idom(X10)
      | c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(X8,X10),X9,X10) = c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(X8,X9,X10),X10)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X10),X9,X10) ),
    inference(variable_rename,[status(thm)],[c_0_1163]) ).

fof(c_0_1961,plain,
    ! [X30,X31,X32,X33] :
      ( c_HOL_Oplus__class_Oplus(X31,X32,tc_nat) != c_HOL_Oplus__class_Oplus(X33,X30,tc_nat)
      | ~ c_HOL_Oord__class_Oless(X33,X32,tc_nat)
      | c_HOL_Oord__class_Oless(X31,X30,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_1164]) ).

fof(c_0_1962,plain,
    ! [X11,X12,X13] :
      ( c_HOL_Oord__class_Oless(X13,X11,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X13,X12,tc_nat),X11,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_1165]) ).

fof(c_0_1963,plain,
    ! [X9,X10] :
      ( c_Ring__and__Field_Odvd__class_Odvd(X10,X9,tc_nat)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X10,c_HOL_Oplus__class_Oplus(X9,X10,tc_nat),tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_1166]) ).

fof(c_0_1964,plain,
    ! [X9,X10,X11] :
      ( c_lessequals(X11,X9,tc_nat)
      | ~ c_lessequals(c_HOL_Oplus__class_Oplus(X10,X11,tc_nat),X9,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_1167]) ).

fof(c_0_1965,plain,
    ! [X9,X10,X11] :
      ( c_lessequals(X10,X9,tc_nat)
      | ~ c_lessequals(c_HOL_Oplus__class_Oplus(X10,X11,tc_nat),X9,tc_nat) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1168])])]) ).

fof(c_0_1966,plain,
    ! [X4,X5,X6] :
      ( ~ class_Ring__and__Field_Oidom(X6)
      | c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X5,c_HOL_Ozero__class_Ozero(X6),X6),c_HOL_Otimes__class_Otimes(X4,c_HOL_Ozero__class_Ozero(X6),X6),X6) ),
    inference(variable_rename,[status(thm)],[c_0_1169]) ).

fof(c_0_1967,plain,
    ! [X4,X5,X6] :
      ( ~ class_Ring__and__Field_Oidom(X6)
      | c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X6),X5,X6),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X6),X4,X6),X6) ),
    inference(variable_rename,[status(thm)],[c_0_1170]) ).

fof(c_0_1968,plain,
    ! [X8,X9,X10] :
      ( ~ class_OrderedGroup_Opordered__comm__monoid__add(X10)
      | c_HOL_Oplus__class_Oplus(X9,X8,X10) != c_HOL_Ozero__class_Ozero(X10)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X10),X8,X10)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X10),X9,X10)
      | X9 = c_HOL_Ozero__class_Ozero(X10) ),
    inference(variable_rename,[status(thm)],[c_0_1171]) ).

fof(c_0_1969,plain,
    ! [X8,X9,X10] :
      ( ~ class_OrderedGroup_Opordered__comm__monoid__add(X10)
      | c_HOL_Oplus__class_Oplus(X9,X8,X10) != c_HOL_Ozero__class_Ozero(X10)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X10),X8,X10)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X10),X9,X10)
      | X8 = c_HOL_Ozero__class_Ozero(X10) ),
    inference(variable_rename,[status(thm)],[c_0_1172]) ).

fof(c_0_1970,plain,
    ! [X6,X7] :
      ( c_Divides_Odiv__class_Omod(X7,X6,tc_nat) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X7,X6,tc_nat),X6,tc_nat)
      | ~ c_lessequals(X6,X7,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_1173]) ).

fof(c_0_1971,plain,
    ! [X4] :
      ( ~ class_OrderedGroup_Opordered__comm__monoid__add(X4)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),c_HOL_Ozero__class_Ozero(X4),X4)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X4),c_HOL_Ozero__class_Ozero(X4),X4)
      | c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X4),c_HOL_Ozero__class_Ozero(X4),X4) = c_HOL_Ozero__class_Ozero(X4) ),
    inference(variable_rename,[status(thm)],[c_0_1174]) ).

fof(c_0_1972,plain,
    ! [X6,X7] :
      ( c_Divides_Odiv__class_Omod(c_Suc(X7),X6,tc_nat) = c_Suc(c_Divides_Odiv__class_Omod(X7,X6,tc_nat))
      | c_Suc(c_Divides_Odiv__class_Omod(X7,X6,tc_nat)) = X6 ),
    inference(variable_rename,[status(thm)],[c_0_1175]) ).

fof(c_0_1973,plain,
    ! [X17,X18,X19] :
      ( c_Ring__and__Field_Odvd__class_Odvd(X19,X17,tc_nat)
      | c_Ring__and__Field_Odvd__class_Odvd(X17,X18,tc_nat)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X18,X17,tc_nat)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X19,X18,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_1176]) ).

fof(c_0_1974,plain,
    ! [X17,X18,X19] :
      ( c_Ring__and__Field_Odvd__class_Odvd(X19,X17,tc_nat)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X18,X17,tc_nat)
      | c_Ring__and__Field_Odvd__class_Odvd(X18,X19,tc_nat)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X19,X18,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_1177]) ).

fof(c_0_1975,plain,
    ! [X6,X7] : c_Ring__and__Field_Odvd__class_Odvd(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),tc_nat),
    inference(variable_rename,[status(thm)],[c_0_1178]) ).

fof(c_0_1976,plain,
    ! [X4,X5] :
      ( ~ class_OrderedGroup_Olordered__ab__group__add(X5)
      | c_lessequals(c_HOL_Oplus__class_Oplus(X4,X4,X5),c_HOL_Ozero__class_Ozero(X5),X5)
      | ~ c_lessequals(X4,c_HOL_Ozero__class_Ozero(X5),X5) ),
    inference(variable_rename,[status(thm)],[c_0_1179]) ).

fof(c_0_1977,plain,
    ! [X4,X5] :
      ( ~ class_OrderedGroup_Olordered__ab__group__add(X5)
      | c_lessequals(c_HOL_Ozero__class_Ozero(X5),c_HOL_Oplus__class_Oplus(X4,X4,X5),X5)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X5),X4,X5) ),
    inference(variable_rename,[status(thm)],[c_0_1180]) ).

fof(c_0_1978,plain,
    ! [X4,X5] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X5)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X4,X4,X5),c_HOL_Ozero__class_Ozero(X5),X5) ),
    inference(variable_rename,[status(thm)],[c_0_1181]) ).

fof(c_0_1979,plain,
    ! [X4,X5] :
      ( ~ class_OrderedGroup_Olordered__ab__group__add(X5)
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),c_HOL_Oplus__class_Oplus(X4,X4,X5),X5)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),X4,X5) ),
    inference(variable_rename,[status(thm)],[c_0_1182]) ).

fof(c_0_1980,plain,
    ! [X4,X5] :
      ( ~ class_Ring__and__Field_Oordered__idom(X5)
      | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X4,X4,X5),c_HOL_Ozero__class_Ozero(X5),X5)
      | ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X5),X5) ),
    inference(variable_rename,[status(thm)],[c_0_1183]) ).

fof(c_0_1981,plain,
    ! [X4,X5] :
      ( ~ class_OrderedGroup_Olordered__ab__group__add(X5)
      | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X4,X4,X5),c_HOL_Ozero__class_Ozero(X5),X5)
      | ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X5),X5) ),
    inference(variable_rename,[status(thm)],[c_0_1184]) ).

fof(c_0_1982,plain,
    ! [X8,X9] :
      ( ~ c_Parity_Oeven__odd__class_Oeven(X8,tc_nat)
      | c_Parity_Oeven__odd__class_Oeven(X9,tc_nat)
      | c_HOL_Oord__class_Oless(X9,X8,tc_nat)
      | ~ c_Parity_Oeven__odd__class_Oeven(c_HOL_Ominus__class_Ominus(X9,X8,tc_nat),tc_nat) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1185])])]) ).

fof(c_0_1983,plain,
    ! [X8,X9] :
      ( ~ c_Parity_Oeven__odd__class_Oeven(X9,tc_nat)
      | c_Parity_Oeven__odd__class_Oeven(X8,tc_nat)
      | c_HOL_Oord__class_Oless(X9,X8,tc_nat)
      | ~ c_Parity_Oeven__odd__class_Oeven(c_HOL_Ominus__class_Ominus(X9,X8,tc_nat),tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_1186]) ).

fof(c_0_1984,plain,
    ! [X8,X9] : c_HOL_Oord__class_Oless(X9,c_Suc(c_HOL_Oplus__class_Oplus(X9,X8,tc_nat)),tc_nat),
    inference(variable_rename,[status(thm)],[c_0_1187]) ).

fof(c_0_1985,plain,
    ! [X11,X12] : c_HOL_Oord__class_Oless(X12,c_Suc(c_HOL_Oplus__class_Oplus(X11,X12,tc_nat)),tc_nat),
    inference(variable_rename,[status(thm)],[c_0_1188]) ).

fof(c_0_1986,plain,
    ! [X11,X12] : c_HOL_Oord__class_Oless(X12,c_Suc(c_HOL_Oplus__class_Oplus(X12,X11,tc_nat)),tc_nat),
    inference(variable_rename,[status(thm)],[c_0_1189]) ).

fof(c_0_1987,plain,
    ! [X6,X7] :
      ( c_Divides_Odiv__class_Omod(X7,X6,tc_nat) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X7,X6,tc_nat),X6,tc_nat)
      | c_HOL_Oord__class_Oless(X7,X6,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_1190]) ).

fof(c_0_1988,plain,
    ! [X4,X5,X6] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add(X6)
      | c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X5,X4,X6),c_HOL_Ozero__class_Ozero(X6),X6)
      | ~ c_HOL_Oord__class_Oless(X5,X4,X6) ),
    inference(variable_rename,[status(thm)],[c_0_1191]) ).

fof(c_0_1989,plain,
    ! [X4,X5,X6] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add(X6)
      | c_lessequals(c_HOL_Ominus__class_Ominus(X5,X4,X6),c_HOL_Ozero__class_Ozero(X6),X6)
      | ~ c_lessequals(X5,X4,X6) ),
    inference(variable_rename,[status(thm)],[c_0_1192]) ).

fof(c_0_1990,plain,
    ! [X11,X12] :
      ( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X11,c_Suc(X12),tc_nat),X11,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X11,tc_nat) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1193])])]) ).

fof(c_0_1991,plain,
    ! [X9,X10,X11] :
      ( c_HOL_Otimes__class_Otimes(X11,X10,tc_nat) != c_HOL_Otimes__class_Otimes(X11,X9,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X11,tc_nat)
      | X10 = X9 ),
    inference(variable_rename,[status(thm)],[c_0_1194]) ).

fof(c_0_1992,plain,
    ! [X6,X7] :
      ( ~ c_Ring__and__Field_Odvd__class_Odvd(X6,X7,tc_nat)
      | ~ c_HOL_Oord__class_Oless(X7,X6,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X7,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_1195]) ).

fof(c_0_1993,plain,
    ! [X8,X9,X10,X11] :
      ( ~ class_Orderings_Olinorder(X11)
      | c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omin(X10,X9,X11),X8,X11)
      | ~ c_HOL_Oord__class_Oless(X10,X8,X11) ),
    inference(variable_rename,[status(thm)],[c_0_1196]) ).

fof(c_0_1994,plain,
    ! [X8,X9,X10,X11] :
      ( ~ class_Orderings_Olinorder(X11)
      | c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omin(X10,X9,X11),X8,X11)
      | ~ c_HOL_Oord__class_Oless(X9,X8,X11) ),
    inference(variable_rename,[status(thm)],[c_0_1197]) ).

fof(c_0_1995,plain,
    ! [X17,X18,X19,X20] :
      ( ~ class_Orderings_Olinorder(X20)
      | c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omin(X19,X18,X20),X17,X20)
      | ~ c_HOL_Oord__class_Oless(X19,X17,X20) ),
    inference(variable_rename,[status(thm)],[c_0_1198]) ).

fof(c_0_1996,plain,
    ! [X17,X18,X19,X20] :
      ( ~ class_Orderings_Olinorder(X20)
      | c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omin(X19,X18,X20),X17,X20)
      | ~ c_HOL_Oord__class_Oless(X18,X17,X20) ),
    inference(variable_rename,[status(thm)],[c_0_1199]) ).

fof(c_0_1997,plain,
    ! [X17,X18,X19,X20] :
      ( ~ class_Orderings_Olinorder(X20)
      | c_lessequals(c_Orderings_Oord__class_Omin(X19,X18,X20),X17,X20)
      | ~ c_lessequals(X18,X17,X20) ),
    inference(variable_rename,[status(thm)],[c_0_1200]) ).

fof(c_0_1998,plain,
    ! [X17,X18,X19,X20] :
      ( ~ class_Orderings_Olinorder(X20)
      | c_lessequals(c_Orderings_Oord__class_Omin(X19,X18,X20),X17,X20)
      | ~ c_lessequals(X19,X17,X20) ),
    inference(variable_rename,[status(thm)],[c_0_1201]) ).

fof(c_0_1999,plain,
    ! [X8,X9,X10,X11] :
      ( ~ class_Orderings_Olinorder(X11)
      | c_lessequals(c_Orderings_Oord__class_Omin(X10,X9,X11),X8,X11)
      | ~ c_lessequals(X9,X8,X11) ),
    inference(variable_rename,[status(thm)],[c_0_1202]) ).

fof(c_0_2000,plain,
    ! [X8,X9,X10,X11] :
      ( ~ class_Orderings_Olinorder(X11)
      | c_lessequals(c_Orderings_Oord__class_Omin(X10,X9,X11),X8,X11)
      | ~ c_lessequals(X10,X8,X11) ),
    inference(variable_rename,[status(thm)],[c_0_1203]) ).

fof(c_0_2001,plain,
    ! [X16,X17,X18,X19] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X19)
      | c_Ring__and__Field_Odvd__class_Odvd(X18,c_HOL_Otimes__class_Otimes(X17,X16,X19),X19)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X18,X17,X19) ),
    inference(variable_rename,[status(thm)],[c_0_1204]) ).

fof(c_0_2002,plain,
    ! [X16,X17,X18,X19] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X19)
      | c_Ring__and__Field_Odvd__class_Odvd(X18,c_HOL_Otimes__class_Otimes(X17,X16,X19),X19)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X18,X16,X19) ),
    inference(variable_rename,[status(thm)],[c_0_1205]) ).

fof(c_0_2003,plain,
    ! [X6,X7] :
      ( c_HOL_Ominus__class_Ominus(c_Suc(X7),X6,tc_nat) = c_Suc(c_HOL_Ominus__class_Ominus(X7,X6,tc_nat))
      | ~ c_lessequals(X6,X7,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_1206]) ).

fof(c_0_2004,plain,
    ! [X4,X5,X6] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X6)
      | c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X5,X4,X6),X6) = c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X4,X5,X6),X6) ),
    inference(variable_rename,[status(thm)],[c_0_1207]) ).

fof(c_0_2005,plain,
    ! [X6,X7] :
      ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oplus__class_Oplus(X7,X6,tc_nat),tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X7,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_1208]) ).

fof(c_0_2006,plain,
    ! [X6,X7] :
      ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oplus__class_Oplus(X7,X6,tc_nat),tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X6,tc_nat) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1209])])]) ).

fof(c_0_2007,plain,
    ! [X11,X12] : ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X11,X12,tc_nat),X12,tc_nat),
    inference(variable_rename,[status(thm)],[c_0_1210]) ).

fof(c_0_2008,plain,
    ! [X11,X12] : ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X12,X11,tc_nat),X12,tc_nat),
    inference(variable_rename,[status(thm)],[c_0_1211]) ).

fof(c_0_2009,plain,
    ! [X6,X7] :
      ( c_HOL_Oord__class_Oless(c_Divides_Odiv__class_Omod(X7,X6,tc_nat),X6,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X6,tc_nat) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1212])])]) ).

fof(c_0_2010,plain,
    ! [X6,X7] :
      ( c_lessequals(c_Divides_Odiv__class_Omod(X7,X6,tc_nat),X6,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X6,tc_nat) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1213])])]) ).

fof(c_0_2011,plain,
    ! [X6,X7] :
      ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ominus__class_Ominus(X6,X7,tc_nat),tc_nat)
      | ~ c_HOL_Oord__class_Oless(X7,X6,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_1214]) ).

fof(c_0_2012,plain,
    ! [X11,X12] :
      ( c_HOL_Ominus__class_Ominus(X11,c_HOL_Ominus__class_Ominus(X11,X12,tc_nat),tc_nat) = X12
      | ~ c_lessequals(X12,X11,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_1215]) ).

fof(c_0_2013,plain,
    ! [X11,X12] :
      ( ~ c_lessequals(X12,X11,tc_nat)
      | X11 = c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X11,X12,tc_nat),X12,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_1216]) ).

fof(c_0_2014,plain,
    ! [X6,X7] :
      ( c_HOL_Oplus__class_Oplus(X6,c_HOL_Ominus__class_Ominus(X7,X6,tc_nat),tc_nat) = X7
      | ~ c_lessequals(X6,X7,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_1217]) ).

fof(c_0_2015,plain,
    ! [X6,X7] :
      ( c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X7,X6,tc_nat),X6,tc_nat) = X7
      | ~ c_lessequals(X6,X7,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_1218]) ).

fof(c_0_2016,plain,
    ! [X10,X11,X12] :
      ( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X12,X10,tc_nat),X11,tc_nat)
      | ~ c_HOL_Oord__class_Oless(X12,X11,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_1219]) ).

fof(c_0_2017,plain,
    ! [X11,X12,X13] :
      ( c_HOL_Oord__class_Oless(X13,c_HOL_Oplus__class_Oplus(X11,X12,tc_nat),tc_nat)
      | ~ c_HOL_Oord__class_Oless(X13,X12,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_1220]) ).

fof(c_0_2018,plain,
    ! [X11,X12,X13] :
      ( c_HOL_Oord__class_Oless(X13,c_HOL_Oplus__class_Oplus(X12,X11,tc_nat),tc_nat)
      | ~ c_HOL_Oord__class_Oless(X13,X12,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_1221]) ).

fof(c_0_2019,plain,
    ! [X17,X18,X19] :
      ( c_HOL_Oord__class_Oless(X19,c_HOL_Oplus__class_Oplus(X18,X17,tc_nat),tc_nat)
      | ~ c_HOL_Oord__class_Oless(X19,X17,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_1222]) ).

fof(c_0_2020,plain,
    ! [X17,X18,X19] :
      ( c_HOL_Oord__class_Oless(X19,c_HOL_Oplus__class_Oplus(X18,X17,tc_nat),tc_nat)
      | ~ c_HOL_Oord__class_Oless(X19,X18,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_1223]) ).

fof(c_0_2021,plain,
    ! [X9,X10] :
      ( c_Ring__and__Field_Odvd__class_Odvd(X10,c_HOL_Oplus__class_Oplus(X9,X10,tc_nat),tc_nat)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X10,X9,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_1224]) ).

fof(c_0_2022,plain,
    ! [X11,X12,X13] :
      ( c_lessequals(X13,c_HOL_Oplus__class_Oplus(X11,X12,tc_nat),tc_nat)
      | ~ c_lessequals(X13,X12,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_1225]) ).

fof(c_0_2023,plain,
    ! [X11,X12,X13] :
      ( c_lessequals(X13,c_HOL_Oplus__class_Oplus(X12,X11,tc_nat),tc_nat)
      | ~ c_lessequals(X13,X12,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_1226]) ).

fof(c_0_2024,plain,
    ! [X17,X18,X19] :
      ( c_lessequals(X19,c_HOL_Oplus__class_Oplus(X18,X17,tc_nat),tc_nat)
      | ~ c_lessequals(X19,X17,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_1227]) ).

fof(c_0_2025,plain,
    ! [X17,X18,X19] :
      ( c_lessequals(X19,c_HOL_Oplus__class_Oplus(X18,X17,tc_nat),tc_nat)
      | ~ c_lessequals(X19,X18,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_1228]) ).

fof(c_0_2026,plain,
    ! [X17,X18,X19,X20] :
      ( ~ class_Orderings_Opreorder(X20)
      | c_HOL_Oord__class_Oless(X19,X17,X20)
      | ~ c_HOL_Oord__class_Oless(X18,X17,X20)
      | ~ c_HOL_Oord__class_Oless(X19,X18,X20) ),
    inference(variable_rename,[status(thm)],[c_0_1229]) ).

fof(c_0_2027,plain,
    ! [X17,X18,X19,X20] :
      ( ~ class_Orderings_Oorder(X20)
      | c_HOL_Oord__class_Oless(X17,X19,X20)
      | ~ c_HOL_Oord__class_Oless(X17,X18,X20)
      | ~ c_HOL_Oord__class_Oless(X18,X19,X20) ),
    inference(variable_rename,[status(thm)],[c_0_1230]) ).

fof(c_0_2028,plain,
    ! [X17,X18,X19,X20] :
      ( ~ class_Orderings_Oorder(X20)
      | c_lessequals(X17,X19,X20)
      | ~ c_lessequals(X17,X18,X20)
      | ~ c_lessequals(X18,X19,X20) ),
    inference(variable_rename,[status(thm)],[c_0_1231]) ).

fof(c_0_2029,plain,
    ! [X17,X18,X19,X20] :
      ( ~ class_Orderings_Opreorder(X20)
      | c_lessequals(X19,X17,X20)
      | ~ c_lessequals(X18,X17,X20)
      | ~ c_lessequals(X19,X18,X20) ),
    inference(variable_rename,[status(thm)],[c_0_1232]) ).

fof(c_0_2030,plain,
    ! [X17,X18,X19,X20] :
      ( ~ class_Orderings_Opreorder(X20)
      | c_HOL_Oord__class_Oless(X19,X17,X20)
      | ~ c_HOL_Oord__class_Oless(X18,X17,X20)
      | ~ c_lessequals(X19,X18,X20) ),
    inference(variable_rename,[status(thm)],[c_0_1233]) ).

fof(c_0_2031,plain,
    ! [X17,X18,X19,X20] :
      ( ~ class_Orderings_Opreorder(X20)
      | c_HOL_Oord__class_Oless(X19,X17,X20)
      | ~ c_lessequals(X18,X17,X20)
      | ~ c_HOL_Oord__class_Oless(X19,X18,X20) ),
    inference(variable_rename,[status(thm)],[c_0_1234]) ).

fof(c_0_2032,plain,
    ! [X17,X18,X19,X20] :
      ( ~ class_Orderings_Oorder(X20)
      | c_HOL_Oord__class_Oless(X17,X19,X20)
      | ~ c_HOL_Oord__class_Oless(X17,X18,X20)
      | ~ c_lessequals(X18,X19,X20) ),
    inference(variable_rename,[status(thm)],[c_0_1235]) ).

fof(c_0_2033,plain,
    ! [X17,X18,X19,X20] :
      ( ~ class_Orderings_Oorder(X20)
      | c_HOL_Oord__class_Oless(X17,X19,X20)
      | ~ c_lessequals(X17,X18,X20)
      | ~ c_HOL_Oord__class_Oless(X18,X19,X20) ),
    inference(variable_rename,[status(thm)],[c_0_1236]) ).

fof(c_0_2034,plain,
    ! [X16,X17,X18,X19] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X19)
      | c_Ring__and__Field_Odvd__class_Odvd(X18,X16,X19)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X17,X16,X19)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X18,X17,X19) ),
    inference(variable_rename,[status(thm)],[c_0_1237]) ).

fof(c_0_2035,plain,
    ! [X4,X5,X6] :
      ( ~ class_Ring__and__Field_Oordered__idom(X6)
      | c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(X5,X4,X6),X6) = c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(X5,X6),c_HOL_Oabs__class_Oabs(X4,X6),X6) ),
    inference(variable_rename,[status(thm)],[c_0_1238]) ).

fof(c_0_2036,plain,
    ! [X6,X7] :
      ( c_Suc(c_Divides_Odiv__class_Omod(X7,X6,tc_nat)) != X6
      | c_Divides_Odiv__class_Omod(c_Suc(X7),X6,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_1239]) ).

fof(c_0_2037,plain,
    ! [X6,X7,X8] :
      ( ~ class_Ring__and__Field_Osemiring__1(X8)
      | c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Otimes__class_Otimes(X7,X6,tc_nat),X8) = c_HOL_Otimes__class_Otimes(c_Nat_Osemiring__1__class_Oof__nat(X7,X8),c_Nat_Osemiring__1__class_Oof__nat(X6,X8),X8) ),
    inference(variable_rename,[status(thm)],[c_0_1240]) ).

fof(c_0_2038,plain,
    ! [X6,X7,X8] :
      ( ~ class_Ring__and__Field_Osemiring__1(X8)
      | c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Oplus__class_Oplus(X7,X6,tc_nat),X8) = c_HOL_Oplus__class_Oplus(c_Nat_Osemiring__1__class_Oof__nat(X7,X8),c_Nat_Osemiring__1__class_Oof__nat(X6,X8),X8) ),
    inference(variable_rename,[status(thm)],[c_0_1241]) ).

fof(c_0_2039,plain,
    ! [X6,X7] :
      ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X7,tc_nat)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X7,X6,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X6,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_1242]) ).

fof(c_0_2040,plain,
    ! [X6,X7,X8] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X8)
      | c_HOL_Oord__class_Oless(X7,X6,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X7,X8),c_Nat_Osemiring__1__class_Oof__nat(X6,X8),X8) ),
    inference(variable_rename,[status(thm)],[c_0_1243]) ).

fof(c_0_2041,plain,
    ! [X6,X7,X8] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X8)
      | c_lessequals(X7,X6,tc_nat)
      | ~ c_lessequals(c_Nat_Osemiring__1__class_Oof__nat(X7,X8),c_Nat_Osemiring__1__class_Oof__nat(X6,X8),X8) ),
    inference(variable_rename,[status(thm)],[c_0_1244]) ).

fof(c_0_2042,plain,
    ! [X11,X12,X13] :
      ( c_HOL_Oord__class_Oless(c_Suc(X13),X11,tc_nat)
      | ~ c_HOL_Oord__class_Oless(X12,X11,tc_nat)
      | ~ c_HOL_Oord__class_Oless(X13,X12,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_1245]) ).

fof(c_0_2043,plain,
    ! [X9,X10] :
      ( c_lessequals(X10,X9,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X9,tc_nat)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X10,X9,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_1246]) ).

fof(c_0_2044,plain,
    ! [X4,X5,X6] :
      ( ~ class_Divides_Osemiring__div(X6)
      | c_Divides_Odiv__class_Omod(c_Divides_Odiv__class_Omod(X5,X4,X6),X4,X6) = c_Divides_Odiv__class_Omod(X5,X4,X6) ),
    inference(variable_rename,[status(thm)],[c_0_1247]) ).

fof(c_0_2045,plain,
    ! [X8,X9,X10] :
      ( ~ class_Orderings_Olinorder(X10)
      | c_Orderings_Oord__class_Omin(X9,c_Orderings_Oord__class_Omin(X9,X8,X10),X10) = c_Orderings_Oord__class_Omin(X9,X8,X10) ),
    inference(variable_rename,[status(thm)],[c_0_1248]) ).

fof(c_0_2046,plain,
    ! [X4,X5,X6] :
      ( ~ class_Divides_Osemiring__div(X6)
      | c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X5,X4,X6),X4,X6) = c_Divides_Odiv__class_Omod(X5,X4,X6) ),
    inference(variable_rename,[status(thm)],[c_0_1249]) ).

fof(c_0_2047,plain,
    ! [X4,X5,X6] :
      ( ~ class_Divides_Osemiring__div(X6)
      | c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X4,X5,X6),X4,X6) = c_Divides_Odiv__class_Omod(X5,X4,X6) ),
    inference(variable_rename,[status(thm)],[c_0_1250]) ).

fof(c_0_2048,plain,
    ! [X8,X9,X10] :
      ( ~ class_OrderedGroup_Oab__semigroup__idem__mult(X10)
      | c_HOL_Otimes__class_Otimes(X9,c_HOL_Otimes__class_Otimes(X9,X8,X10),X10) = c_HOL_Otimes__class_Otimes(X9,X8,X10) ),
    inference(variable_rename,[status(thm)],[c_0_1251]) ).

fof(c_0_2049,plain,
    ! [X5] :
      ( c_Suc(c_HOL_Ominus__class_Ominus(X5,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat)) = X5
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X5,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_1252]) ).

fof(c_0_2050,plain,
    ! [X11,X12,X13] :
      ( c_lessequals(X13,X11,tc_nat)
      | ~ c_lessequals(X12,X11,tc_nat)
      | ~ c_lessequals(X13,X12,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_1253]) ).

fof(c_0_2051,plain,
    ! [X17,X18,X19] :
      ( c_Ring__and__Field_Odvd__class_Odvd(X19,X17,tc_nat)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X18,X17,tc_nat)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X19,X18,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_1254]) ).

fof(c_0_2052,plain,
    ! [X6,X7] :
      ( ~ c_Parity_Oeven__odd__class_Oeven(c_HOL_Oplus__class_Oplus(X7,X6,tc_nat),tc_nat)
      | ~ c_Parity_Oeven__odd__class_Oeven(X6,tc_nat)
      | c_Parity_Oeven__odd__class_Oeven(X7,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_1255]) ).

fof(c_0_2053,plain,
    ! [X6,X7] :
      ( ~ c_Parity_Oeven__odd__class_Oeven(c_HOL_Oplus__class_Oplus(X7,X6,tc_nat),tc_nat)
      | c_Parity_Oeven__odd__class_Oeven(X6,tc_nat)
      | ~ c_Parity_Oeven__odd__class_Oeven(X7,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_1256]) ).

fof(c_0_2054,plain,
    ! [X6,X7] :
      ( c_Parity_Oeven__odd__class_Oeven(X6,tc_nat)
      | ~ c_Parity_Oeven__odd__class_Oeven(X7,tc_nat)
      | ~ c_Parity_Oeven__odd__class_Oeven(c_HOL_Oplus__class_Oplus(X7,X6,tc_nat),tc_nat) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1257])])]) ).

fof(c_0_2055,plain,
    ! [X6,X7] :
      ( c_Parity_Oeven__odd__class_Oeven(X7,tc_nat)
      | ~ c_Parity_Oeven__odd__class_Oeven(X6,tc_nat)
      | ~ c_Parity_Oeven__odd__class_Oeven(c_HOL_Oplus__class_Oplus(X7,X6,tc_nat),tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_1258]) ).

fof(c_0_2056,plain,
    ! [X8,X9] :
      ( ~ c_Parity_Oeven__odd__class_Oeven(X8,tc_nat)
      | c_Parity_Oeven__odd__class_Oeven(X9,tc_nat)
      | ~ c_Parity_Oeven__odd__class_Oeven(c_HOL_Oplus__class_Oplus(X9,X8,tc_nat),tc_nat) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1259])])]) ).

fof(c_0_2057,plain,
    ! [X8,X9] :
      ( ~ c_Parity_Oeven__odd__class_Oeven(X9,tc_nat)
      | c_Parity_Oeven__odd__class_Oeven(X8,tc_nat)
      | ~ c_Parity_Oeven__odd__class_Oeven(c_HOL_Oplus__class_Oplus(X9,X8,tc_nat),tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_1260]) ).

fof(c_0_2058,plain,
    ! [X6,X7] : c_HOL_Otimes__class_Otimes(X7,c_Suc(X6),tc_nat) = c_HOL_Oplus__class_Oplus(X7,c_HOL_Otimes__class_Otimes(X7,X6,tc_nat),tc_nat),
    inference(variable_rename,[status(thm)],[c_0_1261]) ).

fof(c_0_2059,plain,
    ! [X6,X7] : c_HOL_Otimes__class_Otimes(c_Suc(X7),X6,tc_nat) = c_HOL_Oplus__class_Oplus(X6,c_HOL_Otimes__class_Otimes(X7,X6,tc_nat),tc_nat),
    inference(variable_rename,[status(thm)],[c_0_1262]) ).

fof(c_0_2060,plain,
    ! [X6,X7] :
      ( c_HOL_Oplus__class_Oplus(X6,c_HOL_Ominus__class_Ominus(X7,X6,tc_nat),tc_nat) = X7
      | c_HOL_Oord__class_Oless(X7,X6,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_1263]) ).

fof(c_0_2061,plain,
    ! [X8,X9] :
      ( c_Parity_Oeven__odd__class_Oeven(X8,tc_nat)
      | c_Parity_Oeven__odd__class_Oeven(X9,tc_nat)
      | ~ c_Parity_Oeven__odd__class_Oeven(c_HOL_Otimes__class_Otimes(X9,X8,tc_nat),tc_nat) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1264])])]) ).

fof(c_0_2062,plain,
    ! [X8,X9,X10] :
      ( ~ class_Orderings_Opreorder(X10)
      | c_HOL_Oord__class_Oless(X9,X8,X10)
      | c_lessequals(X8,X9,X10)
      | ~ c_lessequals(X9,X8,X10) ),
    inference(variable_rename,[status(thm)],[c_0_1265]) ).

fof(c_0_2063,plain,
    ! [X8,X9] :
      ( c_Parity_Oeven__odd__class_Oeven(c_HOL_Ominus__class_Ominus(X9,X8,tc_nat),tc_nat)
      | ~ c_HOL_Oord__class_Oless(X9,X8,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_1266]) ).

fof(c_0_2064,plain,
    ! [X5,X6] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X6)
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X5,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X6),c_Nat_Osemiring__1__class_Oof__nat(X5,X6),X6) ),
    inference(variable_rename,[status(thm)],[c_0_1267]) ).

fof(c_0_2065,plain,
    ! [X6,X7,X8] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X8)
      | c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X7,X8),c_Nat_Osemiring__1__class_Oof__nat(X6,X8),X8)
      | ~ c_HOL_Oord__class_Oless(X7,X6,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_1268]) ).

fof(c_0_2066,plain,
    ! [X6,X7,X8] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X8)
      | c_lessequals(c_Nat_Osemiring__1__class_Oof__nat(X7,X8),c_Nat_Osemiring__1__class_Oof__nat(X6,X8),X8)
      | ~ c_lessequals(X7,X6,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_1269]) ).

fof(c_0_2067,plain,
    ! [X9,X10,X11] :
      ( ~ class_Ring__and__Field_Oordered__idom(X11)
      | c_Ring__and__Field_Odvd__class_Odvd(X9,X10,X11)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X9,c_HOL_Oabs__class_Oabs(X10,X11),X11) ),
    inference(variable_rename,[status(thm)],[c_0_1270]) ).

fof(c_0_2068,plain,
    ! [X9,X10,X11] :
      ( ~ class_Ring__and__Field_Oordered__idom(X11)
      | c_Ring__and__Field_Odvd__class_Odvd(X9,X10,X11)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oabs__class_Oabs(X9,X11),X10,X11) ),
    inference(variable_rename,[status(thm)],[c_0_1271]) ).

fof(c_0_2069,plain,
    ! [X4,X5,X6] :
      ( ~ class_Ring__and__Field_Oordered__idom(X6)
      | c_HOL_Oord__class_Oless(X5,X4,X6)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(X5,X6),X4,X6) ),
    inference(variable_rename,[status(thm)],[c_0_1272]) ).

fof(c_0_2070,plain,
    ! [X4,X5,X6] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X6)
      | c_lessequals(X5,X4,X6)
      | ~ c_lessequals(c_HOL_Oabs__class_Oabs(X5,X6),X4,X6) ),
    inference(variable_rename,[status(thm)],[c_0_1273]) ).

fof(c_0_2071,plain,
    ! [X17,X18,X19,X20] :
      ( ~ class_Ring__and__Field_Oidom(X20)
      | ~ class_Int_Onumber__ring(X20)
      | c_HOL_Oplus__class_Oplus(X19,X18,X20) != c_HOL_Oplus__class_Oplus(X19,X17,X20)
      | X18 = X17 ),
    inference(variable_rename,[status(thm)],[c_0_1274]) ).

fof(c_0_2072,plain,
    ! [X9,X10,X11] :
      ( c_HOL_Otimes__class_Otimes(c_Suc(X11),X10,tc_nat) != c_HOL_Otimes__class_Otimes(c_Suc(X11),X9,tc_nat)
      | X10 = X9 ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1275])])]) ).

fof(c_0_2073,plain,
    ! [X5,X6] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X6)
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X6),c_Nat_Osemiring__1__class_Oof__nat(X5,X6),X6)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X5,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_1276]) ).

fof(c_0_2074,plain,
    ! [X8,X9,X10] :
      ( ~ class_Orderings_Oorder(X10)
      | X9 = X8
      | ~ c_lessequals(X9,X8,X10)
      | ~ c_lessequals(X8,X9,X10) ),
    inference(variable_rename,[status(thm)],[c_0_1277]) ).

fof(c_0_2075,plain,
    ! [X8,X9,X10] :
      ( ~ class_Orderings_Oorder(X10)
      | X9 = X8
      | ~ c_lessequals(X8,X9,X10)
      | ~ c_lessequals(X9,X8,X10) ),
    inference(variable_rename,[status(thm)],[c_0_1278]) ).

fof(c_0_2076,plain,
    ! [X8,X9,X10] :
      ( ~ class_Orderings_Oorder(X10)
      | X9 = X8
      | ~ c_lessequals(X8,X9,X10)
      | ~ c_lessequals(X9,X8,X10) ),
    inference(variable_rename,[status(thm)],[c_0_1279]) ).

fof(c_0_2077,plain,
    ! [X19,X20,X21,X22] :
      ( ~ class_OrderedGroup_Oab__group__add(X22)
      | c_HOL_Ominus__class_Ominus(X20,X19,X22) != c_HOL_Ominus__class_Ominus(X21,X21,X22)
      | X20 = X19 ),
    inference(variable_rename,[status(thm)],[c_0_1280]) ).

fof(c_0_2078,plain,
    ! [X34,X35,X36,X37] :
      ( ~ class_OrderedGroup_Oab__group__add(X37)
      | c_HOL_Ominus__class_Ominus(X36,X36,X37) != c_HOL_Ominus__class_Ominus(X35,X34,X37)
      | X35 = X34 ),
    inference(variable_rename,[status(thm)],[c_0_1281]) ).

fof(c_0_2079,plain,
    ! [X16,X17,X18,X19] :
      ( ~ class_OrderedGroup_Ocancel__semigroup__add(X19)
      | c_HOL_Oplus__class_Oplus(X17,X18,X19) != c_HOL_Oplus__class_Oplus(X16,X18,X19)
      | X17 = X16 ),
    inference(variable_rename,[status(thm)],[c_0_1282]) ).

fof(c_0_2080,plain,
    ! [X16,X17,X18,X19] :
      ( ~ class_OrderedGroup_Ocancel__semigroup__add(X19)
      | c_HOL_Oplus__class_Oplus(X18,X17,X19) != c_HOL_Oplus__class_Oplus(X18,X16,X19)
      | X17 = X16 ),
    inference(variable_rename,[status(thm)],[c_0_1283]) ).

fof(c_0_2081,plain,
    ! [X16,X17,X18,X19] :
      ( ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X19)
      | c_HOL_Oplus__class_Oplus(X18,X17,X19) != c_HOL_Oplus__class_Oplus(X18,X16,X19)
      | X17 = X16 ),
    inference(variable_rename,[status(thm)],[c_0_1284]) ).

fof(c_0_2082,plain,
    ! [X8,X9,X10] :
      ( ~ class_Orderings_Opreorder(X10)
      | ~ c_HOL_Oord__class_Oless(X8,X9,X10)
      | ~ c_HOL_Oord__class_Oless(X9,X8,X10) ),
    inference(variable_rename,[status(thm)],[c_0_1285]) ).

fof(c_0_2083,plain,
    ! [X4,X5,X6] :
      ( ~ class_Orderings_Opreorder(X6)
      | ~ c_HOL_Oord__class_Oless(X4,X5,X6)
      | ~ c_HOL_Oord__class_Oless(X5,X4,X6) ),
    inference(variable_rename,[status(thm)],[c_0_1286]) ).

fof(c_0_2084,plain,
    ! [X8,X9,X10] :
      ( ~ class_Orderings_Olinorder(X10)
      | ~ c_HOL_Oord__class_Oless(X9,X8,X10)
      | ~ c_HOL_Oord__class_Oless(X8,X9,X10) ),
    inference(variable_rename,[status(thm)],[c_0_1287]) ).

fof(c_0_2085,plain,
    ! [X4,X5,X6] :
      ( ~ class_Orderings_Oorder(X6)
      | ~ c_HOL_Oord__class_Oless(X5,X4,X6)
      | ~ c_HOL_Oord__class_Oless(X4,X5,X6) ),
    inference(variable_rename,[status(thm)],[c_0_1288]) ).

fof(c_0_2086,plain,
    ! [X8,X9,X10] :
      ( ~ class_Orderings_Olinorder(X10)
      | ~ c_lessequals(X9,X8,X10)
      | ~ c_HOL_Oord__class_Oless(X8,X9,X10) ),
    inference(variable_rename,[status(thm)],[c_0_1289]) ).

fof(c_0_2087,plain,
    ! [X8,X9,X10] :
      ( ~ class_Orderings_Olinorder(X10)
      | ~ c_HOL_Oord__class_Oless(X9,X8,X10)
      | ~ c_lessequals(X8,X9,X10) ),
    inference(variable_rename,[status(thm)],[c_0_1290]) ).

fof(c_0_2088,plain,
    ! [X8,X9] :
      ( ~ class_Orderings_Olinorder(X9)
      | ~ c_lessequals(X8,X8,X9)
      | ~ c_HOL_Oord__class_Oless(X8,X8,X9) ),
    inference(variable_rename,[status(thm)],[c_0_1291]) ).

fof(c_0_2089,plain,
    ! [X8,X9,X10] :
      ( ~ class_Orderings_Opreorder(X10)
      | ~ c_lessequals(X8,X9,X10)
      | ~ c_HOL_Oord__class_Oless(X9,X8,X10) ),
    inference(variable_rename,[status(thm)],[c_0_1292]) ).

fof(c_0_2090,plain,
    ! [X6,X7] :
      ( X6 = X7
      | ~ c_HOL_Oord__class_Oless(X6,c_Suc(X7),tc_nat)
      | ~ c_lessequals(X7,X6,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_1293]) ).

fof(c_0_2091,plain,
    ! [X19] : c_Parity_Oeven__odd__class_Oeven(c_HOL_Otimes__class_Otimes(c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),X19,tc_nat),tc_nat),
    inference(variable_rename,[status(thm)],[c_0_1294]) ).

fof(c_0_2092,plain,
    ! [X6,X7] :
      ( ~ c_HOL_Oord__class_Oless(X7,X6,tc_nat)
      | ~ c_HOL_Oord__class_Oless(X6,c_Suc(X7),tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_1295]) ).

fof(c_0_2093,plain,
    ! [X6,X7] :
      ( ~ c_lessequals(X7,X6,tc_nat)
      | ~ c_lessequals(c_Suc(X6),X7,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_1296]) ).

fof(c_0_2094,plain,
    ! [X6,X7] :
      ( c_HOL_Ominus__class_Ominus(X6,X7,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)
      | c_HOL_Ominus__class_Ominus(X7,X6,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)
      | X7 = X6 ),
    inference(variable_rename,[status(thm)],[c_0_1297]) ).

fof(c_0_2095,plain,
    ! [X4,X5] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X5)
      | c_lessequals(c_HOL_Ozero__class_Ozero(X5),c_HOL_Otimes__class_Otimes(X4,X4,X5),X5) ),
    inference(variable_rename,[status(thm)],[c_0_1298]) ).

fof(c_0_2096,plain,
    ! [X9,X10,X11] :
      ( ~ class_Ring__and__Field_Oordered__idom(X11)
      | c_Ring__and__Field_Odvd__class_Odvd(X9,c_HOL_Oabs__class_Oabs(X10,X11),X11)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X9,X10,X11) ),
    inference(variable_rename,[status(thm)],[c_0_1299]) ).

fof(c_0_2097,plain,
    ! [X9,X10,X11] :
      ( ~ class_Ring__and__Field_Oordered__idom(X11)
      | c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oabs__class_Oabs(X9,X11),X10,X11)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X9,X10,X11) ),
    inference(variable_rename,[status(thm)],[c_0_1300]) ).

fof(c_0_2098,plain,
    ! [X6,X7] : c_Orderings_Oord__class_Omin(c_Suc(X7),c_Suc(X6),tc_nat) = c_Suc(c_Orderings_Oord__class_Omin(X7,X6,tc_nat)),
    inference(variable_rename,[status(thm)],[c_0_1301]) ).

fof(c_0_2099,plain,
    ! [X4,X5,X6] :
      ( ~ class_Divides_Osemiring__div(X6)
      | c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X5,X4,X6),X4,X6) = c_HOL_Ozero__class_Ozero(X6) ),
    inference(variable_rename,[status(thm)],[c_0_1302]) ).

fof(c_0_2100,plain,
    ! [X4,X5,X6] :
      ( ~ class_Divides_Osemiring__div(X6)
      | c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X4,X5,X6),X4,X6) = c_HOL_Ozero__class_Ozero(X6) ),
    inference(variable_rename,[status(thm)],[c_0_1303]) ).

fof(c_0_2101,plain,
    ! [X9,X10,X11] :
      ( c_HOL_Otimes__class_Otimes(X11,X10,tc_nat) != c_HOL_Otimes__class_Otimes(X11,X9,tc_nat)
      | X10 = X9
      | X11 = c_HOL_Ozero__class_Ozero(tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_1304]) ).

fof(c_0_2102,plain,
    ! [X9,X10,X11] :
      ( c_HOL_Otimes__class_Otimes(X11,X10,tc_nat) != c_HOL_Otimes__class_Otimes(X11,X9,tc_nat)
      | X11 = c_HOL_Ozero__class_Ozero(tc_nat)
      | X10 = X9 ),
    inference(variable_rename,[status(thm)],[c_0_1305]) ).

fof(c_0_2103,plain,
    ! [X9,X10,X11] :
      ( c_HOL_Otimes__class_Otimes(X10,X11,tc_nat) != c_HOL_Otimes__class_Otimes(X9,X11,tc_nat)
      | X11 = c_HOL_Ozero__class_Ozero(tc_nat)
      | X10 = X9 ),
    inference(variable_rename,[status(thm)],[c_0_1306]) ).

fof(c_0_2104,plain,
    ! [X8,X9] :
      ( X9 = X8
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X8,X9,tc_nat)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X9,X8,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_1307]) ).

fof(c_0_2105,plain,
    ! [X6,X7] :
      ( X7 = X6
      | ~ c_lessequals(X6,X7,tc_nat)
      | ~ c_lessequals(X7,X6,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_1308]) ).

fof(c_0_2106,plain,
    ! [X8,X9] :
      ( X9 = X8
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X8,X9,tc_nat)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X9,X8,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_1309]) ).

fof(c_0_2107,plain,
    ! [X8,X9] :
      ( ~ c_Ring__and__Field_Odvd__class_Odvd(X8,X9,tc_nat)
      | X9 = X8
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X9,X8,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_1310]) ).

fof(c_0_2108,plain,
    ! [X6,X7] :
      ( X7 = X6
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X6,X7,tc_nat)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X7,X6,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_1311]) ).

fof(c_0_2109,plain,
    ! [X8,X9] :
      ( X9 = X8
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X9,X8,tc_nat)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X8,X9,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_1312]) ).

fof(c_0_2110,plain,
    ! [X3,X4] :
      ( ~ c_Ring__and__Field_Odvd__class_Odvd(X3,X4,tc_nat)
      | X4 = X3
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X3,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_1313]) ).

fof(c_0_2111,plain,
    ! [X3,X4] :
      ( ~ c_Ring__and__Field_Odvd__class_Odvd(X3,X4,tc_nat)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X3,tc_nat)
      | X4 = X3 ),
    inference(variable_rename,[status(thm)],[c_0_1314]) ).

fof(c_0_2112,plain,
    ! [X4,X5,X6] :
      ( ~ class_OrderedGroup_Ogroup__add(X6)
      | c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X5,X4,X6),X4,X6) = X5 ),
    inference(variable_rename,[status(thm)],[c_0_1315]) ).

fof(c_0_2113,plain,
    ! [X4,X5,X6] :
      ( ~ class_OrderedGroup_Ogroup__add(X6)
      | c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X5,X4,X6),X4,X6) = X5 ),
    inference(variable_rename,[status(thm)],[c_0_1316]) ).

fof(c_0_2114,plain,
    ! [X17,X18,X19] :
      ( c_HOL_Oplus__class_Oplus(X19,X18,tc_nat) != c_HOL_Oplus__class_Oplus(X19,X17,tc_nat)
      | X18 = X17 ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1317])])]) ).

fof(c_0_2115,plain,
    ! [X9,X10,X11] :
      ( c_HOL_Oplus__class_Oplus(X11,X10,tc_nat) != c_HOL_Oplus__class_Oplus(X11,X9,tc_nat)
      | X10 = X9 ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1318])])]) ).

fof(c_0_2116,plain,
    ! [X9,X10,X11] :
      ( c_HOL_Oplus__class_Oplus(X10,X11,tc_nat) != c_HOL_Oplus__class_Oplus(X9,X11,tc_nat)
      | X10 = X9 ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1319])])]) ).

fof(c_0_2117,plain,
    ! [X9,X10,X11] :
      ( ~ class_Ring__and__Field_Odvd(X11)
      | c_Ring__and__Field_Odvd__class_Odvd(X10,c_HOL_Otimes__class_Otimes(X10,X9,X11),X11) ),
    inference(variable_rename,[status(thm)],[c_0_1320]) ).

fof(c_0_2118,plain,
    ! [X4,X5,X6] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X6)
      | c_Ring__and__Field_Odvd__class_Odvd(X5,c_HOL_Otimes__class_Otimes(X5,X4,X6),X6) ),
    inference(variable_rename,[status(thm)],[c_0_1321]) ).

fof(c_0_2119,plain,
    ! [X4,X5,X6] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X6)
      | c_Ring__and__Field_Odvd__class_Odvd(X5,c_HOL_Otimes__class_Otimes(X4,X5,X6),X6) ),
    inference(variable_rename,[status(thm)],[c_0_1322]) ).

fof(c_0_2120,plain,
    ! [X8,X9,X10] :
      ( ~ class_Orderings_Olinorder(X10)
      | c_lessequals(c_Orderings_Oord__class_Omin(X9,X8,X10),X9,X10) ),
    inference(variable_rename,[status(thm)],[c_0_1323]) ).

fof(c_0_2121,plain,
    ! [X8,X9,X10] :
      ( ~ class_Orderings_Olinorder(X10)
      | c_lessequals(c_Orderings_Oord__class_Omin(X9,X8,X10),X8,X10) ),
    inference(variable_rename,[status(thm)],[c_0_1324]) ).

fof(c_0_2122,plain,
    ! [X4,X5] :
      ( ~ class_Ring__and__Field_Oordered__idom(X5)
      | c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(X4,X5),c_HOL_Oabs__class_Oabs(X4,X5),X5) = c_HOL_Otimes__class_Otimes(X4,X4,X5) ),
    inference(variable_rename,[status(thm)],[c_0_1325]) ).

fof(c_0_2123,plain,
    ! [X6,X7] : c_HOL_Oplus__class_Oplus(X7,c_Suc(X6),tc_nat) = c_Suc(c_HOL_Oplus__class_Oplus(X7,X6,tc_nat)),
    inference(variable_rename,[status(thm)],[c_0_1326]) ).

fof(c_0_2124,plain,
    ! [X6,X7] : c_HOL_Oplus__class_Oplus(c_Suc(X7),X6,tc_nat) = c_Suc(c_HOL_Oplus__class_Oplus(X7,X6,tc_nat)),
    inference(variable_rename,[status(thm)],[c_0_1327]) ).

fof(c_0_2125,plain,
    ! [X6,X7] : c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X7,X6,tc_nat),c_Suc(X7),tc_nat),
    inference(variable_rename,[status(thm)],[c_0_1328]) ).

fof(c_0_2126,plain,
    ! [X4] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X4)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X4),c_HOL_Oabs__class_Oabs(c_HOL_Ozero__class_Ozero(X4),X4),X4) ),
    inference(variable_rename,[status(thm)],[c_0_1329]) ).

fof(c_0_2127,plain,
    ! [X8] :
      ( c_Divides_Odiv__class_Omod(X8,c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
      | ~ c_Parity_Oeven__odd__class_Oeven(X8,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_1330]) ).

fof(c_0_2128,plain,
    ! [X21,X22] : c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X22,X21,tc_nat),X22,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
    inference(variable_rename,[status(thm)],[c_0_1331]) ).

fof(c_0_2129,plain,
    ! [X6,X7] : c_HOL_Ominus__class_Ominus(X6,c_HOL_Oplus__class_Oplus(X6,X7,tc_nat),tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
    inference(variable_rename,[status(thm)],[c_0_1332]) ).

fof(c_0_2130,plain,
    ! [X6,X7] : c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X7,X6,tc_nat),X6,tc_nat) = X7,
    inference(variable_rename,[status(thm)],[c_0_1333]) ).

fof(c_0_2131,plain,
    ! [X6,X7] : c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X6,X7,tc_nat),X6,tc_nat) = X7,
    inference(variable_rename,[status(thm)],[c_0_1334]) ).

fof(c_0_2132,plain,
    ! [X8,X9] :
      ( c_Parity_Oeven__odd__class_Oeven(c_HOL_Ominus__class_Ominus(X9,X8,tc_nat),tc_nat)
      | ~ c_Parity_Oeven__odd__class_Oeven(X8,tc_nat)
      | ~ c_Parity_Oeven__odd__class_Oeven(X9,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_1335]) ).

fof(c_0_2133,plain,
    ! [X6,X7] :
      ( ~ c_Parity_Oeven__odd__class_Oeven(X6,tc_nat)
      | ~ c_Parity_Oeven__odd__class_Oeven(X7,tc_nat)
      | c_Parity_Oeven__odd__class_Oeven(c_HOL_Oplus__class_Oplus(X7,X6,tc_nat),tc_nat) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1336])])]) ).

fof(c_0_2134,plain,
    ! [X6,X7] :
      ( c_Parity_Oeven__odd__class_Oeven(c_HOL_Oplus__class_Oplus(X7,X6,tc_nat),tc_nat)
      | ~ c_Parity_Oeven__odd__class_Oeven(X6,tc_nat)
      | ~ c_Parity_Oeven__odd__class_Oeven(X7,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_1337]) ).

fof(c_0_2135,plain,
    ! [X8,X9] :
      ( c_Parity_Oeven__odd__class_Oeven(c_HOL_Oplus__class_Oplus(X9,X8,tc_nat),tc_nat)
      | ~ c_Parity_Oeven__odd__class_Oeven(X8,tc_nat)
      | ~ c_Parity_Oeven__odd__class_Oeven(X9,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_1338]) ).

fof(c_0_2136,plain,
    ! [X6,X7] : c_lessequals(c_HOL_Ominus__class_Ominus(X7,X6,tc_nat),X7,tc_nat),
    inference(variable_rename,[status(thm)],[c_0_1339]) ).

fof(c_0_2137,plain,
    ! [X6,X7] : c_lessequals(X6,c_HOL_Oplus__class_Oplus(X6,X7,tc_nat),tc_nat),
    inference(variable_rename,[status(thm)],[c_0_1340]) ).

fof(c_0_2138,plain,
    ! [X6,X7] : c_lessequals(X6,c_HOL_Oplus__class_Oplus(X7,X6,tc_nat),tc_nat),
    inference(variable_rename,[status(thm)],[c_0_1341]) ).

fof(c_0_2139,plain,
    ! [X8,X9] : c_lessequals(X9,c_HOL_Oplus__class_Oplus(X9,X8,tc_nat),tc_nat),
    inference(variable_rename,[status(thm)],[c_0_1342]) ).

fof(c_0_2140,plain,
    ! [X9,X10] : c_lessequals(X10,c_HOL_Oplus__class_Oplus(X10,X9,tc_nat),tc_nat),
    inference(variable_rename,[status(thm)],[c_0_1343]) ).

fof(c_0_2141,plain,
    ! [X6] : c_lessequals(X6,c_HOL_Otimes__class_Otimes(X6,X6,tc_nat),tc_nat),
    inference(variable_rename,[status(thm)],[c_0_1344]) ).

fof(c_0_2142,plain,
    ! [X6,X7] : c_lessequals(c_Divides_Odiv__class_Omod(X7,X6,tc_nat),X7,tc_nat),
    inference(variable_rename,[status(thm)],[c_0_1345]) ).

fof(c_0_2143,plain,
    ! [X6,X7] :
      ( c_HOL_Oord__class_Oless(X7,X6,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_Suc(X7),c_Suc(X6),tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_1346]) ).

fof(c_0_2144,plain,
    ! [X6,X7] :
      ( c_lessequals(X6,X7,tc_nat)
      | ~ c_lessequals(c_Suc(X6),c_Suc(X7),tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_1347]) ).

fof(c_0_2145,plain,
    ! [X4,X5,X6] :
      ( ~ class_Divides_Osemiring__div(X6)
      | c_Divides_Odiv__class_Omod(X4,X5,X6) != c_HOL_Ozero__class_Ozero(X6)
      | c_Ring__and__Field_Odvd__class_Odvd(X5,X4,X6) ),
    inference(variable_rename,[status(thm)],[c_0_1348]) ).

fof(c_0_2146,plain,
    ! [X4,X5,X6] :
      ( ~ class_Divides_Osemiring__div(X6)
      | c_Divides_Odiv__class_Omod(X4,X5,X6) = c_HOL_Ozero__class_Ozero(X6)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X5,X4,X6) ),
    inference(variable_rename,[status(thm)],[c_0_1349]) ).

fof(c_0_2147,plain,
    ! [X6,X7] :
      ( X7 = c_Suc(X6)
      | c_lessequals(X7,X6,tc_nat)
      | ~ c_lessequals(X7,c_Suc(X6),tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_1350]) ).

fof(c_0_2148,plain,
    ! [X8,X9,X10] :
      ( ~ class_Orderings_Oorder(X10)
      | c_HOL_Oord__class_Oless(X9,X8,X10)
      | X9 = X8
      | ~ c_lessequals(X9,X8,X10) ),
    inference(variable_rename,[status(thm)],[c_0_1351]) ).

fof(c_0_2149,plain,
    ! [X8,X9,X10] :
      ( ~ class_Orderings_Oorder(X10)
      | X9 = X8
      | c_HOL_Oord__class_Oless(X9,X8,X10)
      | ~ c_lessequals(X9,X8,X10) ),
    inference(variable_rename,[status(thm)],[c_0_1352]) ).

fof(c_0_2150,plain,
    ! [X4,X5,X6] :
      ( ~ class_Orderings_Oorder(X6)
      | c_HOL_Oord__class_Oless(X5,X4,X6)
      | X5 = X4
      | ~ c_lessequals(X5,X4,X6) ),
    inference(variable_rename,[status(thm)],[c_0_1353]) ).

fof(c_0_2151,plain,
    ! [X4,X5,X6] :
      ( ~ class_Orderings_Oorder(X6)
      | c_HOL_Oord__class_Oless(X5,X4,X6)
      | ~ c_lessequals(X5,X4,X6)
      | X5 = X4 ),
    inference(variable_rename,[status(thm)],[c_0_1354]) ).

fof(c_0_2152,plain,
    ! [X8,X9,X10] :
      ( ~ class_Orderings_Olinorder(X10)
      | X9 = X8
      | ~ c_lessequals(X9,X8,X10)
      | c_HOL_Oord__class_Oless(X9,X8,X10) ),
    inference(variable_rename,[status(thm)],[c_0_1355]) ).

fof(c_0_2153,plain,
    ! [X8,X9,X10] :
      ( ~ class_Orderings_Olinorder(X10)
      | X9 = X8
      | c_HOL_Oord__class_Oless(X9,X8,X10)
      | ~ c_lessequals(X9,X8,X10) ),
    inference(variable_rename,[status(thm)],[c_0_1356]) ).

fof(c_0_2154,plain,
    ! [X4,X5,X6] :
      ( ~ class_Orderings_Oorder(X6)
      | c_HOL_Oord__class_Oless(X4,X5,X6)
      | ~ c_lessequals(X4,X5,X6)
      | X5 = X4 ),
    inference(variable_rename,[status(thm)],[c_0_1357]) ).

fof(c_0_2155,plain,
    ! [X4,X5,X6] :
      ( ~ class_Orderings_Oorder(X6)
      | c_HOL_Oord__class_Oless(X4,X5,X6)
      | X5 = X4
      | ~ c_lessequals(X4,X5,X6) ),
    inference(variable_rename,[status(thm)],[c_0_1358]) ).

fof(c_0_2156,plain,
    ! [X8,X9,X10] :
      ( ~ class_Orderings_Olinorder(X10)
      | c_Orderings_Oord__class_Omin(X9,X8,X10) != X9
      | c_lessequals(X9,X8,X10) ),
    inference(variable_rename,[status(thm)],[c_0_1359]) ).

fof(c_0_2157,plain,
    ! [X8,X9] :
      ( c_HOL_Oord__class_Oless(c_Suc(X8),c_Suc(X9),tc_nat)
      | ~ c_HOL_Oord__class_Oless(X8,X9,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_1360]) ).

fof(c_0_2158,plain,
    ! [X6,X7] :
      ( c_HOL_Oord__class_Oless(c_Suc(X7),c_Suc(X6),tc_nat)
      | ~ c_HOL_Oord__class_Oless(X7,X6,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_1361]) ).

fof(c_0_2159,plain,
    ! [X6,X7] :
      ( c_lessequals(c_Suc(X6),c_Suc(X7),tc_nat)
      | ~ c_lessequals(X6,X7,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_1362]) ).

fof(c_0_2160,plain,
    ! [X6,X7] :
      ( X6 = X7
      | ~ c_HOL_Oord__class_Oless(X6,c_Suc(X7),tc_nat)
      | c_HOL_Oord__class_Oless(X6,X7,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_1363]) ).

fof(c_0_2161,plain,
    ! [X6,X7] :
      ( X7 = X6
      | ~ c_HOL_Oord__class_Oless(X6,c_Suc(X7),tc_nat)
      | c_HOL_Oord__class_Oless(X6,X7,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_1364]) ).

fof(c_0_2162,plain,
    ! [X6,X7] :
      ( X7 = X6
      | c_HOL_Oord__class_Oless(X7,X6,tc_nat)
      | ~ c_HOL_Oord__class_Oless(X7,c_Suc(X6),tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_1365]) ).

fof(c_0_2163,plain,
    ! [X8,X9,X10] :
      ( ~ class_Orderings_Olinorder(X10)
      | c_Orderings_Oord__class_Omin(X9,X8,X10) = X8
      | ~ c_lessequals(X8,X9,X10) ),
    inference(variable_rename,[status(thm)],[c_0_1366]) ).

fof(c_0_2164,plain,
    ! [X8,X9,X10] :
      ( ~ class_Orderings_Olinorder(X10)
      | c_Orderings_Oord__class_Omin(X9,X8,X10) = X9
      | ~ c_lessequals(X9,X8,X10) ),
    inference(variable_rename,[status(thm)],[c_0_1367]) ).

fof(c_0_2165,plain,
    ! [X4,X5] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X5)
      | X4 = c_HOL_Ozero__class_Ozero(X5)
      | ~ c_lessequals(c_HOL_Oabs__class_Oabs(X4,X5),c_HOL_Ozero__class_Ozero(X5),X5) ),
    inference(variable_rename,[status(thm)],[c_0_1368]) ).

fof(c_0_2166,plain,
    ! [X6,X7] :
      ( c_HOL_Oord__class_Oless(c_Suc(X7),X6,tc_nat)
      | c_Suc(X7) = X6
      | ~ c_HOL_Oord__class_Oless(X7,X6,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_1369]) ).

fof(c_0_2167,plain,
    ! [X8,X9,X10] :
      ( ~ class_Orderings_Oorder(X10)
      | c_lessequals(X9,X8,X10)
      | ~ c_HOL_Oord__class_Oless(X9,X8,X10) ),
    inference(variable_rename,[status(thm)],[c_0_1370]) ).

fof(c_0_2168,plain,
    ! [X8,X9,X10] :
      ( ~ class_Orderings_Opreorder(X10)
      | c_lessequals(X9,X8,X10)
      | ~ c_HOL_Oord__class_Oless(X9,X8,X10) ),
    inference(variable_rename,[status(thm)],[c_0_1371]) ).

fof(c_0_2169,plain,
    ! [X8] :
      ( c_Divides_Odiv__class_Omod(X8,c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)
      | c_Parity_Oeven__odd__class_Oeven(X8,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_1372]) ).

fof(c_0_2170,plain,
    ! [X6,X7] :
      ( c_HOL_Oord__class_Oless(X7,X6,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_Suc(X7),X6,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_1373]) ).

fof(c_0_2171,plain,
    ! [X6,X7] :
      ( c_lessequals(X7,X6,tc_nat)
      | ~ c_lessequals(c_Suc(X7),X6,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_1374]) ).

fof(c_0_2172,plain,
    ! [X6,X7] :
      ( c_lessequals(X7,X6,tc_nat)
      | ~ c_HOL_Oord__class_Oless(X7,c_Suc(X6),tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_1375]) ).

fof(c_0_2173,plain,
    ! [X6,X7] :
      ( c_HOL_Oord__class_Oless(X6,X7,tc_nat)
      | ~ c_lessequals(c_Suc(X6),X7,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_1376]) ).

fof(c_0_2174,plain,
    ! [X6,X7] :
      ( c_HOL_Oord__class_Oless(X7,X6,tc_nat)
      | ~ c_lessequals(c_Suc(X7),X6,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_1377]) ).

fof(c_0_2175,plain,
    ! [X8] :
      ( X8 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
      | X8 = c_HOL_Ozero__class_Ozero(tc_nat)
      | ~ c_HOL_Oord__class_Oless(X8,c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_1378]) ).

fof(c_0_2176,plain,
    ! [X4,X5] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X5)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(X4,X5),c_HOL_Ozero__class_Ozero(X5),X5) ),
    inference(variable_rename,[status(thm)],[c_0_1379]) ).

fof(c_0_2177,plain,
    ! [X6,X7] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X7)
      | ~ c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X6,X7),c_HOL_Ozero__class_Ozero(X7),X7) ),
    inference(variable_rename,[status(thm)],[c_0_1380]) ).

fof(c_0_2178,plain,
    ! [X6,X7] :
      ( c_HOL_Oord__class_Oless(X7,c_Suc(X6),tc_nat)
      | ~ c_HOL_Oord__class_Oless(X7,X6,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_1381]) ).

fof(c_0_2179,plain,
    ! [X6,X7] :
      ( c_lessequals(X7,c_Suc(X6),tc_nat)
      | ~ c_lessequals(X7,X6,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_1382]) ).

fof(c_0_2180,plain,
    ! [X8] :
      ( ~ c_lessequals(X8,X8,tc_nat)
      | c_HOL_Oord__class_Oless(X8,c_Suc(X8),tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_1383]) ).

fof(c_0_2181,plain,
    ! [X6,X7] :
      ( c_HOL_Oord__class_Oless(X7,c_Suc(X6),tc_nat)
      | ~ c_lessequals(X7,X6,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_1384]) ).

fof(c_0_2182,plain,
    ! [X6,X7] :
      ( c_lessequals(c_Suc(X6),X7,tc_nat)
      | ~ c_HOL_Oord__class_Oless(X6,X7,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_1385]) ).

fof(c_0_2183,plain,
    ! [X6,X7] :
      ( c_lessequals(c_Suc(X7),X6,tc_nat)
      | ~ c_HOL_Oord__class_Oless(X7,X6,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_1386]) ).

fof(c_0_2184,plain,
    ! [X8,X9] :
      ( c_Parity_Oeven__odd__class_Oeven(c_HOL_Ominus__class_Ominus(X9,X8,tc_nat),tc_nat)
      | c_Parity_Oeven__odd__class_Oeven(X8,tc_nat)
      | c_Parity_Oeven__odd__class_Oeven(X9,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_1387]) ).

fof(c_0_2185,plain,
    ! [X6,X7] :
      ( c_Parity_Oeven__odd__class_Oeven(X7,tc_nat)
      | c_Parity_Oeven__odd__class_Oeven(X6,tc_nat)
      | c_Parity_Oeven__odd__class_Oeven(c_HOL_Oplus__class_Oplus(X7,X6,tc_nat),tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_1388]) ).

fof(c_0_2186,plain,
    ! [X6,X7] :
      ( c_Parity_Oeven__odd__class_Oeven(c_HOL_Oplus__class_Oplus(X7,X6,tc_nat),tc_nat)
      | c_Parity_Oeven__odd__class_Oeven(X6,tc_nat)
      | c_Parity_Oeven__odd__class_Oeven(X7,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_1389]) ).

fof(c_0_2187,plain,
    ! [X8,X9] :
      ( c_Parity_Oeven__odd__class_Oeven(c_HOL_Oplus__class_Oplus(X9,X8,tc_nat),tc_nat)
      | c_Parity_Oeven__odd__class_Oeven(X8,tc_nat)
      | c_Parity_Oeven__odd__class_Oeven(X9,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_1390]) ).

fof(c_0_2188,plain,
    ! [X6,X7] :
      ( c_HOL_Ominus__class_Ominus(X7,X6,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)
      | c_lessequals(X7,X6,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_1391]) ).

fof(c_0_2189,plain,
    ! [X6,X7] :
      ( c_HOL_Oord__class_Oless(X7,X6,tc_nat)
      | X7 = X6
      | ~ c_lessequals(X7,X6,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_1392]) ).

fof(c_0_2190,plain,
    ! [X6,X7] :
      ( X7 = X6
      | c_HOL_Oord__class_Oless(X7,X6,tc_nat)
      | ~ c_lessequals(X7,X6,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_1393]) ).

fof(c_0_2191,plain,
    ! [X6,X7] :
      ( c_HOL_Oord__class_Oless(X7,X6,tc_nat)
      | X7 = X6
      | ~ c_lessequals(X7,X6,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_1394]) ).

fof(c_0_2192,plain,
    ! [X6,X7] :
      ( c_HOL_Ominus__class_Ominus(X7,X6,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat)
      | ~ c_lessequals(X7,X6,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_1395]) ).

fof(c_0_2193,plain,
    ! [X6,X7] :
      ( c_Divides_Odiv__class_Omod(X7,X6,tc_nat) = X7
      | ~ c_HOL_Oord__class_Oless(X7,X6,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_1396]) ).

fof(c_0_2194,plain,
    ! [X6,X7] :
      ( c_lessequals(X7,X6,tc_nat)
      | ~ c_HOL_Oord__class_Oless(X7,X6,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_1397]) ).

fof(c_0_2195,plain,
    ! [X8,X9] :
      ( c_lessequals(X9,X8,tc_nat)
      | ~ c_HOL_Oord__class_Oless(X9,X8,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_1398]) ).

fof(c_0_2196,plain,
    ! [X8,X9] :
      ( c_Parity_Oeven__odd__class_Oeven(c_HOL_Otimes__class_Otimes(X9,X8,tc_nat),tc_nat)
      | ~ c_Parity_Oeven__odd__class_Oeven(X9,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_1399]) ).

fof(c_0_2197,plain,
    ! [X8,X9] :
      ( c_Parity_Oeven__odd__class_Oeven(c_HOL_Otimes__class_Otimes(X9,X8,tc_nat),tc_nat)
      | ~ c_Parity_Oeven__odd__class_Oeven(X8,tc_nat) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1400])])]) ).

fof(c_0_2198,plain,
    ! [X8,X9,X10] :
      ( ~ class_Orderings_Olinorder(X10)
      | c_HOL_Oord__class_Oless(X8,X9,X10)
      | c_HOL_Oord__class_Oless(X9,X8,X10)
      | X9 = X8 ),
    inference(variable_rename,[status(thm)],[c_0_1401]) ).

fof(c_0_2199,plain,
    ! [X8,X9,X10] :
      ( ~ class_Orderings_Olinorder(X10)
      | c_HOL_Oord__class_Oless(X8,X9,X10)
      | X9 = X8
      | c_HOL_Oord__class_Oless(X9,X8,X10) ),
    inference(variable_rename,[status(thm)],[c_0_1402]) ).

fof(c_0_2200,plain,
    ! [X8,X9,X10] :
      ( ~ class_Orderings_Olinorder(X10)
      | X9 = X8
      | c_HOL_Oord__class_Oless(X9,X8,X10)
      | c_HOL_Oord__class_Oless(X8,X9,X10) ),
    inference(variable_rename,[status(thm)],[c_0_1403]) ).

fof(c_0_2201,plain,
    ! [X8,X9,X10] :
      ( ~ class_Orderings_Olinorder(X10)
      | X9 = X8
      | c_HOL_Oord__class_Oless(X8,X9,X10)
      | c_HOL_Oord__class_Oless(X9,X8,X10) ),
    inference(variable_rename,[status(thm)],[c_0_1404]) ).

fof(c_0_2202,plain,
    ! [X8,X9,X10] :
      ( ~ class_Ring__and__Field_Oordered__idom(X10)
      | c_HOL_Oord__class_Oless(X8,X9,X10)
      | c_HOL_Oord__class_Oless(X9,X8,X10)
      | X9 = X8 ),
    inference(variable_rename,[status(thm)],[c_0_1405]) ).

fof(c_0_2203,plain,
    ! [X4,X5] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X5)
      | c_HOL_Oabs__class_Oabs(X4,X5) = X4
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),X4,X5) ),
    inference(variable_rename,[status(thm)],[c_0_1406]) ).

fof(c_0_2204,plain,
    ! [X4,X5] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X5)
      | c_HOL_Oabs__class_Oabs(X4,X5) = X4
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X5),X4,X5) ),
    inference(variable_rename,[status(thm)],[c_0_1407]) ).

fof(c_0_2205,plain,
    ! [X6,X7] : c_HOL_Ominus__class_Ominus(c_Suc(X7),c_Suc(X6),tc_nat) = c_HOL_Ominus__class_Ominus(X7,X6,tc_nat),
    inference(variable_rename,[status(thm)],[c_0_1408]) ).

fof(c_0_2206,plain,
    ! [X6,X7] : c_HOL_Oplus__class_Oplus(c_Suc(X7),X6,tc_nat) = c_HOL_Oplus__class_Oplus(X7,c_Suc(X6),tc_nat),
    inference(variable_rename,[status(thm)],[c_0_1409]) ).

fof(c_0_2207,plain,
    ! [X8,X9,X10] :
      ( ~ class_Orderings_Olinorder(X10)
      | c_lessequals(X8,X9,X10)
      | c_lessequals(X9,X8,X10) ),
    inference(variable_rename,[status(thm)],[c_0_1410]) ).

fof(c_0_2208,plain,
    ! [X8,X9,X10] :
      ( ~ class_Orderings_Olinorder(X10)
      | c_HOL_Oord__class_Oless(X8,X9,X10)
      | c_lessequals(X9,X8,X10) ),
    inference(variable_rename,[status(thm)],[c_0_1411]) ).

fof(c_0_2209,plain,
    ! [X8,X9,X10] :
      ( ~ class_Orderings_Olinorder(X10)
      | c_lessequals(X8,X9,X10)
      | c_HOL_Oord__class_Oless(X9,X8,X10) ),
    inference(variable_rename,[status(thm)],[c_0_1412]) ).

fof(c_0_2210,plain,
    ! [X8,X9] :
      ( ~ class_Orderings_Olinorder(X9)
      | c_HOL_Oord__class_Oless(X8,X8,X9)
      | c_lessequals(X8,X8,X9) ),
    inference(variable_rename,[status(thm)],[c_0_1413]) ).

fof(c_0_2211,plain,
    ! [X8,X9,X10] :
      ( ~ class_Orderings_Olinorder(X10)
      | c_HOL_Oord__class_Oless(X9,X8,X10)
      | c_lessequals(X8,X9,X10) ),
    inference(variable_rename,[status(thm)],[c_0_1414]) ).

fof(c_0_2212,plain,
    ! [X4,X5,X6] :
      ( ~ class_OrderedGroup_Ocomm__monoid__add(X6)
      | c_HOL_Oplus__class_Oplus(X5,X4,X6) = c_HOL_Oplus__class_Oplus(X4,X5,X6) ),
    inference(variable_rename,[status(thm)],[c_0_1415]) ).

fof(c_0_2213,plain,
    ! [X8,X9,X10] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X10)
      | c_HOL_Oplus__class_Oplus(X9,X8,X10) = c_HOL_Oplus__class_Oplus(X8,X9,X10) ),
    inference(variable_rename,[status(thm)],[c_0_1416]) ).

fof(c_0_2214,plain,
    ! [X16,X17,X18] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X18)
      | c_HOL_Oplus__class_Oplus(X17,X16,X18) = c_HOL_Oplus__class_Oplus(X16,X17,X18) ),
    inference(variable_rename,[status(thm)],[c_0_1417]) ).

fof(c_0_2215,plain,
    ! [X8,X9,X10] :
      ( ~ class_Orderings_Olinorder(X10)
      | c_Orderings_Oord__class_Omin(X9,X8,X10) = c_Orderings_Oord__class_Omin(X8,X9,X10) ),
    inference(variable_rename,[status(thm)],[c_0_1418]) ).

fof(c_0_2216,plain,
    ! [X4,X5,X6] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X6)
      | c_HOL_Otimes__class_Otimes(X5,X4,X6) = c_HOL_Otimes__class_Otimes(X4,X5,X6) ),
    inference(variable_rename,[status(thm)],[c_0_1419]) ).

fof(c_0_2217,plain,
    ! [X8,X9,X10] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X10)
      | c_HOL_Otimes__class_Otimes(X9,X8,X10) = c_HOL_Otimes__class_Otimes(X8,X9,X10) ),
    inference(variable_rename,[status(thm)],[c_0_1420]) ).

fof(c_0_2218,plain,
    ! [X8] :
      ( c_HOL_Oord__class_Oless(X8,X8,tc_nat)
      | c_HOL_Oord__class_Oless(X8,c_Suc(X8),tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_1421]) ).

fof(c_0_2219,plain,
    ! [X6,X7] :
      ( c_HOL_Oord__class_Oless(X6,c_Suc(X7),tc_nat)
      | c_HOL_Oord__class_Oless(X7,X6,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_1422]) ).

fof(c_0_2220,plain,
    ! [X6,X7] :
      ( c_lessequals(c_Suc(X6),X7,tc_nat)
      | c_lessequals(X7,X6,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_1423]) ).

fof(c_0_2221,plain,
    ! [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_1424]) ).

fof(c_0_2222,plain,
    ! [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_1425]) ).

fof(c_0_2223,plain,
    ! [X6,X7] :
      ( c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != c_HOL_Oplus__class_Oplus(X7,X6,tc_nat)
      | X6 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
      | X7 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
    inference(variable_rename,[status(thm)],[c_0_1426]) ).

fof(c_0_2224,plain,
    ! [X6] :
      ( X6 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X6,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_1427]) ).

fof(c_0_2225,plain,
    ! [X6,X7] :
      ( c_HOL_Oplus__class_Oplus(X7,X6,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
      | X6 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
      | X7 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
    inference(variable_rename,[status(thm)],[c_0_1428]) ).

fof(c_0_2226,plain,
    ! [X4,X5,X6] :
      ( ~ class_Ring__and__Field_Ono__zero__divisors(X6)
      | c_HOL_Otimes__class_Otimes(X5,X4,X6) != c_HOL_Ozero__class_Ozero(X6)
      | X5 = c_HOL_Ozero__class_Ozero(X6)
      | X4 = c_HOL_Ozero__class_Ozero(X6) ),
    inference(variable_rename,[status(thm)],[c_0_1429]) ).

fof(c_0_2227,plain,
    ! [X4,X5,X6] :
      ( ~ class_Ring__and__Field_Ono__zero__divisors(X6)
      | c_HOL_Otimes__class_Otimes(X5,X4,X6) != c_HOL_Ozero__class_Ozero(X6)
      | X4 = c_HOL_Ozero__class_Ozero(X6)
      | X5 = c_HOL_Ozero__class_Ozero(X6) ),
    inference(variable_rename,[status(thm)],[c_0_1430]) ).

fof(c_0_2228,plain,
    ! [X4,X5,X6] :
      ( ~ class_Ring__and__Field_Oring__no__zero__divisors(X6)
      | c_HOL_Otimes__class_Otimes(X5,X4,X6) != c_HOL_Ozero__class_Ozero(X6)
      | X4 = c_HOL_Ozero__class_Ozero(X6)
      | X5 = c_HOL_Ozero__class_Ozero(X6) ),
    inference(variable_rename,[status(thm)],[c_0_1431]) ).

fof(c_0_2229,plain,
    ! [X8,X9] :
      ( c_HOL_Oord__class_Oless(X8,X9,tc_nat)
      | c_HOL_Oord__class_Oless(X9,X8,tc_nat)
      | X9 = X8 ),
    inference(variable_rename,[status(thm)],[c_0_1432]) ).

fof(c_0_2230,plain,
    ! [X6,X7] :
      ( c_HOL_Oord__class_Oless(X6,X7,tc_nat)
      | c_HOL_Oord__class_Oless(X7,X6,tc_nat)
      | X7 = X6 ),
    inference(variable_rename,[status(thm)],[c_0_1433]) ).

fof(c_0_2231,plain,
    ! [X8,X9,X10] :
      ( ~ class_Ring__and__Field_Oidom(X10)
      | ~ class_Int_Onumber__ring(X10)
      | c_HOL_Ominus__class_Ominus(X9,X8,X10) != c_HOL_Ozero__class_Ozero(X10)
      | X9 = X8 ),
    inference(variable_rename,[status(thm)],[c_0_1434]) ).

fof(c_0_2232,plain,
    ! [X4,X5] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X5)
      | X4 = c_HOL_Ozero__class_Ozero(X5)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ozero__class_Ozero(X5),X4,X5) ),
    inference(variable_rename,[status(thm)],[c_0_1435]) ).

fof(c_0_2233,plain,
    ! [X8,X9,X10] :
      ( ~ class_Ring__and__Field_Oidom(X10)
      | ~ class_Int_Onumber__ring(X10)
      | X8 != c_HOL_Oplus__class_Oplus(X8,X9,X10)
      | X9 = c_HOL_Ozero__class_Ozero(X10) ),
    inference(variable_rename,[status(thm)],[c_0_1436]) ).

fof(c_0_2234,plain,
    ! [X6,X7] :
      ( c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != c_HOL_Oplus__class_Oplus(X7,X6,tc_nat)
      | X7 = c_HOL_Ozero__class_Ozero(tc_nat)
      | X7 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
    inference(variable_rename,[status(thm)],[c_0_1437]) ).

fof(c_0_2235,plain,
    ! [X6,X7] :
      ( c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != c_HOL_Oplus__class_Oplus(X7,X6,tc_nat)
      | X6 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
      | X6 = c_HOL_Ozero__class_Ozero(tc_nat) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1438])])]) ).

fof(c_0_2236,plain,
    ! [X6,X7] :
      ( c_HOL_Oplus__class_Oplus(X7,X6,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
      | X6 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
      | X6 = c_HOL_Ozero__class_Ozero(tc_nat) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1439])])]) ).

fof(c_0_2237,plain,
    ! [X6,X7] :
      ( c_HOL_Oplus__class_Oplus(X7,X6,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
      | X7 = c_HOL_Ozero__class_Ozero(tc_nat)
      | X7 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
    inference(variable_rename,[status(thm)],[c_0_1440]) ).

fof(c_0_2238,plain,
    ! [X5] :
      ( X5 = c_HOL_Ozero__class_Ozero(tc_nat)
      | ~ c_HOL_Oord__class_Oless(X5,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_1441]) ).

fof(c_0_2239,plain,
    ! [X6,X7] :
      ( c_lessequals(X6,X7,tc_nat)
      | c_lessequals(X7,X6,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_1442]) ).

fof(c_0_2240,plain,
    ! [X8] :
      ( c_Divides_Odiv__class_Omod(X8,c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat)
      | ~ c_Parity_Oeven__odd__class_Oeven(X8,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_1443]) ).

fof(c_0_2241,plain,
    ! [X30,X31,X32] :
      ( ~ class_Ring__and__Field_Oordered__idom(X32)
      | c_HOL_Oabs__class_Oabs(X30,X32) != c_HOL_Oabs__class_Oabs(X31,X32)
      | c_Ring__and__Field_Odvd__class_Odvd(X30,X31,X32) ),
    inference(variable_rename,[status(thm)],[c_0_1444]) ).

fof(c_0_2242,plain,
    ! [X4] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X4)
      | c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Ozero__class_Ozero(X4),X4),c_HOL_Ozero__class_Ozero(X4),X4) ),
    inference(variable_rename,[status(thm)],[c_0_1445]) ).

fof(c_0_2243,plain,
    ! [X6,X7] : c_HOL_Oplus__class_Oplus(X7,X6,tc_nat) = c_HOL_Oplus__class_Oplus(X6,X7,tc_nat),
    inference(variable_rename,[status(thm)],[c_0_1446]) ).

fof(c_0_2244,plain,
    ! [X6,X7] : c_HOL_Otimes__class_Otimes(X7,X6,tc_nat) = c_HOL_Otimes__class_Otimes(X6,X7,tc_nat),
    inference(variable_rename,[status(thm)],[c_0_1447]) ).

fof(c_0_2245,plain,
    ! [X4,X5] :
      ( ~ class_OrderedGroup_Olordered__ab__group__add(X5)
      | c_HOL_Oplus__class_Oplus(X4,X4,X5) != c_HOL_Ozero__class_Ozero(X5)
      | X4 = c_HOL_Ozero__class_Ozero(X5) ),
    inference(variable_rename,[status(thm)],[c_0_1448]) ).

fof(c_0_2246,plain,
    ! [X8] :
      ( c_Divides_Odiv__class_Omod(X8,c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),tc_nat) = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
      | c_Parity_Oeven__odd__class_Oeven(X8,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_1449]) ).

fof(c_0_2247,plain,
    ! [X6,X7] :
      ( c_HOL_Otimes__class_Otimes(X7,X6,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
      | X6 = 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_1450])])]) ).

fof(c_0_2248,plain,
    ! [X6,X7] :
      ( c_HOL_Otimes__class_Otimes(X7,X6,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
      | X7 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
    inference(variable_rename,[status(thm)],[c_0_1451]) ).

fof(c_0_2249,plain,
    ! [X6,X7] :
      ( c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != c_HOL_Oplus__class_Oplus(X7,X6,tc_nat)
      | X7 = c_HOL_Ozero__class_Ozero(tc_nat)
      | X6 = c_HOL_Ozero__class_Ozero(tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_1452]) ).

fof(c_0_2250,plain,
    ! [X6,X7] :
      ( c_HOL_Oplus__class_Oplus(X7,X6,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
      | X7 = c_HOL_Ozero__class_Ozero(tc_nat)
      | X6 = c_HOL_Ozero__class_Ozero(tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_1453]) ).

fof(c_0_2251,plain,
    ! [X4,X5,X6] :
      ( ~ class_OrderedGroup_Ogroup__add(X6)
      | c_HOL_Ominus__class_Ominus(X5,X4,X6) != c_HOL_Ozero__class_Ozero(X6)
      | X5 = X4 ),
    inference(variable_rename,[status(thm)],[c_0_1454]) ).

fof(c_0_2252,plain,
    ! [X4,X5,X6] :
      ( ~ class_OrderedGroup_Oab__group__add(X6)
      | c_HOL_Ominus__class_Ominus(X5,X4,X6) != c_HOL_Ozero__class_Ozero(X6)
      | X5 = X4 ),
    inference(variable_rename,[status(thm)],[c_0_1455]) ).

fof(c_0_2253,plain,
    ! [X4,X5] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X5)
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),c_HOL_Oabs__class_Oabs(X4,X5),X5)
      | X4 = c_HOL_Ozero__class_Ozero(X5) ),
    inference(variable_rename,[status(thm)],[c_0_1456]) ).

fof(c_0_2254,plain,
    ! [X6,X7] :
      ( c_HOL_Otimes__class_Otimes(X7,X6,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)
      | X6 = c_HOL_Ozero__class_Ozero(tc_nat)
      | X7 = c_HOL_Ozero__class_Ozero(tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_1457]) ).

fof(c_0_2255,plain,
    ! [X4,X5] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X5)
      | c_lessequals(c_HOL_Ozero__class_Ozero(X5),c_HOL_Oabs__class_Oabs(X4,X5),X5) ),
    inference(variable_rename,[status(thm)],[c_0_1458]) ).

fof(c_0_2256,plain,
    ! [X5,X6] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X6)
      | c_lessequals(c_HOL_Ozero__class_Ozero(X6),c_Nat_Osemiring__1__class_Oof__nat(X5,X6),X6) ),
    inference(variable_rename,[status(thm)],[c_0_1459]) ).

fof(c_0_2257,plain,
    ! [X6,X7] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X7)
      | c_lessequals(c_HOL_Ozero__class_Ozero(X7),c_Nat_Osemiring__1__class_Oof__nat(X6,X7),X7) ),
    inference(variable_rename,[status(thm)],[c_0_1460]) ).

fof(c_0_2258,plain,
    ! [X8,X9] :
      ( ~ class_Orderings_Oorder(X9)
      | ~ c_HOL_Oord__class_Oless(X8,X8,X9) ),
    inference(variable_rename,[status(thm)],[c_0_1461]) ).

fof(c_0_2259,plain,
    ! [X8,X9] :
      ( ~ class_Orderings_Olinorder(X9)
      | ~ c_HOL_Oord__class_Oless(X8,X8,X9) ),
    inference(variable_rename,[status(thm)],[c_0_1462]) ).

fof(c_0_2260,plain,
    ! [X8,X9] :
      ( ~ class_Orderings_Opreorder(X9)
      | ~ c_HOL_Oord__class_Oless(X8,X8,X9) ),
    inference(variable_rename,[status(thm)],[c_0_1463]) ).

fof(c_0_2261,plain,
    ! [X5] : ~ c_lessequals(c_Suc(X5),X5,tc_nat),
    inference(variable_rename,[status(thm)],[c_0_1464]) ).

fof(c_0_2262,plain,
    ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
    c_0_1465 ).

fof(c_0_2263,plain,
    ! [X5] :
      ( X5 = c_HOL_Ozero__class_Ozero(tc_nat)
      | ~ c_lessequals(X5,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_1466]) ).

fof(c_0_2264,plain,
    ! [X6,X7] :
      ( c_HOL_Oplus__class_Oplus(X7,X6,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)
      | X6 = c_HOL_Ozero__class_Ozero(tc_nat) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1467])])]) ).

fof(c_0_2265,plain,
    ! [X6,X7] :
      ( c_HOL_Oplus__class_Oplus(X7,X6,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)
      | X7 = c_HOL_Ozero__class_Ozero(tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_1468]) ).

fof(c_0_2266,plain,
    ! [X4,X5] :
      ( ~ class_Orderings_Olinorder(X5)
      | ~ class_OrderedGroup_Olordered__ab__group__add__abs(X5)
      | c_HOL_Oabs__class_Oabs(X4,X5) = X4
      | c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X5),X5) ),
    inference(variable_rename,[status(thm)],[c_0_1469]) ).

fof(c_0_2267,plain,
    ! [X6,X7] :
      ( c_HOL_Oplus__class_Oplus(X7,X6,tc_nat) != X7
      | X6 = c_HOL_Ozero__class_Ozero(tc_nat) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1470])])]) ).

fof(c_0_2268,plain,
    ! [X8,X9] :
      ( X8 != c_HOL_Oplus__class_Oplus(X8,X9,tc_nat)
      | X9 = c_HOL_Ozero__class_Ozero(tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_1471]) ).

fof(c_0_2269,plain,
    ! [X6] : ~ c_HOL_Oord__class_Oless(X6,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
    inference(variable_rename,[status(thm)],[c_0_1472]) ).

fof(c_0_2270,plain,
    ! [X5] : ~ c_HOL_Oord__class_Oless(X5,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
    inference(variable_rename,[status(thm)],[c_0_1473]) ).

fof(c_0_2271,plain,
    ! [X4,X5] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X5)
      | c_lessequals(X4,c_HOL_Oabs__class_Oabs(X4,X5),X5) ),
    inference(variable_rename,[status(thm)],[c_0_1474]) ).

fof(c_0_2272,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)),
    c_0_1475 ).

fof(c_0_2273,plain,
    ! [X5] : ~ c_HOL_Oord__class_Oless(X5,X5,tc_nat),
    inference(variable_rename,[status(thm)],[c_0_1476]) ).

fof(c_0_2274,plain,
    ! [X8] : ~ c_HOL_Oord__class_Oless(X8,X8,tc_nat),
    inference(variable_rename,[status(thm)],[c_0_1477]) ).

fof(c_0_2275,plain,
    ! [X4,X5] :
      ( ~ class_Ring__and__Field_Oabs__if(X5)
      | c_HOL_Oabs__class_Oabs(X4,X5) = X4
      | c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X5),X5) ),
    inference(variable_rename,[status(thm)],[c_0_1478]) ).

fof(c_0_2276,plain,
    ! [X4] :
      ( ~ class_OrderedGroup_Olordered__ab__group__add(X4)
      | c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X4),c_HOL_Ozero__class_Ozero(X4),X4) = c_HOL_Ozero__class_Ozero(X4) ),
    inference(variable_rename,[status(thm)],[c_0_1479]) ).

fof(c_0_2277,axiom,
    c_Ring__and__Field_Odvd__class_Odvd(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),
    c_0_1480 ).

fof(c_0_2278,plain,
    ! [X8,X9] :
      ( ~ class_Ring__and__Field_Oidom(X9)
      | ~ class_Int_Onumber__ring(X9)
      | X8 = c_HOL_Oplus__class_Oplus(X8,c_HOL_Ozero__class_Ozero(X9),X9) ),
    inference(variable_rename,[status(thm)],[c_0_1481]) ).

fof(c_0_2279,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)),
    c_0_1482 ).

fof(c_0_2280,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),
    c_0_1483 ).

fof(c_0_2281,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),
    c_0_1484 ).

fof(c_0_2282,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)),
    c_0_1485 ).

fof(c_0_2283,plain,
    ! [X8,X9] :
      ( ~ class_Ring__and__Field_Oidom(X9)
      | ~ class_Int_Onumber__ring(X9)
      | c_HOL_Ominus__class_Ominus(X8,X8,X9) = c_HOL_Ozero__class_Ozero(X9) ),
    inference(variable_rename,[status(thm)],[c_0_1486]) ).

fof(c_0_2284,plain,
    ! [X4,X5] :
      ( ~ class_Ring__and__Field_Oring__no__zero__divisors(X5)
      | c_HOL_Otimes__class_Otimes(X4,c_HOL_Ozero__class_Ozero(X5),X5) = c_HOL_Ozero__class_Ozero(X5) ),
    inference(variable_rename,[status(thm)],[c_0_1487]) ).

fof(c_0_2285,plain,
    ! [X4,X5] :
      ( ~ class_Ring__and__Field_Oring__no__zero__divisors(X5)
      | c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X5),X4,X5) = c_HOL_Ozero__class_Ozero(X5) ),
    inference(variable_rename,[status(thm)],[c_0_1488]) ).

fof(c_0_2286,plain,
    ! [X4,X5] :
      ( ~ class_Ring__and__Field_Omult__zero(X5)
      | c_HOL_Otimes__class_Otimes(X4,c_HOL_Ozero__class_Ozero(X5),X5) = c_HOL_Ozero__class_Ozero(X5) ),
    inference(variable_rename,[status(thm)],[c_0_1489]) ).

fof(c_0_2287,plain,
    ! [X4,X5] :
      ( ~ class_Ring__and__Field_Omult__zero(X5)
      | c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X5),X4,X5) = c_HOL_Ozero__class_Ozero(X5) ),
    inference(variable_rename,[status(thm)],[c_0_1490]) ).

fof(c_0_2288,plain,
    ! [X8,X9] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X9)
      | c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X9),X8,X9) = c_HOL_Ozero__class_Ozero(X9) ),
    inference(variable_rename,[status(thm)],[c_0_1491]) ).

fof(c_0_2289,plain,
    ! [X8,X9] :
      ( ~ class_RealVector_Oreal__normed__algebra(X9)
      | c_HOL_Otimes__class_Otimes(X8,c_HOL_Ozero__class_Ozero(X9),X9) = c_HOL_Ozero__class_Ozero(X9) ),
    inference(variable_rename,[status(thm)],[c_0_1492]) ).

fof(c_0_2290,plain,
    ! [X4,X5] :
      ( ~ class_RealVector_Oreal__normed__algebra(X5)
      | c_HOL_Otimes__class_Otimes(X4,c_HOL_Ozero__class_Ozero(X5),X5) = c_HOL_Ozero__class_Ozero(X5) ),
    inference(variable_rename,[status(thm)],[c_0_1493]) ).

fof(c_0_2291,plain,
    ! [X4,X5] :
      ( ~ class_RealVector_Oreal__normed__algebra(X5)
      | c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X5),X4,X5) = c_HOL_Ozero__class_Ozero(X5) ),
    inference(variable_rename,[status(thm)],[c_0_1494]) ).

fof(c_0_2292,plain,
    ! [X7,X8] :
      ( ~ class_RealVector_Oreal__normed__algebra(X8)
      | c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X8),X7,X8) = c_HOL_Ozero__class_Ozero(X8) ),
    inference(variable_rename,[status(thm)],[c_0_1495]) ).

fof(c_0_2293,plain,
    ! [X4,X5] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X5)
      | c_HOL_Otimes__class_Otimes(X4,c_HOL_Ozero__class_Ozero(X5),X5) = c_HOL_Ozero__class_Ozero(X5) ),
    inference(variable_rename,[status(thm)],[c_0_1496]) ).

fof(c_0_2294,plain,
    ! [X4,X5] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X5)
      | c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X5),X4,X5) = c_HOL_Ozero__class_Ozero(X5) ),
    inference(variable_rename,[status(thm)],[c_0_1497]) ).

fof(c_0_2295,plain,
    ! [X4,X5] :
      ( ~ class_Divides_Osemiring__div(X5)
      | c_Divides_Odiv__class_Omod(c_HOL_Ozero__class_Ozero(X5),X4,X5) = c_HOL_Ozero__class_Ozero(X5) ),
    inference(variable_rename,[status(thm)],[c_0_1498]) ).

fof(c_0_2296,plain,
    ! [X5] :
      ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X5,tc_nat)
      | c_Parity_Oeven__odd__class_Oeven(X5,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_1499]) ).

fof(c_0_2297,plain,
    ! [X4,X5] :
      ( ~ class_OrderedGroup_Ogroup__add(X5)
      | c_HOL_Ominus__class_Ominus(X4,c_HOL_Ozero__class_Ozero(X5),X5) = X4 ),
    inference(variable_rename,[status(thm)],[c_0_1500]) ).

fof(c_0_2298,plain,
    ! [X4,X5] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X5)
      | c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X5),X4,X5) = X4 ),
    inference(variable_rename,[status(thm)],[c_0_1501]) ).

fof(c_0_2299,plain,
    ! [X4,X5] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X5)
      | c_HOL_Oplus__class_Oplus(X4,c_HOL_Ozero__class_Ozero(X5),X5) = X4 ),
    inference(variable_rename,[status(thm)],[c_0_1502]) ).

fof(c_0_2300,plain,
    ! [X4,X5] :
      ( ~ class_OrderedGroup_Ocomm__monoid__add(X5)
      | c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X5),X4,X5) = X4 ),
    inference(variable_rename,[status(thm)],[c_0_1503]) ).

fof(c_0_2301,plain,
    ! [X8,X9] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X9)
      | c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X9),X8,X9) = X8 ),
    inference(variable_rename,[status(thm)],[c_0_1504]) ).

fof(c_0_2302,plain,
    ! [X4,X5] :
      ( ~ class_OrderedGroup_Ocomm__monoid__add(X5)
      | c_HOL_Oplus__class_Oplus(X4,c_HOL_Ozero__class_Ozero(X5),X5) = X4 ),
    inference(variable_rename,[status(thm)],[c_0_1505]) ).

fof(c_0_2303,plain,
    ! [X4,X5] :
      ( ~ class_OrderedGroup_Omonoid__add(X5)
      | c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X5),X4,X5) = X4 ),
    inference(variable_rename,[status(thm)],[c_0_1506]) ).

fof(c_0_2304,plain,
    ! [X4,X5] :
      ( ~ class_OrderedGroup_Omonoid__add(X5)
      | c_HOL_Oplus__class_Oplus(X4,c_HOL_Ozero__class_Ozero(X5),X5) = X4 ),
    inference(variable_rename,[status(thm)],[c_0_1507]) ).

fof(c_0_2305,plain,
    ! [X4,X5] :
      ( ~ class_Divides_Osemiring__div(X5)
      | c_Divides_Odiv__class_Omod(X4,c_HOL_Ozero__class_Ozero(X5),X5) = X4 ),
    inference(variable_rename,[status(thm)],[c_0_1508]) ).

fof(c_0_2306,axiom,
    c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),
    c_0_1509 ).

fof(c_0_2307,plain,
    ! [X4,X5] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X5)
      | c_Ring__and__Field_Odvd__class_Odvd(X4,c_HOL_Ozero__class_Ozero(X5),X5) ),
    inference(variable_rename,[status(thm)],[c_0_1510]) ).

fof(c_0_2308,plain,
    ! [X6] : c_Divides_Odiv__class_Omod(X6,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
    inference(variable_rename,[status(thm)],[c_0_1511]) ).

fof(c_0_2309,plain,
    ! [X4,X5] :
      ( ~ class_OrderedGroup_Ogroup__add(X5)
      | c_HOL_Ominus__class_Ominus(X4,X4,X5) = c_HOL_Ozero__class_Ozero(X5) ),
    inference(variable_rename,[status(thm)],[c_0_1512]) ).

fof(c_0_2310,plain,
    ! [X8,X9] :
      ( ~ class_OrderedGroup_Ogroup__add(X9)
      | c_HOL_Ominus__class_Ominus(X8,X8,X9) = c_HOL_Ozero__class_Ozero(X9) ),
    inference(variable_rename,[status(thm)],[c_0_1513]) ).

fof(c_0_2311,plain,
    ! [X8,X9] :
      ( ~ class_OrderedGroup_Oab__group__add(X9)
      | c_HOL_Ominus__class_Ominus(X8,X8,X9) = c_HOL_Ozero__class_Ozero(X9) ),
    inference(variable_rename,[status(thm)],[c_0_1514]) ).

fof(c_0_2312,plain,
    ! [X4,X5] :
      ( ~ class_Divides_Osemiring__div(X5)
      | c_Divides_Odiv__class_Omod(X4,X4,X5) = c_HOL_Ozero__class_Ozero(X5) ),
    inference(variable_rename,[status(thm)],[c_0_1515]) ).

fof(c_0_2313,plain,
    ! [X5] : c_lessequals(c_Suc(X5),c_Suc(X5),tc_nat),
    inference(variable_rename,[status(thm)],[c_0_1516]) ).

fof(c_0_2314,plain,
    ! [X9] : c_Ring__and__Field_Odvd__class_Odvd(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X9,tc_nat),
    inference(variable_rename,[status(thm)],[c_0_1517]) ).

fof(c_0_2315,plain,
    ! [X8,X9] :
      ( ~ class_OrderedGroup_Oab__semigroup__idem__mult(X9)
      | c_HOL_Otimes__class_Otimes(X8,X8,X9) = X8 ),
    inference(variable_rename,[status(thm)],[c_0_1518]) ).

fof(c_0_2316,plain,
    ! [X8,X9] :
      ( ~ class_Orderings_Olinorder(X9)
      | c_Orderings_Oord__class_Omin(X8,X8,X9) = X8 ),
    inference(variable_rename,[status(thm)],[c_0_1519]) ).

fof(c_0_2317,plain,
    ! [X5] : c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(X5),tc_nat),
    inference(variable_rename,[status(thm)],[c_0_1520]) ).

fof(c_0_2318,plain,
    ! [X8] : c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(X8),tc_nat),
    inference(variable_rename,[status(thm)],[c_0_1521]) ).

fof(c_0_2319,plain,
    ! [X8,X9] :
      ( ~ class_Orderings_Oorder(X9)
      | c_lessequals(X8,X8,X9) ),
    inference(variable_rename,[status(thm)],[c_0_1522]) ).

fof(c_0_2320,plain,
    ! [X8,X9] :
      ( ~ class_Orderings_Opreorder(X9)
      | c_lessequals(X8,X8,X9) ),
    inference(variable_rename,[status(thm)],[c_0_1523]) ).

fof(c_0_2321,plain,
    ! [X4,X5] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X5)
      | c_Ring__and__Field_Odvd__class_Odvd(X4,X4,X5) ),
    inference(variable_rename,[status(thm)],[c_0_1524]) ).

fof(c_0_2322,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),
    c_0_1525 ).

fof(c_0_2323,plain,
    ! [X4,X5] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X5)
      | c_HOL_Oabs__class_Oabs(c_HOL_Oabs__class_Oabs(X4,X5),X5) = c_HOL_Oabs__class_Oabs(X4,X5) ),
    inference(variable_rename,[status(thm)],[c_0_1526]) ).

fof(c_0_2324,plain,
    ! [X5,X6] :
      ( ~ class_Ring__and__Field_Oordered__idom(X6)
      | c_HOL_Oabs__class_Oabs(c_Nat_Osemiring__1__class_Oof__nat(X5,X6),X6) = c_Nat_Osemiring__1__class_Oof__nat(X5,X6) ),
    inference(variable_rename,[status(thm)],[c_0_1527]) ).

fof(c_0_2325,plain,
    ! [X5] :
      ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X5,tc_nat)
      | X5 = c_HOL_Ozero__class_Ozero(tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_1528]) ).

fof(c_0_2326,plain,
    ! [X8] : c_HOL_Oord__class_Oless(X8,c_Suc(X8),tc_nat),
    inference(variable_rename,[status(thm)],[c_0_1529]) ).

fof(c_0_2327,plain,
    ! [X5] : c_HOL_Oord__class_Oless(X5,c_Suc(X5),tc_nat),
    inference(variable_rename,[status(thm)],[c_0_1530]) ).

fof(c_0_2328,axiom,
    c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
    c_0_1531 ).

fof(c_0_2329,plain,
    ! [X5] : c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(tc_nat),X5,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
    inference(variable_rename,[status(thm)],[c_0_1532]) ).

fof(c_0_2330,plain,
    ! [X5] : c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),X5,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
    inference(variable_rename,[status(thm)],[c_0_1533]) ).

fof(c_0_2331,plain,
    ! [X6] : c_HOL_Otimes__class_Otimes(X6,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
    inference(variable_rename,[status(thm)],[c_0_1534]) ).

fof(c_0_2332,plain,
    ! [X5] : c_Orderings_Oord__class_Omin(X5,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
    inference(variable_rename,[status(thm)],[c_0_1535]) ).

fof(c_0_2333,plain,
    ! [X5] : c_Orderings_Oord__class_Omin(c_HOL_Ozero__class_Ozero(tc_nat),X5,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
    inference(variable_rename,[status(thm)],[c_0_1536]) ).

fof(c_0_2334,plain,
    ! [X6] : c_HOL_Ominus__class_Ominus(X6,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = X6,
    inference(variable_rename,[status(thm)],[c_0_1537]) ).

fof(c_0_2335,plain,
    ! [X5] : c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),X5,tc_nat) = X5,
    inference(variable_rename,[status(thm)],[c_0_1538]) ).

fof(c_0_2336,plain,
    ! [X6] : c_HOL_Oplus__class_Oplus(X6,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = X6,
    inference(variable_rename,[status(thm)],[c_0_1539]) ).

fof(c_0_2337,plain,
    ! [X8] : X8 = c_HOL_Oplus__class_Oplus(X8,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
    inference(variable_rename,[status(thm)],[c_0_1540]) ).

fof(c_0_2338,plain,
    ! [X8] : c_Ring__and__Field_Odvd__class_Odvd(X8,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
    inference(variable_rename,[status(thm)],[c_0_1541]) ).

fof(c_0_2339,plain,
    ! [X5] : c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),X5,tc_nat),
    inference(variable_rename,[status(thm)],[c_0_1542]) ).

fof(c_0_2340,plain,
    ! [X6] : c_HOL_Ominus__class_Ominus(X6,X6,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
    inference(variable_rename,[status(thm)],[c_0_1543]) ).

fof(c_0_2341,plain,
    ! [X6,X7,X8] :
      ( ~ class_Nat_Osemiring__char__0(X8)
      | c_Nat_Osemiring__1__class_Oof__nat(X7,X8) != c_Nat_Osemiring__1__class_Oof__nat(X6,X8)
      | X7 = X6 ),
    inference(variable_rename,[status(thm)],[c_0_1544]) ).

fof(c_0_2342,plain,
    ! [X5] : c_lessequals(X5,X5,tc_nat),
    inference(variable_rename,[status(thm)],[c_0_1545]) ).

fof(c_0_2343,plain,
    ! [X8] : c_lessequals(X8,X8,tc_nat),
    inference(variable_rename,[status(thm)],[c_0_1546]) ).

fof(c_0_2344,plain,
    ! [X8] : c_Ring__and__Field_Odvd__class_Odvd(X8,X8,tc_nat),
    inference(variable_rename,[status(thm)],[c_0_1547]) ).

fof(c_0_2345,axiom,
    c_HOL_Oord__class_Oless(v_i,v_n,tc_nat),
    c_0_1548 ).

fof(c_0_2346,axiom,
    c_HOL_Oord__class_Oless(v_i,v_n,tc_nat),
    c_0_1549 ).

fof(c_0_2347,plain,
    ! [X8] :
      ( ~ c_Parity_Oeven__odd__class_Oeven(X8,tc_nat)
      | ~ c_Parity_Oeven__odd__class_Oeven(c_Suc(X8),tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_1550]) ).

fof(c_0_2348,plain,
    ! [X4,X5] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X5)
      | c_HOL_Oabs__class_Oabs(X4,X5) != c_HOL_Ozero__class_Ozero(X5)
      | X4 = c_HOL_Ozero__class_Ozero(X5) ),
    inference(variable_rename,[status(thm)],[c_0_1551]) ).

fof(c_0_2349,plain,
    ! [X8] :
      ( c_Parity_Oeven__odd__class_Oeven(c_Suc(X8),tc_nat)
      | c_Parity_Oeven__odd__class_Oeven(X8,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_1552]) ).

fof(c_0_2350,plain,
    ! [X4] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X4)
      | c_HOL_Oabs__class_Oabs(c_HOL_Ozero__class_Ozero(X4),X4) = c_HOL_Ozero__class_Ozero(X4) ),
    inference(variable_rename,[status(thm)],[c_0_1553]) ).

fof(c_0_2351,plain,
    ! [X4] :
      ( ~ class_Ring__and__Field_Osemiring__1(X4)
      | c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Ozero__class_Ozero(tc_nat),X4) = c_HOL_Ozero__class_Ozero(X4) ),
    inference(variable_rename,[status(thm)],[c_0_1554]) ).

fof(c_0_2352,axiom,
    c_Parity_Oeven__odd__class_Oeven(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
    c_0_1555 ).

fof(c_0_2353,plain,
    ! [X8,X9] :
      ( c_Suc(X9) != c_Suc(X8)
      | X9 = X8 ),
    inference(variable_rename,[status(thm)],[c_0_1556]) ).

fof(c_0_2354,plain,
    ! [X31,X32] :
      ( c_Suc(X32) != c_Suc(X31)
      | X32 = X31 ),
    inference(variable_rename,[status(thm)],[c_0_1557]) ).

fof(c_0_2355,plain,
    ! [X22] : c_Suc(X22) != c_HOL_Ozero__class_Ozero(tc_nat),
    inference(variable_rename,[status(thm)],[c_0_1558]) ).

fof(c_0_2356,plain,
    ! [X6] : c_Suc(X6) != c_HOL_Ozero__class_Ozero(tc_nat),
    inference(variable_rename,[status(thm)],[c_0_1559]) ).

fof(c_0_2357,plain,
    ! [X6] : c_HOL_Ozero__class_Ozero(tc_nat) != c_Suc(X6),
    inference(variable_rename,[status(thm)],[c_0_1560]) ).

fof(c_0_2358,plain,
    ! [X22] : c_HOL_Ozero__class_Ozero(tc_nat) != c_Suc(X22),
    inference(variable_rename,[status(thm)],[c_0_1561]) ).

fof(c_0_2359,plain,
    ! [X5] : c_Suc(X5) != X5,
    inference(variable_rename,[status(thm)],[c_0_1562]) ).

fof(c_0_2360,plain,
    ! [X5] : X5 != c_Suc(X5),
    inference(variable_rename,[status(thm)],[c_0_1563]) ).

fof(c_0_2361,axiom,
    class_Orderings_Oorder(tc_nat),
    c_0_1564 ).

fof(c_0_2362,axiom,
    class_Orderings_Olinorder(tc_nat),
    c_0_1565 ).

fof(c_0_2363,axiom,
    class_Orderings_Opreorder(tc_nat),
    c_0_1566 ).

fof(c_0_2364,axiom,
    class_Ring__and__Field_Odvd(tc_nat),
    c_0_1567 ).

fof(c_0_2365,axiom,
    class_Nat_Osemiring__char__0(tc_nat),
    c_0_1568 ).

fof(c_0_2366,axiom,
    class_Divides_Osemiring__div(tc_nat),
    c_0_1569 ).

fof(c_0_2367,axiom,
    class_OrderedGroup_Omonoid__add(tc_nat),
    c_0_1570 ).

fof(c_0_2368,axiom,
    class_Ring__and__Field_Osemiring(tc_nat),
    c_0_1571 ).

fof(c_0_2369,axiom,
    class_Ring__and__Field_Omult__mono(tc_nat),
    c_0_1572 ).

fof(c_0_2370,axiom,
    class_Ring__and__Field_Omult__zero(tc_nat),
    c_0_1573 ).

fof(c_0_2371,axiom,
    class_Ring__and__Field_Omult__mono1(tc_nat),
    c_0_1574 ).

fof(c_0_2372,axiom,
    class_Ring__and__Field_Osemiring__1(tc_nat),
    c_0_1575 ).

fof(c_0_2373,axiom,
    class_OrderedGroup_Ocomm__monoid__add(tc_nat),
    c_0_1576 ).

fof(c_0_2374,axiom,
    class_Ring__and__Field_Ocomm__semiring(tc_nat),
    c_0_1577 ).

fof(c_0_2375,axiom,
    class_OrderedGroup_Oab__semigroup__add(tc_nat),
    c_0_1578 ).

fof(c_0_2376,axiom,
    class_OrderedGroup_Oab__semigroup__mult(tc_nat),
    c_0_1579 ).

fof(c_0_2377,axiom,
    class_Ring__and__Field_Ocomm__semiring__1(tc_nat),
    c_0_1580 ).

fof(c_0_2378,axiom,
    class_Ring__and__Field_Oordered__semidom(tc_nat),
    c_0_1581 ).

fof(c_0_2379,axiom,
    class_Ring__and__Field_Ono__zero__divisors(tc_nat),
    c_0_1582 ).

fof(c_0_2380,axiom,
    class_Ring__and__Field_Oordered__semiring(tc_nat),
    c_0_1583 ).

fof(c_0_2381,axiom,
    class_Ring__and__Field_Opordered__semiring(tc_nat),
    c_0_1584 ).

fof(c_0_2382,axiom,
    class_OrderedGroup_Ocancel__semigroup__add(tc_nat),
    c_0_1585 ).

fof(c_0_2383,axiom,
    class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat),
    c_0_1586 ).

fof(c_0_2384,axiom,
    class_OrderedGroup_Opordered__comm__monoid__add(tc_nat),
    c_0_1587 ).

fof(c_0_2385,axiom,
    class_OrderedGroup_Opordered__ab__semigroup__add(tc_nat),
    c_0_1588 ).

fof(c_0_2386,axiom,
    class_Ring__and__Field_Oordered__semiring__strict(tc_nat),
    c_0_1589 ).

fof(c_0_2387,axiom,
    class_Ring__and__Field_Opordered__cancel__semiring(tc_nat),
    c_0_1590 ).

fof(c_0_2388,axiom,
    class_Ring__and__Field_Oordered__comm__semiring__strict(tc_nat),
    c_0_1591 ).

fof(c_0_2389,axiom,
    class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat),
    c_0_1592 ).

fof(c_0_2390,axiom,
    class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat),
    c_0_1593 ).

cnf(c_0_2391,plain,
    ( c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X4,X5,X3),X3) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,X4,X3),c_HOL_Ominus__class_Ominus(X2,X5,X3),X3),c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,X4,X3),X5,X3),X3),c_HOL_Otimes__class_Otimes(X4,c_HOL_Ominus__class_Ominus(X2,X5,X3),X3),X3)
    | ~ class_RealVector_Oreal__normed__algebra(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1594]) ).

cnf(c_0_2392,plain,
    ( c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X1,X2,X3),c_HOL_Oplus__class_Oplus(X4,X5,X3),X3),X3),c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X1,X4,X3),X3),c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X2,X5,X3),X3),X3),X3)
    | ~ class_OrderedGroup_Opordered__ab__group__add__abs(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1595]) ).

cnf(c_0_2393,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_1596]) ).

cnf(c_0_2394,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_1597]) ).

cnf(c_0_2395,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_1598]) ).

cnf(c_0_2396,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_1599]) ).

cnf(c_0_2397,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_1600]) ).

cnf(c_0_2398,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_1601]) ).

cnf(c_0_2399,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_1602]) ).

cnf(c_0_2400,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_1603]) ).

cnf(c_0_2401,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_1604]) ).

cnf(c_0_2402,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_1605]) ).

cnf(c_0_2403,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_1606]) ).

cnf(c_0_2404,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_1607]) ).

cnf(c_0_2405,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_1608]) ).

cnf(c_0_2406,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_1609]) ).

cnf(c_0_2407,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_1610]) ).

cnf(c_0_2408,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_1611]) ).

cnf(c_0_2409,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_1612]) ).

cnf(c_0_2410,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_1613]) ).

cnf(c_0_2411,plain,
    ( c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Oplus__class_Oplus(X4,X6,X3),X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X4,c_HOL_Otimes__class_Otimes(X5,X2,X3),X3),X6,X3),X3)
    | ~ class_Ring__and__Field_Ocomm__ring(X3)
    | ~ class_Ring__and__Field_Odvd(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1614]) ).

cnf(c_0_2412,plain,
    ( c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X4,c_HOL_Otimes__class_Otimes(X6,X2,X3),X3),X5,X3),X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Oplus__class_Oplus(X4,X5,X3),X3)
    | ~ class_Ring__and__Field_Ocomm__ring(X3)
    | ~ class_Ring__and__Field_Odvd(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1615]) ).

cnf(c_0_2413,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_1616]) ).

cnf(c_0_2414,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_1617]) ).

cnf(c_0_2415,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_1618]) ).

cnf(c_0_2416,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_1619]) ).

cnf(c_0_2417,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_1620]) ).

cnf(c_0_2418,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_1621]) ).

cnf(c_0_2419,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_1622]) ).

cnf(c_0_2420,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_1623]) ).

cnf(c_0_2421,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_1624]) ).

cnf(c_0_2422,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_1625]) ).

cnf(c_0_2423,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_1626]) ).

cnf(c_0_2424,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_1627]) ).

cnf(c_0_2425,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_1628]) ).

cnf(c_0_2426,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_1629]) ).

cnf(c_0_2427,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_1630]) ).

cnf(c_0_2428,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_1631]) ).

cnf(c_0_2429,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(X3,X2,tc_nat),X4,tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X1,X3,tc_nat),X2,tc_nat),X4,tc_nat),
    inference(split_conjunct,[status(thm)],[c_0_1632]) ).

cnf(c_0_2430,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_1633]) ).

cnf(c_0_2431,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_1634]) ).

cnf(c_0_2432,plain,
    ( c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X4,X1,X3),X3),X2,X3)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,X2,X3),X4,X3)
    | ~ c_HOL_Oord__class_Oless(X4,c_HOL_Oplus__class_Oplus(X1,X2,X3),X3)
    | ~ class_Ring__and__Field_Oordered__idom(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1635]) ).

cnf(c_0_2433,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_1636]) ).

cnf(c_0_2434,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_1637]) ).

cnf(c_0_2435,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_1638]) ).

cnf(c_0_2436,plain,
    ( c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(c_HOL_Oabs__class_Oabs(X1,X2),c_HOL_Oabs__class_Oabs(X3,X2),X2),X2),c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X1,X3,X2),X2),X2)
    | ~ class_OrderedGroup_Opordered__ab__group__add__abs(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_1639]) ).

cnf(c_0_2437,plain,
    c_Divides_Odiv__class_Omod(c_Suc(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),X3,tc_nat)),X2,tc_nat) = c_Divides_Odiv__class_Omod(c_Suc(X3),X2,tc_nat),
    inference(split_conjunct,[status(thm)],[c_0_1640]) ).

cnf(c_0_2438,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_1641]) ).

cnf(c_0_2439,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_1642]) ).

cnf(c_0_2440,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_1643]) ).

cnf(c_0_2441,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_1644]) ).

cnf(c_0_2442,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_1645]) ).

cnf(c_0_2443,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_1646]) ).

cnf(c_0_2444,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_1647]) ).

cnf(c_0_2445,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_1648]) ).

cnf(c_0_2446,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_1649]) ).

cnf(c_0_2447,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_1650]) ).

cnf(c_0_2448,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_1651]) ).

cnf(c_0_2449,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_1652]) ).

cnf(c_0_2450,plain,
    ( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(X1,X2),c_HOL_Oabs__class_Oabs(X4,X2),X2),c_HOL_Otimes__class_Otimes(X3,X5,X2),X2)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(X1,X2),X3,X2)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(X4,X2),X5,X2)
    | ~ class_Ring__and__Field_Oordered__idom(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_1653]) ).

cnf(c_0_2451,plain,
    ( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X2,X4,X3),X1,X3)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X1,X2,X3),X3),X4,X3)
    | ~ class_Ring__and__Field_Oordered__idom(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1654]) ).

cnf(c_0_2452,plain,
    ( c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(X2,X4,X3),X3)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X1,X2,X3),X3),X4,X3)
    | ~ class_Ring__and__Field_Oordered__idom(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1655]) ).

cnf(c_0_2453,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_1656]) ).

cnf(c_0_2454,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_1657]) ).

cnf(c_0_2455,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_1658]) ).

cnf(c_0_2456,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_1659]) ).

cnf(c_0_2457,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_1660]) ).

cnf(c_0_2458,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_1661]) ).

cnf(c_0_2459,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_1662]) ).

cnf(c_0_2460,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_1663]) ).

cnf(c_0_2461,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_1664]) ).

cnf(c_0_2462,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_1665]) ).

cnf(c_0_2463,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_1666]) ).

cnf(c_0_2464,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_1667]) ).

cnf(c_0_2465,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_1668]) ).

cnf(c_0_2466,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_1669]) ).

cnf(c_0_2467,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_1670]) ).

cnf(c_0_2468,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_1671]) ).

cnf(c_0_2469,plain,
    ( c_Ring__and__Field_Odvd__class_Odvd(X2,X3,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_1672]) ).

cnf(c_0_2470,plain,
    ( c_Ring__and__Field_Odvd__class_Odvd(X2,X3,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_1673]) ).

cnf(c_0_2471,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_1674]) ).

cnf(c_0_2472,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_1675]) ).

cnf(c_0_2473,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_1676]) ).

cnf(c_0_2474,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_1677]) ).

cnf(c_0_2475,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_1678]) ).

cnf(c_0_2476,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_1679]) ).

cnf(c_0_2477,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_1680]) ).

cnf(c_0_2478,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_1681]) ).

cnf(c_0_2479,plain,
    ~ c_Parity_Oeven__odd__class_Oeven(c_Suc(c_HOL_Otimes__class_Otimes(c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),X1,tc_nat)),tc_nat),
    inference(split_conjunct,[status(thm)],[c_0_1682]) ).

cnf(c_0_2480,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_1683]) ).

cnf(c_0_2481,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_1684]) ).

cnf(c_0_2482,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_1685]) ).

cnf(c_0_2483,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_1686]) ).

cnf(c_0_2484,plain,
    ( c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X1,X2,X3),c_HOL_Oplus__class_Oplus(X4,X5,X3),X3) = c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X1,X4,X3),c_HOL_Ominus__class_Ominus(X2,X5,X3),X3)
    | ~ class_OrderedGroup_Oab__group__add(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1687]) ).

cnf(c_0_2485,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_1688]) ).

cnf(c_0_2486,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_1689]) ).

cnf(c_0_2487,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_1690]) ).

cnf(c_0_2488,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_1691]) ).

cnf(c_0_2489,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_1692]) ).

cnf(c_0_2490,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_1693]) ).

cnf(c_0_2491,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_1694]) ).

cnf(c_0_2492,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_1695]) ).

cnf(c_0_2493,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_1696]) ).

cnf(c_0_2494,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_1697]) ).

cnf(c_0_2495,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_1698]) ).

cnf(c_0_2496,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_1699]) ).

cnf(c_0_2497,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_1700]) ).

cnf(c_0_2498,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_1701]) ).

cnf(c_0_2499,plain,
    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) = 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),
    inference(split_conjunct,[status(thm)],[c_0_1702]) ).

cnf(c_0_2500,plain,
    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) = 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),
    inference(split_conjunct,[status(thm)],[c_0_1703]) ).

cnf(c_0_2501,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_1704]) ).

cnf(c_0_2502,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_1705]) ).

cnf(c_0_2503,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_1706]) ).

cnf(c_0_2504,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_1707]) ).

cnf(c_0_2505,plain,
    ( c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X1,X2,X3),X3),c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(X1,X3),c_HOL_Oabs__class_Oabs(X2,X3),X3),X3)
    | ~ class_OrderedGroup_Opordered__ab__group__add__abs(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1708]) ).

cnf(c_0_2506,plain,
    ( c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Oplus__class_Oplus(X1,X2,X3),X3),c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(X1,X3),c_HOL_Oabs__class_Oabs(X2,X3),X3),X3)
    | ~ class_OrderedGroup_Opordered__ab__group__add__abs(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1709]) ).

cnf(c_0_2507,plain,
    ( c_lessequals(c_HOL_Ominus__class_Ominus(c_HOL_Oabs__class_Oabs(X1,X2),c_HOL_Oabs__class_Oabs(X3,X2),X2),c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X1,X3,X2),X2),X2)
    | ~ class_OrderedGroup_Opordered__ab__group__add__abs(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_1710]) ).

cnf(c_0_2508,plain,
    ( c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(X1,X2,X3),X3),c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(X1,X3),c_HOL_Oabs__class_Oabs(X2,X3),X3),X3)
    | ~ class_Ring__and__Field_Olordered__ring(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1711]) ).

cnf(c_0_2509,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_1712]) ).

cnf(c_0_2510,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_1713]) ).

cnf(c_0_2511,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_1714]) ).

cnf(c_0_2512,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_1715]) ).

cnf(c_0_2513,plain,
    ( X1 = c_HOL_Ozero__class_Ozero(X3)
    | c_Ring__and__Field_Odvd__class_Odvd(X2,X4,X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X1,X4,X3),X3)
    | ~ class_Ring__and__Field_Oidom(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1716]) ).

cnf(c_0_2514,plain,
    ( X2 = c_HOL_Ozero__class_Ozero(X3)
    | c_Ring__and__Field_Odvd__class_Odvd(X1,X4,X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X4,X2,X3),X3)
    | ~ class_Ring__and__Field_Oidom(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1717]) ).

cnf(c_0_2515,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_1718]) ).

cnf(c_0_2516,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_1719]) ).

cnf(c_0_2517,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_1720]) ).

cnf(c_0_2518,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_1721]) ).

cnf(c_0_2519,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_1722]) ).

cnf(c_0_2520,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_1723]) ).

cnf(c_0_2521,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_1724]) ).

cnf(c_0_2522,plain,
    ( c_lessequals(X1,c_HOL_Oplus__class_Oplus(X4,c_HOL_Oabs__class_Oabs(X2,X3),X3),X3)
    | ~ c_lessequals(c_HOL_Oplus__class_Oplus(X1,X2,X3),X4,X3)
    | ~ class_OrderedGroup_Olordered__ab__group__add__abs(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1725]) ).

cnf(c_0_2523,plain,
    ( c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Ominus__class_Ominus(X2,X3,tc_nat),tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X3,tc_nat)
    | ~ c_lessequals(X3,X2,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_1726]) ).

cnf(c_0_2524,plain,
    ( c_Ring__and__Field_Odvd__class_Odvd(X1,X3,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Ominus__class_Ominus(X2,X3,tc_nat),tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
    | ~ c_lessequals(X3,X2,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_1727]) ).

cnf(c_0_2525,plain,
    ( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
    | c_Ring__and__Field_Odvd__class_Odvd(X2,X3,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_1728]) ).

cnf(c_0_2526,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_1729]) ).

cnf(c_0_2527,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_1730]) ).

cnf(c_0_2528,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_1731]) ).

cnf(c_0_2529,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_1732]) ).

cnf(c_0_2530,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_1733]) ).

cnf(c_0_2531,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_1734]) ).

cnf(c_0_2532,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_1735]) ).

cnf(c_0_2533,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_1736]) ).

cnf(c_0_2534,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_1737]) ).

cnf(c_0_2535,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_1738]) ).

cnf(c_0_2536,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_1739]) ).

cnf(c_0_2537,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_1740]) ).

cnf(c_0_2538,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_1741]) ).

cnf(c_0_2539,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_1742]) ).

cnf(c_0_2540,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_1743]) ).

cnf(c_0_2541,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_1744]) ).

cnf(c_0_2542,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_1745]) ).

cnf(c_0_2543,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_1746]) ).

cnf(c_0_2544,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_1747]) ).

cnf(c_0_2545,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_1748]) ).

cnf(c_0_2546,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_1749]) ).

cnf(c_0_2547,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_1750]) ).

cnf(c_0_2548,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_1751]) ).

cnf(c_0_2549,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_1752]) ).

cnf(c_0_2550,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_1753]) ).

cnf(c_0_2551,plain,
    ( c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X2,X5,X3),X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X5,X3)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1754]) ).

cnf(c_0_2552,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_1755]) ).

cnf(c_0_2553,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_1756]) ).

cnf(c_0_2554,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_1757]) ).

cnf(c_0_2555,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_1758]) ).

cnf(c_0_2556,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_1759]) ).

cnf(c_0_2557,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_1760]) ).

cnf(c_0_2558,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_1761]) ).

cnf(c_0_2559,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_1762]) ).

cnf(c_0_2560,plain,
    ( c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,X2,X3),X4,X3) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X2,X4,X3),X3)
    | ~ class_RealVector_Oreal__normed__algebra(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1763]) ).

cnf(c_0_2561,plain,
    ( c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,X2,X3),X4,X3) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X2,X4,X3),X3)
    | ~ class_RealVector_Oreal__normed__algebra(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1764]) ).

cnf(c_0_2562,plain,
    ( c_HOL_Otimes__class_Otimes(X1,c_HOL_Ominus__class_Ominus(X2,X3,X4),X4) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X1,X2,X4),c_HOL_Otimes__class_Otimes(X1,X3,X4),X4)
    | ~ class_RealVector_Oreal__normed__algebra(X4) ),
    inference(split_conjunct,[status(thm)],[c_0_1765]) ).

cnf(c_0_2563,plain,
    ( c_HOL_Otimes__class_Otimes(X1,c_HOL_Ominus__class_Ominus(X2,X3,X4),X4) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X1,X2,X4),c_HOL_Otimes__class_Otimes(X1,X3,X4),X4)
    | ~ class_RealVector_Oreal__normed__algebra(X4) ),
    inference(split_conjunct,[status(thm)],[c_0_1766]) ).

cnf(c_0_2564,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_1767]) ).

cnf(c_0_2565,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_1768]) ).

cnf(c_0_2566,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_1769]) ).

cnf(c_0_2567,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_1770]) ).

cnf(c_0_2568,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_1771]) ).

cnf(c_0_2569,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_1772]) ).

cnf(c_0_2570,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_1773]) ).

cnf(c_0_2571,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_RealVector_Oreal__normed__algebra(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1774]) ).

cnf(c_0_2572,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_RealVector_Oreal__normed__algebra(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1775]) ).

cnf(c_0_2573,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_RealVector_Oreal__normed__algebra(X4) ),
    inference(split_conjunct,[status(thm)],[c_0_1776]) ).

cnf(c_0_2574,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_RealVector_Oreal__normed__algebra(X4) ),
    inference(split_conjunct,[status(thm)],[c_0_1777]) ).

cnf(c_0_2575,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_1778]) ).

cnf(c_0_2576,plain,
    ( c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X3,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_1779]) ).

cnf(c_0_2577,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_1780]) ).

cnf(c_0_2578,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_1781]) ).

cnf(c_0_2579,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_1782]) ).

cnf(c_0_2580,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_1783]) ).

cnf(c_0_2581,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_1784]) ).

cnf(c_0_2582,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_1785]) ).

cnf(c_0_2583,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_1786]) ).

cnf(c_0_2584,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_1787]) ).

cnf(c_0_2585,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_1788]) ).

cnf(c_0_2586,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_1789]) ).

cnf(c_0_2587,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_1790]) ).

cnf(c_0_2588,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_1791]) ).

cnf(c_0_2589,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_1792]) ).

cnf(c_0_2590,plain,
    ( c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(X1,X3,X2),X2) = c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(X1,X2),c_HOL_Oabs__class_Oabs(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__abs(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_1793]) ).

cnf(c_0_2591,plain,
    ( c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(X1,X3,X2),X2) = c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(X1,X2),c_HOL_Oabs__class_Oabs(X3,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__ring__abs(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_1794]) ).

cnf(c_0_2592,plain,
    ( c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(X2,X3,X1),X1) = c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(X2,X1),c_HOL_Oabs__class_Oabs(X3,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__ring__abs(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1795]) ).

cnf(c_0_2593,plain,
    ( c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(X2,X3,X1),X1) = c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(X2,X1),c_HOL_Oabs__class_Oabs(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__abs(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1796]) ).

cnf(c_0_2594,plain,
    c_HOL_Otimes__class_Otimes(X1,c_HOL_Ominus__class_Ominus(X2,X3,tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(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_1797]) ).

cnf(c_0_2595,plain,
    c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),X3,tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),c_HOL_Otimes__class_Otimes(X2,X3,tc_nat),tc_nat),
    inference(split_conjunct,[status(thm)],[c_0_1798]) ).

cnf(c_0_2596,plain,
    c_Orderings_Oord__class_Omin(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),c_HOL_Ominus__class_Ominus(X3,X2,tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(c_Orderings_Oord__class_Omin(X1,X3,tc_nat),X2,tc_nat),
    inference(split_conjunct,[status(thm)],[c_0_1799]) ).

cnf(c_0_2597,plain,
    c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),X3,tc_nat),X2,tc_nat) = c_Divides_Odiv__class_Omod(X3,X2,tc_nat),
    inference(split_conjunct,[status(thm)],[c_0_1800]) ).

cnf(c_0_2598,plain,
    c_HOL_Otimes__class_Otimes(X1,c_Divides_Odiv__class_Omod(X2,X3,tc_nat),tc_nat) = c_Divides_Odiv__class_Omod(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_1801]) ).

cnf(c_0_2599,plain,
    c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(X1,X2,tc_nat),X3,tc_nat) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),c_HOL_Otimes__class_Otimes(X2,X3,tc_nat),tc_nat),
    inference(split_conjunct,[status(thm)],[c_0_1802]) ).

cnf(c_0_2600,plain,
    c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),X3,tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),c_HOL_Otimes__class_Otimes(X2,X3,tc_nat),tc_nat),
    inference(split_conjunct,[status(thm)],[c_0_1803]) ).

cnf(c_0_2601,plain,
    c_HOL_Otimes__class_Otimes(X1,c_HOL_Oplus__class_Oplus(X2,X3,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(split_conjunct,[status(thm)],[c_0_1804]) ).

cnf(c_0_2602,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_1805]) ).

cnf(c_0_2603,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_1806]) ).

cnf(c_0_2604,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_1807]) ).

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) ),
    inference(split_conjunct,[status(thm)],[c_0_1808]) ).

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) ),
    inference(split_conjunct,[status(thm)],[c_0_1809]) ).

cnf(c_0_2607,plain,
    ( c_Ring__and__Field_Odvd__class_Odvd(X1,X4,X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,c_Divides_Odiv__class_Omod(X4,X2,X3),X3)
    | ~ class_Divides_Osemiring__div(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1810]) ).

cnf(c_0_2608,plain,
    ( c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X4)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,c_Divides_Odiv__class_Omod(X2,X3,X4),X4)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X3,X4)
    | ~ class_Divides_Osemiring__div(X4) ),
    inference(split_conjunct,[status(thm)],[c_0_1811]) ).

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) ),
    inference(split_conjunct,[status(thm)],[c_0_1812]) ).

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) ),
    inference(split_conjunct,[status(thm)],[c_0_1813]) ).

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) ),
    inference(split_conjunct,[status(thm)],[c_0_1814]) ).

cnf(c_0_2612,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_1815]) ).

cnf(c_0_2613,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_1816]) ).

cnf(c_0_2614,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_1817]) ).

cnf(c_0_2615,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_1818]) ).

cnf(c_0_2616,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_1819]) ).

cnf(c_0_2617,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_1820]) ).

cnf(c_0_2618,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_1821]) ).

cnf(c_0_2619,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_1822]) ).

cnf(c_0_2620,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_1823]) ).

cnf(c_0_2621,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_1824]) ).

cnf(c_0_2622,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_1825]) ).

cnf(c_0_2623,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_1826]) ).

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) ),
    inference(split_conjunct,[status(thm)],[c_0_1827]) ).

cnf(c_0_2625,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_1828]) ).

cnf(c_0_2626,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_1829]) ).

cnf(c_0_2627,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_1830]) ).

cnf(c_0_2628,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_1831]) ).

cnf(c_0_2629,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_1832]) ).

cnf(c_0_2630,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_1833]) ).

cnf(c_0_2631,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_1834]) ).

cnf(c_0_2632,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_1835]) ).

cnf(c_0_2633,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_1836]) ).

cnf(c_0_2634,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_1837]) ).

cnf(c_0_2635,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_1838]) ).

cnf(c_0_2636,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_1839]) ).

cnf(c_0_2637,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_1840]) ).

cnf(c_0_2638,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_1841]) ).

cnf(c_0_2639,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_1842]) ).

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) ),
    inference(split_conjunct,[status(thm)],[c_0_1843]) ).

cnf(c_0_2641,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_1844]) ).

cnf(c_0_2642,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_1845]) ).

cnf(c_0_2643,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_1846]) ).

cnf(c_0_2644,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_1847]) ).

cnf(c_0_2645,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_1848]) ).

cnf(c_0_2646,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_1849]) ).

cnf(c_0_2647,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_1850]) ).

cnf(c_0_2648,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_1851]) ).

cnf(c_0_2649,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_1852]) ).

cnf(c_0_2650,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_1853]) ).

cnf(c_0_2651,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_1854]) ).

cnf(c_0_2652,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_1855]) ).

cnf(c_0_2653,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_1856]) ).

cnf(c_0_2654,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_1857]) ).

cnf(c_0_2655,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_1858]) ).

cnf(c_0_2656,plain,
    c_lessequals(X1,c_HOL_Otimes__class_Otimes(X1,c_HOL_Otimes__class_Otimes(X1,X1,tc_nat),tc_nat),tc_nat),
    inference(split_conjunct,[status(thm)],[c_0_1859]) ).

cnf(c_0_2657,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_1860]) ).

cnf(c_0_2658,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_1861]) ).

cnf(c_0_2659,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_1862]) ).

cnf(c_0_2660,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_1863]) ).

cnf(c_0_2661,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_1864]) ).

cnf(c_0_2662,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_1865]) ).

cnf(c_0_2663,plain,
    ( c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X2,X4,X3),X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
    | ~ class_Ring__and__Field_Oidom(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1866]) ).

cnf(c_0_2664,plain,
    ( c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X4,X1,X3),c_HOL_Otimes__class_Otimes(X4,X2,X3),X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
    | ~ class_Ring__and__Field_Oidom(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1867]) ).

cnf(c_0_2665,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_1868]) ).

cnf(c_0_2666,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_1869]) ).

cnf(c_0_2667,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_1870]) ).

cnf(c_0_2668,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_1871]) ).

cnf(c_0_2669,plain,
    ( c_Ring__and__Field_Odvd__class_Odvd(X2,X1,tc_nat)
    | c_Ring__and__Field_Odvd__class_Odvd(X3,X2,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X3,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X3,X1,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_1872]) ).

cnf(c_0_2670,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_1873]) ).

cnf(c_0_2671,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_1874]) ).

cnf(c_0_2672,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_1875]) ).

cnf(c_0_2673,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_1876]) ).

cnf(c_0_2674,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_1877]) ).

cnf(c_0_2675,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_1878]) ).

cnf(c_0_2676,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_1879]) ).

cnf(c_0_2677,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_1880]) ).

cnf(c_0_2678,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_1881]) ).

cnf(c_0_2679,plain,
    ( c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X3,X1,tc_nat),c_HOL_Otimes__class_Otimes(X3,X2,tc_nat),tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_1882]) ).

cnf(c_0_2680,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_1883]) ).

cnf(c_0_2681,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_1884]) ).

cnf(c_0_2682,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_1885]) ).

cnf(c_0_2683,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_1886]) ).

cnf(c_0_2684,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_1887]) ).

cnf(c_0_2685,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_1888]) ).

cnf(c_0_2686,plain,
    ( c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Ominus__class_Ominus(X2,X4,X3),X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X4,X3)
    | ~ class_Ring__and__Field_Ocomm__ring__1(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1889]) ).

cnf(c_0_2687,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_1890]) ).

cnf(c_0_2688,plain,
    ( c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Oplus__class_Oplus(X2,X4,X3),X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X4,X3)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1891]) ).

cnf(c_0_2689,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_1892]) ).

cnf(c_0_2690,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_1893]) ).

cnf(c_0_2691,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_1894]) ).

cnf(c_0_2692,plain,
    ( c_Ring__and__Field_Odvd__class_Odvd(X1,c_Divides_Odiv__class_Omod(X2,X4,X3),X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X4,X3)
    | ~ class_Divides_Osemiring__div(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1895]) ).

cnf(c_0_2693,plain,
    ( c_Ring__and__Field_Odvd__class_Odvd(X1,c_Divides_Odiv__class_Omod(X4,X2,X3),X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X4,X3)
    | ~ class_Divides_Osemiring__div(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1896]) ).

cnf(c_0_2694,plain,
    ( c_HOL_Oabs__class_Oabs(c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(X1,X2),c_HOL_Oabs__class_Oabs(X3,X2),X2),X2) = c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(X1,X2),c_HOL_Oabs__class_Oabs(X3,X2),X2)
    | ~ class_OrderedGroup_Opordered__ab__group__add__abs(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_1897]) ).

cnf(c_0_2695,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_1898]) ).

cnf(c_0_2696,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_1899]) ).

cnf(c_0_2697,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_1900]) ).

cnf(c_0_2698,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_1901]) ).

cnf(c_0_2699,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_1902]) ).

cnf(c_0_2700,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_1903]) ).

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_Ring__and__Field_Oordered__idom(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_1904]) ).

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_OrderedGroup_Olordered__ab__group__add(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_1905]) ).

cnf(c_0_2703,plain,
    c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(c_Suc(X1),X2,tc_nat),c_Suc(X3),tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),X3,tc_nat),
    inference(split_conjunct,[status(thm)],[c_0_1906]) ).

cnf(c_0_2704,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_1907]) ).

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) ),
    inference(split_conjunct,[status(thm)],[c_0_1908]) ).

cnf(c_0_2706,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_1909]) ).

cnf(c_0_2707,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_1910]) ).

cnf(c_0_2708,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_1911]) ).

cnf(c_0_2709,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_1912]) ).

cnf(c_0_2710,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_1913]) ).

cnf(c_0_2711,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_1914]) ).

cnf(c_0_2712,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_1915]) ).

cnf(c_0_2713,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_1916]) ).

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(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_1917]) ).

cnf(c_0_2715,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_1918]) ).

cnf(c_0_2716,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_1919]) ).

cnf(c_0_2717,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_1920]) ).

cnf(c_0_2718,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_1921]) ).

cnf(c_0_2719,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_1922]) ).

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) ),
    inference(split_conjunct,[status(thm)],[c_0_1923]) ).

cnf(c_0_2721,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_1924]) ).

cnf(c_0_2722,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_1925]) ).

cnf(c_0_2723,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_1926]) ).

cnf(c_0_2724,plain,
    ( c_Ring__and__Field_Odvd__class_Odvd(X2,X1,tc_nat)
    | c_Ring__and__Field_Odvd__class_Odvd(X3,X2,tc_nat)
    | c_Ring__and__Field_Odvd__class_Odvd(X1,X3,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X3,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_1927]) ).

cnf(c_0_2725,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_1928]) ).

cnf(c_0_2726,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_1929]) ).

cnf(c_0_2727,plain,
    c_Divides_Odiv__class_Omod(c_Suc(X1),X2,tc_nat) = c_Divides_Odiv__class_Omod(c_Suc(c_Divides_Odiv__class_Omod(X1,X2,tc_nat)),X2,tc_nat),
    inference(split_conjunct,[status(thm)],[c_0_1930]) ).

cnf(c_0_2728,plain,
    ( c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Ominus__class_Ominus(X2,X3,tc_nat),tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X3,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_1931]) ).

cnf(c_0_2729,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_1932]) ).

cnf(c_0_2730,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_1933]) ).

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) ),
    inference(split_conjunct,[status(thm)],[c_0_1934]) ).

cnf(c_0_2732,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_1935]) ).

cnf(c_0_2733,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_1936]) ).

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(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_1937]) ).

cnf(c_0_2735,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_1938]) ).

cnf(c_0_2736,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_1939]) ).

cnf(c_0_2737,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_1940]) ).

cnf(c_0_2738,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_1941]) ).

cnf(c_0_2739,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_1942]) ).

cnf(c_0_2740,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_1943]) ).

cnf(c_0_2741,plain,
    ( c_Ring__and__Field_Odvd__class_Odvd(X2,X4,X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1944]) ).

cnf(c_0_2742,plain,
    ( c_Ring__and__Field_Odvd__class_Odvd(X1,X4,X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1945]) ).

cnf(c_0_2743,plain,
    ( c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),X3) = c_HOL_Ominus__class_Ominus(c_Nat_Osemiring__1__class_Oof__nat(X2,X3),c_Nat_Osemiring__1__class_Oof__nat(X1,X3),X3)
    | ~ c_lessequals(X1,X2,tc_nat)
    | ~ class_Ring__and__Field_Oring__1(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1946]) ).

cnf(c_0_2744,plain,
    c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),X3,tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X1,X3,tc_nat),X2,tc_nat),
    inference(split_conjunct,[status(thm)],[c_0_1947]) ).

cnf(c_0_2745,plain,
    c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),X3,tc_nat) = c_HOL_Ominus__class_Ominus(X1,c_HOL_Oplus__class_Oplus(X2,X3,tc_nat),tc_nat),
    inference(split_conjunct,[status(thm)],[c_0_1948]) ).

cnf(c_0_2746,plain,
    c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),c_HOL_Oplus__class_Oplus(X3,X2,tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(X1,X3,tc_nat),
    inference(split_conjunct,[status(thm)],[c_0_1949]) ).

cnf(c_0_2747,plain,
    c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),c_HOL_Oplus__class_Oplus(X1,X3,tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(X2,X3,tc_nat),
    inference(split_conjunct,[status(thm)],[c_0_1950]) ).

cnf(c_0_2748,plain,
    c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X2,X3,tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(X2,c_HOL_Oplus__class_Oplus(X1,X3,tc_nat),tc_nat),
    inference(split_conjunct,[status(thm)],[c_0_1951]) ).

cnf(c_0_2749,plain,
    c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),X3,tc_nat) = c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X2,X3,tc_nat),tc_nat),
    inference(split_conjunct,[status(thm)],[c_0_1952]) ).

cnf(c_0_2750,plain,
    c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),X3,tc_nat) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Otimes__class_Otimes(X2,X3,tc_nat),tc_nat),
    inference(split_conjunct,[status(thm)],[c_0_1953]) ).

cnf(c_0_2751,plain,
    ( c_Divides_Odiv__class_Omod(c_Divides_Odiv__class_Omod(X4,X2,X3),X1,X3) = c_Divides_Odiv__class_Omod(X4,X1,X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
    | ~ class_Divides_Osemiring__div(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1954]) ).

cnf(c_0_2752,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_1955]) ).

cnf(c_0_2753,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_1956]) ).

cnf(c_0_2754,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_1957]) ).

cnf(c_0_2755,plain,
    ( c_Ring__and__Field_Odvd__class_Odvd(X2,X1,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X3,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X3,X1,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_1958]) ).

cnf(c_0_2756,plain,
    ( c_Ring__and__Field_Odvd__class_Odvd(X3,X2,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X3,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X3,X1,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_1959]) ).

cnf(c_0_2757,plain,
    ( c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(X3,X1),X2,X1) = c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(X3,X2,X1),X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1960]) ).

cnf(c_0_2758,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_1961]) ).

cnf(c_0_2759,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_1962]) ).

cnf(c_0_2760,plain,
    ( c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Oplus__class_Oplus(X2,X1,tc_nat),tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_1963]) ).

cnf(c_0_2761,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_1964]) ).

cnf(c_0_2762,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_1965]) ).

cnf(c_0_2763,plain,
    ( c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X1,c_HOL_Ozero__class_Ozero(X2),X2),c_HOL_Otimes__class_Otimes(X3,c_HOL_Ozero__class_Ozero(X2),X2),X2)
    | ~ class_Ring__and__Field_Oidom(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_1966]) ).

cnf(c_0_2764,plain,
    ( c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),X2,X1),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),X3,X1),X1)
    | ~ class_Ring__and__Field_Oidom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1967]) ).

cnf(c_0_2765,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_1968]) ).

cnf(c_0_2766,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_1969]) ).

cnf(c_0_2767,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_1970]) ).

cnf(c_0_2768,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_1971]) ).

cnf(c_0_2769,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_1972]) ).

cnf(c_0_2770,plain,
    ( c_Ring__and__Field_Odvd__class_Odvd(X3,X2,tc_nat)
    | c_Ring__and__Field_Odvd__class_Odvd(X1,X3,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X3,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_1973]) ).

cnf(c_0_2771,plain,
    ( c_Ring__and__Field_Odvd__class_Odvd(X2,X1,tc_nat)
    | c_Ring__and__Field_Odvd__class_Odvd(X1,X3,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X3,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_1974]) ).

cnf(c_0_2772,plain,
    c_Ring__and__Field_Odvd__class_Odvd(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),tc_nat),
    inference(split_conjunct,[status(thm)],[c_0_1975]) ).

cnf(c_0_2773,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_1976]) ).

cnf(c_0_2774,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_1977]) ).

cnf(c_0_2775,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_1978]) ).

cnf(c_0_2776,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_1979]) ).

cnf(c_0_2777,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_1980]) ).

cnf(c_0_2778,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_1981]) ).

cnf(c_0_2779,plain,
    ( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | c_Parity_Oeven__odd__class_Oeven(X1,tc_nat)
    | ~ c_Parity_Oeven__odd__class_Oeven(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),tc_nat)
    | ~ c_Parity_Oeven__odd__class_Oeven(X2,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_1982]) ).

cnf(c_0_2780,plain,
    ( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | c_Parity_Oeven__odd__class_Oeven(X2,tc_nat)
    | ~ c_Parity_Oeven__odd__class_Oeven(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),tc_nat)
    | ~ c_Parity_Oeven__odd__class_Oeven(X1,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_1983]) ).

cnf(c_0_2781,plain,
    c_HOL_Oord__class_Oless(X1,c_Suc(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat)),tc_nat),
    inference(split_conjunct,[status(thm)],[c_0_1984]) ).

cnf(c_0_2782,plain,
    c_HOL_Oord__class_Oless(X1,c_Suc(c_HOL_Oplus__class_Oplus(X2,X1,tc_nat)),tc_nat),
    inference(split_conjunct,[status(thm)],[c_0_1985]) ).

cnf(c_0_2783,plain,
    c_HOL_Oord__class_Oless(X1,c_Suc(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat)),tc_nat),
    inference(split_conjunct,[status(thm)],[c_0_1986]) ).

cnf(c_0_2784,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_1987]) ).

cnf(c_0_2785,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_1988]) ).

cnf(c_0_2786,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_1989]) ).

cnf(c_0_2787,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_1990]) ).

cnf(c_0_2788,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_1991]) ).

cnf(c_0_2789,plain,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
    | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X1,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_1992]) ).

cnf(c_0_2790,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_1993]) ).

cnf(c_0_2791,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_1994]) ).

cnf(c_0_2792,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_1995]) ).

cnf(c_0_2793,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_1996]) ).

cnf(c_0_2794,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_1997]) ).

cnf(c_0_2795,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_1998]) ).

cnf(c_0_2796,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_1999]) ).

cnf(c_0_2797,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_2000]) ).

cnf(c_0_2798,plain,
    ( c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Otimes__class_Otimes(X2,X4,X3),X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_2001]) ).

cnf(c_0_2799,plain,
    ( c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Otimes__class_Otimes(X4,X2,X3),X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_2002]) ).

cnf(c_0_2800,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_2003]) ).

cnf(c_0_2801,plain,
    ( c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X1,X2,X3),X3) = c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X2,X1,X3),X3)
    | ~ class_OrderedGroup_Opordered__ab__group__add__abs(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_2004]) ).

cnf(c_0_2802,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_2005]) ).

cnf(c_0_2803,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_2006]) ).

cnf(c_0_2804,plain,
    ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),X2,tc_nat),
    inference(split_conjunct,[status(thm)],[c_0_2007]) ).

cnf(c_0_2805,plain,
    ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),X1,tc_nat),
    inference(split_conjunct,[status(thm)],[c_0_2008]) ).

cnf(c_0_2806,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_2009]) ).

cnf(c_0_2807,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_2010]) ).

cnf(c_0_2808,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_2011]) ).

cnf(c_0_2809,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_2012]) ).

cnf(c_0_2810,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_2013]) ).

cnf(c_0_2811,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_2014]) ).

cnf(c_0_2812,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_2015]) ).

cnf(c_0_2813,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_2016]) ).

cnf(c_0_2814,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_2017]) ).

cnf(c_0_2815,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_2018]) ).

cnf(c_0_2816,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_2019]) ).

cnf(c_0_2817,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_2020]) ).

cnf(c_0_2818,plain,
    ( c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Oplus__class_Oplus(X2,X1,tc_nat),tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_2021]) ).

cnf(c_0_2819,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_2022]) ).

cnf(c_0_2820,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_2023]) ).

cnf(c_0_2821,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_2024]) ).

cnf(c_0_2822,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_2025]) ).

cnf(c_0_2823,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_2026]) ).

cnf(c_0_2824,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_2027]) ).

cnf(c_0_2825,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_2028]) ).

cnf(c_0_2826,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_2029]) ).

cnf(c_0_2827,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_2030]) ).

cnf(c_0_2828,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_2031]) ).

cnf(c_0_2829,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_2032]) ).

cnf(c_0_2830,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_2033]) ).

cnf(c_0_2831,plain,
    ( c_Ring__and__Field_Odvd__class_Odvd(X1,X4,X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X4,X3)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_2034]) ).

cnf(c_0_2832,plain,
    ( c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(X1,X2,X3),X3) = c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(X1,X3),c_HOL_Oabs__class_Oabs(X2,X3),X3)
    | ~ class_Ring__and__Field_Oordered__idom(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_2035]) ).

cnf(c_0_2833,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_2036]) ).

cnf(c_0_2834,plain,
    ( c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),X3) = c_HOL_Otimes__class_Otimes(c_Nat_Osemiring__1__class_Oof__nat(X1,X3),c_Nat_Osemiring__1__class_Oof__nat(X2,X3),X3)
    | ~ class_Ring__and__Field_Osemiring__1(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_2037]) ).

cnf(c_0_2835,plain,
    ( c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),X3) = c_HOL_Oplus__class_Oplus(c_Nat_Osemiring__1__class_Oof__nat(X1,X3),c_Nat_Osemiring__1__class_Oof__nat(X2,X3),X3)
    | ~ class_Ring__and__Field_Osemiring__1(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_2038]) ).

cnf(c_0_2836,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),X1,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X1,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_2039]) ).

cnf(c_0_2837,plain,
    ( c_HOL_Oord__class_Oless(X1,X3,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X1,X2),c_Nat_Osemiring__1__class_Oof__nat(X3,X2),X2)
    | ~ class_Ring__and__Field_Oordered__semidom(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_2040]) ).

cnf(c_0_2838,plain,
    ( c_lessequals(X1,X3,tc_nat)
    | ~ c_lessequals(c_Nat_Osemiring__1__class_Oof__nat(X1,X2),c_Nat_Osemiring__1__class_Oof__nat(X3,X2),X2)
    | ~ class_Ring__and__Field_Oordered__semidom(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_2041]) ).

cnf(c_0_2839,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_2042]) ).

cnf(c_0_2840,plain,
    ( c_lessequals(X1,X2,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_2043]) ).

cnf(c_0_2841,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_2044]) ).

cnf(c_0_2842,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_2045]) ).

cnf(c_0_2843,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_2046]) ).

cnf(c_0_2844,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_2047]) ).

cnf(c_0_2845,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_2048]) ).

cnf(c_0_2846,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_2049]) ).

cnf(c_0_2847,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_2050]) ).

cnf(c_0_2848,plain,
    ( c_Ring__and__Field_Odvd__class_Odvd(X1,X3,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X3,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_2051]) ).

cnf(c_0_2849,plain,
    ( c_Parity_Oeven__odd__class_Oeven(X1,tc_nat)
    | ~ c_Parity_Oeven__odd__class_Oeven(X2,tc_nat)
    | ~ c_Parity_Oeven__odd__class_Oeven(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_2052]) ).

cnf(c_0_2850,plain,
    ( c_Parity_Oeven__odd__class_Oeven(X2,tc_nat)
    | ~ c_Parity_Oeven__odd__class_Oeven(X1,tc_nat)
    | ~ c_Parity_Oeven__odd__class_Oeven(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_2053]) ).

cnf(c_0_2851,plain,
    ( c_Parity_Oeven__odd__class_Oeven(X2,tc_nat)
    | ~ c_Parity_Oeven__odd__class_Oeven(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat)
    | ~ c_Parity_Oeven__odd__class_Oeven(X1,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_2054]) ).

cnf(c_0_2852,plain,
    ( c_Parity_Oeven__odd__class_Oeven(X1,tc_nat)
    | ~ c_Parity_Oeven__odd__class_Oeven(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat)
    | ~ c_Parity_Oeven__odd__class_Oeven(X2,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_2055]) ).

cnf(c_0_2853,plain,
    ( c_Parity_Oeven__odd__class_Oeven(X1,tc_nat)
    | ~ c_Parity_Oeven__odd__class_Oeven(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat)
    | ~ c_Parity_Oeven__odd__class_Oeven(X2,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_2056]) ).

cnf(c_0_2854,plain,
    ( c_Parity_Oeven__odd__class_Oeven(X2,tc_nat)
    | ~ c_Parity_Oeven__odd__class_Oeven(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat)
    | ~ c_Parity_Oeven__odd__class_Oeven(X1,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_2057]) ).

cnf(c_0_2855,plain,
    c_HOL_Otimes__class_Otimes(X1,c_Suc(X2),tc_nat) = c_HOL_Oplus__class_Oplus(X1,c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),tc_nat),
    inference(split_conjunct,[status(thm)],[c_0_2058]) ).

cnf(c_0_2856,plain,
    c_HOL_Otimes__class_Otimes(c_Suc(X1),X2,tc_nat) = c_HOL_Oplus__class_Oplus(X2,c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),tc_nat),
    inference(split_conjunct,[status(thm)],[c_0_2059]) ).

cnf(c_0_2857,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_2060]) ).

cnf(c_0_2858,plain,
    ( c_Parity_Oeven__odd__class_Oeven(X1,tc_nat)
    | c_Parity_Oeven__odd__class_Oeven(X2,tc_nat)
    | ~ c_Parity_Oeven__odd__class_Oeven(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_2061]) ).

cnf(c_0_2859,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_2062]) ).

cnf(c_0_2860,plain,
    ( c_Parity_Oeven__odd__class_Oeven(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),tc_nat)
    | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_2063]) ).

cnf(c_0_2861,plain,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Nat_Osemiring__1__class_Oof__nat(X2,X1),X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2064]) ).

cnf(c_0_2862,plain,
    ( c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X1,X3),c_Nat_Osemiring__1__class_Oof__nat(X2,X3),X3)
    | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | ~ class_Ring__and__Field_Oordered__semidom(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_2065]) ).

cnf(c_0_2863,plain,
    ( c_lessequals(c_Nat_Osemiring__1__class_Oof__nat(X1,X3),c_Nat_Osemiring__1__class_Oof__nat(X2,X3),X3)
    | ~ c_lessequals(X1,X2,tc_nat)
    | ~ class_Ring__and__Field_Oordered__semidom(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_2066]) ).

cnf(c_0_2864,plain,
    ( c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Oabs__class_Oabs(X2,X3),X3)
    | ~ class_Ring__and__Field_Oordered__idom(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_2067]) ).

cnf(c_0_2865,plain,
    ( c_Ring__and__Field_Odvd__class_Odvd(X1,X3,X2)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oabs__class_Oabs(X1,X2),X3,X2)
    | ~ class_Ring__and__Field_Oordered__idom(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_2068]) ).

cnf(c_0_2866,plain,
    ( c_HOL_Oord__class_Oless(X1,X3,X2)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(X1,X2),X3,X2)
    | ~ class_Ring__and__Field_Oordered__idom(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_2069]) ).

cnf(c_0_2867,plain,
    ( c_lessequals(X1,X3,X2)
    | ~ c_lessequals(c_HOL_Oabs__class_Oabs(X1,X2),X3,X2)
    | ~ class_OrderedGroup_Opordered__ab__group__add__abs(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_2070]) ).

cnf(c_0_2868,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_2071]) ).

cnf(c_0_2869,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_2072]) ).

cnf(c_0_2870,plain,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),c_Nat_Osemiring__1__class_Oof__nat(X1,X2),X2)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
    | ~ class_Ring__and__Field_Oordered__semidom(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_2073]) ).

cnf(c_0_2871,plain,
    ( X2 = X1
    | ~ c_lessequals(X1,X2,X3)
    | ~ c_lessequals(X2,X1,X3)
    | ~ class_Orderings_Oorder(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_2074]) ).

cnf(c_0_2872,plain,
    ( X1 = X2
    | ~ c_lessequals(X1,X2,X3)
    | ~ c_lessequals(X2,X1,X3)
    | ~ class_Orderings_Oorder(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_2075]) ).

cnf(c_0_2873,plain,
    ( X1 = X2
    | ~ c_lessequals(X1,X2,X3)
    | ~ c_lessequals(X2,X1,X3)
    | ~ class_Orderings_Oorder(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_2076]) ).

cnf(c_0_2874,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_2077]) ).

cnf(c_0_2875,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_2078]) ).

cnf(c_0_2876,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_2079]) ).

cnf(c_0_2877,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_2080]) ).

cnf(c_0_2878,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_2081]) ).

cnf(c_0_2879,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_2082]) ).

cnf(c_0_2880,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_2083]) ).

cnf(c_0_2881,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_2084]) ).

cnf(c_0_2882,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_2085]) ).

cnf(c_0_2883,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_2086]) ).

cnf(c_0_2884,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_2087]) ).

cnf(c_0_2885,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_2088]) ).

cnf(c_0_2886,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_2089]) ).

cnf(c_0_2887,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_2090]) ).

cnf(c_0_2888,plain,
    c_Parity_Oeven__odd__class_Oeven(c_HOL_Otimes__class_Otimes(c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),X1,tc_nat),tc_nat),
    inference(split_conjunct,[status(thm)],[c_0_2091]) ).

cnf(c_0_2889,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_2092]) ).

cnf(c_0_2890,plain,
    ( ~ c_lessequals(c_Suc(X1),X2,tc_nat)
    | ~ c_lessequals(X2,X1,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_2093]) ).

cnf(c_0_2891,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_2094]) ).

cnf(c_0_2892,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_2095]) ).

cnf(c_0_2893,plain,
    ( c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Oabs__class_Oabs(X2,X3),X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
    | ~ class_Ring__and__Field_Oordered__idom(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_2096]) ).

cnf(c_0_2894,plain,
    ( c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oabs__class_Oabs(X1,X3),X2,X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
    | ~ class_Ring__and__Field_Oordered__idom(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_2097]) ).

cnf(c_0_2895,plain,
    c_Orderings_Oord__class_Omin(c_Suc(X1),c_Suc(X2),tc_nat) = c_Suc(c_Orderings_Oord__class_Omin(X1,X2,tc_nat)),
    inference(split_conjunct,[status(thm)],[c_0_2098]) ).

cnf(c_0_2896,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_2099]) ).

cnf(c_0_2897,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_2100]) ).

cnf(c_0_2898,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_2101]) ).

cnf(c_0_2899,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_2102]) ).

cnf(c_0_2900,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_2103]) ).

cnf(c_0_2901,plain,
    ( X1 = X2
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X1,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_2104]) ).

cnf(c_0_2902,plain,
    ( X1 = X2
    | ~ c_lessequals(X1,X2,tc_nat)
    | ~ c_lessequals(X2,X1,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_2105]) ).

cnf(c_0_2903,plain,
    ( X1 = X2
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X1,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_2106]) ).

cnf(c_0_2904,plain,
    ( X1 = X2
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X1,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_2107]) ).

cnf(c_0_2905,plain,
    ( X1 = X2
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X1,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_2108]) ).

cnf(c_0_2906,plain,
    ( X2 = X1
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X1,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_2109]) ).

cnf(c_0_2907,plain,
    ( X1 = X2
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X1,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_2110]) ).

cnf(c_0_2908,plain,
    ( X1 = X2
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X1,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_2111]) ).

cnf(c_0_2909,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_2112]) ).

cnf(c_0_2910,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_2113]) ).

cnf(c_0_2911,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_2114]) ).

cnf(c_0_2912,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_2115]) ).

cnf(c_0_2913,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_2116]) ).

cnf(c_0_2914,plain,
    ( c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Otimes__class_Otimes(X1,X2,X3),X3)
    | ~ class_Ring__and__Field_Odvd(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_2117]) ).

cnf(c_0_2915,plain,
    ( c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Otimes__class_Otimes(X1,X2,X3),X3)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_2118]) ).

cnf(c_0_2916,plain,
    ( c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Otimes__class_Otimes(X2,X1,X3),X3)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_2119]) ).

cnf(c_0_2917,plain,
    ( c_lessequals(c_Orderings_Oord__class_Omin(X1,X2,X3),X1,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_2120]) ).

cnf(c_0_2918,plain,
    ( c_lessequals(c_Orderings_Oord__class_Omin(X1,X2,X3),X2,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_2121]) ).

cnf(c_0_2919,plain,
    ( c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(X1,X2),c_HOL_Oabs__class_Oabs(X1,X2),X2) = c_HOL_Otimes__class_Otimes(X1,X1,X2)
    | ~ class_Ring__and__Field_Oordered__idom(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_2122]) ).

cnf(c_0_2920,plain,
    c_HOL_Oplus__class_Oplus(X1,c_Suc(X2),tc_nat) = c_Suc(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat)),
    inference(split_conjunct,[status(thm)],[c_0_2123]) ).

cnf(c_0_2921,plain,
    c_HOL_Oplus__class_Oplus(c_Suc(X1),X2,tc_nat) = c_Suc(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat)),
    inference(split_conjunct,[status(thm)],[c_0_2124]) ).

cnf(c_0_2922,plain,
    c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),c_Suc(X1),tc_nat),
    inference(split_conjunct,[status(thm)],[c_0_2125]) ).

cnf(c_0_2923,plain,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oabs__class_Oabs(c_HOL_Ozero__class_Ozero(X1),X1),X1)
    | ~ class_OrderedGroup_Opordered__ab__group__add__abs(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2126]) ).

cnf(c_0_2924,plain,
    ( ~ c_Parity_Oeven__odd__class_Oeven(X1,tc_nat)
    | c_Divides_Odiv__class_Omod(X1,c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
    inference(split_conjunct,[status(thm)],[c_0_2127]) ).

cnf(c_0_2925,plain,
    c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),X1,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
    inference(split_conjunct,[status(thm)],[c_0_2128]) ).

cnf(c_0_2926,plain,
    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(split_conjunct,[status(thm)],[c_0_2129]) ).

cnf(c_0_2927,plain,
    c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),X2,tc_nat) = X1,
    inference(split_conjunct,[status(thm)],[c_0_2130]) ).

cnf(c_0_2928,plain,
    c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),X1,tc_nat) = X2,
    inference(split_conjunct,[status(thm)],[c_0_2131]) ).

cnf(c_0_2929,plain,
    ( c_Parity_Oeven__odd__class_Oeven(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),tc_nat)
    | ~ c_Parity_Oeven__odd__class_Oeven(X1,tc_nat)
    | ~ c_Parity_Oeven__odd__class_Oeven(X2,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_2132]) ).

cnf(c_0_2930,plain,
    ( c_Parity_Oeven__odd__class_Oeven(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat)
    | ~ c_Parity_Oeven__odd__class_Oeven(X1,tc_nat)
    | ~ c_Parity_Oeven__odd__class_Oeven(X2,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_2133]) ).

cnf(c_0_2931,plain,
    ( c_Parity_Oeven__odd__class_Oeven(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat)
    | ~ c_Parity_Oeven__odd__class_Oeven(X1,tc_nat)
    | ~ c_Parity_Oeven__odd__class_Oeven(X2,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_2134]) ).

cnf(c_0_2932,plain,
    ( c_Parity_Oeven__odd__class_Oeven(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat)
    | ~ c_Parity_Oeven__odd__class_Oeven(X1,tc_nat)
    | ~ c_Parity_Oeven__odd__class_Oeven(X2,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_2135]) ).

cnf(c_0_2933,plain,
    c_lessequals(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),X1,tc_nat),
    inference(split_conjunct,[status(thm)],[c_0_2136]) ).

cnf(c_0_2934,plain,
    c_lessequals(X1,c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat),
    inference(split_conjunct,[status(thm)],[c_0_2137]) ).

cnf(c_0_2935,plain,
    c_lessequals(X1,c_HOL_Oplus__class_Oplus(X2,X1,tc_nat),tc_nat),
    inference(split_conjunct,[status(thm)],[c_0_2138]) ).

cnf(c_0_2936,plain,
    c_lessequals(X1,c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat),
    inference(split_conjunct,[status(thm)],[c_0_2139]) ).

cnf(c_0_2937,plain,
    c_lessequals(X1,c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat),
    inference(split_conjunct,[status(thm)],[c_0_2140]) ).

cnf(c_0_2938,plain,
    c_lessequals(X1,c_HOL_Otimes__class_Otimes(X1,X1,tc_nat),tc_nat),
    inference(split_conjunct,[status(thm)],[c_0_2141]) ).

cnf(c_0_2939,plain,
    c_lessequals(c_Divides_Odiv__class_Omod(X1,X2,tc_nat),X1,tc_nat),
    inference(split_conjunct,[status(thm)],[c_0_2142]) ).

cnf(c_0_2940,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_2143]) ).

cnf(c_0_2941,plain,
    ( c_lessequals(X1,X2,tc_nat)
    | ~ c_lessequals(c_Suc(X1),c_Suc(X2),tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_2144]) ).

cnf(c_0_2942,plain,
    ( c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
    | c_Divides_Odiv__class_Omod(X2,X1,X3) != c_HOL_Ozero__class_Ozero(X3)
    | ~ class_Divides_Osemiring__div(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_2145]) ).

cnf(c_0_2943,plain,
    ( c_Divides_Odiv__class_Omod(X2,X1,X3) = c_HOL_Ozero__class_Ozero(X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
    | ~ class_Divides_Osemiring__div(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_2146]) ).

cnf(c_0_2944,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_2147]) ).

cnf(c_0_2945,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_2148]) ).

cnf(c_0_2946,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_2149]) ).

cnf(c_0_2947,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_2150]) ).

cnf(c_0_2948,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_2151]) ).

cnf(c_0_2949,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_2152]) ).

cnf(c_0_2950,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_2153]) ).

cnf(c_0_2951,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_2154]) ).

cnf(c_0_2952,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_2155]) ).

cnf(c_0_2953,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_2156]) ).

cnf(c_0_2954,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_2157]) ).

cnf(c_0_2955,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_2158]) ).

cnf(c_0_2956,plain,
    ( c_lessequals(c_Suc(X1),c_Suc(X2),tc_nat)
    | ~ c_lessequals(X1,X2,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_2159]) ).

cnf(c_0_2957,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_2160]) ).

cnf(c_0_2958,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_2161]) ).

cnf(c_0_2959,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_2162]) ).

cnf(c_0_2960,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_2163]) ).

cnf(c_0_2961,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_2164]) ).

cnf(c_0_2962,plain,
    ( X1 = c_HOL_Ozero__class_Ozero(X2)
    | ~ c_lessequals(c_HOL_Oabs__class_Oabs(X1,X2),c_HOL_Ozero__class_Ozero(X2),X2)
    | ~ class_OrderedGroup_Opordered__ab__group__add__abs(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_2165]) ).

cnf(c_0_2963,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_2166]) ).

cnf(c_0_2964,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_2167]) ).

cnf(c_0_2965,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_2168]) ).

cnf(c_0_2966,plain,
    ( c_Parity_Oeven__odd__class_Oeven(X1,tc_nat)
    | c_Divides_Odiv__class_Omod(X1,c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_2169]) ).

cnf(c_0_2967,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_2170]) ).

cnf(c_0_2968,plain,
    ( c_lessequals(X1,X2,tc_nat)
    | ~ c_lessequals(c_Suc(X1),X2,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_2171]) ).

cnf(c_0_2969,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_2172]) ).

cnf(c_0_2970,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_2173]) ).

cnf(c_0_2971,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_2174]) ).

cnf(c_0_2972,plain,
    ( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
    | X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
    | ~ c_HOL_Oord__class_Oless(X1,c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_2175]) ).

cnf(c_0_2973,plain,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(X1,X2),c_HOL_Ozero__class_Ozero(X2),X2)
    | ~ class_OrderedGroup_Opordered__ab__group__add__abs(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_2176]) ).

cnf(c_0_2974,plain,
    ( ~ c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X1,X2),c_HOL_Ozero__class_Ozero(X2),X2)
    | ~ class_Ring__and__Field_Oordered__semidom(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_2177]) ).

cnf(c_0_2975,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_2178]) ).

cnf(c_0_2976,plain,
    ( c_lessequals(X1,c_Suc(X2),tc_nat)
    | ~ c_lessequals(X1,X2,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_2179]) ).

cnf(c_0_2977,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_2180]) ).

cnf(c_0_2978,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_2181]) ).

cnf(c_0_2979,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_2182]) ).

cnf(c_0_2980,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_2183]) ).

cnf(c_0_2981,plain,
    ( c_Parity_Oeven__odd__class_Oeven(X1,tc_nat)
    | c_Parity_Oeven__odd__class_Oeven(X2,tc_nat)
    | c_Parity_Oeven__odd__class_Oeven(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_2184]) ).

cnf(c_0_2982,plain,
    ( c_Parity_Oeven__odd__class_Oeven(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat)
    | c_Parity_Oeven__odd__class_Oeven(X2,tc_nat)
    | c_Parity_Oeven__odd__class_Oeven(X1,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_2185]) ).

cnf(c_0_2983,plain,
    ( c_Parity_Oeven__odd__class_Oeven(X1,tc_nat)
    | c_Parity_Oeven__odd__class_Oeven(X2,tc_nat)
    | c_Parity_Oeven__odd__class_Oeven(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_2186]) ).

cnf(c_0_2984,plain,
    ( c_Parity_Oeven__odd__class_Oeven(X1,tc_nat)
    | c_Parity_Oeven__odd__class_Oeven(X2,tc_nat)
    | c_Parity_Oeven__odd__class_Oeven(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_2187]) ).

cnf(c_0_2985,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_2188]) ).

cnf(c_0_2986,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_2189]) ).

cnf(c_0_2987,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_2190]) ).

cnf(c_0_2988,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_2191]) ).

cnf(c_0_2989,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_2192]) ).

cnf(c_0_2990,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_2193]) ).

cnf(c_0_2991,plain,
    ( c_lessequals(X1,X2,tc_nat)
    | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_2194]) ).

cnf(c_0_2992,plain,
    ( c_lessequals(X1,X2,tc_nat)
    | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_2195]) ).

cnf(c_0_2993,plain,
    ( c_Parity_Oeven__odd__class_Oeven(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),tc_nat)
    | ~ c_Parity_Oeven__odd__class_Oeven(X1,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_2196]) ).

cnf(c_0_2994,plain,
    ( c_Parity_Oeven__odd__class_Oeven(c_HOL_Otimes__class_Otimes(X2,X1,tc_nat),tc_nat)
    | ~ c_Parity_Oeven__odd__class_Oeven(X1,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_2197]) ).

cnf(c_0_2995,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_2198]) ).

cnf(c_0_2996,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_2199]) ).

cnf(c_0_2997,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_2200]) ).

cnf(c_0_2998,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_2201]) ).

cnf(c_0_2999,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_2202]) ).

cnf(c_0_3000,plain,
    ( c_HOL_Oabs__class_Oabs(X2,X1) = X2
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | ~ class_OrderedGroup_Opordered__ab__group__add__abs(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2203]) ).

cnf(c_0_3001,plain,
    ( c_HOL_Oabs__class_Oabs(X2,X1) = X2
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | ~ class_OrderedGroup_Opordered__ab__group__add__abs(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2204]) ).

cnf(c_0_3002,plain,
    c_HOL_Ominus__class_Ominus(c_Suc(X1),c_Suc(X2),tc_nat) = c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),
    inference(split_conjunct,[status(thm)],[c_0_2205]) ).

cnf(c_0_3003,plain,
    c_HOL_Oplus__class_Oplus(c_Suc(X1),X2,tc_nat) = c_HOL_Oplus__class_Oplus(X1,c_Suc(X2),tc_nat),
    inference(split_conjunct,[status(thm)],[c_0_2206]) ).

cnf(c_0_3004,plain,
    ( c_lessequals(X1,X2,X3)
    | c_lessequals(X2,X1,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_2207]) ).

cnf(c_0_3005,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_2208]) ).

cnf(c_0_3006,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_2209]) ).

cnf(c_0_3007,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_2210]) ).

cnf(c_0_3008,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_2211]) ).

cnf(c_0_3009,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_2212]) ).

cnf(c_0_3010,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_2213]) ).

cnf(c_0_3011,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_2214]) ).

cnf(c_0_3012,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_2215]) ).

cnf(c_0_3013,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_2216]) ).

cnf(c_0_3014,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_2217]) ).

cnf(c_0_3015,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_2218]) ).

cnf(c_0_3016,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_2219]) ).

cnf(c_0_3017,plain,
    ( c_lessequals(X1,X2,tc_nat)
    | c_lessequals(c_Suc(X2),X1,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_2220]) ).

cnf(c_0_3018,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),
    inference(split_conjunct,[status(thm)],[c_0_2221]) ).

cnf(c_0_3019,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),
    inference(split_conjunct,[status(thm)],[c_0_2222]) ).

cnf(c_0_3020,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_2223]) ).

cnf(c_0_3021,plain,
    ( X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_2224]) ).

cnf(c_0_3022,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_2225]) ).

cnf(c_0_3023,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_2226]) ).

cnf(c_0_3024,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_2227]) ).

cnf(c_0_3025,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_2228]) ).

cnf(c_0_3026,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_2229]) ).

cnf(c_0_3027,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_2230]) ).

cnf(c_0_3028,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_2231]) ).

cnf(c_0_3029,plain,
    ( X2 = c_HOL_Ozero__class_Ozero(X1)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2232]) ).

cnf(c_0_3030,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_2233]) ).

cnf(c_0_3031,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_2234]) ).

cnf(c_0_3032,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_2235]) ).

cnf(c_0_3033,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_2236]) ).

cnf(c_0_3034,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_2237]) ).

cnf(c_0_3035,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_2238]) ).

cnf(c_0_3036,plain,
    ( c_lessequals(X1,X2,tc_nat)
    | c_lessequals(X2,X1,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_2239]) ).

cnf(c_0_3037,plain,
    ( c_Divides_Odiv__class_Omod(X1,c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat)
    | ~ c_Parity_Oeven__odd__class_Oeven(X1,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_2240]) ).

cnf(c_0_3038,plain,
    ( c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
    | c_HOL_Oabs__class_Oabs(X1,X3) != c_HOL_Oabs__class_Oabs(X2,X3)
    | ~ class_Ring__and__Field_Oordered__idom(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_2241]) ).

cnf(c_0_3039,plain,
    ( c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Ozero__class_Ozero(X1),X1),c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ class_OrderedGroup_Opordered__ab__group__add__abs(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2242]) ).

cnf(c_0_3040,plain,
    c_HOL_Oplus__class_Oplus(X1,X2,tc_nat) = c_HOL_Oplus__class_Oplus(X2,X1,tc_nat),
    inference(split_conjunct,[status(thm)],[c_0_2243]) ).

cnf(c_0_3041,plain,
    c_HOL_Otimes__class_Otimes(X1,X2,tc_nat) = c_HOL_Otimes__class_Otimes(X2,X1,tc_nat),
    inference(split_conjunct,[status(thm)],[c_0_2244]) ).

cnf(c_0_3042,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_2245]) ).

cnf(c_0_3043,plain,
    ( c_Parity_Oeven__odd__class_Oeven(X1,tc_nat)
    | c_Divides_Odiv__class_Omod(X1,c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),tc_nat) = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
    inference(split_conjunct,[status(thm)],[c_0_2246]) ).

cnf(c_0_3044,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_2247]) ).

cnf(c_0_3045,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_2248]) ).

cnf(c_0_3046,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_2249]) ).

cnf(c_0_3047,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_2250]) ).

cnf(c_0_3048,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_2251]) ).

cnf(c_0_3049,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_2252]) ).

cnf(c_0_3050,plain,
    ( X1 = c_HOL_Ozero__class_Ozero(X2)
    | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),c_HOL_Oabs__class_Oabs(X1,X2),X2)
    | ~ class_OrderedGroup_Opordered__ab__group__add__abs(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_2253]) ).

cnf(c_0_3051,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_2254]) ).

cnf(c_0_3052,plain,
    ( c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oabs__class_Oabs(X2,X1),X1)
    | ~ class_OrderedGroup_Opordered__ab__group__add__abs(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2255]) ).

cnf(c_0_3053,plain,
    ( c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_Nat_Osemiring__1__class_Oof__nat(X2,X1),X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2256]) ).

cnf(c_0_3054,plain,
    ( c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_Nat_Osemiring__1__class_Oof__nat(X2,X1),X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2257]) ).

cnf(c_0_3055,plain,
    ( ~ c_HOL_Oord__class_Oless(X1,X1,X2)
    | ~ class_Orderings_Oorder(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_2258]) ).

cnf(c_0_3056,plain,
    ( ~ c_HOL_Oord__class_Oless(X1,X1,X2)
    | ~ class_Orderings_Olinorder(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_2259]) ).

cnf(c_0_3057,plain,
    ( ~ c_HOL_Oord__class_Oless(X1,X1,X2)
    | ~ class_Orderings_Opreorder(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_2260]) ).

cnf(c_0_3058,plain,
    ~ c_lessequals(c_Suc(X1),X1,tc_nat),
    inference(split_conjunct,[status(thm)],[c_0_2261]) ).

cnf(c_0_3059,plain,
    ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
    inference(split_conjunct,[status(thm)],[c_0_2262]) ).

cnf(c_0_3060,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_2263]) ).

cnf(c_0_3061,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_2264]) ).

cnf(c_0_3062,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_2265]) ).

cnf(c_0_3063,plain,
    ( c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
    | c_HOL_Oabs__class_Oabs(X1,X2) = X1
    | ~ class_OrderedGroup_Olordered__ab__group__add__abs(X2)
    | ~ class_Orderings_Olinorder(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_2266]) ).

cnf(c_0_3064,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_2267]) ).

cnf(c_0_3065,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_2268]) ).

cnf(c_0_3066,plain,
    ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
    inference(split_conjunct,[status(thm)],[c_0_2269]) ).

cnf(c_0_3067,plain,
    ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
    inference(split_conjunct,[status(thm)],[c_0_2270]) ).

cnf(c_0_3068,plain,
    ( c_lessequals(X1,c_HOL_Oabs__class_Oabs(X1,X2),X2)
    | ~ class_OrderedGroup_Opordered__ab__group__add__abs(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_2271]) ).

cnf(c_0_3069,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)),
    inference(split_conjunct,[status(thm)],[c_0_2272]) ).

cnf(c_0_3070,plain,
    ~ c_HOL_Oord__class_Oless(X1,X1,tc_nat),
    inference(split_conjunct,[status(thm)],[c_0_2273]) ).

cnf(c_0_3071,plain,
    ~ c_HOL_Oord__class_Oless(X1,X1,tc_nat),
    inference(split_conjunct,[status(thm)],[c_0_2274]) ).

cnf(c_0_3072,plain,
    ( c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
    | c_HOL_Oabs__class_Oabs(X1,X2) = X1
    | ~ class_Ring__and__Field_Oabs__if(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_2275]) ).

cnf(c_0_3073,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_2276]) ).

cnf(c_0_3074,plain,
    c_Ring__and__Field_Odvd__class_Odvd(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),
    inference(split_conjunct,[status(thm)],[c_0_2277]) ).

cnf(c_0_3075,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_2278]) ).

cnf(c_0_3076,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)),
    inference(split_conjunct,[status(thm)],[c_0_2279]) ).

cnf(c_0_3077,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),
    inference(split_conjunct,[status(thm)],[c_0_2280]) ).

cnf(c_0_3078,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),
    inference(split_conjunct,[status(thm)],[c_0_2281]) ).

cnf(c_0_3079,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)),
    inference(split_conjunct,[status(thm)],[c_0_2282]) ).

cnf(c_0_3080,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_2283]) ).

cnf(c_0_3081,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_2284]) ).

cnf(c_0_3082,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_2285]) ).

cnf(c_0_3083,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_2286]) ).

cnf(c_0_3084,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_2287]) ).

cnf(c_0_3085,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_2288]) ).

cnf(c_0_3086,plain,
    ( c_HOL_Otimes__class_Otimes(X1,c_HOL_Ozero__class_Ozero(X2),X2) = c_HOL_Ozero__class_Ozero(X2)
    | ~ class_RealVector_Oreal__normed__algebra(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_2289]) ).

cnf(c_0_3087,plain,
    ( c_HOL_Otimes__class_Otimes(X1,c_HOL_Ozero__class_Ozero(X2),X2) = c_HOL_Ozero__class_Ozero(X2)
    | ~ class_RealVector_Oreal__normed__algebra(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_2290]) ).

cnf(c_0_3088,plain,
    ( c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),X2,X1) = c_HOL_Ozero__class_Ozero(X1)
    | ~ class_RealVector_Oreal__normed__algebra(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2291]) ).

cnf(c_0_3089,plain,
    ( c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),X2,X1) = c_HOL_Ozero__class_Ozero(X1)
    | ~ class_RealVector_Oreal__normed__algebra(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2292]) ).

cnf(c_0_3090,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_2293]) ).

cnf(c_0_3091,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_2294]) ).

cnf(c_0_3092,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_2295]) ).

cnf(c_0_3093,plain,
    ( c_Parity_Oeven__odd__class_Oeven(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_2296]) ).

cnf(c_0_3094,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_2297]) ).

cnf(c_0_3095,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_2298]) ).

cnf(c_0_3096,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_2299]) ).

cnf(c_0_3097,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_2300]) ).

cnf(c_0_3098,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_2301]) ).

cnf(c_0_3099,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_2302]) ).

cnf(c_0_3100,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_2303]) ).

cnf(c_0_3101,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_2304]) ).

cnf(c_0_3102,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_2305]) ).

cnf(c_0_3103,plain,
    c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),
    inference(split_conjunct,[status(thm)],[c_0_2306]) ).

cnf(c_0_3104,plain,
    ( c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Ozero__class_Ozero(X2),X2)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_2307]) ).

cnf(c_0_3105,plain,
    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(split_conjunct,[status(thm)],[c_0_2308]) ).

cnf(c_0_3106,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_2309]) ).

cnf(c_0_3107,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_2310]) ).

cnf(c_0_3108,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_2311]) ).

cnf(c_0_3109,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_2312]) ).

cnf(c_0_3110,plain,
    c_lessequals(c_Suc(X1),c_Suc(X1),tc_nat),
    inference(split_conjunct,[status(thm)],[c_0_2313]) ).

cnf(c_0_3111,plain,
    c_Ring__and__Field_Odvd__class_Odvd(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X1,tc_nat),
    inference(split_conjunct,[status(thm)],[c_0_2314]) ).

cnf(c_0_3112,plain,
    ( c_HOL_Otimes__class_Otimes(X1,X1,X2) = X1
    | ~ class_OrderedGroup_Oab__semigroup__idem__mult(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_2315]) ).

cnf(c_0_3113,plain,
    ( c_Orderings_Oord__class_Omin(X1,X1,X2) = X1
    | ~ class_Orderings_Olinorder(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_2316]) ).

cnf(c_0_3114,plain,
    c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(X1),tc_nat),
    inference(split_conjunct,[status(thm)],[c_0_2317]) ).

cnf(c_0_3115,plain,
    c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(X1),tc_nat),
    inference(split_conjunct,[status(thm)],[c_0_2318]) ).

cnf(c_0_3116,plain,
    ( c_lessequals(X1,X1,X2)
    | ~ class_Orderings_Oorder(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_2319]) ).

cnf(c_0_3117,plain,
    ( c_lessequals(X1,X1,X2)
    | ~ class_Orderings_Opreorder(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_2320]) ).

cnf(c_0_3118,plain,
    ( c_Ring__and__Field_Odvd__class_Odvd(X1,X1,X2)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_2321]) ).

cnf(c_0_3119,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),
    inference(split_conjunct,[status(thm)],[c_0_2322]) ).

cnf(c_0_3120,plain,
    ( c_HOL_Oabs__class_Oabs(c_HOL_Oabs__class_Oabs(X1,X2),X2) = c_HOL_Oabs__class_Oabs(X1,X2)
    | ~ class_OrderedGroup_Opordered__ab__group__add__abs(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_2323]) ).

cnf(c_0_3121,plain,
    ( c_HOL_Oabs__class_Oabs(c_Nat_Osemiring__1__class_Oof__nat(X1,X2),X2) = c_Nat_Osemiring__1__class_Oof__nat(X1,X2)
    | ~ class_Ring__and__Field_Oordered__idom(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_2324]) ).

cnf(c_0_3122,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_2325]) ).

cnf(c_0_3123,plain,
    c_HOL_Oord__class_Oless(X1,c_Suc(X1),tc_nat),
    inference(split_conjunct,[status(thm)],[c_0_2326]) ).

cnf(c_0_3124,plain,
    c_HOL_Oord__class_Oless(X1,c_Suc(X1),tc_nat),
    inference(split_conjunct,[status(thm)],[c_0_2327]) ).

cnf(c_0_3125,plain,
    c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
    inference(split_conjunct,[status(thm)],[c_0_2328]) ).

cnf(c_0_3126,plain,
    c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
    inference(split_conjunct,[status(thm)],[c_0_2329]) ).

cnf(c_0_3127,plain,
    c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
    inference(split_conjunct,[status(thm)],[c_0_2330]) ).

cnf(c_0_3128,plain,
    c_HOL_Otimes__class_Otimes(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
    inference(split_conjunct,[status(thm)],[c_0_2331]) ).

cnf(c_0_3129,plain,
    c_Orderings_Oord__class_Omin(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
    inference(split_conjunct,[status(thm)],[c_0_2332]) ).

cnf(c_0_3130,plain,
    c_Orderings_Oord__class_Omin(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
    inference(split_conjunct,[status(thm)],[c_0_2333]) ).

cnf(c_0_3131,plain,
    c_HOL_Ominus__class_Ominus(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = X1,
    inference(split_conjunct,[status(thm)],[c_0_2334]) ).

cnf(c_0_3132,plain,
    c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) = X1,
    inference(split_conjunct,[status(thm)],[c_0_2335]) ).

cnf(c_0_3133,plain,
    c_HOL_Oplus__class_Oplus(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = X1,
    inference(split_conjunct,[status(thm)],[c_0_2336]) ).

cnf(c_0_3134,plain,
    X1 = c_HOL_Oplus__class_Oplus(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
    inference(split_conjunct,[status(thm)],[c_0_2337]) ).

cnf(c_0_3135,plain,
    c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
    inference(split_conjunct,[status(thm)],[c_0_2338]) ).

cnf(c_0_3136,plain,
    c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat),
    inference(split_conjunct,[status(thm)],[c_0_2339]) ).

cnf(c_0_3137,plain,
    c_HOL_Ominus__class_Ominus(X1,X1,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
    inference(split_conjunct,[status(thm)],[c_0_2340]) ).

cnf(c_0_3138,plain,
    ( X1 = X2
    | c_Nat_Osemiring__1__class_Oof__nat(X1,X3) != c_Nat_Osemiring__1__class_Oof__nat(X2,X3)
    | ~ class_Nat_Osemiring__char__0(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_2341]) ).

cnf(c_0_3139,plain,
    c_lessequals(X1,X1,tc_nat),
    inference(split_conjunct,[status(thm)],[c_0_2342]) ).

cnf(c_0_3140,plain,
    c_lessequals(X1,X1,tc_nat),
    inference(split_conjunct,[status(thm)],[c_0_2343]) ).

cnf(c_0_3141,plain,
    c_Ring__and__Field_Odvd__class_Odvd(X1,X1,tc_nat),
    inference(split_conjunct,[status(thm)],[c_0_2344]) ).

cnf(c_0_3142,plain,
    c_HOL_Oord__class_Oless(v_i,v_n,tc_nat),
    inference(split_conjunct,[status(thm)],[c_0_2345]) ).

cnf(c_0_3143,plain,
    c_HOL_Oord__class_Oless(v_i,v_n,tc_nat),
    inference(split_conjunct,[status(thm)],[c_0_2346]) ).

cnf(c_0_3144,plain,
    ( ~ c_Parity_Oeven__odd__class_Oeven(c_Suc(X1),tc_nat)
    | ~ c_Parity_Oeven__odd__class_Oeven(X1,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_2347]) ).

cnf(c_0_3145,plain,
    ( X1 = c_HOL_Ozero__class_Ozero(X2)
    | c_HOL_Oabs__class_Oabs(X1,X2) != c_HOL_Ozero__class_Ozero(X2)
    | ~ class_OrderedGroup_Opordered__ab__group__add__abs(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_2348]) ).

cnf(c_0_3146,plain,
    ( c_Parity_Oeven__odd__class_Oeven(X1,tc_nat)
    | c_Parity_Oeven__odd__class_Oeven(c_Suc(X1),tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_2349]) ).

cnf(c_0_3147,plain,
    ( c_HOL_Oabs__class_Oabs(c_HOL_Ozero__class_Ozero(X1),X1) = c_HOL_Ozero__class_Ozero(X1)
    | ~ class_OrderedGroup_Opordered__ab__group__add__abs(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2350]) ).

cnf(c_0_3148,plain,
    ( c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Ozero__class_Ozero(tc_nat),X1) = c_HOL_Ozero__class_Ozero(X1)
    | ~ class_Ring__and__Field_Osemiring__1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2351]) ).

cnf(c_0_3149,plain,
    c_Parity_Oeven__odd__class_Oeven(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
    inference(split_conjunct,[status(thm)],[c_0_2352]) ).

cnf(c_0_3150,plain,
    ( X1 = X2
    | c_Suc(X1) != c_Suc(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_2353]) ).

cnf(c_0_3151,plain,
    ( X1 = X2
    | c_Suc(X1) != c_Suc(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_2354]) ).

cnf(c_0_3152,plain,
    c_Suc(X1) != c_HOL_Ozero__class_Ozero(tc_nat),
    inference(split_conjunct,[status(thm)],[c_0_2355]) ).

cnf(c_0_3153,plain,
    c_Suc(X1) != c_HOL_Ozero__class_Ozero(tc_nat),
    inference(split_conjunct,[status(thm)],[c_0_2356]) ).

cnf(c_0_3154,plain,
    c_HOL_Ozero__class_Ozero(tc_nat) != c_Suc(X1),
    inference(split_conjunct,[status(thm)],[c_0_2357]) ).

cnf(c_0_3155,plain,
    c_HOL_Ozero__class_Ozero(tc_nat) != c_Suc(X1),
    inference(split_conjunct,[status(thm)],[c_0_2358]) ).

cnf(c_0_3156,plain,
    c_Suc(X1) != X1,
    inference(split_conjunct,[status(thm)],[c_0_2359]) ).

cnf(c_0_3157,plain,
    X1 != c_Suc(X1),
    inference(split_conjunct,[status(thm)],[c_0_2360]) ).

cnf(c_0_3158,plain,
    class_Orderings_Oorder(tc_nat),
    inference(split_conjunct,[status(thm)],[c_0_2361]) ).

cnf(c_0_3159,plain,
    class_Orderings_Olinorder(tc_nat),
    inference(split_conjunct,[status(thm)],[c_0_2362]) ).

cnf(c_0_3160,plain,
    class_Orderings_Opreorder(tc_nat),
    inference(split_conjunct,[status(thm)],[c_0_2363]) ).

cnf(c_0_3161,plain,
    class_Ring__and__Field_Odvd(tc_nat),
    inference(split_conjunct,[status(thm)],[c_0_2364]) ).

cnf(c_0_3162,plain,
    class_Nat_Osemiring__char__0(tc_nat),
    inference(split_conjunct,[status(thm)],[c_0_2365]) ).

cnf(c_0_3163,plain,
    class_Divides_Osemiring__div(tc_nat),
    inference(split_conjunct,[status(thm)],[c_0_2366]) ).

cnf(c_0_3164,plain,
    class_OrderedGroup_Omonoid__add(tc_nat),
    inference(split_conjunct,[status(thm)],[c_0_2367]) ).

cnf(c_0_3165,plain,
    class_Ring__and__Field_Osemiring(tc_nat),
    inference(split_conjunct,[status(thm)],[c_0_2368]) ).

cnf(c_0_3166,plain,
    class_Ring__and__Field_Omult__mono(tc_nat),
    inference(split_conjunct,[status(thm)],[c_0_2369]) ).

cnf(c_0_3167,plain,
    class_Ring__and__Field_Omult__zero(tc_nat),
    inference(split_conjunct,[status(thm)],[c_0_2370]) ).

cnf(c_0_3168,plain,
    class_Ring__and__Field_Omult__mono1(tc_nat),
    inference(split_conjunct,[status(thm)],[c_0_2371]) ).

cnf(c_0_3169,plain,
    class_Ring__and__Field_Osemiring__1(tc_nat),
    inference(split_conjunct,[status(thm)],[c_0_2372]) ).

cnf(c_0_3170,plain,
    class_OrderedGroup_Ocomm__monoid__add(tc_nat),
    inference(split_conjunct,[status(thm)],[c_0_2373]) ).

cnf(c_0_3171,plain,
    class_Ring__and__Field_Ocomm__semiring(tc_nat),
    inference(split_conjunct,[status(thm)],[c_0_2374]) ).

cnf(c_0_3172,plain,
    class_OrderedGroup_Oab__semigroup__add(tc_nat),
    inference(split_conjunct,[status(thm)],[c_0_2375]) ).

cnf(c_0_3173,plain,
    class_OrderedGroup_Oab__semigroup__mult(tc_nat),
    inference(split_conjunct,[status(thm)],[c_0_2376]) ).

cnf(c_0_3174,plain,
    class_Ring__and__Field_Ocomm__semiring__1(tc_nat),
    inference(split_conjunct,[status(thm)],[c_0_2377]) ).

cnf(c_0_3175,plain,
    class_Ring__and__Field_Oordered__semidom(tc_nat),
    inference(split_conjunct,[status(thm)],[c_0_2378]) ).

cnf(c_0_3176,plain,
    class_Ring__and__Field_Ono__zero__divisors(tc_nat),
    inference(split_conjunct,[status(thm)],[c_0_2379]) ).

cnf(c_0_3177,plain,
    class_Ring__and__Field_Oordered__semiring(tc_nat),
    inference(split_conjunct,[status(thm)],[c_0_2380]) ).

cnf(c_0_3178,plain,
    class_Ring__and__Field_Opordered__semiring(tc_nat),
    inference(split_conjunct,[status(thm)],[c_0_2381]) ).

cnf(c_0_3179,plain,
    class_OrderedGroup_Ocancel__semigroup__add(tc_nat),
    inference(split_conjunct,[status(thm)],[c_0_2382]) ).

cnf(c_0_3180,plain,
    class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat),
    inference(split_conjunct,[status(thm)],[c_0_2383]) ).

cnf(c_0_3181,plain,
    class_OrderedGroup_Opordered__comm__monoid__add(tc_nat),
    inference(split_conjunct,[status(thm)],[c_0_2384]) ).

cnf(c_0_3182,plain,
    class_OrderedGroup_Opordered__ab__semigroup__add(tc_nat),
    inference(split_conjunct,[status(thm)],[c_0_2385]) ).

cnf(c_0_3183,plain,
    class_Ring__and__Field_Oordered__semiring__strict(tc_nat),
    inference(split_conjunct,[status(thm)],[c_0_2386]) ).

cnf(c_0_3184,plain,
    class_Ring__and__Field_Opordered__cancel__semiring(tc_nat),
    inference(split_conjunct,[status(thm)],[c_0_2387]) ).

cnf(c_0_3185,plain,
    class_Ring__and__Field_Oordered__comm__semiring__strict(tc_nat),
    inference(split_conjunct,[status(thm)],[c_0_2388]) ).

cnf(c_0_3186,plain,
    class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat),
    inference(split_conjunct,[status(thm)],[c_0_2389]) ).

cnf(c_0_3187,plain,
    class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat),
    inference(split_conjunct,[status(thm)],[c_0_2390]) ).

cnf(c_0_3188,plain,
    ( c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,X4,X3),c_HOL_Ominus__class_Ominus(X2,X5,X3),X3),c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,X4,X3),X5,X3),X3),c_HOL_Otimes__class_Otimes(X4,c_HOL_Ominus__class_Ominus(X2,X5,X3),X3),X3) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X4,X5,X3),X3)
    | ~ class_RealVector_Oreal__normed__algebra(X3) ),
    c_0_2391,
    [final] ).

cnf(c_0_3189,plain,
    ( c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X1,X2,X3),c_HOL_Oplus__class_Oplus(X4,X5,X3),X3),X3),c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X1,X4,X3),X3),c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X2,X5,X3),X3),X3),X3)
    | ~ class_OrderedGroup_Opordered__ab__group__add__abs(X3) ),
    c_0_2392,
    [final] ).

cnf(c_0_3190,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_2393,
    [final] ).

cnf(c_0_3191,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_2394,
    [final] ).

cnf(c_0_3192,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_2395,
    [final] ).

cnf(c_0_3193,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_2396,
    [final] ).

cnf(c_0_3194,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_2397,
    [final] ).

cnf(c_0_3195,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_2398,
    [final] ).

cnf(c_0_3196,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_2399,
    [final] ).

cnf(c_0_3197,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_2400,
    [final] ).

cnf(c_0_3198,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_2401,
    [final] ).

cnf(c_0_3199,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_2402,
    [final] ).

cnf(c_0_3200,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_2403,
    [final] ).

cnf(c_0_3201,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_2404,
    [final] ).

cnf(c_0_3202,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_2405,
    [final] ).

cnf(c_0_3203,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_2406,
    [final] ).

cnf(c_0_3204,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_2407,
    [final] ).

cnf(c_0_3205,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_2408,
    [final] ).

cnf(c_0_3206,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_2409,
    [final] ).

cnf(c_0_3207,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_2410,
    [final] ).

cnf(c_0_3208,plain,
    ( c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Oplus__class_Oplus(X4,X6,X3),X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X4,c_HOL_Otimes__class_Otimes(X5,X2,X3),X3),X6,X3),X3)
    | ~ class_Ring__and__Field_Ocomm__ring(X3)
    | ~ class_Ring__and__Field_Odvd(X3) ),
    c_0_2411,
    [final] ).

cnf(c_0_3209,plain,
    ( c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X4,c_HOL_Otimes__class_Otimes(X6,X2,X3),X3),X5,X3),X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Oplus__class_Oplus(X4,X5,X3),X3)
    | ~ class_Ring__and__Field_Ocomm__ring(X3)
    | ~ class_Ring__and__Field_Odvd(X3) ),
    c_0_2412,
    [final] ).

cnf(c_0_3210,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_2413,
    [final] ).

cnf(c_0_3211,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_2414,
    [final] ).

cnf(c_0_3212,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_2415,
    [final] ).

cnf(c_0_3213,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_2416,
    [final] ).

cnf(c_0_3214,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_2417,
    [final] ).

cnf(c_0_3215,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_2418,
    [final] ).

cnf(c_0_3216,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_2419,
    [final] ).

cnf(c_0_3217,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_2420,
    [final] ).

cnf(c_0_3218,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_2421,
    [final] ).

cnf(c_0_3219,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_2422,
    [final] ).

cnf(c_0_3220,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_2423,
    [final] ).

cnf(c_0_3221,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_2424,
    [final] ).

cnf(c_0_3222,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_2425,
    [final] ).

cnf(c_0_3223,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_2426,
    [final] ).

cnf(c_0_3224,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_2427,
    [final] ).

cnf(c_0_3225,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_2428,
    [final] ).

cnf(c_0_3226,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(X3,X2,tc_nat),X4,tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X1,X3,tc_nat),X2,tc_nat),X4,tc_nat),
    c_0_2429,
    [final] ).

cnf(c_0_3227,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_2430,
    [final] ).

cnf(c_0_3228,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_2431,
    [final] ).

cnf(c_0_3229,plain,
    ( c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X4,X1,X3),X3),X2,X3)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,X2,X3),X4,X3)
    | ~ c_HOL_Oord__class_Oless(X4,c_HOL_Oplus__class_Oplus(X1,X2,X3),X3)
    | ~ class_Ring__and__Field_Oordered__idom(X3) ),
    c_0_2432,
    [final] ).

cnf(c_0_3230,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_2433,
    [final] ).

cnf(c_0_3231,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_2434,
    [final] ).

cnf(c_0_3232,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_2435,
    [final] ).

cnf(c_0_3233,plain,
    ( c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(c_HOL_Oabs__class_Oabs(X1,X2),c_HOL_Oabs__class_Oabs(X3,X2),X2),X2),c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X1,X3,X2),X2),X2)
    | ~ class_OrderedGroup_Opordered__ab__group__add__abs(X2) ),
    c_0_2436,
    [final] ).

cnf(c_0_3234,plain,
    c_Divides_Odiv__class_Omod(c_Suc(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),X3,tc_nat)),X2,tc_nat) = c_Divides_Odiv__class_Omod(c_Suc(X3),X2,tc_nat),
    c_0_2437,
    [final] ).

cnf(c_0_3235,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_2438,
    [final] ).

cnf(c_0_3236,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_2439,
    [final] ).

cnf(c_0_3237,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_2440,
    [final] ).

cnf(c_0_3238,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_2441,
    [final] ).

cnf(c_0_3239,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_2442,
    [final] ).

cnf(c_0_3240,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_2443,
    [final] ).

cnf(c_0_3241,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_2444,
    [final] ).

cnf(c_0_3242,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_2445,
    [final] ).

cnf(c_0_3243,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_2446,
    [final] ).

cnf(c_0_3244,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_2447,
    [final] ).

cnf(c_0_3245,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_2448,
    [final] ).

cnf(c_0_3246,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_2449,
    [final] ).

cnf(c_0_3247,plain,
    ( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(X1,X2),c_HOL_Oabs__class_Oabs(X4,X2),X2),c_HOL_Otimes__class_Otimes(X3,X5,X2),X2)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(X1,X2),X3,X2)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(X4,X2),X5,X2)
    | ~ class_Ring__and__Field_Oordered__idom(X2) ),
    c_0_2450,
    [final] ).

cnf(c_0_3248,plain,
    ( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X2,X4,X3),X1,X3)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X1,X2,X3),X3),X4,X3)
    | ~ class_Ring__and__Field_Oordered__idom(X3) ),
    c_0_2451,
    [final] ).

cnf(c_0_3249,plain,
    ( c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(X2,X4,X3),X3)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X1,X2,X3),X3),X4,X3)
    | ~ class_Ring__and__Field_Oordered__idom(X3) ),
    c_0_2452,
    [final] ).

cnf(c_0_3250,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_2453,
    [final] ).

cnf(c_0_3251,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_2454,
    [final] ).

cnf(c_0_3252,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_2455,
    [final] ).

cnf(c_0_3253,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_2456,
    [final] ).

cnf(c_0_3254,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_2457,
    [final] ).

cnf(c_0_3255,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_2458,
    [final] ).

cnf(c_0_3256,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_2459,
    [final] ).

cnf(c_0_3257,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_2460,
    [final] ).

cnf(c_0_3258,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_2461,
    [final] ).

cnf(c_0_3259,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_2462,
    [final] ).

cnf(c_0_3260,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_2463,
    [final] ).

cnf(c_0_3261,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_2464,
    [final] ).

cnf(c_0_3262,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_2465,
    [final] ).

cnf(c_0_3263,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_2466,
    [final] ).

cnf(c_0_3264,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_2467,
    [final] ).

cnf(c_0_3265,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_2468,
    [final] ).

cnf(c_0_3266,plain,
    ( c_Ring__and__Field_Odvd__class_Odvd(X2,X3,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat) ),
    c_0_2469,
    [final] ).

cnf(c_0_3267,plain,
    ( c_Ring__and__Field_Odvd__class_Odvd(X2,X3,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
    c_0_2470,
    [final] ).

cnf(c_0_3268,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_2471,
    [final] ).

cnf(c_0_3269,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_2472,
    [final] ).

cnf(c_0_3270,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_2473,
    [final] ).

cnf(c_0_3271,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_2474,
    [final] ).

cnf(c_0_3272,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_2475,
    [final] ).

cnf(c_0_3273,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_2476,
    [final] ).

cnf(c_0_3274,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_2477,
    [final] ).

cnf(c_0_3275,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_2478,
    [final] ).

cnf(c_0_3276,plain,
    ~ c_Parity_Oeven__odd__class_Oeven(c_Suc(c_HOL_Otimes__class_Otimes(c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),X1,tc_nat)),tc_nat),
    c_0_2479,
    [final] ).

cnf(c_0_3277,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_2480,
    [final] ).

cnf(c_0_3278,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_2481,
    [final] ).

cnf(c_0_3279,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_2482,
    [final] ).

cnf(c_0_3280,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_2483,
    [final] ).

cnf(c_0_3281,plain,
    ( c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X1,X2,X3),c_HOL_Oplus__class_Oplus(X4,X5,X3),X3) = c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X1,X4,X3),c_HOL_Ominus__class_Ominus(X2,X5,X3),X3)
    | ~ class_OrderedGroup_Oab__group__add(X3) ),
    c_0_2484,
    [final] ).

cnf(c_0_3282,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_2485,
    [final] ).

cnf(c_0_3283,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_2486,
    [final] ).

cnf(c_0_3284,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_2487,
    [final] ).

cnf(c_0_3285,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_2488,
    [final] ).

cnf(c_0_3286,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_2489,
    [final] ).

cnf(c_0_3287,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_2490,
    [final] ).

cnf(c_0_3288,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_2491,
    [final] ).

cnf(c_0_3289,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_2492,
    [final] ).

cnf(c_0_3290,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_2493,
    [final] ).

cnf(c_0_3291,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_2494,
    [final] ).

cnf(c_0_3292,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_2495,
    [final] ).

cnf(c_0_3293,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_2496,
    [final] ).

cnf(c_0_3294,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_2497,
    [final] ).

cnf(c_0_3295,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_2498,
    [final] ).

cnf(c_0_3296,plain,
    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) = 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_0_2499,
    [final] ).

cnf(c_0_3297,plain,
    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) = 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_0_2500,
    [final] ).

cnf(c_0_3298,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_2501,
    [final] ).

cnf(c_0_3299,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_2502,
    [final] ).

cnf(c_0_3300,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_2503,
    [final] ).

cnf(c_0_3301,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_2504,
    [final] ).

cnf(c_0_3302,plain,
    ( c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X1,X2,X3),X3),c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(X1,X3),c_HOL_Oabs__class_Oabs(X2,X3),X3),X3)
    | ~ class_OrderedGroup_Opordered__ab__group__add__abs(X3) ),
    c_0_2505,
    [final] ).

cnf(c_0_3303,plain,
    ( c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Oplus__class_Oplus(X1,X2,X3),X3),c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(X1,X3),c_HOL_Oabs__class_Oabs(X2,X3),X3),X3)
    | ~ class_OrderedGroup_Opordered__ab__group__add__abs(X3) ),
    c_0_2506,
    [final] ).

cnf(c_0_3304,plain,
    ( c_lessequals(c_HOL_Ominus__class_Ominus(c_HOL_Oabs__class_Oabs(X1,X2),c_HOL_Oabs__class_Oabs(X3,X2),X2),c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X1,X3,X2),X2),X2)
    | ~ class_OrderedGroup_Opordered__ab__group__add__abs(X2) ),
    c_0_2507,
    [final] ).

cnf(c_0_3305,plain,
    ( c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(X1,X2,X3),X3),c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(X1,X3),c_HOL_Oabs__class_Oabs(X2,X3),X3),X3)
    | ~ class_Ring__and__Field_Olordered__ring(X3) ),
    c_0_2508,
    [final] ).

cnf(c_0_3306,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_2509,
    [final] ).

cnf(c_0_3307,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_2510,
    [final] ).

cnf(c_0_3308,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_2511,
    [final] ).

cnf(c_0_3309,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_2512,
    [final] ).

cnf(c_0_3310,plain,
    ( X1 = c_HOL_Ozero__class_Ozero(X3)
    | c_Ring__and__Field_Odvd__class_Odvd(X2,X4,X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X1,X4,X3),X3)
    | ~ class_Ring__and__Field_Oidom(X3) ),
    c_0_2513,
    [final] ).

cnf(c_0_3311,plain,
    ( X2 = c_HOL_Ozero__class_Ozero(X3)
    | c_Ring__and__Field_Odvd__class_Odvd(X1,X4,X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X4,X2,X3),X3)
    | ~ class_Ring__and__Field_Oidom(X3) ),
    c_0_2514,
    [final] ).

cnf(c_0_3312,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_2515,
    [final] ).

cnf(c_0_3313,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_2516,
    [final] ).

cnf(c_0_3314,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_2517,
    [final] ).

cnf(c_0_3315,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_2518,
    [final] ).

cnf(c_0_3316,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_2519,
    [final] ).

cnf(c_0_3317,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_2520,
    [final] ).

cnf(c_0_3318,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_2521,
    [final] ).

cnf(c_0_3319,plain,
    ( c_lessequals(X1,c_HOL_Oplus__class_Oplus(X4,c_HOL_Oabs__class_Oabs(X2,X3),X3),X3)
    | ~ c_lessequals(c_HOL_Oplus__class_Oplus(X1,X2,X3),X4,X3)
    | ~ class_OrderedGroup_Olordered__ab__group__add__abs(X3) ),
    c_0_2522,
    [final] ).

cnf(c_0_3320,plain,
    ( c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Ominus__class_Ominus(X2,X3,tc_nat),tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X3,tc_nat)
    | ~ c_lessequals(X3,X2,tc_nat) ),
    c_0_2523,
    [final] ).

cnf(c_0_3321,plain,
    ( c_Ring__and__Field_Odvd__class_Odvd(X1,X3,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Ominus__class_Ominus(X2,X3,tc_nat),tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
    | ~ c_lessequals(X3,X2,tc_nat) ),
    c_0_2524,
    [final] ).

cnf(c_0_3322,plain,
    ( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
    | c_Ring__and__Field_Odvd__class_Odvd(X2,X3,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat) ),
    c_0_2525,
    [final] ).

cnf(c_0_3323,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_2526,
    [final] ).

cnf(c_0_3324,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_2527,
    [final] ).

cnf(c_0_3325,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_2528,
    [final] ).

cnf(c_0_3326,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_2529,
    [final] ).

cnf(c_0_3327,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_2530,
    [final] ).

cnf(c_0_3328,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_2531,
    [final] ).

cnf(c_0_3329,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_2532,
    [final] ).

cnf(c_0_3330,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_2533,
    [final] ).

cnf(c_0_3331,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_2534,
    [final] ).

cnf(c_0_3332,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_2535,
    [final] ).

cnf(c_0_3333,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_2536,
    [final] ).

cnf(c_0_3334,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_2537,
    [final] ).

cnf(c_0_3335,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_2538,
    [final] ).

cnf(c_0_3336,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_2539,
    [final] ).

cnf(c_0_3337,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_2540,
    [final] ).

cnf(c_0_3338,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_2541,
    [final] ).

cnf(c_0_3339,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_2542,
    [final] ).

cnf(c_0_3340,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_2543,
    [final] ).

cnf(c_0_3341,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_2544,
    [final] ).

cnf(c_0_3342,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_2545,
    [final] ).

cnf(c_0_3343,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_2546,
    [final] ).

cnf(c_0_3344,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_2547,
    [final] ).

cnf(c_0_3345,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_2548,
    [final] ).

cnf(c_0_3346,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_2549,
    [final] ).

cnf(c_0_3347,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_2550,
    [final] ).

cnf(c_0_3348,plain,
    ( c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X2,X5,X3),X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X5,X3)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
    c_0_2551,
    [final] ).

cnf(c_0_3349,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_2552,
    [final] ).

cnf(c_0_3350,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_2553,
    [final] ).

cnf(c_0_3351,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_2554,
    [final] ).

cnf(c_0_3352,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_2555,
    [final] ).

cnf(c_0_3353,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_2556,
    [final] ).

cnf(c_0_3354,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_2557,
    [final] ).

cnf(c_0_3355,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_2558,
    [final] ).

cnf(c_0_3356,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_2559,
    [final] ).

cnf(c_0_3357,plain,
    ( c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X2,X4,X3),X3) = c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,X2,X3),X4,X3)
    | ~ class_RealVector_Oreal__normed__algebra(X3) ),
    c_0_2560,
    [final] ).

cnf(c_0_3358,plain,
    ( c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X2,X4,X3),X3) = c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,X2,X3),X4,X3)
    | ~ class_RealVector_Oreal__normed__algebra(X3) ),
    c_0_2561,
    [final] ).

cnf(c_0_3359,plain,
    ( c_HOL_Ominus__class_Ominus(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_Ominus__class_Ominus(X2,X3,X4),X4)
    | ~ class_RealVector_Oreal__normed__algebra(X4) ),
    c_0_2562,
    [final] ).

cnf(c_0_3360,plain,
    ( c_HOL_Ominus__class_Ominus(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_Ominus__class_Ominus(X2,X3,X4),X4)
    | ~ class_RealVector_Oreal__normed__algebra(X4) ),
    c_0_2563,
    [final] ).

cnf(c_0_3361,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_2564,
    [final] ).

cnf(c_0_3362,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_2565,
    [final] ).

cnf(c_0_3363,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_2566,
    [final] ).

cnf(c_0_3364,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_2567,
    [final] ).

cnf(c_0_3365,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_2568,
    [final] ).

cnf(c_0_3366,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_2569,
    [final] ).

cnf(c_0_3367,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_2570,
    [final] ).

cnf(c_0_3368,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_RealVector_Oreal__normed__algebra(X3) ),
    c_0_2571,
    [final] ).

cnf(c_0_3369,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_RealVector_Oreal__normed__algebra(X3) ),
    c_0_2572,
    [final] ).

cnf(c_0_3370,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_RealVector_Oreal__normed__algebra(X4) ),
    c_0_2573,
    [final] ).

cnf(c_0_3371,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_RealVector_Oreal__normed__algebra(X4) ),
    c_0_2574,
    [final] ).

cnf(c_0_3372,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_2575,
    [final] ).

cnf(c_0_3373,plain,
    ( c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X3,tc_nat) ),
    c_0_2576,
    [final] ).

cnf(c_0_3374,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_2577,
    [final] ).

cnf(c_0_3375,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_2578,
    [final] ).

cnf(c_0_3376,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_2579,
    [final] ).

cnf(c_0_3377,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_2580,
    [final] ).

cnf(c_0_3378,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_2581,
    [final] ).

cnf(c_0_3379,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_2582,
    [final] ).

cnf(c_0_3380,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_2583,
    [final] ).

cnf(c_0_3381,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_2584,
    [final] ).

cnf(c_0_3382,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_2585,
    [final] ).

cnf(c_0_3383,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_2586,
    [final] ).

cnf(c_0_3384,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_2587,
    [final] ).

cnf(c_0_3385,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_2588,
    [final] ).

cnf(c_0_3386,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_2589,
    [final] ).

cnf(c_0_3387,plain,
    ( c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(X1,X2),c_HOL_Oabs__class_Oabs(X3,X2),X2) = c_HOL_Oabs__class_Oabs(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__abs(X2) ),
    c_0_2590,
    [final] ).

cnf(c_0_3388,plain,
    ( c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(X1,X2),c_HOL_Oabs__class_Oabs(X3,X2),X2) = c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(X1,X3,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__ring__abs(X2) ),
    c_0_2591,
    [final] ).

cnf(c_0_3389,plain,
    ( c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(X2,X1),c_HOL_Oabs__class_Oabs(X3,X1),X1) = c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(X2,X3,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__ring__abs(X1) ),
    c_0_2592,
    [final] ).

cnf(c_0_3390,plain,
    ( c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(X2,X1),c_HOL_Oabs__class_Oabs(X3,X1),X1) = c_HOL_Oabs__class_Oabs(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__abs(X1) ),
    c_0_2593,
    [final] ).

cnf(c_0_3391,plain,
    c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Ominus__class_Ominus(X2,X3,tc_nat),tc_nat),
    c_0_2594,
    [final] ).

cnf(c_0_3392,plain,
    c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),c_HOL_Otimes__class_Otimes(X2,X3,tc_nat),tc_nat) = c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),X3,tc_nat),
    c_0_2595,
    [final] ).

cnf(c_0_3393,plain,
    c_Orderings_Oord__class_Omin(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),c_HOL_Ominus__class_Ominus(X3,X2,tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(c_Orderings_Oord__class_Omin(X1,X3,tc_nat),X2,tc_nat),
    c_0_2596,
    [final] ).

cnf(c_0_3394,plain,
    c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),X3,tc_nat),X2,tc_nat) = c_Divides_Odiv__class_Omod(X3,X2,tc_nat),
    c_0_2597,
    [final] ).

cnf(c_0_3395,plain,
    c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat) = c_HOL_Otimes__class_Otimes(X1,c_Divides_Odiv__class_Omod(X2,X3,tc_nat),tc_nat),
    c_0_2598,
    [final] ).

cnf(c_0_3396,plain,
    c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),c_HOL_Otimes__class_Otimes(X2,X3,tc_nat),tc_nat) = c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(X1,X2,tc_nat),X3,tc_nat),
    c_0_2599,
    [final] ).

cnf(c_0_3397,plain,
    c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),c_HOL_Otimes__class_Otimes(X2,X3,tc_nat),tc_nat) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),X3,tc_nat),
    c_0_2600,
    [final] ).

cnf(c_0_3398,plain,
    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) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Oplus__class_Oplus(X2,X3,tc_nat),tc_nat),
    c_0_2601,
    [final] ).

cnf(c_0_3399,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_2602,
    [final] ).

cnf(c_0_3400,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_2603,
    [final] ).

cnf(c_0_3401,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_2604,
    [final] ).

cnf(c_0_3402,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_2605,
    [final] ).

cnf(c_0_3403,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_2606,
    [final] ).

cnf(c_0_3404,plain,
    ( c_Ring__and__Field_Odvd__class_Odvd(X1,X4,X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,c_Divides_Odiv__class_Omod(X4,X2,X3),X3)
    | ~ class_Divides_Osemiring__div(X3) ),
    c_0_2607,
    [final] ).

cnf(c_0_3405,plain,
    ( c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X4)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,c_Divides_Odiv__class_Omod(X2,X3,X4),X4)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X3,X4)
    | ~ class_Divides_Osemiring__div(X4) ),
    c_0_2608,
    [final] ).

cnf(c_0_3406,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_2609,
    [final] ).

cnf(c_0_3407,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) ),
    c_0_2610,
    [final] ).

cnf(c_0_3408,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) ),
    c_0_2611,
    [final] ).

cnf(c_0_3409,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_2612,
    [final] ).

cnf(c_0_3410,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) ),
    c_0_2613,
    [final] ).

cnf(c_0_3411,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) ),
    c_0_2614,
    [final] ).

cnf(c_0_3412,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_2615,
    [final] ).

cnf(c_0_3413,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_2616,
    [final] ).

cnf(c_0_3414,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_2617,
    [final] ).

cnf(c_0_3415,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_2618,
    [final] ).

cnf(c_0_3416,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_2619,
    [final] ).

cnf(c_0_3417,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_2620,
    [final] ).

cnf(c_0_3418,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_2621,
    [final] ).

cnf(c_0_3419,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_2622,
    [final] ).

cnf(c_0_3420,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_2623,
    [final] ).

cnf(c_0_3421,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_2624,
    [final] ).

cnf(c_0_3422,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_2625,
    [final] ).

cnf(c_0_3423,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_2626,
    [final] ).

cnf(c_0_3424,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_2627,
    [final] ).

cnf(c_0_3425,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_2628,
    [final] ).

cnf(c_0_3426,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_2629,
    [final] ).

cnf(c_0_3427,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_2630,
    [final] ).

cnf(c_0_3428,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_2631,
    [final] ).

cnf(c_0_3429,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_2632,
    [final] ).

cnf(c_0_3430,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_2633,
    [final] ).

cnf(c_0_3431,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_2634,
    [final] ).

cnf(c_0_3432,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_2635,
    [final] ).

cnf(c_0_3433,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_2636,
    [final] ).

cnf(c_0_3434,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_2637,
    [final] ).

cnf(c_0_3435,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_2638,
    [final] ).

cnf(c_0_3436,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_2639,
    [final] ).

cnf(c_0_3437,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_2640,
    [final] ).

cnf(c_0_3438,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_2641,
    [final] ).

cnf(c_0_3439,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_2642,
    [final] ).

cnf(c_0_3440,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_2643,
    [final] ).

cnf(c_0_3441,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_2644,
    [final] ).

cnf(c_0_3442,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_2645,
    [final] ).

cnf(c_0_3443,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_2646,
    [final] ).

cnf(c_0_3444,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_2647,
    [final] ).

cnf(c_0_3445,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_2648,
    [final] ).

cnf(c_0_3446,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_2649,
    [final] ).

cnf(c_0_3447,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_2650,
    [final] ).

cnf(c_0_3448,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_2651,
    [final] ).

cnf(c_0_3449,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_2652,
    [final] ).

cnf(c_0_3450,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_2653,
    [final] ).

cnf(c_0_3451,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_2654,
    [final] ).

cnf(c_0_3452,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_2655,
    [final] ).

cnf(c_0_3453,plain,
    c_lessequals(X1,c_HOL_Otimes__class_Otimes(X1,c_HOL_Otimes__class_Otimes(X1,X1,tc_nat),tc_nat),tc_nat),
    c_0_2656,
    [final] ).

cnf(c_0_3454,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_2657,
    [final] ).

cnf(c_0_3455,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_2658,
    [final] ).

cnf(c_0_3456,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_2659,
    [final] ).

cnf(c_0_3457,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_2660,
    [final] ).

cnf(c_0_3458,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_2661,
    [final] ).

cnf(c_0_3459,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_2662,
    [final] ).

cnf(c_0_3460,plain,
    ( c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X2,X4,X3),X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
    | ~ class_Ring__and__Field_Oidom(X3) ),
    c_0_2663,
    [final] ).

cnf(c_0_3461,plain,
    ( c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X4,X1,X3),c_HOL_Otimes__class_Otimes(X4,X2,X3),X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
    | ~ class_Ring__and__Field_Oidom(X3) ),
    c_0_2664,
    [final] ).

cnf(c_0_3462,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_2665,
    [final] ).

cnf(c_0_3463,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_2666,
    [final] ).

cnf(c_0_3464,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_2667,
    [final] ).

cnf(c_0_3465,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_2668,
    [final] ).

cnf(c_0_3466,plain,
    ( c_Ring__and__Field_Odvd__class_Odvd(X2,X1,tc_nat)
    | c_Ring__and__Field_Odvd__class_Odvd(X3,X2,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X3,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X3,X1,tc_nat) ),
    c_0_2669,
    [final] ).

cnf(c_0_3467,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_2670,
    [final] ).

cnf(c_0_3468,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_2671,
    [final] ).

cnf(c_0_3469,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_2672,
    [final] ).

cnf(c_0_3470,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_2673,
    [final] ).

cnf(c_0_3471,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_2674,
    [final] ).

cnf(c_0_3472,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_2675,
    [final] ).

cnf(c_0_3473,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_2676,
    [final] ).

cnf(c_0_3474,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_2677,
    [final] ).

cnf(c_0_3475,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_2678,
    [final] ).

cnf(c_0_3476,plain,
    ( c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X3,X1,tc_nat),c_HOL_Otimes__class_Otimes(X3,X2,tc_nat),tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat) ),
    c_0_2679,
    [final] ).

cnf(c_0_3477,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_2680,
    [final] ).

cnf(c_0_3478,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_2681,
    [final] ).

cnf(c_0_3479,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_2682,
    [final] ).

cnf(c_0_3480,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_2683,
    [final] ).

cnf(c_0_3481,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_2684,
    [final] ).

cnf(c_0_3482,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_2685,
    [final] ).

cnf(c_0_3483,plain,
    ( c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Ominus__class_Ominus(X2,X4,X3),X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X4,X3)
    | ~ class_Ring__and__Field_Ocomm__ring__1(X3) ),
    c_0_2686,
    [final] ).

cnf(c_0_3484,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_2687,
    [final] ).

cnf(c_0_3485,plain,
    ( c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Oplus__class_Oplus(X2,X4,X3),X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X4,X3)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
    c_0_2688,
    [final] ).

cnf(c_0_3486,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_2689,
    [final] ).

cnf(c_0_3487,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_2690,
    [final] ).

cnf(c_0_3488,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_2691,
    [final] ).

cnf(c_0_3489,plain,
    ( c_Ring__and__Field_Odvd__class_Odvd(X1,c_Divides_Odiv__class_Omod(X2,X4,X3),X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X4,X3)
    | ~ class_Divides_Osemiring__div(X3) ),
    c_0_2692,
    [final] ).

cnf(c_0_3490,plain,
    ( c_Ring__and__Field_Odvd__class_Odvd(X1,c_Divides_Odiv__class_Omod(X4,X2,X3),X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X4,X3)
    | ~ class_Divides_Osemiring__div(X3) ),
    c_0_2693,
    [final] ).

cnf(c_0_3491,plain,
    ( c_HOL_Oabs__class_Oabs(c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(X1,X2),c_HOL_Oabs__class_Oabs(X3,X2),X2),X2) = c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(X1,X2),c_HOL_Oabs__class_Oabs(X3,X2),X2)
    | ~ class_OrderedGroup_Opordered__ab__group__add__abs(X2) ),
    c_0_2694,
    [final] ).

cnf(c_0_3492,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_2695,
    [final] ).

cnf(c_0_3493,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_2696,
    [final] ).

cnf(c_0_3494,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_2697,
    [final] ).

cnf(c_0_3495,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_2698,
    [final] ).

cnf(c_0_3496,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_2699,
    [final] ).

cnf(c_0_3497,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_2700,
    [final] ).

cnf(c_0_3498,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_2701,
    [final] ).

cnf(c_0_3499,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_2702,
    [final] ).

cnf(c_0_3500,plain,
    c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(c_Suc(X1),X2,tc_nat),c_Suc(X3),tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),X3,tc_nat),
    c_0_2703,
    [final] ).

cnf(c_0_3501,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_2704,
    [final] ).

cnf(c_0_3502,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_2705,
    [final] ).

cnf(c_0_3503,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_2706,
    [final] ).

cnf(c_0_3504,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_2707,
    [final] ).

cnf(c_0_3505,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_2708,
    [final] ).

cnf(c_0_3506,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_2709,
    [final] ).

cnf(c_0_3507,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_2710,
    [final] ).

cnf(c_0_3508,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_2711,
    [final] ).

cnf(c_0_3509,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_2712,
    [final] ).

cnf(c_0_3510,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_2713,
    [final] ).

cnf(c_0_3511,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_2714,
    [final] ).

cnf(c_0_3512,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_2715,
    [final] ).

cnf(c_0_3513,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_2716,
    [final] ).

cnf(c_0_3514,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_2717,
    [final] ).

cnf(c_0_3515,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_2718,
    [final] ).

cnf(c_0_3516,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_2719,
    [final] ).

cnf(c_0_3517,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_2720,
    [final] ).

cnf(c_0_3518,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_2721,
    [final] ).

cnf(c_0_3519,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_2722,
    [final] ).

cnf(c_0_3520,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_2723,
    [final] ).

cnf(c_0_3521,plain,
    ( c_Ring__and__Field_Odvd__class_Odvd(X2,X1,tc_nat)
    | c_Ring__and__Field_Odvd__class_Odvd(X3,X2,tc_nat)
    | c_Ring__and__Field_Odvd__class_Odvd(X1,X3,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X3,tc_nat) ),
    c_0_2724,
    [final] ).

cnf(c_0_3522,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_2725,
    [final] ).

cnf(c_0_3523,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_2726,
    [final] ).

cnf(c_0_3524,plain,
    c_Divides_Odiv__class_Omod(c_Suc(c_Divides_Odiv__class_Omod(X1,X2,tc_nat)),X2,tc_nat) = c_Divides_Odiv__class_Omod(c_Suc(X1),X2,tc_nat),
    c_0_2727,
    [final] ).

cnf(c_0_3525,plain,
    ( c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Ominus__class_Ominus(X2,X3,tc_nat),tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X3,tc_nat) ),
    c_0_2728,
    [final] ).

cnf(c_0_3526,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_2729,
    [final] ).

cnf(c_0_3527,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_2730,
    [final] ).

cnf(c_0_3528,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_2731,
    [final] ).

cnf(c_0_3529,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_2732,
    [final] ).

cnf(c_0_3530,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_2733,
    [final] ).

cnf(c_0_3531,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_2734,
    [final] ).

cnf(c_0_3532,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_2735,
    [final] ).

cnf(c_0_3533,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_2736,
    [final] ).

cnf(c_0_3534,plain,
    ( c_lessequals(X1,X3,X4)
    | ~ c_lessequals(X1,c_Orderings_Oord__class_Omin(X2,X3,X4),X4)
    | ~ class_Orderings_Olinorder(X4) ),
    c_0_2737,
    [final] ).

cnf(c_0_3535,plain,
    ( c_lessequals(X1,X2,X4)
    | ~ c_lessequals(X1,c_Orderings_Oord__class_Omin(X2,X3,X4),X4)
    | ~ class_Orderings_Olinorder(X4) ),
    c_0_2738,
    [final] ).

cnf(c_0_3536,plain,
    ( c_lessequals(X1,X3,X4)
    | ~ c_lessequals(X1,c_Orderings_Oord__class_Omin(X2,X3,X4),X4)
    | ~ class_Orderings_Olinorder(X4) ),
    c_0_2739,
    [final] ).

cnf(c_0_3537,plain,
    ( c_lessequals(X1,X2,X4)
    | ~ c_lessequals(X1,c_Orderings_Oord__class_Omin(X2,X3,X4),X4)
    | ~ class_Orderings_Olinorder(X4) ),
    c_0_2740,
    [final] ).

cnf(c_0_3538,plain,
    ( c_Ring__and__Field_Odvd__class_Odvd(X2,X4,X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
    c_0_2741,
    [final] ).

cnf(c_0_3539,plain,
    ( c_Ring__and__Field_Odvd__class_Odvd(X1,X4,X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
    c_0_2742,
    [final] ).

cnf(c_0_3540,plain,
    ( c_HOL_Ominus__class_Ominus(c_Nat_Osemiring__1__class_Oof__nat(X2,X3),c_Nat_Osemiring__1__class_Oof__nat(X1,X3),X3) = c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),X3)
    | ~ c_lessequals(X1,X2,tc_nat)
    | ~ class_Ring__and__Field_Oring__1(X3) ),
    c_0_2743,
    [final] ).

cnf(c_0_3541,plain,
    c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),X3,tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X1,X3,tc_nat),X2,tc_nat),
    c_0_2744,
    [final] ).

cnf(c_0_3542,plain,
    c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),X3,tc_nat) = c_HOL_Ominus__class_Ominus(X1,c_HOL_Oplus__class_Oplus(X2,X3,tc_nat),tc_nat),
    c_0_2745,
    [final] ).

cnf(c_0_3543,plain,
    c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),c_HOL_Oplus__class_Oplus(X3,X2,tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(X1,X3,tc_nat),
    c_0_2746,
    [final] ).

cnf(c_0_3544,plain,
    c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),c_HOL_Oplus__class_Oplus(X1,X3,tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(X2,X3,tc_nat),
    c_0_2747,
    [final] ).

cnf(c_0_3545,plain,
    c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X2,X3,tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(X2,c_HOL_Oplus__class_Oplus(X1,X3,tc_nat),tc_nat),
    c_0_2748,
    [final] ).

cnf(c_0_3546,plain,
    c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),X3,tc_nat) = c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X2,X3,tc_nat),tc_nat),
    c_0_2749,
    [final] ).

cnf(c_0_3547,plain,
    c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),X3,tc_nat) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Otimes__class_Otimes(X2,X3,tc_nat),tc_nat),
    c_0_2750,
    [final] ).

cnf(c_0_3548,plain,
    ( c_Divides_Odiv__class_Omod(c_Divides_Odiv__class_Omod(X4,X2,X3),X1,X3) = c_Divides_Odiv__class_Omod(X4,X1,X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
    | ~ class_Divides_Osemiring__div(X3) ),
    c_0_2751,
    [final] ).

cnf(c_0_3549,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_2752,
    [final] ).

cnf(c_0_3550,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_2753,
    [final] ).

cnf(c_0_3551,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_2754,
    [final] ).

cnf(c_0_3552,plain,
    ( c_Ring__and__Field_Odvd__class_Odvd(X2,X1,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X3,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X3,X1,tc_nat) ),
    c_0_2755,
    [final] ).

cnf(c_0_3553,plain,
    ( c_Ring__and__Field_Odvd__class_Odvd(X3,X2,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X3,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X3,X1,tc_nat) ),
    c_0_2756,
    [final] ).

cnf(c_0_3554,plain,
    ( c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(X3,X1),X2,X1) = c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(X3,X2,X1),X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    c_0_2757,
    [final] ).

cnf(c_0_3555,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_2758,
    [final] ).

cnf(c_0_3556,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_2759,
    [final] ).

cnf(c_0_3557,plain,
    ( c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Oplus__class_Oplus(X2,X1,tc_nat),tc_nat) ),
    c_0_2760,
    [final] ).

cnf(c_0_3558,plain,
    ( c_lessequals(X2,X3,tc_nat)
    | ~ c_lessequals(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),X3,tc_nat) ),
    c_0_2761,
    [final] ).

cnf(c_0_3559,plain,
    ( c_lessequals(X1,X3,tc_nat)
    | ~ c_lessequals(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),X3,tc_nat) ),
    c_0_2762,
    [final] ).

cnf(c_0_3560,plain,
    ( c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X1,c_HOL_Ozero__class_Ozero(X2),X2),c_HOL_Otimes__class_Otimes(X3,c_HOL_Ozero__class_Ozero(X2),X2),X2)
    | ~ class_Ring__and__Field_Oidom(X2) ),
    c_0_2763,
    [final] ).

cnf(c_0_3561,plain,
    ( c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),X2,X1),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),X3,X1),X1)
    | ~ class_Ring__and__Field_Oidom(X1) ),
    c_0_2764,
    [final] ).

cnf(c_0_3562,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_2765,
    [final] ).

cnf(c_0_3563,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_2766,
    [final] ).

cnf(c_0_3564,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_2767,
    [final] ).

cnf(c_0_3565,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_2768,
    [final] ).

cnf(c_0_3566,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_2769,
    [final] ).

cnf(c_0_3567,plain,
    ( c_Ring__and__Field_Odvd__class_Odvd(X3,X2,tc_nat)
    | c_Ring__and__Field_Odvd__class_Odvd(X1,X3,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X3,tc_nat) ),
    c_0_2770,
    [final] ).

cnf(c_0_3568,plain,
    ( c_Ring__and__Field_Odvd__class_Odvd(X2,X1,tc_nat)
    | c_Ring__and__Field_Odvd__class_Odvd(X1,X3,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X3,tc_nat) ),
    c_0_2771,
    [final] ).

cnf(c_0_3569,plain,
    c_Ring__and__Field_Odvd__class_Odvd(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),tc_nat),
    c_0_2772,
    [final] ).

cnf(c_0_3570,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_2773,
    [final] ).

cnf(c_0_3571,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_2774,
    [final] ).

cnf(c_0_3572,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_2775,
    [final] ).

cnf(c_0_3573,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_2776,
    [final] ).

cnf(c_0_3574,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_2777,
    [final] ).

cnf(c_0_3575,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_2778,
    [final] ).

cnf(c_0_3576,plain,
    ( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | c_Parity_Oeven__odd__class_Oeven(X1,tc_nat)
    | ~ c_Parity_Oeven__odd__class_Oeven(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),tc_nat)
    | ~ c_Parity_Oeven__odd__class_Oeven(X2,tc_nat) ),
    c_0_2779,
    [final] ).

cnf(c_0_3577,plain,
    ( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | c_Parity_Oeven__odd__class_Oeven(X2,tc_nat)
    | ~ c_Parity_Oeven__odd__class_Oeven(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),tc_nat)
    | ~ c_Parity_Oeven__odd__class_Oeven(X1,tc_nat) ),
    c_0_2780,
    [final] ).

cnf(c_0_3578,plain,
    c_HOL_Oord__class_Oless(X1,c_Suc(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat)),tc_nat),
    c_0_2781,
    [final] ).

cnf(c_0_3579,plain,
    c_HOL_Oord__class_Oless(X1,c_Suc(c_HOL_Oplus__class_Oplus(X2,X1,tc_nat)),tc_nat),
    c_0_2782,
    [final] ).

cnf(c_0_3580,plain,
    c_HOL_Oord__class_Oless(X1,c_Suc(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat)),tc_nat),
    c_0_2783,
    [final] ).

cnf(c_0_3581,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_2784,
    [final] ).

cnf(c_0_3582,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_2785,
    [final] ).

cnf(c_0_3583,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_2786,
    [final] ).

cnf(c_0_3584,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_2787,
    [final] ).

cnf(c_0_3585,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_2788,
    [final] ).

cnf(c_0_3586,plain,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
    | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X1,tc_nat) ),
    c_0_2789,
    [final] ).

cnf(c_0_3587,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_2790,
    [final] ).

cnf(c_0_3588,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_2791,
    [final] ).

cnf(c_0_3589,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_2792,
    [final] ).

cnf(c_0_3590,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_2793,
    [final] ).

cnf(c_0_3591,plain,
    ( c_lessequals(c_Orderings_Oord__class_Omin(X4,X1,X3),X2,X3)
    | ~ c_lessequals(X1,X2,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    c_0_2794,
    [final] ).

cnf(c_0_3592,plain,
    ( c_lessequals(c_Orderings_Oord__class_Omin(X1,X4,X3),X2,X3)
    | ~ c_lessequals(X1,X2,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    c_0_2795,
    [final] ).

cnf(c_0_3593,plain,
    ( c_lessequals(c_Orderings_Oord__class_Omin(X4,X1,X3),X2,X3)
    | ~ c_lessequals(X1,X2,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    c_0_2796,
    [final] ).

cnf(c_0_3594,plain,
    ( c_lessequals(c_Orderings_Oord__class_Omin(X1,X4,X3),X2,X3)
    | ~ c_lessequals(X1,X2,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    c_0_2797,
    [final] ).

cnf(c_0_3595,plain,
    ( c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Otimes__class_Otimes(X2,X4,X3),X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
    c_0_2798,
    [final] ).

cnf(c_0_3596,plain,
    ( c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Otimes__class_Otimes(X4,X2,X3),X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
    c_0_2799,
    [final] ).

cnf(c_0_3597,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_2800,
    [final] ).

cnf(c_0_3598,plain,
    ( c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X1,X2,X3),X3) = c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X2,X1,X3),X3)
    | ~ class_OrderedGroup_Opordered__ab__group__add__abs(X3) ),
    c_0_2801,
    [final] ).

cnf(c_0_3599,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_2802,
    [final] ).

cnf(c_0_3600,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_2803,
    [final] ).

cnf(c_0_3601,plain,
    ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),X2,tc_nat),
    c_0_2804,
    [final] ).

cnf(c_0_3602,plain,
    ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),X1,tc_nat),
    c_0_2805,
    [final] ).

cnf(c_0_3603,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_2806,
    [final] ).

cnf(c_0_3604,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_2807,
    [final] ).

cnf(c_0_3605,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_2808,
    [final] ).

cnf(c_0_3606,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_2809,
    [final] ).

cnf(c_0_3607,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_2810,
    [final] ).

cnf(c_0_3608,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_2811,
    [final] ).

cnf(c_0_3609,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_2812,
    [final] ).

cnf(c_0_3610,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_2813,
    [final] ).

cnf(c_0_3611,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_2814,
    [final] ).

cnf(c_0_3612,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_2815,
    [final] ).

cnf(c_0_3613,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_2816,
    [final] ).

cnf(c_0_3614,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_2817,
    [final] ).

cnf(c_0_3615,plain,
    ( c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Oplus__class_Oplus(X2,X1,tc_nat),tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat) ),
    c_0_2818,
    [final] ).

cnf(c_0_3616,plain,
    ( c_lessequals(X1,c_HOL_Oplus__class_Oplus(X3,X2,tc_nat),tc_nat)
    | ~ c_lessequals(X1,X2,tc_nat) ),
    c_0_2819,
    [final] ).

cnf(c_0_3617,plain,
    ( c_lessequals(X1,c_HOL_Oplus__class_Oplus(X2,X3,tc_nat),tc_nat)
    | ~ c_lessequals(X1,X2,tc_nat) ),
    c_0_2820,
    [final] ).

cnf(c_0_3618,plain,
    ( c_lessequals(X1,c_HOL_Oplus__class_Oplus(X3,X2,tc_nat),tc_nat)
    | ~ c_lessequals(X1,X2,tc_nat) ),
    c_0_2821,
    [final] ).

cnf(c_0_3619,plain,
    ( c_lessequals(X1,c_HOL_Oplus__class_Oplus(X2,X3,tc_nat),tc_nat)
    | ~ c_lessequals(X1,X2,tc_nat) ),
    c_0_2822,
    [final] ).

cnf(c_0_3620,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_2823,
    [final] ).

cnf(c_0_3621,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_2824,
    [final] ).

cnf(c_0_3622,plain,
    ( c_lessequals(X4,X2,X3)
    | ~ c_lessequals(X1,X2,X3)
    | ~ c_lessequals(X4,X1,X3)
    | ~ class_Orderings_Oorder(X3) ),
    c_0_2825,
    [final] ).

cnf(c_0_3623,plain,
    ( c_lessequals(X1,X4,X3)
    | ~ c_lessequals(X1,X2,X3)
    | ~ c_lessequals(X2,X4,X3)
    | ~ class_Orderings_Opreorder(X3) ),
    c_0_2826,
    [final] ).

cnf(c_0_3624,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_2827,
    [final] ).

cnf(c_0_3625,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_2828,
    [final] ).

cnf(c_0_3626,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_2829,
    [final] ).

cnf(c_0_3627,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_2830,
    [final] ).

cnf(c_0_3628,plain,
    ( c_Ring__and__Field_Odvd__class_Odvd(X1,X4,X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X4,X3)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
    c_0_2831,
    [final] ).

cnf(c_0_3629,plain,
    ( c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(X1,X3),c_HOL_Oabs__class_Oabs(X2,X3),X3) = c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(X1,X2,X3),X3)
    | ~ class_Ring__and__Field_Oordered__idom(X3) ),
    c_0_2832,
    [final] ).

cnf(c_0_3630,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_2833,
    [final] ).

cnf(c_0_3631,plain,
    ( c_HOL_Otimes__class_Otimes(c_Nat_Osemiring__1__class_Oof__nat(X1,X3),c_Nat_Osemiring__1__class_Oof__nat(X2,X3),X3) = c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),X3)
    | ~ class_Ring__and__Field_Osemiring__1(X3) ),
    c_0_2834,
    [final] ).

cnf(c_0_3632,plain,
    ( c_HOL_Oplus__class_Oplus(c_Nat_Osemiring__1__class_Oof__nat(X1,X3),c_Nat_Osemiring__1__class_Oof__nat(X2,X3),X3) = c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),X3)
    | ~ class_Ring__and__Field_Osemiring__1(X3) ),
    c_0_2835,
    [final] ).

cnf(c_0_3633,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),X1,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X1,tc_nat) ),
    c_0_2836,
    [final] ).

cnf(c_0_3634,plain,
    ( c_HOL_Oord__class_Oless(X1,X3,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X1,X2),c_Nat_Osemiring__1__class_Oof__nat(X3,X2),X2)
    | ~ class_Ring__and__Field_Oordered__semidom(X2) ),
    c_0_2837,
    [final] ).

cnf(c_0_3635,plain,
    ( c_lessequals(X1,X3,tc_nat)
    | ~ c_lessequals(c_Nat_Osemiring__1__class_Oof__nat(X1,X2),c_Nat_Osemiring__1__class_Oof__nat(X3,X2),X2)
    | ~ class_Ring__and__Field_Oordered__semidom(X2) ),
    c_0_2838,
    [final] ).

cnf(c_0_3636,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_2839,
    [final] ).

cnf(c_0_3637,plain,
    ( c_lessequals(X1,X2,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat) ),
    c_0_2840,
    [final] ).

cnf(c_0_3638,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_2841,
    [final] ).

cnf(c_0_3639,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_2842,
    [final] ).

cnf(c_0_3640,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_2843,
    [final] ).

cnf(c_0_3641,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_2844,
    [final] ).

cnf(c_0_3642,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_2845,
    [final] ).

cnf(c_0_3643,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_2846,
    [final] ).

cnf(c_0_3644,plain,
    ( c_lessequals(X1,X3,tc_nat)
    | ~ c_lessequals(X1,X2,tc_nat)
    | ~ c_lessequals(X2,X3,tc_nat) ),
    c_0_2847,
    [final] ).

cnf(c_0_3645,plain,
    ( c_Ring__and__Field_Odvd__class_Odvd(X1,X3,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X3,tc_nat) ),
    c_0_2848,
    [final] ).

cnf(c_0_3646,plain,
    ( c_Parity_Oeven__odd__class_Oeven(X1,tc_nat)
    | ~ c_Parity_Oeven__odd__class_Oeven(X2,tc_nat)
    | ~ c_Parity_Oeven__odd__class_Oeven(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat) ),
    c_0_2849,
    [final] ).

cnf(c_0_3647,plain,
    ( c_Parity_Oeven__odd__class_Oeven(X2,tc_nat)
    | ~ c_Parity_Oeven__odd__class_Oeven(X1,tc_nat)
    | ~ c_Parity_Oeven__odd__class_Oeven(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat) ),
    c_0_2850,
    [final] ).

cnf(c_0_3648,plain,
    ( c_Parity_Oeven__odd__class_Oeven(X2,tc_nat)
    | ~ c_Parity_Oeven__odd__class_Oeven(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat)
    | ~ c_Parity_Oeven__odd__class_Oeven(X1,tc_nat) ),
    c_0_2851,
    [final] ).

cnf(c_0_3649,plain,
    ( c_Parity_Oeven__odd__class_Oeven(X1,tc_nat)
    | ~ c_Parity_Oeven__odd__class_Oeven(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat)
    | ~ c_Parity_Oeven__odd__class_Oeven(X2,tc_nat) ),
    c_0_2852,
    [final] ).

cnf(c_0_3650,plain,
    ( c_Parity_Oeven__odd__class_Oeven(X1,tc_nat)
    | ~ c_Parity_Oeven__odd__class_Oeven(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat)
    | ~ c_Parity_Oeven__odd__class_Oeven(X2,tc_nat) ),
    c_0_2853,
    [final] ).

cnf(c_0_3651,plain,
    ( c_Parity_Oeven__odd__class_Oeven(X2,tc_nat)
    | ~ c_Parity_Oeven__odd__class_Oeven(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat)
    | ~ c_Parity_Oeven__odd__class_Oeven(X1,tc_nat) ),
    c_0_2854,
    [final] ).

cnf(c_0_3652,plain,
    c_HOL_Oplus__class_Oplus(X1,c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),tc_nat) = c_HOL_Otimes__class_Otimes(X1,c_Suc(X2),tc_nat),
    c_0_2855,
    [final] ).

cnf(c_0_3653,plain,
    c_HOL_Oplus__class_Oplus(X2,c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),tc_nat) = c_HOL_Otimes__class_Otimes(c_Suc(X1),X2,tc_nat),
    c_0_2856,
    [final] ).

cnf(c_0_3654,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_2857,
    [final] ).

cnf(c_0_3655,plain,
    ( c_Parity_Oeven__odd__class_Oeven(X1,tc_nat)
    | c_Parity_Oeven__odd__class_Oeven(X2,tc_nat)
    | ~ c_Parity_Oeven__odd__class_Oeven(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),tc_nat) ),
    c_0_2858,
    [final] ).

cnf(c_0_3656,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_2859,
    [final] ).

cnf(c_0_3657,plain,
    ( c_Parity_Oeven__odd__class_Oeven(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),tc_nat)
    | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
    c_0_2860,
    [final] ).

cnf(c_0_3658,plain,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Nat_Osemiring__1__class_Oof__nat(X2,X1),X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    c_0_2861,
    [final] ).

cnf(c_0_3659,plain,
    ( c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X1,X3),c_Nat_Osemiring__1__class_Oof__nat(X2,X3),X3)
    | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | ~ class_Ring__and__Field_Oordered__semidom(X3) ),
    c_0_2862,
    [final] ).

cnf(c_0_3660,plain,
    ( c_lessequals(c_Nat_Osemiring__1__class_Oof__nat(X1,X3),c_Nat_Osemiring__1__class_Oof__nat(X2,X3),X3)
    | ~ c_lessequals(X1,X2,tc_nat)
    | ~ class_Ring__and__Field_Oordered__semidom(X3) ),
    c_0_2863,
    [final] ).

cnf(c_0_3661,plain,
    ( c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Oabs__class_Oabs(X2,X3),X3)
    | ~ class_Ring__and__Field_Oordered__idom(X3) ),
    c_0_2864,
    [final] ).

cnf(c_0_3662,plain,
    ( c_Ring__and__Field_Odvd__class_Odvd(X1,X3,X2)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oabs__class_Oabs(X1,X2),X3,X2)
    | ~ class_Ring__and__Field_Oordered__idom(X2) ),
    c_0_2865,
    [final] ).

cnf(c_0_3663,plain,
    ( c_HOL_Oord__class_Oless(X1,X3,X2)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(X1,X2),X3,X2)
    | ~ class_Ring__and__Field_Oordered__idom(X2) ),
    c_0_2866,
    [final] ).

cnf(c_0_3664,plain,
    ( c_lessequals(X1,X3,X2)
    | ~ c_lessequals(c_HOL_Oabs__class_Oabs(X1,X2),X3,X2)
    | ~ class_OrderedGroup_Opordered__ab__group__add__abs(X2) ),
    c_0_2867,
    [final] ).

cnf(c_0_3665,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_2868,
    [final] ).

cnf(c_0_3666,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_2869,
    [final] ).

cnf(c_0_3667,plain,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),c_Nat_Osemiring__1__class_Oof__nat(X1,X2),X2)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
    | ~ class_Ring__and__Field_Oordered__semidom(X2) ),
    c_0_2870,
    [final] ).

cnf(c_0_3668,plain,
    ( X2 = X1
    | ~ c_lessequals(X1,X2,X3)
    | ~ c_lessequals(X2,X1,X3)
    | ~ class_Orderings_Oorder(X3) ),
    c_0_2871,
    [final] ).

cnf(c_0_3669,plain,
    ( X1 = X2
    | ~ c_lessequals(X1,X2,X3)
    | ~ c_lessequals(X2,X1,X3)
    | ~ class_Orderings_Oorder(X3) ),
    c_0_2872,
    [final] ).

cnf(c_0_3670,plain,
    ( X1 = X2
    | ~ c_lessequals(X1,X2,X3)
    | ~ c_lessequals(X2,X1,X3)
    | ~ class_Orderings_Oorder(X3) ),
    c_0_2873,
    [final] ).

cnf(c_0_3671,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_2874,
    [final] ).

cnf(c_0_3672,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_2875,
    [final] ).

cnf(c_0_3673,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_2876,
    [final] ).

cnf(c_0_3674,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_2877,
    [final] ).

cnf(c_0_3675,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_2878,
    [final] ).

cnf(c_0_3676,plain,
    ( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | ~ c_HOL_Oord__class_Oless(X2,X1,X3)
    | ~ class_Orderings_Opreorder(X3) ),
    c_0_2879,
    [final] ).

cnf(c_0_3677,plain,
    ( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | ~ c_HOL_Oord__class_Oless(X2,X1,X3)
    | ~ class_Orderings_Opreorder(X3) ),
    c_0_2880,
    [final] ).

cnf(c_0_3678,plain,
    ( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | ~ c_HOL_Oord__class_Oless(X2,X1,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    c_0_2881,
    [final] ).

cnf(c_0_3679,plain,
    ( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | ~ c_HOL_Oord__class_Oless(X2,X1,X3)
    | ~ class_Orderings_Oorder(X3) ),
    c_0_2882,
    [final] ).

cnf(c_0_3680,plain,
    ( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | ~ c_lessequals(X2,X1,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    c_0_2883,
    [final] ).

cnf(c_0_3681,plain,
    ( ~ c_lessequals(X1,X2,X3)
    | ~ c_HOL_Oord__class_Oless(X2,X1,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    c_0_2884,
    [final] ).

cnf(c_0_3682,plain,
    ( ~ c_HOL_Oord__class_Oless(X1,X1,X2)
    | ~ c_lessequals(X1,X1,X2)
    | ~ class_Orderings_Olinorder(X2) ),
    c_0_2885,
    [final] ).

cnf(c_0_3683,plain,
    ( ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | ~ c_lessequals(X2,X1,X3)
    | ~ class_Orderings_Opreorder(X3) ),
    c_0_2886,
    [final] ).

cnf(c_0_3684,plain,
    ( X2 = X1
    | ~ c_lessequals(X1,X2,tc_nat)
    | ~ c_HOL_Oord__class_Oless(X2,c_Suc(X1),tc_nat) ),
    c_0_2887,
    [final] ).

cnf(c_0_3685,plain,
    c_Parity_Oeven__odd__class_Oeven(c_HOL_Otimes__class_Otimes(c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),X1,tc_nat),tc_nat),
    c_0_2888,
    [final] ).

cnf(c_0_3686,plain,
    ( ~ c_HOL_Oord__class_Oless(X1,c_Suc(X2),tc_nat)
    | ~ c_HOL_Oord__class_Oless(X2,X1,tc_nat) ),
    c_0_2889,
    [final] ).

cnf(c_0_3687,plain,
    ( ~ c_lessequals(c_Suc(X1),X2,tc_nat)
    | ~ c_lessequals(X2,X1,tc_nat) ),
    c_0_2890,
    [final] ).

cnf(c_0_3688,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_2891,
    [final] ).

cnf(c_0_3689,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_2892,
    [final] ).

cnf(c_0_3690,plain,
    ( c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Oabs__class_Oabs(X2,X3),X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
    | ~ class_Ring__and__Field_Oordered__idom(X3) ),
    c_0_2893,
    [final] ).

cnf(c_0_3691,plain,
    ( c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oabs__class_Oabs(X1,X3),X2,X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
    | ~ class_Ring__and__Field_Oordered__idom(X3) ),
    c_0_2894,
    [final] ).

cnf(c_0_3692,plain,
    c_Orderings_Oord__class_Omin(c_Suc(X1),c_Suc(X2),tc_nat) = c_Suc(c_Orderings_Oord__class_Omin(X1,X2,tc_nat)),
    c_0_2895,
    [final] ).

cnf(c_0_3693,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_2896,
    [final] ).

cnf(c_0_3694,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_2897,
    [final] ).

cnf(c_0_3695,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_2898,
    [final] ).

cnf(c_0_3696,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_2899,
    [final] ).

cnf(c_0_3697,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_2900,
    [final] ).

cnf(c_0_3698,plain,
    ( X1 = X2
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X1,tc_nat) ),
    c_0_2901,
    [final] ).

cnf(c_0_3699,plain,
    ( X1 = X2
    | ~ c_lessequals(X1,X2,tc_nat)
    | ~ c_lessequals(X2,X1,tc_nat) ),
    c_0_2902,
    [final] ).

cnf(c_0_3700,plain,
    ( X1 = X2
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X1,tc_nat) ),
    c_0_2903,
    [final] ).

cnf(c_0_3701,plain,
    ( X1 = X2
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X1,tc_nat) ),
    c_0_2904,
    [final] ).

cnf(c_0_3702,plain,
    ( X1 = X2
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X1,tc_nat) ),
    c_0_2905,
    [final] ).

cnf(c_0_3703,plain,
    ( X2 = X1
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X1,tc_nat) ),
    c_0_2906,
    [final] ).

cnf(c_0_3704,plain,
    ( X1 = X2
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X1,tc_nat) ),
    c_0_2907,
    [final] ).

cnf(c_0_3705,plain,
    ( X1 = X2
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X1,tc_nat) ),
    c_0_2908,
    [final] ).

cnf(c_0_3706,plain,
    ( c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X1,X2,X3),X2,X3) = X1
    | ~ class_OrderedGroup_Ogroup__add(X3) ),
    c_0_2909,
    [final] ).

cnf(c_0_3707,plain,
    ( c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X1,X2,X3),X2,X3) = X1
    | ~ class_OrderedGroup_Ogroup__add(X3) ),
    c_0_2910,
    [final] ).

cnf(c_0_3708,plain,
    ( X1 = X2
    | c_HOL_Oplus__class_Oplus(X3,X1,tc_nat) != c_HOL_Oplus__class_Oplus(X3,X2,tc_nat) ),
    c_0_2911,
    [final] ).

cnf(c_0_3709,plain,
    ( X1 = X2
    | c_HOL_Oplus__class_Oplus(X3,X1,tc_nat) != c_HOL_Oplus__class_Oplus(X3,X2,tc_nat) ),
    c_0_2912,
    [final] ).

cnf(c_0_3710,plain,
    ( X1 = X2
    | c_HOL_Oplus__class_Oplus(X1,X3,tc_nat) != c_HOL_Oplus__class_Oplus(X2,X3,tc_nat) ),
    c_0_2913,
    [final] ).

cnf(c_0_3711,plain,
    ( c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Otimes__class_Otimes(X1,X2,X3),X3)
    | ~ class_Ring__and__Field_Odvd(X3) ),
    c_0_2914,
    [final] ).

cnf(c_0_3712,plain,
    ( c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Otimes__class_Otimes(X1,X2,X3),X3)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
    c_0_2915,
    [final] ).

cnf(c_0_3713,plain,
    ( c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Otimes__class_Otimes(X2,X1,X3),X3)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
    c_0_2916,
    [final] ).

cnf(c_0_3714,plain,
    ( c_lessequals(c_Orderings_Oord__class_Omin(X1,X2,X3),X1,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    c_0_2917,
    [final] ).

cnf(c_0_3715,plain,
    ( c_lessequals(c_Orderings_Oord__class_Omin(X1,X2,X3),X2,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    c_0_2918,
    [final] ).

cnf(c_0_3716,plain,
    ( c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(X1,X2),c_HOL_Oabs__class_Oabs(X1,X2),X2) = c_HOL_Otimes__class_Otimes(X1,X1,X2)
    | ~ class_Ring__and__Field_Oordered__idom(X2) ),
    c_0_2919,
    [final] ).

cnf(c_0_3717,plain,
    c_Suc(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat)) = c_HOL_Oplus__class_Oplus(X1,c_Suc(X2),tc_nat),
    c_0_2920,
    [final] ).

cnf(c_0_3718,plain,
    c_Suc(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat)) = c_HOL_Oplus__class_Oplus(c_Suc(X1),X2,tc_nat),
    c_0_2921,
    [final] ).

cnf(c_0_3719,plain,
    c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),c_Suc(X1),tc_nat),
    c_0_2922,
    [final] ).

cnf(c_0_3720,plain,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oabs__class_Oabs(c_HOL_Ozero__class_Ozero(X1),X1),X1)
    | ~ class_OrderedGroup_Opordered__ab__group__add__abs(X1) ),
    c_0_2923,
    [final] ).

cnf(c_0_3721,plain,
    ( ~ c_Parity_Oeven__odd__class_Oeven(X1,tc_nat)
    | c_Divides_Odiv__class_Omod(X1,c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
    c_0_2924,
    [final] ).

cnf(c_0_3722,plain,
    c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),X1,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
    c_0_2925,
    [final] ).

cnf(c_0_3723,plain,
    c_HOL_Ominus__class_Ominus(X1,c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
    c_0_2926,
    [final] ).

cnf(c_0_3724,plain,
    c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),X2,tc_nat) = X1,
    c_0_2927,
    [final] ).

cnf(c_0_3725,plain,
    c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),X1,tc_nat) = X2,
    c_0_2928,
    [final] ).

cnf(c_0_3726,plain,
    ( c_Parity_Oeven__odd__class_Oeven(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),tc_nat)
    | ~ c_Parity_Oeven__odd__class_Oeven(X1,tc_nat)
    | ~ c_Parity_Oeven__odd__class_Oeven(X2,tc_nat) ),
    c_0_2929,
    [final] ).

cnf(c_0_3727,plain,
    ( c_Parity_Oeven__odd__class_Oeven(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat)
    | ~ c_Parity_Oeven__odd__class_Oeven(X1,tc_nat)
    | ~ c_Parity_Oeven__odd__class_Oeven(X2,tc_nat) ),
    c_0_2930,
    [final] ).

cnf(c_0_3728,plain,
    ( c_Parity_Oeven__odd__class_Oeven(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat)
    | ~ c_Parity_Oeven__odd__class_Oeven(X1,tc_nat)
    | ~ c_Parity_Oeven__odd__class_Oeven(X2,tc_nat) ),
    c_0_2931,
    [final] ).

cnf(c_0_3729,plain,
    ( c_Parity_Oeven__odd__class_Oeven(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat)
    | ~ c_Parity_Oeven__odd__class_Oeven(X1,tc_nat)
    | ~ c_Parity_Oeven__odd__class_Oeven(X2,tc_nat) ),
    c_0_2932,
    [final] ).

cnf(c_0_3730,plain,
    c_lessequals(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),X1,tc_nat),
    c_0_2933,
    [final] ).

cnf(c_0_3731,plain,
    c_lessequals(X1,c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat),
    c_0_2934,
    [final] ).

cnf(c_0_3732,plain,
    c_lessequals(X1,c_HOL_Oplus__class_Oplus(X2,X1,tc_nat),tc_nat),
    c_0_2935,
    [final] ).

cnf(c_0_3733,plain,
    c_lessequals(X1,c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat),
    c_0_2936,
    [final] ).

cnf(c_0_3734,plain,
    c_lessequals(X1,c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat),
    c_0_2937,
    [final] ).

cnf(c_0_3735,plain,
    c_lessequals(X1,c_HOL_Otimes__class_Otimes(X1,X1,tc_nat),tc_nat),
    c_0_2938,
    [final] ).

cnf(c_0_3736,plain,
    c_lessequals(c_Divides_Odiv__class_Omod(X1,X2,tc_nat),X1,tc_nat),
    c_0_2939,
    [final] ).

cnf(c_0_3737,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_2940,
    [final] ).

cnf(c_0_3738,plain,
    ( c_lessequals(X1,X2,tc_nat)
    | ~ c_lessequals(c_Suc(X1),c_Suc(X2),tc_nat) ),
    c_0_2941,
    [final] ).

cnf(c_0_3739,plain,
    ( c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
    | c_Divides_Odiv__class_Omod(X2,X1,X3) != c_HOL_Ozero__class_Ozero(X3)
    | ~ class_Divides_Osemiring__div(X3) ),
    c_0_2942,
    [final] ).

cnf(c_0_3740,plain,
    ( c_Divides_Odiv__class_Omod(X2,X1,X3) = c_HOL_Ozero__class_Ozero(X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
    | ~ class_Divides_Osemiring__div(X3) ),
    c_0_2943,
    [final] ).

cnf(c_0_3741,plain,
    ( c_lessequals(X1,X2,tc_nat)
    | X1 = c_Suc(X2)
    | ~ c_lessequals(X1,c_Suc(X2),tc_nat) ),
    c_0_2944,
    [final] ).

cnf(c_0_3742,plain,
    ( X1 = X2
    | c_HOL_Oord__class_Oless(X1,X2,X3)
    | ~ c_lessequals(X1,X2,X3)
    | ~ class_Orderings_Oorder(X3) ),
    c_0_2945,
    [final] ).

cnf(c_0_3743,plain,
    ( c_HOL_Oord__class_Oless(X1,X2,X3)
    | X1 = X2
    | ~ c_lessequals(X1,X2,X3)
    | ~ class_Orderings_Oorder(X3) ),
    c_0_2946,
    [final] ).

cnf(c_0_3744,plain,
    ( X1 = X2
    | c_HOL_Oord__class_Oless(X1,X2,X3)
    | ~ c_lessequals(X1,X2,X3)
    | ~ class_Orderings_Oorder(X3) ),
    c_0_2947,
    [final] ).

cnf(c_0_3745,plain,
    ( X1 = X2
    | c_HOL_Oord__class_Oless(X1,X2,X3)
    | ~ c_lessequals(X1,X2,X3)
    | ~ class_Orderings_Oorder(X3) ),
    c_0_2948,
    [final] ).

cnf(c_0_3746,plain,
    ( c_HOL_Oord__class_Oless(X1,X2,X3)
    | X1 = X2
    | ~ c_lessequals(X1,X2,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    c_0_2949,
    [final] ).

cnf(c_0_3747,plain,
    ( c_HOL_Oord__class_Oless(X1,X2,X3)
    | X1 = X2
    | ~ c_lessequals(X1,X2,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    c_0_2950,
    [final] ).

cnf(c_0_3748,plain,
    ( X1 = X2
    | c_HOL_Oord__class_Oless(X2,X1,X3)
    | ~ c_lessequals(X2,X1,X3)
    | ~ class_Orderings_Oorder(X3) ),
    c_0_2951,
    [final] ).

cnf(c_0_3749,plain,
    ( X2 = X1
    | c_HOL_Oord__class_Oless(X1,X2,X3)
    | ~ c_lessequals(X1,X2,X3)
    | ~ class_Orderings_Oorder(X3) ),
    c_0_2952,
    [final] ).

cnf(c_0_3750,plain,
    ( c_lessequals(X1,X2,X3)
    | c_Orderings_Oord__class_Omin(X1,X2,X3) != X1
    | ~ class_Orderings_Olinorder(X3) ),
    c_0_2953,
    [final] ).

cnf(c_0_3751,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_2954,
    [final] ).

cnf(c_0_3752,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_2955,
    [final] ).

cnf(c_0_3753,plain,
    ( c_lessequals(c_Suc(X1),c_Suc(X2),tc_nat)
    | ~ c_lessequals(X1,X2,tc_nat) ),
    c_0_2956,
    [final] ).

cnf(c_0_3754,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_2957,
    [final] ).

cnf(c_0_3755,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_2958,
    [final] ).

cnf(c_0_3756,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_2959,
    [final] ).

cnf(c_0_3757,plain,
    ( c_Orderings_Oord__class_Omin(X2,X1,X3) = X1
    | ~ c_lessequals(X1,X2,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    c_0_2960,
    [final] ).

cnf(c_0_3758,plain,
    ( c_Orderings_Oord__class_Omin(X1,X2,X3) = X1
    | ~ c_lessequals(X1,X2,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    c_0_2961,
    [final] ).

cnf(c_0_3759,plain,
    ( X1 = c_HOL_Ozero__class_Ozero(X2)
    | ~ c_lessequals(c_HOL_Oabs__class_Oabs(X1,X2),c_HOL_Ozero__class_Ozero(X2),X2)
    | ~ class_OrderedGroup_Opordered__ab__group__add__abs(X2) ),
    c_0_2962,
    [final] ).

cnf(c_0_3760,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_2963,
    [final] ).

cnf(c_0_3761,plain,
    ( c_lessequals(X1,X2,X3)
    | ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | ~ class_Orderings_Oorder(X3) ),
    c_0_2964,
    [final] ).

cnf(c_0_3762,plain,
    ( c_lessequals(X1,X2,X3)
    | ~ c_HOL_Oord__class_Oless(X1,X2,X3)
    | ~ class_Orderings_Opreorder(X3) ),
    c_0_2965,
    [final] ).

cnf(c_0_3763,plain,
    ( c_Parity_Oeven__odd__class_Oeven(X1,tc_nat)
    | c_Divides_Odiv__class_Omod(X1,c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) ),
    c_0_2966,
    [final] ).

cnf(c_0_3764,plain,
    ( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_Suc(X1),X2,tc_nat) ),
    c_0_2967,
    [final] ).

cnf(c_0_3765,plain,
    ( c_lessequals(X1,X2,tc_nat)
    | ~ c_lessequals(c_Suc(X1),X2,tc_nat) ),
    c_0_2968,
    [final] ).

cnf(c_0_3766,plain,
    ( c_lessequals(X1,X2,tc_nat)
    | ~ c_HOL_Oord__class_Oless(X1,c_Suc(X2),tc_nat) ),
    c_0_2969,
    [final] ).

cnf(c_0_3767,plain,
    ( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | ~ c_lessequals(c_Suc(X1),X2,tc_nat) ),
    c_0_2970,
    [final] ).

cnf(c_0_3768,plain,
    ( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | ~ c_lessequals(c_Suc(X1),X2,tc_nat) ),
    c_0_2971,
    [final] ).

cnf(c_0_3769,plain,
    ( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
    | X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
    | ~ c_HOL_Oord__class_Oless(X1,c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),tc_nat) ),
    c_0_2972,
    [final] ).

cnf(c_0_3770,plain,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(X1,X2),c_HOL_Ozero__class_Ozero(X2),X2)
    | ~ class_OrderedGroup_Opordered__ab__group__add__abs(X2) ),
    c_0_2973,
    [final] ).

cnf(c_0_3771,plain,
    ( ~ c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X1,X2),c_HOL_Ozero__class_Ozero(X2),X2)
    | ~ class_Ring__and__Field_Oordered__semidom(X2) ),
    c_0_2974,
    [final] ).

cnf(c_0_3772,plain,
    ( c_HOL_Oord__class_Oless(X1,c_Suc(X2),tc_nat)
    | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
    c_0_2975,
    [final] ).

cnf(c_0_3773,plain,
    ( c_lessequals(X1,c_Suc(X2),tc_nat)
    | ~ c_lessequals(X1,X2,tc_nat) ),
    c_0_2976,
    [final] ).

cnf(c_0_3774,plain,
    ( c_HOL_Oord__class_Oless(X1,c_Suc(X1),tc_nat)
    | ~ c_lessequals(X1,X1,tc_nat) ),
    c_0_2977,
    [final] ).

cnf(c_0_3775,plain,
    ( c_HOL_Oord__class_Oless(X1,c_Suc(X2),tc_nat)
    | ~ c_lessequals(X1,X2,tc_nat) ),
    c_0_2978,
    [final] ).

cnf(c_0_3776,plain,
    ( c_lessequals(c_Suc(X1),X2,tc_nat)
    | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
    c_0_2979,
    [final] ).

cnf(c_0_3777,plain,
    ( c_lessequals(c_Suc(X1),X2,tc_nat)
    | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
    c_0_2980,
    [final] ).

cnf(c_0_3778,plain,
    ( c_Parity_Oeven__odd__class_Oeven(X1,tc_nat)
    | c_Parity_Oeven__odd__class_Oeven(X2,tc_nat)
    | c_Parity_Oeven__odd__class_Oeven(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),tc_nat) ),
    c_0_2981,
    [final] ).

cnf(c_0_3779,plain,
    ( c_Parity_Oeven__odd__class_Oeven(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat)
    | c_Parity_Oeven__odd__class_Oeven(X2,tc_nat)
    | c_Parity_Oeven__odd__class_Oeven(X1,tc_nat) ),
    c_0_2982,
    [final] ).

cnf(c_0_3780,plain,
    ( c_Parity_Oeven__odd__class_Oeven(X1,tc_nat)
    | c_Parity_Oeven__odd__class_Oeven(X2,tc_nat)
    | c_Parity_Oeven__odd__class_Oeven(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat) ),
    c_0_2983,
    [final] ).

cnf(c_0_3781,plain,
    ( c_Parity_Oeven__odd__class_Oeven(X1,tc_nat)
    | c_Parity_Oeven__odd__class_Oeven(X2,tc_nat)
    | c_Parity_Oeven__odd__class_Oeven(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat) ),
    c_0_2984,
    [final] ).

cnf(c_0_3782,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_2985,
    [final] ).

cnf(c_0_3783,plain,
    ( X1 = X2
    | c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | ~ c_lessequals(X1,X2,tc_nat) ),
    c_0_2986,
    [final] ).

cnf(c_0_3784,plain,
    ( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | X1 = X2
    | ~ c_lessequals(X1,X2,tc_nat) ),
    c_0_2987,
    [final] ).

cnf(c_0_3785,plain,
    ( X1 = X2
    | c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | ~ c_lessequals(X1,X2,tc_nat) ),
    c_0_2988,
    [final] ).

cnf(c_0_3786,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_2989,
    [final] ).

cnf(c_0_3787,plain,
    ( c_Divides_Odiv__class_Omod(X1,X2,tc_nat) = X1
    | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
    c_0_2990,
    [final] ).

cnf(c_0_3788,plain,
    ( c_lessequals(X1,X2,tc_nat)
    | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
    c_0_2991,
    [final] ).

cnf(c_0_3789,plain,
    ( c_lessequals(X1,X2,tc_nat)
    | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
    c_0_2992,
    [final] ).

cnf(c_0_3790,plain,
    ( c_Parity_Oeven__odd__class_Oeven(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),tc_nat)
    | ~ c_Parity_Oeven__odd__class_Oeven(X1,tc_nat) ),
    c_0_2993,
    [final] ).

cnf(c_0_3791,plain,
    ( c_Parity_Oeven__odd__class_Oeven(c_HOL_Otimes__class_Otimes(X2,X1,tc_nat),tc_nat)
    | ~ c_Parity_Oeven__odd__class_Oeven(X1,tc_nat) ),
    c_0_2994,
    [final] ).

cnf(c_0_3792,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_2995,
    [final] ).

cnf(c_0_3793,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_2996,
    [final] ).

cnf(c_0_3794,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_2997,
    [final] ).

cnf(c_0_3795,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_2998,
    [final] ).

cnf(c_0_3796,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_2999,
    [final] ).

cnf(c_0_3797,plain,
    ( c_HOL_Oabs__class_Oabs(X2,X1) = X2
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | ~ class_OrderedGroup_Opordered__ab__group__add__abs(X1) ),
    c_0_3000,
    [final] ).

cnf(c_0_3798,plain,
    ( c_HOL_Oabs__class_Oabs(X2,X1) = X2
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | ~ class_OrderedGroup_Opordered__ab__group__add__abs(X1) ),
    c_0_3001,
    [final] ).

cnf(c_0_3799,plain,
    c_HOL_Ominus__class_Ominus(c_Suc(X1),c_Suc(X2),tc_nat) = c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),
    c_0_3002,
    [final] ).

cnf(c_0_3800,plain,
    c_HOL_Oplus__class_Oplus(c_Suc(X1),X2,tc_nat) = c_HOL_Oplus__class_Oplus(X1,c_Suc(X2),tc_nat),
    c_0_3003,
    [final] ).

cnf(c_0_3801,plain,
    ( c_lessequals(X1,X2,X3)
    | c_lessequals(X2,X1,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    c_0_3004,
    [final] ).

cnf(c_0_3802,plain,
    ( c_lessequals(X1,X2,X3)
    | c_HOL_Oord__class_Oless(X2,X1,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    c_0_3005,
    [final] ).

cnf(c_0_3803,plain,
    ( c_HOL_Oord__class_Oless(X1,X2,X3)
    | c_lessequals(X2,X1,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    c_0_3006,
    [final] ).

cnf(c_0_3804,plain,
    ( c_lessequals(X1,X1,X2)
    | c_HOL_Oord__class_Oless(X1,X1,X2)
    | ~ class_Orderings_Olinorder(X2) ),
    c_0_3007,
    [final] ).

cnf(c_0_3805,plain,
    ( c_lessequals(X1,X2,X3)
    | c_HOL_Oord__class_Oless(X2,X1,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    c_0_3008,
    [final] ).

cnf(c_0_3806,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_3009,
    [final] ).

cnf(c_0_3807,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_3010,
    [final] ).

cnf(c_0_3808,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_3011,
    [final] ).

cnf(c_0_3809,plain,
    ( c_Orderings_Oord__class_Omin(X1,X2,X3) = c_Orderings_Oord__class_Omin(X2,X1,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    c_0_3012,
    [final] ).

cnf(c_0_3810,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_3013,
    [final] ).

cnf(c_0_3811,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_3014,
    [final] ).

cnf(c_0_3812,plain,
    ( c_HOL_Oord__class_Oless(X1,c_Suc(X1),tc_nat)
    | c_HOL_Oord__class_Oless(X1,X1,tc_nat) ),
    c_0_3015,
    [final] ).

cnf(c_0_3813,plain,
    ( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | c_HOL_Oord__class_Oless(X2,c_Suc(X1),tc_nat) ),
    c_0_3016,
    [final] ).

cnf(c_0_3814,plain,
    ( c_lessequals(X1,X2,tc_nat)
    | c_lessequals(c_Suc(X2),X1,tc_nat) ),
    c_0_3017,
    [final] ).

cnf(c_0_3815,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),
    c_0_3018,
    [final] ).

cnf(c_0_3816,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),
    c_0_3019,
    [final] ).

cnf(c_0_3817,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_3020,
    [final] ).

cnf(c_0_3818,plain,
    ( X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) ),
    c_0_3021,
    [final] ).

cnf(c_0_3819,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_3022,
    [final] ).

cnf(c_0_3820,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_3023,
    [final] ).

cnf(c_0_3821,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_3024,
    [final] ).

cnf(c_0_3822,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_3025,
    [final] ).

cnf(c_0_3823,plain,
    ( X1 = X2
    | c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | c_HOL_Oord__class_Oless(X2,X1,tc_nat) ),
    c_0_3026,
    [final] ).

cnf(c_0_3824,plain,
    ( X1 = X2
    | c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | c_HOL_Oord__class_Oless(X2,X1,tc_nat) ),
    c_0_3027,
    [final] ).

cnf(c_0_3825,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_3028,
    [final] ).

cnf(c_0_3826,plain,
    ( X2 = c_HOL_Ozero__class_Ozero(X1)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    c_0_3029,
    [final] ).

cnf(c_0_3827,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_3030,
    [final] ).

cnf(c_0_3828,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_3031,
    [final] ).

cnf(c_0_3829,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_3032,
    [final] ).

cnf(c_0_3830,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_3033,
    [final] ).

cnf(c_0_3831,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_3034,
    [final] ).

cnf(c_0_3832,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_3035,
    [final] ).

cnf(c_0_3833,plain,
    ( c_lessequals(X1,X2,tc_nat)
    | c_lessequals(X2,X1,tc_nat) ),
    c_0_3036,
    [final] ).

cnf(c_0_3834,plain,
    ( c_Divides_Odiv__class_Omod(X1,c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat)
    | ~ c_Parity_Oeven__odd__class_Oeven(X1,tc_nat) ),
    c_0_3037,
    [final] ).

cnf(c_0_3835,plain,
    ( c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
    | c_HOL_Oabs__class_Oabs(X1,X3) != c_HOL_Oabs__class_Oabs(X2,X3)
    | ~ class_Ring__and__Field_Oordered__idom(X3) ),
    c_0_3038,
    [final] ).

cnf(c_0_3836,plain,
    ( c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Ozero__class_Ozero(X1),X1),c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ class_OrderedGroup_Opordered__ab__group__add__abs(X1) ),
    c_0_3039,
    [final] ).

cnf(c_0_3837,plain,
    c_HOL_Oplus__class_Oplus(X1,X2,tc_nat) = c_HOL_Oplus__class_Oplus(X2,X1,tc_nat),
    c_0_3040,
    [final] ).

cnf(c_0_3838,plain,
    c_HOL_Otimes__class_Otimes(X1,X2,tc_nat) = c_HOL_Otimes__class_Otimes(X2,X1,tc_nat),
    c_0_3041,
    [final] ).

cnf(c_0_3839,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_3042,
    [final] ).

cnf(c_0_3840,plain,
    ( c_Parity_Oeven__odd__class_Oeven(X1,tc_nat)
    | c_Divides_Odiv__class_Omod(X1,c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),tc_nat) = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
    c_0_3043,
    [final] ).

cnf(c_0_3841,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_3044,
    [final] ).

cnf(c_0_3842,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_3045,
    [final] ).

cnf(c_0_3843,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_3046,
    [final] ).

cnf(c_0_3844,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_3047,
    [final] ).

cnf(c_0_3845,plain,
    ( X1 = X2
    | c_HOL_Ominus__class_Ominus(X1,X2,X3) != c_HOL_Ozero__class_Ozero(X3)
    | ~ class_OrderedGroup_Ogroup__add(X3) ),
    c_0_3048,
    [final] ).

cnf(c_0_3846,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_3049,
    [final] ).

cnf(c_0_3847,plain,
    ( X1 = c_HOL_Ozero__class_Ozero(X2)
    | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),c_HOL_Oabs__class_Oabs(X1,X2),X2)
    | ~ class_OrderedGroup_Opordered__ab__group__add__abs(X2) ),
    c_0_3050,
    [final] ).

cnf(c_0_3848,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_3051,
    [final] ).

cnf(c_0_3849,plain,
    ( c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oabs__class_Oabs(X2,X1),X1)
    | ~ class_OrderedGroup_Opordered__ab__group__add__abs(X1) ),
    c_0_3052,
    [final] ).

cnf(c_0_3850,plain,
    ( c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_Nat_Osemiring__1__class_Oof__nat(X2,X1),X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    c_0_3053,
    [final] ).

cnf(c_0_3851,plain,
    ( c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_Nat_Osemiring__1__class_Oof__nat(X2,X1),X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    c_0_3054,
    [final] ).

cnf(c_0_3852,plain,
    ( ~ c_HOL_Oord__class_Oless(X1,X1,X2)
    | ~ class_Orderings_Oorder(X2) ),
    c_0_3055,
    [final] ).

cnf(c_0_3853,plain,
    ( ~ c_HOL_Oord__class_Oless(X1,X1,X2)
    | ~ class_Orderings_Olinorder(X2) ),
    c_0_3056,
    [final] ).

cnf(c_0_3854,plain,
    ( ~ c_HOL_Oord__class_Oless(X1,X1,X2)
    | ~ class_Orderings_Opreorder(X2) ),
    c_0_3057,
    [final] ).

cnf(c_0_3855,plain,
    ~ c_lessequals(c_Suc(X1),X1,tc_nat),
    c_0_3058,
    [final] ).

cnf(c_0_3856,plain,
    ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
    c_0_3059,
    [final] ).

cnf(c_0_3857,plain,
    ( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
    | ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ),
    c_0_3060,
    [final] ).

cnf(c_0_3858,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_3061,
    [final] ).

cnf(c_0_3859,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_3062,
    [final] ).

cnf(c_0_3860,plain,
    ( c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
    | c_HOL_Oabs__class_Oabs(X1,X2) = X1
    | ~ class_OrderedGroup_Olordered__ab__group__add__abs(X2)
    | ~ class_Orderings_Olinorder(X2) ),
    c_0_3063,
    [final] ).

cnf(c_0_3861,plain,
    ( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
    | c_HOL_Oplus__class_Oplus(X2,X1,tc_nat) != X2 ),
    c_0_3064,
    [final] ).

cnf(c_0_3862,plain,
    ( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
    | c_HOL_Oplus__class_Oplus(X2,X1,tc_nat) != X2 ),
    c_0_3065,
    [final] ).

cnf(c_0_3863,plain,
    ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
    c_0_3066,
    [final] ).

cnf(c_0_3864,plain,
    ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
    c_0_3067,
    [final] ).

cnf(c_0_3865,plain,
    ( c_lessequals(X1,c_HOL_Oabs__class_Oabs(X1,X2),X2)
    | ~ class_OrderedGroup_Opordered__ab__group__add__abs(X2) ),
    c_0_3068,
    [final] ).

cnf(c_0_3866,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)),
    c_0_3069,
    [final] ).

cnf(c_0_3867,plain,
    ~ c_HOL_Oord__class_Oless(X1,X1,tc_nat),
    c_0_3070,
    [final] ).

cnf(c_0_3868,plain,
    ~ c_HOL_Oord__class_Oless(X1,X1,tc_nat),
    c_0_3071,
    [final] ).

cnf(c_0_3869,plain,
    ( c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
    | c_HOL_Oabs__class_Oabs(X1,X2) = X1
    | ~ class_Ring__and__Field_Oabs__if(X2) ),
    c_0_3072,
    [final] ).

cnf(c_0_3870,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_3073,
    [final] ).

cnf(c_0_3871,plain,
    c_Ring__and__Field_Odvd__class_Odvd(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),
    c_0_3074,
    [final] ).

cnf(c_0_3872,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_3075,
    [final] ).

cnf(c_0_3873,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)),
    c_0_3076,
    [final] ).

cnf(c_0_3874,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)),
    c_0_3077,
    [final] ).

cnf(c_0_3875,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)),
    c_0_3078,
    [final] ).

cnf(c_0_3876,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)),
    c_0_3079,
    [final] ).

cnf(c_0_3877,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_3080,
    [final] ).

cnf(c_0_3878,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_3081,
    [final] ).

cnf(c_0_3879,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_3082,
    [final] ).

cnf(c_0_3880,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_3083,
    [final] ).

cnf(c_0_3881,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_3084,
    [final] ).

cnf(c_0_3882,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_3085,
    [final] ).

cnf(c_0_3883,plain,
    ( c_HOL_Otimes__class_Otimes(X1,c_HOL_Ozero__class_Ozero(X2),X2) = c_HOL_Ozero__class_Ozero(X2)
    | ~ class_RealVector_Oreal__normed__algebra(X2) ),
    c_0_3086,
    [final] ).

cnf(c_0_3884,plain,
    ( c_HOL_Otimes__class_Otimes(X1,c_HOL_Ozero__class_Ozero(X2),X2) = c_HOL_Ozero__class_Ozero(X2)
    | ~ class_RealVector_Oreal__normed__algebra(X2) ),
    c_0_3087,
    [final] ).

cnf(c_0_3885,plain,
    ( c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),X2,X1) = c_HOL_Ozero__class_Ozero(X1)
    | ~ class_RealVector_Oreal__normed__algebra(X1) ),
    c_0_3088,
    [final] ).

cnf(c_0_3886,plain,
    ( c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),X2,X1) = c_HOL_Ozero__class_Ozero(X1)
    | ~ class_RealVector_Oreal__normed__algebra(X1) ),
    c_0_3089,
    [final] ).

cnf(c_0_3887,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_3090,
    [final] ).

cnf(c_0_3888,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_3091,
    [final] ).

cnf(c_0_3889,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_3092,
    [final] ).

cnf(c_0_3890,plain,
    ( c_Parity_Oeven__odd__class_Oeven(X1,tc_nat)
    | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
    c_0_3093,
    [final] ).

cnf(c_0_3891,plain,
    ( c_HOL_Ominus__class_Ominus(X1,c_HOL_Ozero__class_Ozero(X2),X2) = X1
    | ~ class_OrderedGroup_Ogroup__add(X2) ),
    c_0_3094,
    [final] ).

cnf(c_0_3892,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_3095,
    [final] ).

cnf(c_0_3893,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_3096,
    [final] ).

cnf(c_0_3894,plain,
    ( c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X1),X2,X1) = X2
    | ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
    c_0_3097,
    [final] ).

cnf(c_0_3895,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_3098,
    [final] ).

cnf(c_0_3896,plain,
    ( c_HOL_Oplus__class_Oplus(X1,c_HOL_Ozero__class_Ozero(X2),X2) = X1
    | ~ class_OrderedGroup_Ocomm__monoid__add(X2) ),
    c_0_3099,
    [final] ).

cnf(c_0_3897,plain,
    ( c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X1),X2,X1) = X2
    | ~ class_OrderedGroup_Omonoid__add(X1) ),
    c_0_3100,
    [final] ).

cnf(c_0_3898,plain,
    ( c_HOL_Oplus__class_Oplus(X1,c_HOL_Ozero__class_Ozero(X2),X2) = X1
    | ~ class_OrderedGroup_Omonoid__add(X2) ),
    c_0_3101,
    [final] ).

cnf(c_0_3899,plain,
    ( c_Divides_Odiv__class_Omod(X1,c_HOL_Ozero__class_Ozero(X2),X2) = X1
    | ~ class_Divides_Osemiring__div(X2) ),
    c_0_3102,
    [final] ).

cnf(c_0_3900,plain,
    c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),
    c_0_3103,
    [final] ).

cnf(c_0_3901,plain,
    ( c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Ozero__class_Ozero(X2),X2)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X2) ),
    c_0_3104,
    [final] ).

cnf(c_0_3902,plain,
    c_Divides_Odiv__class_Omod(X1,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
    c_0_3105,
    [final] ).

cnf(c_0_3903,plain,
    ( c_HOL_Ominus__class_Ominus(X1,X1,X2) = c_HOL_Ozero__class_Ozero(X2)
    | ~ class_OrderedGroup_Ogroup__add(X2) ),
    c_0_3106,
    [final] ).

cnf(c_0_3904,plain,
    ( c_HOL_Ominus__class_Ominus(X1,X1,X2) = c_HOL_Ozero__class_Ozero(X2)
    | ~ class_OrderedGroup_Ogroup__add(X2) ),
    c_0_3107,
    [final] ).

cnf(c_0_3905,plain,
    ( c_HOL_Ominus__class_Ominus(X1,X1,X2) = c_HOL_Ozero__class_Ozero(X2)
    | ~ class_OrderedGroup_Oab__group__add(X2) ),
    c_0_3108,
    [final] ).

cnf(c_0_3906,plain,
    ( c_Divides_Odiv__class_Omod(X1,X1,X2) = c_HOL_Ozero__class_Ozero(X2)
    | ~ class_Divides_Osemiring__div(X2) ),
    c_0_3109,
    [final] ).

cnf(c_0_3907,plain,
    c_lessequals(c_Suc(X1),c_Suc(X1),tc_nat),
    c_0_3110,
    [final] ).

cnf(c_0_3908,plain,
    c_Ring__and__Field_Odvd__class_Odvd(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X1,tc_nat),
    c_0_3111,
    [final] ).

cnf(c_0_3909,plain,
    ( c_HOL_Otimes__class_Otimes(X1,X1,X2) = X1
    | ~ class_OrderedGroup_Oab__semigroup__idem__mult(X2) ),
    c_0_3112,
    [final] ).

cnf(c_0_3910,plain,
    ( c_Orderings_Oord__class_Omin(X1,X1,X2) = X1
    | ~ class_Orderings_Olinorder(X2) ),
    c_0_3113,
    [final] ).

cnf(c_0_3911,plain,
    c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(X1),tc_nat),
    c_0_3114,
    [final] ).

cnf(c_0_3912,plain,
    c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(X1),tc_nat),
    c_0_3115,
    [final] ).

cnf(c_0_3913,plain,
    ( c_lessequals(X1,X1,X2)
    | ~ class_Orderings_Oorder(X2) ),
    c_0_3116,
    [final] ).

cnf(c_0_3914,plain,
    ( c_lessequals(X1,X1,X2)
    | ~ class_Orderings_Opreorder(X2) ),
    c_0_3117,
    [final] ).

cnf(c_0_3915,plain,
    ( c_Ring__and__Field_Odvd__class_Odvd(X1,X1,X2)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X2) ),
    c_0_3118,
    [final] ).

cnf(c_0_3916,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),
    c_0_3119,
    [final] ).

cnf(c_0_3917,plain,
    ( c_HOL_Oabs__class_Oabs(c_HOL_Oabs__class_Oabs(X1,X2),X2) = c_HOL_Oabs__class_Oabs(X1,X2)
    | ~ class_OrderedGroup_Opordered__ab__group__add__abs(X2) ),
    c_0_3120,
    [final] ).

cnf(c_0_3918,plain,
    ( c_HOL_Oabs__class_Oabs(c_Nat_Osemiring__1__class_Oof__nat(X1,X2),X2) = c_Nat_Osemiring__1__class_Oof__nat(X1,X2)
    | ~ class_Ring__and__Field_Oordered__idom(X2) ),
    c_0_3121,
    [final] ).

cnf(c_0_3919,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_3122,
    [final] ).

cnf(c_0_3920,plain,
    c_HOL_Oord__class_Oless(X1,c_Suc(X1),tc_nat),
    c_0_3123,
    [final] ).

cnf(c_0_3921,plain,
    c_HOL_Oord__class_Oless(X1,c_Suc(X1),tc_nat),
    c_0_3124,
    [final] ).

cnf(c_0_3922,plain,
    c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
    c_0_3125,
    [final] ).

cnf(c_0_3923,plain,
    c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
    c_0_3126,
    [final] ).

cnf(c_0_3924,plain,
    c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
    c_0_3127,
    [final] ).

cnf(c_0_3925,plain,
    c_HOL_Otimes__class_Otimes(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
    c_0_3128,
    [final] ).

cnf(c_0_3926,plain,
    c_Orderings_Oord__class_Omin(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
    c_0_3129,
    [final] ).

cnf(c_0_3927,plain,
    c_Orderings_Oord__class_Omin(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
    c_0_3130,
    [final] ).

cnf(c_0_3928,plain,
    c_HOL_Ominus__class_Ominus(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = X1,
    c_0_3131,
    [final] ).

cnf(c_0_3929,plain,
    c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) = X1,
    c_0_3132,
    [final] ).

cnf(c_0_3930,plain,
    c_HOL_Oplus__class_Oplus(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = X1,
    c_0_3133,
    [final] ).

cnf(c_0_3931,plain,
    c_HOL_Oplus__class_Oplus(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = X1,
    c_0_3134,
    [final] ).

cnf(c_0_3932,plain,
    c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
    c_0_3135,
    [final] ).

cnf(c_0_3933,plain,
    c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat),
    c_0_3136,
    [final] ).

cnf(c_0_3934,plain,
    c_HOL_Ominus__class_Ominus(X1,X1,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
    c_0_3137,
    [final] ).

cnf(c_0_3935,plain,
    ( X1 = X2
    | c_Nat_Osemiring__1__class_Oof__nat(X1,X3) != c_Nat_Osemiring__1__class_Oof__nat(X2,X3)
    | ~ class_Nat_Osemiring__char__0(X3) ),
    c_0_3138,
    [final] ).

cnf(c_0_3936,plain,
    c_lessequals(X1,X1,tc_nat),
    c_0_3139,
    [final] ).

cnf(c_0_3937,plain,
    c_lessequals(X1,X1,tc_nat),
    c_0_3140,
    [final] ).

cnf(c_0_3938,plain,
    c_Ring__and__Field_Odvd__class_Odvd(X1,X1,tc_nat),
    c_0_3141,
    [final] ).

cnf(c_0_3939,plain,
    c_HOL_Oord__class_Oless(v_i,v_n,tc_nat),
    c_0_3142,
    [final] ).

cnf(c_0_3940,plain,
    c_HOL_Oord__class_Oless(v_i,v_n,tc_nat),
    c_0_3143,
    [final] ).

cnf(c_0_3941,plain,
    ( ~ c_Parity_Oeven__odd__class_Oeven(c_Suc(X1),tc_nat)
    | ~ c_Parity_Oeven__odd__class_Oeven(X1,tc_nat) ),
    c_0_3144,
    [final] ).

cnf(c_0_3942,plain,
    ( X1 = c_HOL_Ozero__class_Ozero(X2)
    | c_HOL_Oabs__class_Oabs(X1,X2) != c_HOL_Ozero__class_Ozero(X2)
    | ~ class_OrderedGroup_Opordered__ab__group__add__abs(X2) ),
    c_0_3145,
    [final] ).

cnf(c_0_3943,plain,
    ( c_Parity_Oeven__odd__class_Oeven(X1,tc_nat)
    | c_Parity_Oeven__odd__class_Oeven(c_Suc(X1),tc_nat) ),
    c_0_3146,
    [final] ).

cnf(c_0_3944,plain,
    ( c_HOL_Oabs__class_Oabs(c_HOL_Ozero__class_Ozero(X1),X1) = c_HOL_Ozero__class_Ozero(X1)
    | ~ class_OrderedGroup_Opordered__ab__group__add__abs(X1) ),
    c_0_3147,
    [final] ).

cnf(c_0_3945,plain,
    ( c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Ozero__class_Ozero(tc_nat),X1) = c_HOL_Ozero__class_Ozero(X1)
    | ~ class_Ring__and__Field_Osemiring__1(X1) ),
    c_0_3148,
    [final] ).

cnf(c_0_3946,plain,
    c_Parity_Oeven__odd__class_Oeven(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
    c_0_3149,
    [final] ).

cnf(c_0_3947,plain,
    ( X1 = X2
    | c_Suc(X1) != c_Suc(X2) ),
    c_0_3150,
    [final] ).

cnf(c_0_3948,plain,
    ( X1 = X2
    | c_Suc(X1) != c_Suc(X2) ),
    c_0_3151,
    [final] ).

cnf(c_0_3949,plain,
    c_Suc(X1) != c_HOL_Ozero__class_Ozero(tc_nat),
    c_0_3152,
    [final] ).

cnf(c_0_3950,plain,
    c_Suc(X1) != c_HOL_Ozero__class_Ozero(tc_nat),
    c_0_3153,
    [final] ).

cnf(c_0_3951,plain,
    c_Suc(X1) != c_HOL_Ozero__class_Ozero(tc_nat),
    c_0_3154,
    [final] ).

cnf(c_0_3952,plain,
    c_Suc(X1) != c_HOL_Ozero__class_Ozero(tc_nat),
    c_0_3155,
    [final] ).

cnf(c_0_3953,plain,
    c_Suc(X1) != X1,
    c_0_3156,
    [final] ).

cnf(c_0_3954,plain,
    c_Suc(X1) != X1,
    c_0_3157,
    [final] ).

cnf(c_0_3955,plain,
    class_Orderings_Oorder(tc_nat),
    c_0_3158,
    [final] ).

cnf(c_0_3956,plain,
    class_Orderings_Olinorder(tc_nat),
    c_0_3159,
    [final] ).

cnf(c_0_3957,plain,
    class_Orderings_Opreorder(tc_nat),
    c_0_3160,
    [final] ).

cnf(c_0_3958,plain,
    class_Ring__and__Field_Odvd(tc_nat),
    c_0_3161,
    [final] ).

cnf(c_0_3959,plain,
    class_Nat_Osemiring__char__0(tc_nat),
    c_0_3162,
    [final] ).

cnf(c_0_3960,plain,
    class_Divides_Osemiring__div(tc_nat),
    c_0_3163,
    [final] ).

cnf(c_0_3961,plain,
    class_OrderedGroup_Omonoid__add(tc_nat),
    c_0_3164,
    [final] ).

cnf(c_0_3962,plain,
    class_Ring__and__Field_Osemiring(tc_nat),
    c_0_3165,
    [final] ).

cnf(c_0_3963,plain,
    class_Ring__and__Field_Omult__mono(tc_nat),
    c_0_3166,
    [final] ).

cnf(c_0_3964,plain,
    class_Ring__and__Field_Omult__zero(tc_nat),
    c_0_3167,
    [final] ).

cnf(c_0_3965,plain,
    class_Ring__and__Field_Omult__mono1(tc_nat),
    c_0_3168,
    [final] ).

cnf(c_0_3966,plain,
    class_Ring__and__Field_Osemiring__1(tc_nat),
    c_0_3169,
    [final] ).

cnf(c_0_3967,plain,
    class_OrderedGroup_Ocomm__monoid__add(tc_nat),
    c_0_3170,
    [final] ).

cnf(c_0_3968,plain,
    class_Ring__and__Field_Ocomm__semiring(tc_nat),
    c_0_3171,
    [final] ).

cnf(c_0_3969,plain,
    class_OrderedGroup_Oab__semigroup__add(tc_nat),
    c_0_3172,
    [final] ).

cnf(c_0_3970,plain,
    class_OrderedGroup_Oab__semigroup__mult(tc_nat),
    c_0_3173,
    [final] ).

cnf(c_0_3971,plain,
    class_Ring__and__Field_Ocomm__semiring__1(tc_nat),
    c_0_3174,
    [final] ).

cnf(c_0_3972,plain,
    class_Ring__and__Field_Oordered__semidom(tc_nat),
    c_0_3175,
    [final] ).

cnf(c_0_3973,plain,
    class_Ring__and__Field_Ono__zero__divisors(tc_nat),
    c_0_3176,
    [final] ).

cnf(c_0_3974,plain,
    class_Ring__and__Field_Oordered__semiring(tc_nat),
    c_0_3177,
    [final] ).

cnf(c_0_3975,plain,
    class_Ring__and__Field_Opordered__semiring(tc_nat),
    c_0_3178,
    [final] ).

cnf(c_0_3976,plain,
    class_OrderedGroup_Ocancel__semigroup__add(tc_nat),
    c_0_3179,
    [final] ).

cnf(c_0_3977,plain,
    class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat),
    c_0_3180,
    [final] ).

cnf(c_0_3978,plain,
    class_OrderedGroup_Opordered__comm__monoid__add(tc_nat),
    c_0_3181,
    [final] ).

cnf(c_0_3979,plain,
    class_OrderedGroup_Opordered__ab__semigroup__add(tc_nat),
    c_0_3182,
    [final] ).

cnf(c_0_3980,plain,
    class_Ring__and__Field_Oordered__semiring__strict(tc_nat),
    c_0_3183,
    [final] ).

cnf(c_0_3981,plain,
    class_Ring__and__Field_Opordered__cancel__semiring(tc_nat),
    c_0_3184,
    [final] ).

cnf(c_0_3982,plain,
    class_Ring__and__Field_Oordered__comm__semiring__strict(tc_nat),
    c_0_3185,
    [final] ).

cnf(c_0_3983,plain,
    class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat),
    c_0_3186,
    [final] ).

cnf(c_0_3984,plain,
    class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat),
    c_0_3187,
    [final] ).

% End CNF derivation
% Generating one_way clauses for all literals in the CNF.
cnf(c_0_3188_0,axiom,
    ( c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,X4,X3),c_HOL_Ominus__class_Ominus(X2,X5,X3),X3),c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,X4,X3),X5,X3),X3),c_HOL_Otimes__class_Otimes(X4,c_HOL_Ominus__class_Ominus(X2,X5,X3),X3),X3) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X4,X5,X3),X3)
    | ~ class_RealVector_Oreal__normed__algebra(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_3188]) ).

cnf(c_0_3188_1,axiom,
    ( ~ class_RealVector_Oreal__normed__algebra(X3)
    | c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,X4,X3),c_HOL_Ominus__class_Ominus(X2,X5,X3),X3),c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,X4,X3),X5,X3),X3),c_HOL_Otimes__class_Otimes(X4,c_HOL_Ominus__class_Ominus(X2,X5,X3),X3),X3) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X4,X5,X3),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_3188]) ).

cnf(c_0_3189_0,axiom,
    ( c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X1,X2,X3),c_HOL_Oplus__class_Oplus(X4,X5,X3),X3),X3),c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X1,X4,X3),X3),c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X2,X5,X3),X3),X3),X3)
    | ~ class_OrderedGroup_Opordered__ab__group__add__abs(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_3189]) ).

cnf(c_0_3189_1,axiom,
    ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X3)
    | c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X1,X2,X3),c_HOL_Oplus__class_Oplus(X4,X5,X3),X3),X3),c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X1,X4,X3),X3),c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X2,X5,X3),X3),X3),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_3189]) ).

cnf(c_0_3190_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_3190]) ).

cnf(c_0_3190_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_3190]) ).

cnf(c_0_3190_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_3190]) ).

cnf(c_0_3191_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_3191]) ).

cnf(c_0_3191_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_3191]) ).

cnf(c_0_3191_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_3191]) ).

cnf(c_0_3192_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_3192]) ).

cnf(c_0_3192_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_3192]) ).

cnf(c_0_3192_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_3192]) ).

cnf(c_0_3193_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_3193]) ).

cnf(c_0_3193_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_3193]) ).

cnf(c_0_3193_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_3193]) ).

cnf(c_0_3194_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_3194]) ).

cnf(c_0_3194_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_3194]) ).

cnf(c_0_3194_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_3194]) ).

cnf(c_0_3195_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_3195]) ).

cnf(c_0_3195_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_3195]) ).

cnf(c_0_3195_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_3195]) ).

cnf(c_0_3196_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_3196]) ).

cnf(c_0_3196_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_3196]) ).

cnf(c_0_3196_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_3196]) ).

cnf(c_0_3197_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_3197]) ).

cnf(c_0_3197_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_3197]) ).

cnf(c_0_3197_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_3197]) ).

cnf(c_0_3198_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_3198]) ).

cnf(c_0_3198_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_3198]) ).

cnf(c_0_3198_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_3198]) ).

cnf(c_0_3199_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_3199]) ).

cnf(c_0_3199_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_3199]) ).

cnf(c_0_3199_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_3199]) ).

cnf(c_0_3200_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_3200]) ).

cnf(c_0_3200_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_3200]) ).

cnf(c_0_3200_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_3200]) ).

cnf(c_0_3201_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_3201]) ).

cnf(c_0_3201_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_3201]) ).

cnf(c_0_3201_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_3201]) ).

cnf(c_0_3202_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_3202]) ).

cnf(c_0_3202_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_3202]) ).

cnf(c_0_3202_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_3202]) ).

cnf(c_0_3203_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_3203]) ).

cnf(c_0_3203_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_3203]) ).

cnf(c_0_3203_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_3203]) ).

cnf(c_0_3204_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_3204]) ).

cnf(c_0_3204_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_3204]) ).

cnf(c_0_3204_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_3204]) ).

cnf(c_0_3205_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_3205]) ).

cnf(c_0_3205_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_3205]) ).

cnf(c_0_3205_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_3205]) ).

cnf(c_0_3206_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_3206]) ).

cnf(c_0_3206_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_3206]) ).

cnf(c_0_3207_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_3207]) ).

cnf(c_0_3207_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_3207]) ).

cnf(c_0_3208_0,axiom,
    ( c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Oplus__class_Oplus(X4,X6,X3),X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X4,c_HOL_Otimes__class_Otimes(X5,X2,X3),X3),X6,X3),X3)
    | ~ class_Ring__and__Field_Ocomm__ring(X3)
    | ~ class_Ring__and__Field_Odvd(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_3208]) ).

cnf(c_0_3208_1,axiom,
    ( ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
    | c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Oplus__class_Oplus(X4,X6,X3),X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X4,c_HOL_Otimes__class_Otimes(X5,X2,X3),X3),X6,X3),X3)
    | ~ class_Ring__and__Field_Ocomm__ring(X3)
    | ~ class_Ring__and__Field_Odvd(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_3208]) ).

cnf(c_0_3208_2,axiom,
    ( ~ c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X4,c_HOL_Otimes__class_Otimes(X5,X2,X3),X3),X6,X3),X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
    | c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Oplus__class_Oplus(X4,X6,X3),X3)
    | ~ class_Ring__and__Field_Ocomm__ring(X3)
    | ~ class_Ring__and__Field_Odvd(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_3208]) ).

cnf(c_0_3208_3,axiom,
    ( ~ class_Ring__and__Field_Ocomm__ring(X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X4,c_HOL_Otimes__class_Otimes(X5,X2,X3),X3),X6,X3),X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
    | c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Oplus__class_Oplus(X4,X6,X3),X3)
    | ~ class_Ring__and__Field_Odvd(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_3208]) ).

cnf(c_0_3208_4,axiom,
    ( ~ class_Ring__and__Field_Odvd(X3)
    | ~ class_Ring__and__Field_Ocomm__ring(X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X4,c_HOL_Otimes__class_Otimes(X5,X2,X3),X3),X6,X3),X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
    | c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Oplus__class_Oplus(X4,X6,X3),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_3208]) ).

cnf(c_0_3209_0,axiom,
    ( c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X4,c_HOL_Otimes__class_Otimes(X6,X2,X3),X3),X5,X3),X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Oplus__class_Oplus(X4,X5,X3),X3)
    | ~ class_Ring__and__Field_Ocomm__ring(X3)
    | ~ class_Ring__and__Field_Odvd(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_3209]) ).

cnf(c_0_3209_1,axiom,
    ( ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
    | c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X4,c_HOL_Otimes__class_Otimes(X6,X2,X3),X3),X5,X3),X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Oplus__class_Oplus(X4,X5,X3),X3)
    | ~ class_Ring__and__Field_Ocomm__ring(X3)
    | ~ class_Ring__and__Field_Odvd(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_3209]) ).

cnf(c_0_3209_2,axiom,
    ( ~ c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Oplus__class_Oplus(X4,X5,X3),X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
    | c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X4,c_HOL_Otimes__class_Otimes(X6,X2,X3),X3),X5,X3),X3)
    | ~ class_Ring__and__Field_Ocomm__ring(X3)
    | ~ class_Ring__and__Field_Odvd(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_3209]) ).

cnf(c_0_3209_3,axiom,
    ( ~ class_Ring__and__Field_Ocomm__ring(X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Oplus__class_Oplus(X4,X5,X3),X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
    | c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X4,c_HOL_Otimes__class_Otimes(X6,X2,X3),X3),X5,X3),X3)
    | ~ class_Ring__and__Field_Odvd(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_3209]) ).

cnf(c_0_3209_4,axiom,
    ( ~ class_Ring__and__Field_Odvd(X3)
    | ~ class_Ring__and__Field_Ocomm__ring(X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Oplus__class_Oplus(X4,X5,X3),X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
    | c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X4,c_HOL_Otimes__class_Otimes(X6,X2,X3),X3),X5,X3),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_3209]) ).

cnf(c_0_3210_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_3210]) ).

cnf(c_0_3210_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_3210]) ).

cnf(c_0_3211_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_3211]) ).

cnf(c_0_3211_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_3211]) ).

cnf(c_0_3212_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_3212]) ).

cnf(c_0_3212_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_3212]) ).

cnf(c_0_3213_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_3213]) ).

cnf(c_0_3213_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_3213]) ).

cnf(c_0_3214_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_3214]) ).

cnf(c_0_3214_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_3214]) ).

cnf(c_0_3215_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_3215]) ).

cnf(c_0_3215_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_3215]) ).

cnf(c_0_3215_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_3215]) ).

cnf(c_0_3216_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_3216]) ).

cnf(c_0_3216_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_3216]) ).

cnf(c_0_3216_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_3216]) ).

cnf(c_0_3217_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_3217]) ).

cnf(c_0_3217_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_3217]) ).

cnf(c_0_3217_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_3217]) ).

cnf(c_0_3218_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_3218]) ).

cnf(c_0_3218_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_3218]) ).

cnf(c_0_3219_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_3219]) ).

cnf(c_0_3219_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_3219]) ).

cnf(c_0_3219_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_3219]) ).

cnf(c_0_3220_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_3220]) ).

cnf(c_0_3220_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_3220]) ).

cnf(c_0_3220_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_3220]) ).

cnf(c_0_3221_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_3221]) ).

cnf(c_0_3221_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_3221]) ).

cnf(c_0_3221_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_3221]) ).

cnf(c_0_3222_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_3222]) ).

cnf(c_0_3222_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_3222]) ).

cnf(c_0_3222_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_3222]) ).

cnf(c_0_3223_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_3223]) ).

cnf(c_0_3223_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_3223]) ).

cnf(c_0_3224_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_3224]) ).

cnf(c_0_3224_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_3224]) ).

cnf(c_0_3224_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_3224]) ).

cnf(c_0_3224_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_3224]) ).

cnf(c_0_3224_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_3224]) ).

cnf(c_0_3225_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_3225]) ).

cnf(c_0_3225_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_3225]) ).

cnf(c_0_3225_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_3225]) ).

cnf(c_0_3225_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_3225]) ).

cnf(c_0_3225_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_3225]) ).

cnf(c_0_3227_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_3227]) ).

cnf(c_0_3227_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_3227]) ).

cnf(c_0_3227_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_3227]) ).

cnf(c_0_3228_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_3228]) ).

cnf(c_0_3228_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_3228]) ).

cnf(c_0_3228_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_3228]) ).

cnf(c_0_3229_0,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X4,X1,X3),X3),X2,X3)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,X2,X3),X4,X3)
    | ~ c_HOL_Oord__class_Oless(X4,c_HOL_Oplus__class_Oplus(X1,X2,X3),X3)
    | ~ class_Ring__and__Field_Oordered__idom(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_3229]) ).

cnf(c_0_3229_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,X2,X3),X4,X3)
    | c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X4,X1,X3),X3),X2,X3)
    | ~ c_HOL_Oord__class_Oless(X4,c_HOL_Oplus__class_Oplus(X1,X2,X3),X3)
    | ~ class_Ring__and__Field_Oordered__idom(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_3229]) ).

cnf(c_0_3229_2,axiom,
    ( ~ c_HOL_Oord__class_Oless(X4,c_HOL_Oplus__class_Oplus(X1,X2,X3),X3)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,X2,X3),X4,X3)
    | c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X4,X1,X3),X3),X2,X3)
    | ~ class_Ring__and__Field_Oordered__idom(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_3229]) ).

cnf(c_0_3229_3,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(X3)
    | ~ c_HOL_Oord__class_Oless(X4,c_HOL_Oplus__class_Oplus(X1,X2,X3),X3)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,X2,X3),X4,X3)
    | c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X4,X1,X3),X3),X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_3229]) ).

cnf(c_0_3230_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_3230]) ).

cnf(c_0_3230_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_3230]) ).

cnf(c_0_3231_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_3231]) ).

cnf(c_0_3231_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_3231]) ).

cnf(c_0_3232_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_3232]) ).

cnf(c_0_3232_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_3232]) ).

cnf(c_0_3233_0,axiom,
    ( c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(c_HOL_Oabs__class_Oabs(X1,X2),c_HOL_Oabs__class_Oabs(X3,X2),X2),X2),c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X1,X3,X2),X2),X2)
    | ~ class_OrderedGroup_Opordered__ab__group__add__abs(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_3233]) ).

cnf(c_0_3233_1,axiom,
    ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X2)
    | c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(c_HOL_Oabs__class_Oabs(X1,X2),c_HOL_Oabs__class_Oabs(X3,X2),X2),X2),c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X1,X3,X2),X2),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_3233]) ).

cnf(c_0_3235_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_3235]) ).

cnf(c_0_3235_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_3235]) ).

cnf(c_0_3236_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_3236]) ).

cnf(c_0_3236_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_3236]) ).

cnf(c_0_3236_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_3236]) ).

cnf(c_0_3236_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_3236]) ).

cnf(c_0_3237_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_3237]) ).

cnf(c_0_3237_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_3237]) ).

cnf(c_0_3237_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_3237]) ).

cnf(c_0_3237_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_3237]) ).

cnf(c_0_3238_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_3238]) ).

cnf(c_0_3238_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_3238]) ).

cnf(c_0_3238_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_3238]) ).

cnf(c_0_3238_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_3238]) ).

cnf(c_0_3239_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_3239]) ).

cnf(c_0_3239_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_3239]) ).

cnf(c_0_3240_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_3240]) ).

cnf(c_0_3240_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_3240]) ).

cnf(c_0_3241_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_3241]) ).

cnf(c_0_3241_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_3241]) ).

cnf(c_0_3241_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_3241]) ).

cnf(c_0_3241_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_3241]) ).

cnf(c_0_3241_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_3241]) ).

cnf(c_0_3241_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_3241]) ).

cnf(c_0_3242_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_3242]) ).

cnf(c_0_3242_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_3242]) ).

cnf(c_0_3242_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_3242]) ).

cnf(c_0_3242_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_3242]) ).

cnf(c_0_3242_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_3242]) ).

cnf(c_0_3242_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_3242]) ).

cnf(c_0_3243_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_3243]) ).

cnf(c_0_3243_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_3243]) ).

cnf(c_0_3243_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_3243]) ).

cnf(c_0_3243_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_3243]) ).

cnf(c_0_3243_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_3243]) ).

cnf(c_0_3243_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_3243]) ).

cnf(c_0_3244_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_3244]) ).

cnf(c_0_3244_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_3244]) ).

cnf(c_0_3244_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_3244]) ).

cnf(c_0_3244_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_3244]) ).

cnf(c_0_3244_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_3244]) ).

cnf(c_0_3244_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_3244]) ).

cnf(c_0_3245_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_3245]) ).

cnf(c_0_3245_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_3245]) ).

cnf(c_0_3245_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_3245]) ).

cnf(c_0_3245_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_3245]) ).

cnf(c_0_3245_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_3245]) ).

cnf(c_0_3245_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_3245]) ).

cnf(c_0_3246_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_3246]) ).

cnf(c_0_3246_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_3246]) ).

cnf(c_0_3246_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_3246]) ).

cnf(c_0_3246_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_3246]) ).

cnf(c_0_3246_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_3246]) ).

cnf(c_0_3246_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_3246]) ).

cnf(c_0_3247_0,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(X1,X2),c_HOL_Oabs__class_Oabs(X4,X2),X2),c_HOL_Otimes__class_Otimes(X3,X5,X2),X2)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(X1,X2),X3,X2)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(X4,X2),X5,X2)
    | ~ class_Ring__and__Field_Oordered__idom(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_3247]) ).

cnf(c_0_3247_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(X1,X2),X3,X2)
    | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(X1,X2),c_HOL_Oabs__class_Oabs(X4,X2),X2),c_HOL_Otimes__class_Otimes(X3,X5,X2),X2)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(X4,X2),X5,X2)
    | ~ class_Ring__and__Field_Oordered__idom(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_3247]) ).

cnf(c_0_3247_2,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(X4,X2),X5,X2)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(X1,X2),X3,X2)
    | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(X1,X2),c_HOL_Oabs__class_Oabs(X4,X2),X2),c_HOL_Otimes__class_Otimes(X3,X5,X2),X2)
    | ~ class_Ring__and__Field_Oordered__idom(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_3247]) ).

cnf(c_0_3247_3,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(X2)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(X4,X2),X5,X2)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(X1,X2),X3,X2)
    | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(X1,X2),c_HOL_Oabs__class_Oabs(X4,X2),X2),c_HOL_Otimes__class_Otimes(X3,X5,X2),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_3247]) ).

cnf(c_0_3248_0,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X2,X4,X3),X1,X3)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X1,X2,X3),X3),X4,X3)
    | ~ class_Ring__and__Field_Oordered__idom(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_3248]) ).

cnf(c_0_3248_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X1,X2,X3),X3),X4,X3)
    | c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X2,X4,X3),X1,X3)
    | ~ class_Ring__and__Field_Oordered__idom(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_3248]) ).

cnf(c_0_3248_2,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(X3)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X1,X2,X3),X3),X4,X3)
    | c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X2,X4,X3),X1,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_3248]) ).

cnf(c_0_3249_0,axiom,
    ( c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(X2,X4,X3),X3)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X1,X2,X3),X3),X4,X3)
    | ~ class_Ring__and__Field_Oordered__idom(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_3249]) ).

cnf(c_0_3249_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X1,X2,X3),X3),X4,X3)
    | c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(X2,X4,X3),X3)
    | ~ class_Ring__and__Field_Oordered__idom(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_3249]) ).

cnf(c_0_3249_2,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(X3)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X1,X2,X3),X3),X4,X3)
    | c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(X2,X4,X3),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_3249]) ).

cnf(c_0_3250_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_3250]) ).

cnf(c_0_3250_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_3250]) ).

cnf(c_0_3250_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_3250]) ).

cnf(c_0_3250_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_3250]) ).

cnf(c_0_3251_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_3251]) ).

cnf(c_0_3251_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_3251]) ).

cnf(c_0_3251_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_3251]) ).

cnf(c_0_3251_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_3251]) ).

cnf(c_0_3252_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_3252]) ).

cnf(c_0_3252_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_3252]) ).

cnf(c_0_3252_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_3252]) ).

cnf(c_0_3253_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_3253]) ).

cnf(c_0_3253_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_3253]) ).

cnf(c_0_3253_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_3253]) ).

cnf(c_0_3254_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_3254]) ).

cnf(c_0_3254_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_3254]) ).

cnf(c_0_3255_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_3255]) ).

cnf(c_0_3255_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_3255]) ).

cnf(c_0_3256_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_3256]) ).

cnf(c_0_3256_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_3256]) ).

cnf(c_0_3256_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_3256]) ).

cnf(c_0_3256_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_3256]) ).

cnf(c_0_3257_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_3257]) ).

cnf(c_0_3257_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_3257]) ).

cnf(c_0_3257_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_3257]) ).

cnf(c_0_3257_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_3257]) ).

cnf(c_0_3258_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_3258]) ).

cnf(c_0_3258_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_3258]) ).

cnf(c_0_3258_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_3258]) ).

cnf(c_0_3258_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_3258]) ).

cnf(c_0_3259_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_3259]) ).

cnf(c_0_3259_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_3259]) ).

cnf(c_0_3259_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_3259]) ).

cnf(c_0_3259_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_3259]) ).

cnf(c_0_3260_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_3260]) ).

cnf(c_0_3260_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_3260]) ).

cnf(c_0_3260_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_3260]) ).

cnf(c_0_3260_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_3260]) ).

cnf(c_0_3261_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_3261]) ).

cnf(c_0_3261_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_3261]) ).

cnf(c_0_3261_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_3261]) ).

cnf(c_0_3261_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_3261]) ).

cnf(c_0_3262_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_3262]) ).

cnf(c_0_3262_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_3262]) ).

cnf(c_0_3262_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_3262]) ).

cnf(c_0_3262_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_3262]) ).

cnf(c_0_3263_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_3263]) ).

cnf(c_0_3263_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_3263]) ).

cnf(c_0_3263_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_3263]) ).

cnf(c_0_3263_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_3263]) ).

cnf(c_0_3264_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_3264]) ).

cnf(c_0_3264_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_3264]) ).

cnf(c_0_3264_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_3264]) ).

cnf(c_0_3264_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_3264]) ).

cnf(c_0_3265_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_3265]) ).

cnf(c_0_3265_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_3265]) ).

cnf(c_0_3265_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_3265]) ).

cnf(c_0_3265_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_3265]) ).

cnf(c_0_3266_0,axiom,
    ( c_Ring__and__Field_Odvd__class_Odvd(X2,X3,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_3266]) ).

cnf(c_0_3266_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
    | c_Ring__and__Field_Odvd__class_Odvd(X2,X3,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_3266]) ).

cnf(c_0_3266_2,axiom,
    ( ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
    | c_Ring__and__Field_Odvd__class_Odvd(X2,X3,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_3266]) ).

cnf(c_0_3267_0,axiom,
    ( c_Ring__and__Field_Odvd__class_Odvd(X2,X3,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_3267]) ).

cnf(c_0_3267_1,axiom,
    ( ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat)
    | c_Ring__and__Field_Odvd__class_Odvd(X2,X3,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_3267]) ).

cnf(c_0_3267_2,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat)
    | c_Ring__and__Field_Odvd__class_Odvd(X2,X3,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_3267]) ).

cnf(c_0_3268_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_3268]) ).

cnf(c_0_3268_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_3268]) ).

cnf(c_0_3268_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_3268]) ).

cnf(c_0_3269_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_3269]) ).

cnf(c_0_3269_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_3269]) ).

cnf(c_0_3269_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_3269]) ).

cnf(c_0_3270_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_3270]) ).

cnf(c_0_3270_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_3270]) ).

cnf(c_0_3270_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_3270]) ).

cnf(c_0_3271_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_3271]) ).

cnf(c_0_3271_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_3271]) ).

cnf(c_0_3271_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_3271]) ).

cnf(c_0_3272_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_3272]) ).

cnf(c_0_3272_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_3272]) ).

cnf(c_0_3272_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_3272]) ).

cnf(c_0_3272_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_3272]) ).

cnf(c_0_3273_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_3273]) ).

cnf(c_0_3273_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_3273]) ).

cnf(c_0_3273_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_3273]) ).

cnf(c_0_3273_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_3273]) ).

cnf(c_0_3274_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_3274]) ).

cnf(c_0_3274_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_3274]) ).

cnf(c_0_3274_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_3274]) ).

cnf(c_0_3275_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_3275]) ).

cnf(c_0_3275_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_3275]) ).

cnf(c_0_3275_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_3275]) ).

cnf(c_0_3277_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_3277]) ).

cnf(c_0_3277_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_3277]) ).

cnf(c_0_3277_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_3277]) ).

cnf(c_0_3277_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_3277]) ).

cnf(c_0_3278_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_3278]) ).

cnf(c_0_3278_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_3278]) ).

cnf(c_0_3278_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_3278]) ).

cnf(c_0_3278_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_3278]) ).

cnf(c_0_3279_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_3279]) ).

cnf(c_0_3279_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_3279]) ).

cnf(c_0_3279_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_3279]) ).

cnf(c_0_3279_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_3279]) ).

cnf(c_0_3280_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_3280]) ).

cnf(c_0_3280_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_3280]) ).

cnf(c_0_3280_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_3280]) ).

cnf(c_0_3280_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_3280]) ).

cnf(c_0_3281_0,axiom,
    ( c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X1,X2,X3),c_HOL_Oplus__class_Oplus(X4,X5,X3),X3) = c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X1,X4,X3),c_HOL_Ominus__class_Ominus(X2,X5,X3),X3)
    | ~ class_OrderedGroup_Oab__group__add(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_3281]) ).

cnf(c_0_3281_1,axiom,
    ( ~ class_OrderedGroup_Oab__group__add(X3)
    | c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X1,X2,X3),c_HOL_Oplus__class_Oplus(X4,X5,X3),X3) = c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X1,X4,X3),c_HOL_Ominus__class_Ominus(X2,X5,X3),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_3281]) ).

cnf(c_0_3282_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_3282]) ).

cnf(c_0_3282_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_3282]) ).

cnf(c_0_3283_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_3283]) ).

cnf(c_0_3283_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_3283]) ).

cnf(c_0_3284_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_3284]) ).

cnf(c_0_3284_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_3284]) ).

cnf(c_0_3285_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_3285]) ).

cnf(c_0_3285_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_3285]) ).

cnf(c_0_3286_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_3286]) ).

cnf(c_0_3286_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_3286]) ).

cnf(c_0_3287_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_3287]) ).

cnf(c_0_3287_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_3287]) ).

cnf(c_0_3288_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_3288]) ).

cnf(c_0_3288_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_3288]) ).

cnf(c_0_3289_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_3289]) ).

cnf(c_0_3289_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_3289]) ).

cnf(c_0_3290_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_3290]) ).

cnf(c_0_3290_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_3290]) ).

cnf(c_0_3291_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_3291]) ).

cnf(c_0_3291_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_3291]) ).

cnf(c_0_3292_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_3292]) ).

cnf(c_0_3292_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_3292]) ).

cnf(c_0_3293_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_3293]) ).

cnf(c_0_3293_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_3293]) ).

cnf(c_0_3293_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_3293]) ).

cnf(c_0_3293_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_3293]) ).

cnf(c_0_3294_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_3294]) ).

cnf(c_0_3294_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_3294]) ).

cnf(c_0_3294_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_3294]) ).

cnf(c_0_3294_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_3294]) ).

cnf(c_0_3295_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_3295]) ).

cnf(c_0_3295_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_3295]) ).

cnf(c_0_3295_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_3295]) ).

cnf(c_0_3295_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_3295]) ).

cnf(c_0_3295_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_3295]) ).

cnf(c_0_3298_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_3298]) ).

cnf(c_0_3298_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_3298]) ).

cnf(c_0_3299_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_3299]) ).

cnf(c_0_3299_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_3299]) ).

cnf(c_0_3300_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_3300]) ).

cnf(c_0_3300_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_3300]) ).

cnf(c_0_3300_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_3300]) ).

cnf(c_0_3300_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_3300]) ).

cnf(c_0_3301_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_3301]) ).

cnf(c_0_3301_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_3301]) ).

cnf(c_0_3301_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_3301]) ).

cnf(c_0_3301_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_3301]) ).

cnf(c_0_3302_0,axiom,
    ( c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X1,X2,X3),X3),c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(X1,X3),c_HOL_Oabs__class_Oabs(X2,X3),X3),X3)
    | ~ class_OrderedGroup_Opordered__ab__group__add__abs(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_3302]) ).

cnf(c_0_3302_1,axiom,
    ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X3)
    | c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X1,X2,X3),X3),c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(X1,X3),c_HOL_Oabs__class_Oabs(X2,X3),X3),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_3302]) ).

cnf(c_0_3303_0,axiom,
    ( c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Oplus__class_Oplus(X1,X2,X3),X3),c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(X1,X3),c_HOL_Oabs__class_Oabs(X2,X3),X3),X3)
    | ~ class_OrderedGroup_Opordered__ab__group__add__abs(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_3303]) ).

cnf(c_0_3303_1,axiom,
    ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X3)
    | c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Oplus__class_Oplus(X1,X2,X3),X3),c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(X1,X3),c_HOL_Oabs__class_Oabs(X2,X3),X3),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_3303]) ).

cnf(c_0_3304_0,axiom,
    ( c_lessequals(c_HOL_Ominus__class_Ominus(c_HOL_Oabs__class_Oabs(X1,X2),c_HOL_Oabs__class_Oabs(X3,X2),X2),c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X1,X3,X2),X2),X2)
    | ~ class_OrderedGroup_Opordered__ab__group__add__abs(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_3304]) ).

cnf(c_0_3304_1,axiom,
    ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X2)
    | c_lessequals(c_HOL_Ominus__class_Ominus(c_HOL_Oabs__class_Oabs(X1,X2),c_HOL_Oabs__class_Oabs(X3,X2),X2),c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X1,X3,X2),X2),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_3304]) ).

cnf(c_0_3305_0,axiom,
    ( c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(X1,X2,X3),X3),c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(X1,X3),c_HOL_Oabs__class_Oabs(X2,X3),X3),X3)
    | ~ class_Ring__and__Field_Olordered__ring(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_3305]) ).

cnf(c_0_3305_1,axiom,
    ( ~ class_Ring__and__Field_Olordered__ring(X3)
    | c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(X1,X2,X3),X3),c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(X1,X3),c_HOL_Oabs__class_Oabs(X2,X3),X3),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_3305]) ).

cnf(c_0_3306_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_3306]) ).

cnf(c_0_3306_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_3306]) ).

cnf(c_0_3306_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_3306]) ).

cnf(c_0_3306_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_3306]) ).

cnf(c_0_3307_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_3307]) ).

cnf(c_0_3307_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_3307]) ).

cnf(c_0_3308_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_3308]) ).

cnf(c_0_3308_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_3308]) ).

cnf(c_0_3309_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_3309]) ).

cnf(c_0_3309_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_3309]) ).

cnf(c_0_3309_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_3309]) ).

cnf(c_0_3310_0,axiom,
    ( X1 = c_HOL_Ozero__class_Ozero(X3)
    | c_Ring__and__Field_Odvd__class_Odvd(X2,X4,X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X1,X4,X3),X3)
    | ~ class_Ring__and__Field_Oidom(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_3310]) ).

cnf(c_0_3310_1,axiom,
    ( c_Ring__and__Field_Odvd__class_Odvd(X2,X4,X3)
    | X1 = c_HOL_Ozero__class_Ozero(X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X1,X4,X3),X3)
    | ~ class_Ring__and__Field_Oidom(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_3310]) ).

cnf(c_0_3310_2,axiom,
    ( ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X1,X4,X3),X3)
    | c_Ring__and__Field_Odvd__class_Odvd(X2,X4,X3)
    | X1 = c_HOL_Ozero__class_Ozero(X3)
    | ~ class_Ring__and__Field_Oidom(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_3310]) ).

cnf(c_0_3310_3,axiom,
    ( ~ class_Ring__and__Field_Oidom(X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X1,X4,X3),X3)
    | c_Ring__and__Field_Odvd__class_Odvd(X2,X4,X3)
    | X1 = c_HOL_Ozero__class_Ozero(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_3310]) ).

cnf(c_0_3311_0,axiom,
    ( X2 = c_HOL_Ozero__class_Ozero(X3)
    | c_Ring__and__Field_Odvd__class_Odvd(X1,X4,X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X4,X2,X3),X3)
    | ~ class_Ring__and__Field_Oidom(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_3311]) ).

cnf(c_0_3311_1,axiom,
    ( c_Ring__and__Field_Odvd__class_Odvd(X1,X4,X3)
    | X2 = c_HOL_Ozero__class_Ozero(X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X4,X2,X3),X3)
    | ~ class_Ring__and__Field_Oidom(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_3311]) ).

cnf(c_0_3311_2,axiom,
    ( ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X4,X2,X3),X3)
    | c_Ring__and__Field_Odvd__class_Odvd(X1,X4,X3)
    | X2 = c_HOL_Ozero__class_Ozero(X3)
    | ~ class_Ring__and__Field_Oidom(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_3311]) ).

cnf(c_0_3311_3,axiom,
    ( ~ class_Ring__and__Field_Oidom(X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X4,X2,X3),X3)
    | c_Ring__and__Field_Odvd__class_Odvd(X1,X4,X3)
    | X2 = c_HOL_Ozero__class_Ozero(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_3311]) ).

cnf(c_0_3312_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_3312]) ).

cnf(c_0_3312_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_3312]) ).

cnf(c_0_3312_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_3312]) ).

cnf(c_0_3313_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_3313]) ).

cnf(c_0_3313_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_3313]) ).

cnf(c_0_3313_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_3313]) ).

cnf(c_0_3314_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_3314]) ).

cnf(c_0_3314_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_3314]) ).

cnf(c_0_3314_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_3314]) ).

cnf(c_0_3315_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_3315]) ).

cnf(c_0_3315_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_3315]) ).

cnf(c_0_3315_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_3315]) ).

cnf(c_0_3316_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_3316]) ).

cnf(c_0_3316_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_3316]) ).

cnf(c_0_3316_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_3316]) ).

cnf(c_0_3317_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_3317]) ).

cnf(c_0_3317_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_3317]) ).

cnf(c_0_3317_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_3317]) ).

cnf(c_0_3318_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_3318]) ).

cnf(c_0_3318_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_3318]) ).

cnf(c_0_3318_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_3318]) ).

cnf(c_0_3319_0,axiom,
    ( c_lessequals(X1,c_HOL_Oplus__class_Oplus(X4,c_HOL_Oabs__class_Oabs(X2,X3),X3),X3)
    | ~ c_lessequals(c_HOL_Oplus__class_Oplus(X1,X2,X3),X4,X3)
    | ~ class_OrderedGroup_Olordered__ab__group__add__abs(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_3319]) ).

cnf(c_0_3319_1,axiom,
    ( ~ c_lessequals(c_HOL_Oplus__class_Oplus(X1,X2,X3),X4,X3)
    | c_lessequals(X1,c_HOL_Oplus__class_Oplus(X4,c_HOL_Oabs__class_Oabs(X2,X3),X3),X3)
    | ~ class_OrderedGroup_Olordered__ab__group__add__abs(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_3319]) ).

cnf(c_0_3319_2,axiom,
    ( ~ class_OrderedGroup_Olordered__ab__group__add__abs(X3)
    | ~ c_lessequals(c_HOL_Oplus__class_Oplus(X1,X2,X3),X4,X3)
    | c_lessequals(X1,c_HOL_Oplus__class_Oplus(X4,c_HOL_Oabs__class_Oabs(X2,X3),X3),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_3319]) ).

cnf(c_0_3320_0,axiom,
    ( c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Ominus__class_Ominus(X2,X3,tc_nat),tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X3,tc_nat)
    | ~ c_lessequals(X3,X2,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_3320]) ).

cnf(c_0_3320_1,axiom,
    ( ~ c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Ominus__class_Ominus(X2,X3,tc_nat),tc_nat)
    | c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X3,tc_nat)
    | ~ c_lessequals(X3,X2,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_3320]) ).

cnf(c_0_3320_2,axiom,
    ( ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X3,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Ominus__class_Ominus(X2,X3,tc_nat),tc_nat)
    | c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
    | ~ c_lessequals(X3,X2,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_3320]) ).

cnf(c_0_3320_3,axiom,
    ( ~ c_lessequals(X3,X2,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X3,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Ominus__class_Ominus(X2,X3,tc_nat),tc_nat)
    | c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_3320]) ).

cnf(c_0_3321_0,axiom,
    ( c_Ring__and__Field_Odvd__class_Odvd(X1,X3,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Ominus__class_Ominus(X2,X3,tc_nat),tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
    | ~ c_lessequals(X3,X2,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_3321]) ).

cnf(c_0_3321_1,axiom,
    ( ~ c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Ominus__class_Ominus(X2,X3,tc_nat),tc_nat)
    | c_Ring__and__Field_Odvd__class_Odvd(X1,X3,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
    | ~ c_lessequals(X3,X2,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_3321]) ).

cnf(c_0_3321_2,axiom,
    ( ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Ominus__class_Ominus(X2,X3,tc_nat),tc_nat)
    | c_Ring__and__Field_Odvd__class_Odvd(X1,X3,tc_nat)
    | ~ c_lessequals(X3,X2,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_3321]) ).

cnf(c_0_3321_3,axiom,
    ( ~ c_lessequals(X3,X2,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Ominus__class_Ominus(X2,X3,tc_nat),tc_nat)
    | c_Ring__and__Field_Odvd__class_Odvd(X1,X3,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_3321]) ).

cnf(c_0_3322_0,axiom,
    ( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
    | c_Ring__and__Field_Odvd__class_Odvd(X2,X3,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_3322]) ).

cnf(c_0_3322_1,axiom,
    ( c_Ring__and__Field_Odvd__class_Odvd(X2,X3,tc_nat)
    | X1 = c_HOL_Ozero__class_Ozero(tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_3322]) ).

cnf(c_0_3322_2,axiom,
    ( ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat)
    | c_Ring__and__Field_Odvd__class_Odvd(X2,X3,tc_nat)
    | X1 = c_HOL_Ozero__class_Ozero(tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_3322]) ).

cnf(c_0_3323_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_3323]) ).

cnf(c_0_3323_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_3323]) ).

cnf(c_0_3324_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_3324]) ).

cnf(c_0_3324_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_3324]) ).

cnf(c_0_3325_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_3325]) ).

cnf(c_0_3325_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_3325]) ).

cnf(c_0_3326_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_3326]) ).

cnf(c_0_3326_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_3326]) ).

cnf(c_0_3327_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_3327]) ).

cnf(c_0_3327_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_3327]) ).

cnf(c_0_3328_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_3328]) ).

cnf(c_0_3328_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_3328]) ).

cnf(c_0_3329_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_3329]) ).

cnf(c_0_3329_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_3329]) ).

cnf(c_0_3329_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_3329]) ).

cnf(c_0_3329_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_3329]) ).

cnf(c_0_3330_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_3330]) ).

cnf(c_0_3330_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_3330]) ).

cnf(c_0_3330_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_3330]) ).

cnf(c_0_3330_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_3330]) ).

cnf(c_0_3331_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_3331]) ).

cnf(c_0_3331_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_3331]) ).

cnf(c_0_3331_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_3331]) ).

cnf(c_0_3331_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_3331]) ).

cnf(c_0_3332_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_3332]) ).

cnf(c_0_3332_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_3332]) ).

cnf(c_0_3332_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_3332]) ).

cnf(c_0_3332_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_3332]) ).

cnf(c_0_3333_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_3333]) ).

cnf(c_0_3333_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_3333]) ).

cnf(c_0_3333_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_3333]) ).

cnf(c_0_3333_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_3333]) ).

cnf(c_0_3334_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_3334]) ).

cnf(c_0_3334_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_3334]) ).

cnf(c_0_3334_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_3334]) ).

cnf(c_0_3334_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_3334]) ).

cnf(c_0_3335_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_3335]) ).

cnf(c_0_3335_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_3335]) ).

cnf(c_0_3335_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_3335]) ).

cnf(c_0_3335_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_3335]) ).

cnf(c_0_3336_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_3336]) ).

cnf(c_0_3336_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_3336]) ).

cnf(c_0_3336_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_3336]) ).

cnf(c_0_3336_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_3336]) ).

cnf(c_0_3337_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_3337]) ).

cnf(c_0_3337_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_3337]) ).

cnf(c_0_3337_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_3337]) ).

cnf(c_0_3337_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_3337]) ).

cnf(c_0_3338_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_3338]) ).

cnf(c_0_3338_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_3338]) ).

cnf(c_0_3338_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_3338]) ).

cnf(c_0_3338_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_3338]) ).

cnf(c_0_3339_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_3339]) ).

cnf(c_0_3339_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_3339]) ).

cnf(c_0_3339_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_3339]) ).

cnf(c_0_3339_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_3339]) ).

cnf(c_0_3340_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_3340]) ).

cnf(c_0_3340_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_3340]) ).

cnf(c_0_3340_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_3340]) ).

cnf(c_0_3340_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_3340]) ).

cnf(c_0_3341_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_3341]) ).

cnf(c_0_3341_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_3341]) ).

cnf(c_0_3341_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_3341]) ).

cnf(c_0_3341_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_3341]) ).

cnf(c_0_3342_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_3342]) ).

cnf(c_0_3342_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_3342]) ).

cnf(c_0_3342_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_3342]) ).

cnf(c_0_3342_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_3342]) ).

cnf(c_0_3343_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_3343]) ).

cnf(c_0_3343_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_3343]) ).

cnf(c_0_3343_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_3343]) ).

cnf(c_0_3343_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_3343]) ).

cnf(c_0_3344_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_3344]) ).

cnf(c_0_3344_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_3344]) ).

cnf(c_0_3344_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_3344]) ).

cnf(c_0_3344_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_3344]) ).

cnf(c_0_3345_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_3345]) ).

cnf(c_0_3345_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_3345]) ).

cnf(c_0_3345_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_3345]) ).

cnf(c_0_3345_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_3345]) ).

cnf(c_0_3346_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_3346]) ).

cnf(c_0_3346_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_3346]) ).

cnf(c_0_3346_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_3346]) ).

cnf(c_0_3346_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_3346]) ).

cnf(c_0_3347_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_3347]) ).

cnf(c_0_3347_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_3347]) ).

cnf(c_0_3348_0,axiom,
    ( c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X2,X5,X3),X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X5,X3)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_3348]) ).

cnf(c_0_3348_1,axiom,
    ( ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
    | c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X2,X5,X3),X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X5,X3)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_3348]) ).

cnf(c_0_3348_2,axiom,
    ( ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X5,X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
    | c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X2,X5,X3),X3)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_3348]) ).

cnf(c_0_3348_3,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X5,X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
    | c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X2,X5,X3),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_3348]) ).

cnf(c_0_3349_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_3349]) ).

cnf(c_0_3349_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_3349]) ).

cnf(c_0_3349_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_3349]) ).

cnf(c_0_3349_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_3349]) ).

cnf(c_0_3350_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_3350]) ).

cnf(c_0_3350_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_3350]) ).

cnf(c_0_3350_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_3350]) ).

cnf(c_0_3350_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_3350]) ).

cnf(c_0_3351_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_3351]) ).

cnf(c_0_3351_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_3351]) ).

cnf(c_0_3351_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_3351]) ).

cnf(c_0_3351_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_3351]) ).

cnf(c_0_3352_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_3352]) ).

cnf(c_0_3352_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_3352]) ).

cnf(c_0_3352_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_3352]) ).

cnf(c_0_3352_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_3352]) ).

cnf(c_0_3353_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_3353]) ).

cnf(c_0_3353_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_3353]) ).

cnf(c_0_3353_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_3353]) ).

cnf(c_0_3354_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_3354]) ).

cnf(c_0_3354_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_3354]) ).

cnf(c_0_3354_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_3354]) ).

cnf(c_0_3355_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_3355]) ).

cnf(c_0_3355_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_3355]) ).

cnf(c_0_3356_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_3356]) ).

cnf(c_0_3356_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_3356]) ).

cnf(c_0_3357_0,axiom,
    ( c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X2,X4,X3),X3) = c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,X2,X3),X4,X3)
    | ~ class_RealVector_Oreal__normed__algebra(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_3357]) ).

cnf(c_0_3357_1,axiom,
    ( ~ class_RealVector_Oreal__normed__algebra(X3)
    | c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X2,X4,X3),X3) = c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,X2,X3),X4,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_3357]) ).

cnf(c_0_3358_0,axiom,
    ( c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X2,X4,X3),X3) = c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,X2,X3),X4,X3)
    | ~ class_RealVector_Oreal__normed__algebra(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_3358]) ).

cnf(c_0_3358_1,axiom,
    ( ~ class_RealVector_Oreal__normed__algebra(X3)
    | c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X2,X4,X3),X3) = c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,X2,X3),X4,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_3358]) ).

cnf(c_0_3359_0,axiom,
    ( c_HOL_Ominus__class_Ominus(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_Ominus__class_Ominus(X2,X3,X4),X4)
    | ~ class_RealVector_Oreal__normed__algebra(X4) ),
    inference(literals_permutation,[status(thm)],[c_0_3359]) ).

cnf(c_0_3359_1,axiom,
    ( ~ class_RealVector_Oreal__normed__algebra(X4)
    | c_HOL_Ominus__class_Ominus(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_Ominus__class_Ominus(X2,X3,X4),X4) ),
    inference(literals_permutation,[status(thm)],[c_0_3359]) ).

cnf(c_0_3360_0,axiom,
    ( c_HOL_Ominus__class_Ominus(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_Ominus__class_Ominus(X2,X3,X4),X4)
    | ~ class_RealVector_Oreal__normed__algebra(X4) ),
    inference(literals_permutation,[status(thm)],[c_0_3360]) ).

cnf(c_0_3360_1,axiom,
    ( ~ class_RealVector_Oreal__normed__algebra(X4)
    | c_HOL_Ominus__class_Ominus(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_Ominus__class_Ominus(X2,X3,X4),X4) ),
    inference(literals_permutation,[status(thm)],[c_0_3360]) ).

cnf(c_0_3361_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_3361]) ).

cnf(c_0_3361_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_3361]) ).

cnf(c_0_3362_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_3362]) ).

cnf(c_0_3362_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_3362]) ).

cnf(c_0_3363_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_3363]) ).

cnf(c_0_3363_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_3363]) ).

cnf(c_0_3364_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_3364]) ).

cnf(c_0_3364_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_3364]) ).

cnf(c_0_3365_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_3365]) ).

cnf(c_0_3365_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_3365]) ).

cnf(c_0_3366_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_3366]) ).

cnf(c_0_3366_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_3366]) ).

cnf(c_0_3367_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_3367]) ).

cnf(c_0_3367_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_3367]) ).

cnf(c_0_3368_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_RealVector_Oreal__normed__algebra(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_3368]) ).

cnf(c_0_3368_1,axiom,
    ( ~ class_RealVector_Oreal__normed__algebra(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_3368]) ).

cnf(c_0_3369_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_RealVector_Oreal__normed__algebra(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_3369]) ).

cnf(c_0_3369_1,axiom,
    ( ~ class_RealVector_Oreal__normed__algebra(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_3369]) ).

cnf(c_0_3370_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_RealVector_Oreal__normed__algebra(X4) ),
    inference(literals_permutation,[status(thm)],[c_0_3370]) ).

cnf(c_0_3370_1,axiom,
    ( ~ class_RealVector_Oreal__normed__algebra(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_3370]) ).

cnf(c_0_3371_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_RealVector_Oreal__normed__algebra(X4) ),
    inference(literals_permutation,[status(thm)],[c_0_3371]) ).

cnf(c_0_3371_1,axiom,
    ( ~ class_RealVector_Oreal__normed__algebra(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_3371]) ).

cnf(c_0_3372_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_3372]) ).

cnf(c_0_3372_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_3372]) ).

cnf(c_0_3373_0,axiom,
    ( c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X3,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_3373]) ).

cnf(c_0_3373_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
    | c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X3,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_3373]) ).

cnf(c_0_3373_2,axiom,
    ( ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X3,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
    | c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_3373]) ).

cnf(c_0_3374_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_3374]) ).

cnf(c_0_3374_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_3374]) ).

cnf(c_0_3374_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_3374]) ).

cnf(c_0_3375_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_3375]) ).

cnf(c_0_3375_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_3375]) ).

cnf(c_0_3375_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_3375]) ).

cnf(c_0_3376_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_3376]) ).

cnf(c_0_3376_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_3376]) ).

cnf(c_0_3376_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_3376]) ).

cnf(c_0_3377_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_3377]) ).

cnf(c_0_3377_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_3377]) ).

cnf(c_0_3377_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_3377]) ).

cnf(c_0_3378_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_3378]) ).

cnf(c_0_3378_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_3378]) ).

cnf(c_0_3378_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_3378]) ).

cnf(c_0_3379_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_3379]) ).

cnf(c_0_3379_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_3379]) ).

cnf(c_0_3379_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_3379]) ).

cnf(c_0_3380_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_3380]) ).

cnf(c_0_3380_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_3380]) ).

cnf(c_0_3380_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_3380]) ).

cnf(c_0_3381_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_3381]) ).

cnf(c_0_3381_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_3381]) ).

cnf(c_0_3381_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_3381]) ).

cnf(c_0_3382_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_3382]) ).

cnf(c_0_3382_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_3382]) ).

cnf(c_0_3382_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_3382]) ).

cnf(c_0_3383_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_3383]) ).

cnf(c_0_3383_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_3383]) ).

cnf(c_0_3383_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_3383]) ).

cnf(c_0_3384_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_3384]) ).

cnf(c_0_3384_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_3384]) ).

cnf(c_0_3384_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_3384]) ).

cnf(c_0_3385_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_3385]) ).

cnf(c_0_3385_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_3385]) ).

cnf(c_0_3385_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_3385]) ).

cnf(c_0_3385_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_3385]) ).

cnf(c_0_3386_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_3386]) ).

cnf(c_0_3386_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_3386]) ).

cnf(c_0_3386_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_3386]) ).

cnf(c_0_3386_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_3386]) ).

cnf(c_0_3387_0,axiom,
    ( c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(X1,X2),c_HOL_Oabs__class_Oabs(X3,X2),X2) = c_HOL_Oabs__class_Oabs(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__abs(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_3387]) ).

cnf(c_0_3387_1,axiom,
    ( ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
    | c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(X1,X2),c_HOL_Oabs__class_Oabs(X3,X2),X2) = c_HOL_Oabs__class_Oabs(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__abs(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_3387]) ).

cnf(c_0_3387_2,axiom,
    ( ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X2),X2)
    | ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
    | c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(X1,X2),c_HOL_Oabs__class_Oabs(X3,X2),X2) = c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(X1,X3,X2),X2)
    | ~ class_Ring__and__Field_Opordered__ring__abs(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_3387]) ).

cnf(c_0_3387_3,axiom,
    ( ~ class_Ring__and__Field_Opordered__ring__abs(X2)
    | ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X2),X2)
    | ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
    | c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(X1,X2),c_HOL_Oabs__class_Oabs(X3,X2),X2) = c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(X1,X3,X2),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_3387]) ).

cnf(c_0_3388_0,axiom,
    ( c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(X1,X2),c_HOL_Oabs__class_Oabs(X3,X2),X2) = c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(X1,X3,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__ring__abs(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_3388]) ).

cnf(c_0_3388_1,axiom,
    ( ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
    | c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(X1,X2),c_HOL_Oabs__class_Oabs(X3,X2),X2) = c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(X1,X3,X2),X2)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X3,X2)
    | ~ class_Ring__and__Field_Opordered__ring__abs(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_3388]) ).

cnf(c_0_3388_2,axiom,
    ( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X3,X2)
    | ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
    | c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(X1,X2),c_HOL_Oabs__class_Oabs(X3,X2),X2) = c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(X1,X3,X2),X2)
    | ~ class_Ring__and__Field_Opordered__ring__abs(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_3388]) ).

cnf(c_0_3388_3,axiom,
    ( ~ class_Ring__and__Field_Opordered__ring__abs(X2)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X3,X2)
    | ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X2),X2)
    | c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(X1,X2),c_HOL_Oabs__class_Oabs(X3,X2),X2) = c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(X1,X3,X2),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_3388]) ).

cnf(c_0_3389_0,axiom,
    ( c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(X2,X1),c_HOL_Oabs__class_Oabs(X3,X1),X1) = c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(X2,X3,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__ring__abs(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3389]) ).

cnf(c_0_3389_1,axiom,
    ( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(X2,X1),c_HOL_Oabs__class_Oabs(X3,X1),X1) = c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
    | ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ class_Ring__and__Field_Opordered__ring__abs(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3389]) ).

cnf(c_0_3389_2,axiom,
    ( ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(X2,X1),c_HOL_Oabs__class_Oabs(X3,X1),X1) = c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
    | ~ class_Ring__and__Field_Opordered__ring__abs(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3389]) ).

cnf(c_0_3389_3,axiom,
    ( ~ class_Ring__and__Field_Opordered__ring__abs(X1)
    | ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(X2,X1),c_HOL_Oabs__class_Oabs(X3,X1),X1) = c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(X2,X3,X1),X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3389]) ).

cnf(c_0_3390_0,axiom,
    ( c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(X2,X1),c_HOL_Oabs__class_Oabs(X3,X1),X1) = c_HOL_Oabs__class_Oabs(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__abs(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3390]) ).

cnf(c_0_3390_1,axiom,
    ( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(X2,X1),c_HOL_Oabs__class_Oabs(X3,X1),X1) = c_HOL_Oabs__class_Oabs(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__abs(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3390]) ).

cnf(c_0_3390_2,axiom,
    ( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(X2,X1),c_HOL_Oabs__class_Oabs(X3,X1),X1) = c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
    | ~ class_Ring__and__Field_Opordered__ring__abs(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3390]) ).

cnf(c_0_3390_3,axiom,
    ( ~ class_Ring__and__Field_Opordered__ring__abs(X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(X2,X1),c_HOL_Oabs__class_Oabs(X3,X1),X1) = c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(X2,X3,X1),X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3390]) ).

cnf(c_0_3399_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_3399]) ).

cnf(c_0_3399_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_3399]) ).

cnf(c_0_3400_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_3400]) ).

cnf(c_0_3400_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_3400]) ).

cnf(c_0_3401_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_3401]) ).

cnf(c_0_3401_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_3401]) ).

cnf(c_0_3402_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_3402]) ).

cnf(c_0_3402_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_3402]) ).

cnf(c_0_3403_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_3403]) ).

cnf(c_0_3403_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_3403]) ).

cnf(c_0_3404_0,axiom,
    ( c_Ring__and__Field_Odvd__class_Odvd(X1,X4,X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,c_Divides_Odiv__class_Omod(X4,X2,X3),X3)
    | ~ class_Divides_Osemiring__div(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_3404]) ).

cnf(c_0_3404_1,axiom,
    ( ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
    | c_Ring__and__Field_Odvd__class_Odvd(X1,X4,X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,c_Divides_Odiv__class_Omod(X4,X2,X3),X3)
    | ~ class_Divides_Osemiring__div(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_3404]) ).

cnf(c_0_3404_2,axiom,
    ( ~ c_Ring__and__Field_Odvd__class_Odvd(X1,c_Divides_Odiv__class_Omod(X4,X2,X3),X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
    | c_Ring__and__Field_Odvd__class_Odvd(X1,X4,X3)
    | ~ class_Divides_Osemiring__div(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_3404]) ).

cnf(c_0_3404_3,axiom,
    ( ~ class_Divides_Osemiring__div(X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,c_Divides_Odiv__class_Omod(X4,X2,X3),X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
    | c_Ring__and__Field_Odvd__class_Odvd(X1,X4,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_3404]) ).

cnf(c_0_3405_0,axiom,
    ( c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X4)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,c_Divides_Odiv__class_Omod(X2,X3,X4),X4)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X3,X4)
    | ~ class_Divides_Osemiring__div(X4) ),
    inference(literals_permutation,[status(thm)],[c_0_3405]) ).

cnf(c_0_3405_1,axiom,
    ( ~ c_Ring__and__Field_Odvd__class_Odvd(X1,c_Divides_Odiv__class_Omod(X2,X3,X4),X4)
    | c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X4)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X3,X4)
    | ~ class_Divides_Osemiring__div(X4) ),
    inference(literals_permutation,[status(thm)],[c_0_3405]) ).

cnf(c_0_3405_2,axiom,
    ( ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X3,X4)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,c_Divides_Odiv__class_Omod(X2,X3,X4),X4)
    | c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X4)
    | ~ class_Divides_Osemiring__div(X4) ),
    inference(literals_permutation,[status(thm)],[c_0_3405]) ).

cnf(c_0_3405_3,axiom,
    ( ~ class_Divides_Osemiring__div(X4)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X3,X4)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,c_Divides_Odiv__class_Omod(X2,X3,X4),X4)
    | c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X4) ),
    inference(literals_permutation,[status(thm)],[c_0_3405]) ).

cnf(c_0_3406_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_3406]) ).

cnf(c_0_3406_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_3406]) ).

cnf(c_0_3406_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_3406]) ).

cnf(c_0_3407_0,axiom,
    ( 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(literals_permutation,[status(thm)],[c_0_3407]) ).

cnf(c_0_3407_1,axiom,
    ( ~ c_lessequals(X1,X2,tc_nat)
    | 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) ),
    inference(literals_permutation,[status(thm)],[c_0_3407]) ).

cnf(c_0_3408_0,axiom,
    ( 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(literals_permutation,[status(thm)],[c_0_3408]) ).

cnf(c_0_3408_1,axiom,
    ( ~ c_lessequals(X1,X2,tc_nat)
    | 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) ),
    inference(literals_permutation,[status(thm)],[c_0_3408]) ).

cnf(c_0_3409_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_3409]) ).

cnf(c_0_3409_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_3409]) ).

cnf(c_0_3410_0,axiom,
    ( 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(literals_permutation,[status(thm)],[c_0_3410]) ).

cnf(c_0_3410_1,axiom,
    ( ~ c_lessequals(X1,X2,tc_nat)
    | 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) ),
    inference(literals_permutation,[status(thm)],[c_0_3410]) ).

cnf(c_0_3411_0,axiom,
    ( 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(literals_permutation,[status(thm)],[c_0_3411]) ).

cnf(c_0_3411_1,axiom,
    ( ~ c_lessequals(X1,X2,tc_nat)
    | 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) ),
    inference(literals_permutation,[status(thm)],[c_0_3411]) ).

cnf(c_0_3412_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_3412]) ).

cnf(c_0_3412_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_3412]) ).

cnf(c_0_3412_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_3412]) ).

cnf(c_0_3412_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_3412]) ).

cnf(c_0_3413_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_3413]) ).

cnf(c_0_3413_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_3413]) ).

cnf(c_0_3413_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_3413]) ).

cnf(c_0_3413_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_3413]) ).

cnf(c_0_3414_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_3414]) ).

cnf(c_0_3414_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_3414]) ).

cnf(c_0_3414_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_3414]) ).

cnf(c_0_3414_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_3414]) ).

cnf(c_0_3415_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_3415]) ).

cnf(c_0_3415_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_3415]) ).

cnf(c_0_3415_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_3415]) ).

cnf(c_0_3415_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_3415]) ).

cnf(c_0_3416_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_3416]) ).

cnf(c_0_3416_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_3416]) ).

cnf(c_0_3416_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_3416]) ).

cnf(c_0_3416_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_3416]) ).

cnf(c_0_3417_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_3417]) ).

cnf(c_0_3417_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_3417]) ).

cnf(c_0_3417_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_3417]) ).

cnf(c_0_3417_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_3417]) ).

cnf(c_0_3418_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_3418]) ).

cnf(c_0_3418_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_3418]) ).

cnf(c_0_3418_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_3418]) ).

cnf(c_0_3418_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_3418]) ).

cnf(c_0_3419_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_3419]) ).

cnf(c_0_3419_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_3419]) ).

cnf(c_0_3419_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_3419]) ).

cnf(c_0_3419_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_3419]) ).

cnf(c_0_3420_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_3420]) ).

cnf(c_0_3420_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_3420]) ).

cnf(c_0_3420_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_3420]) ).

cnf(c_0_3421_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_3421]) ).

cnf(c_0_3421_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_3421]) ).

cnf(c_0_3421_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_3421]) ).

cnf(c_0_3422_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_3422]) ).

cnf(c_0_3422_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_3422]) ).

cnf(c_0_3422_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_3422]) ).

cnf(c_0_3422_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_3422]) ).

cnf(c_0_3423_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_3423]) ).

cnf(c_0_3423_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_3423]) ).

cnf(c_0_3423_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_3423]) ).

cnf(c_0_3423_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_3423]) ).

cnf(c_0_3424_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_3424]) ).

cnf(c_0_3424_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_3424]) ).

cnf(c_0_3425_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_3425]) ).

cnf(c_0_3425_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_3425]) ).

cnf(c_0_3426_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_3426]) ).

cnf(c_0_3426_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_3426]) ).

cnf(c_0_3426_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_3426]) ).

cnf(c_0_3426_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_3426]) ).

cnf(c_0_3427_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_3427]) ).

cnf(c_0_3427_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_3427]) ).

cnf(c_0_3427_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_3427]) ).

cnf(c_0_3427_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_3427]) ).

cnf(c_0_3428_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_3428]) ).

cnf(c_0_3428_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_3428]) ).

cnf(c_0_3428_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_3428]) ).

cnf(c_0_3428_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_3428]) ).

cnf(c_0_3429_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_3429]) ).

cnf(c_0_3429_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_3429]) ).

cnf(c_0_3429_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_3429]) ).

cnf(c_0_3429_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_3429]) ).

cnf(c_0_3430_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_3430]) ).

cnf(c_0_3430_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_3430]) ).

cnf(c_0_3430_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_3430]) ).

cnf(c_0_3430_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_3430]) ).

cnf(c_0_3431_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_3431]) ).

cnf(c_0_3431_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_3431]) ).

cnf(c_0_3431_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_3431]) ).

cnf(c_0_3431_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_3431]) ).

cnf(c_0_3432_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_3432]) ).

cnf(c_0_3432_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_3432]) ).

cnf(c_0_3432_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_3432]) ).

cnf(c_0_3432_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_3432]) ).

cnf(c_0_3433_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_3433]) ).

cnf(c_0_3433_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_3433]) ).

cnf(c_0_3433_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_3433]) ).

cnf(c_0_3433_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_3433]) ).

cnf(c_0_3434_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_3434]) ).

cnf(c_0_3434_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_3434]) ).

cnf(c_0_3434_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_3434]) ).

cnf(c_0_3434_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_3434]) ).

cnf(c_0_3435_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_3435]) ).

cnf(c_0_3435_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_3435]) ).

cnf(c_0_3435_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_3435]) ).

cnf(c_0_3435_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_3435]) ).

cnf(c_0_3436_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_3436]) ).

cnf(c_0_3436_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_3436]) ).

cnf(c_0_3436_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_3436]) ).

cnf(c_0_3436_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_3436]) ).

cnf(c_0_3437_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_3437]) ).

cnf(c_0_3437_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_3437]) ).

cnf(c_0_3437_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_3437]) ).

cnf(c_0_3437_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_3437]) ).

cnf(c_0_3438_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_3438]) ).

cnf(c_0_3438_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_3438]) ).

cnf(c_0_3438_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_3438]) ).

cnf(c_0_3438_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_3438]) ).

cnf(c_0_3439_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_3439]) ).

cnf(c_0_3439_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_3439]) ).

cnf(c_0_3439_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_3439]) ).

cnf(c_0_3439_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_3439]) ).

cnf(c_0_3440_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_3440]) ).

cnf(c_0_3440_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_3440]) ).

cnf(c_0_3440_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_3440]) ).

cnf(c_0_3440_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_3440]) ).

cnf(c_0_3441_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_3441]) ).

cnf(c_0_3441_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_3441]) ).

cnf(c_0_3441_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_3441]) ).

cnf(c_0_3441_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_3441]) ).

cnf(c_0_3442_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_3442]) ).

cnf(c_0_3442_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_3442]) ).

cnf(c_0_3442_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_3442]) ).

cnf(c_0_3442_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_3442]) ).

cnf(c_0_3443_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_3443]) ).

cnf(c_0_3443_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_3443]) ).

cnf(c_0_3443_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_3443]) ).

cnf(c_0_3443_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_3443]) ).

cnf(c_0_3444_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_3444]) ).

cnf(c_0_3444_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_3444]) ).

cnf(c_0_3444_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_3444]) ).

cnf(c_0_3444_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_3444]) ).

cnf(c_0_3445_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_3445]) ).

cnf(c_0_3445_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_3445]) ).

cnf(c_0_3445_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_3445]) ).

cnf(c_0_3445_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_3445]) ).

cnf(c_0_3446_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_3446]) ).

cnf(c_0_3446_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_3446]) ).

cnf(c_0_3446_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_3446]) ).

cnf(c_0_3446_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_3446]) ).

cnf(c_0_3447_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_3447]) ).

cnf(c_0_3447_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_3447]) ).

cnf(c_0_3447_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_3447]) ).

cnf(c_0_3447_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_3447]) ).

cnf(c_0_3448_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_3448]) ).

cnf(c_0_3448_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_3448]) ).

cnf(c_0_3448_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_3448]) ).

cnf(c_0_3448_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_3448]) ).

cnf(c_0_3449_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_3449]) ).

cnf(c_0_3449_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_3449]) ).

cnf(c_0_3449_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_3449]) ).

cnf(c_0_3449_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_3449]) ).

cnf(c_0_3450_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_3450]) ).

cnf(c_0_3450_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_3450]) ).

cnf(c_0_3450_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_3450]) ).

cnf(c_0_3450_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_3450]) ).

cnf(c_0_3451_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_3451]) ).

cnf(c_0_3451_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_3451]) ).

cnf(c_0_3451_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_3451]) ).

cnf(c_0_3451_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_3451]) ).

cnf(c_0_3452_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_3452]) ).

cnf(c_0_3452_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_3452]) ).

cnf(c_0_3452_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_3452]) ).

cnf(c_0_3454_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_3454]) ).

cnf(c_0_3454_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_3454]) ).

cnf(c_0_3454_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_3454]) ).

cnf(c_0_3455_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_3455]) ).

cnf(c_0_3455_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_3455]) ).

cnf(c_0_3455_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_3455]) ).

cnf(c_0_3456_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_3456]) ).

cnf(c_0_3456_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_3456]) ).

cnf(c_0_3456_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_3456]) ).

cnf(c_0_3457_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_3457]) ).

cnf(c_0_3457_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_3457]) ).

cnf(c_0_3457_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_3457]) ).

cnf(c_0_3458_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_3458]) ).

cnf(c_0_3458_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_3458]) ).

cnf(c_0_3458_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_3458]) ).

cnf(c_0_3459_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_3459]) ).

cnf(c_0_3459_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_3459]) ).

cnf(c_0_3459_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_3459]) ).

cnf(c_0_3460_0,axiom,
    ( c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X2,X4,X3),X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
    | ~ class_Ring__and__Field_Oidom(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_3460]) ).

cnf(c_0_3460_1,axiom,
    ( ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
    | c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X2,X4,X3),X3)
    | ~ class_Ring__and__Field_Oidom(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_3460]) ).

cnf(c_0_3460_2,axiom,
    ( ~ class_Ring__and__Field_Oidom(X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
    | c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X1,X4,X3),c_HOL_Otimes__class_Otimes(X2,X4,X3),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_3460]) ).

cnf(c_0_3461_0,axiom,
    ( c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X4,X1,X3),c_HOL_Otimes__class_Otimes(X4,X2,X3),X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
    | ~ class_Ring__and__Field_Oidom(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_3461]) ).

cnf(c_0_3461_1,axiom,
    ( ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
    | c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X4,X1,X3),c_HOL_Otimes__class_Otimes(X4,X2,X3),X3)
    | ~ class_Ring__and__Field_Oidom(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_3461]) ).

cnf(c_0_3461_2,axiom,
    ( ~ class_Ring__and__Field_Oidom(X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
    | c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X4,X1,X3),c_HOL_Otimes__class_Otimes(X4,X2,X3),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_3461]) ).

cnf(c_0_3462_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_3462]) ).

cnf(c_0_3462_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_3462]) ).

cnf(c_0_3462_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_3462]) ).

cnf(c_0_3463_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_3463]) ).

cnf(c_0_3463_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_3463]) ).

cnf(c_0_3463_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_3463]) ).

cnf(c_0_3464_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_3464]) ).

cnf(c_0_3464_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_3464]) ).

cnf(c_0_3464_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_3464]) ).

cnf(c_0_3465_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_3465]) ).

cnf(c_0_3465_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_3465]) ).

cnf(c_0_3465_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_3465]) ).

cnf(c_0_3466_0,axiom,
    ( c_Ring__and__Field_Odvd__class_Odvd(X2,X1,tc_nat)
    | c_Ring__and__Field_Odvd__class_Odvd(X3,X2,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X3,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X3,X1,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_3466]) ).

cnf(c_0_3466_1,axiom,
    ( c_Ring__and__Field_Odvd__class_Odvd(X3,X2,tc_nat)
    | c_Ring__and__Field_Odvd__class_Odvd(X2,X1,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X3,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X3,X1,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_3466]) ).

cnf(c_0_3466_2,axiom,
    ( ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
    | c_Ring__and__Field_Odvd__class_Odvd(X3,X2,tc_nat)
    | c_Ring__and__Field_Odvd__class_Odvd(X2,X1,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X3,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X3,X1,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_3466]) ).

cnf(c_0_3466_3,axiom,
    ( ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X3,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
    | c_Ring__and__Field_Odvd__class_Odvd(X3,X2,tc_nat)
    | c_Ring__and__Field_Odvd__class_Odvd(X2,X1,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X3,X1,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_3466]) ).

cnf(c_0_3466_4,axiom,
    ( ~ c_Ring__and__Field_Odvd__class_Odvd(X3,X1,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X3,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
    | c_Ring__and__Field_Odvd__class_Odvd(X3,X2,tc_nat)
    | c_Ring__and__Field_Odvd__class_Odvd(X2,X1,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_3466]) ).

cnf(c_0_3467_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_3467]) ).

cnf(c_0_3467_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_3467]) ).

cnf(c_0_3467_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_3467]) ).

cnf(c_0_3467_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_3467]) ).

cnf(c_0_3467_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_3467]) ).

cnf(c_0_3468_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_3468]) ).

cnf(c_0_3468_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_3468]) ).

cnf(c_0_3468_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_3468]) ).

cnf(c_0_3468_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_3468]) ).

cnf(c_0_3468_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_3468]) ).

cnf(c_0_3469_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_3469]) ).

cnf(c_0_3469_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_3469]) ).

cnf(c_0_3469_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_3469]) ).

cnf(c_0_3469_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_3469]) ).

cnf(c_0_3469_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_3469]) ).

cnf(c_0_3470_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_3470]) ).

cnf(c_0_3470_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_3470]) ).

cnf(c_0_3470_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_3470]) ).

cnf(c_0_3470_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_3470]) ).

cnf(c_0_3470_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_3470]) ).

cnf(c_0_3471_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_3471]) ).

cnf(c_0_3471_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_3471]) ).

cnf(c_0_3471_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_3471]) ).

cnf(c_0_3471_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_3471]) ).

cnf(c_0_3472_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_3472]) ).

cnf(c_0_3472_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_3472]) ).

cnf(c_0_3473_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_3473]) ).

cnf(c_0_3473_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_3473]) ).

cnf(c_0_3474_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_3474]) ).

cnf(c_0_3474_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_3474]) ).

cnf(c_0_3475_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_3475]) ).

cnf(c_0_3475_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_3475]) ).

cnf(c_0_3476_0,axiom,
    ( c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X3,X1,tc_nat),c_HOL_Otimes__class_Otimes(X3,X2,tc_nat),tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_3476]) ).

cnf(c_0_3476_1,axiom,
    ( ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
    | c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X3,X1,tc_nat),c_HOL_Otimes__class_Otimes(X3,X2,tc_nat),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_3476]) ).

cnf(c_0_3477_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_3477]) ).

cnf(c_0_3477_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_3477]) ).

cnf(c_0_3478_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_3478]) ).

cnf(c_0_3478_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_3478]) ).

cnf(c_0_3479_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_3479]) ).

cnf(c_0_3479_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_3479]) ).

cnf(c_0_3480_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_3480]) ).

cnf(c_0_3480_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_3480]) ).

cnf(c_0_3481_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_3481]) ).

cnf(c_0_3481_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_3481]) ).

cnf(c_0_3482_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_3482]) ).

cnf(c_0_3482_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_3482]) ).

cnf(c_0_3483_0,axiom,
    ( c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Ominus__class_Ominus(X2,X4,X3),X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X4,X3)
    | ~ class_Ring__and__Field_Ocomm__ring__1(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_3483]) ).

cnf(c_0_3483_1,axiom,
    ( ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
    | c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Ominus__class_Ominus(X2,X4,X3),X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X4,X3)
    | ~ class_Ring__and__Field_Ocomm__ring__1(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_3483]) ).

cnf(c_0_3483_2,axiom,
    ( ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X4,X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
    | c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Ominus__class_Ominus(X2,X4,X3),X3)
    | ~ class_Ring__and__Field_Ocomm__ring__1(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_3483]) ).

cnf(c_0_3483_3,axiom,
    ( ~ class_Ring__and__Field_Ocomm__ring__1(X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X4,X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
    | c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Ominus__class_Ominus(X2,X4,X3),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_3483]) ).

cnf(c_0_3484_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_3484]) ).

cnf(c_0_3484_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_3484]) ).

cnf(c_0_3484_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_3484]) ).

cnf(c_0_3484_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_3484]) ).

cnf(c_0_3485_0,axiom,
    ( c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Oplus__class_Oplus(X2,X4,X3),X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X4,X3)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_3485]) ).

cnf(c_0_3485_1,axiom,
    ( ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
    | c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Oplus__class_Oplus(X2,X4,X3),X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X4,X3)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_3485]) ).

cnf(c_0_3485_2,axiom,
    ( ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X4,X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
    | c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Oplus__class_Oplus(X2,X4,X3),X3)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_3485]) ).

cnf(c_0_3485_3,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X4,X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
    | c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Oplus__class_Oplus(X2,X4,X3),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_3485]) ).

cnf(c_0_3486_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_3486]) ).

cnf(c_0_3486_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_3486]) ).

cnf(c_0_3486_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_3486]) ).

cnf(c_0_3486_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_3486]) ).

cnf(c_0_3487_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_3487]) ).

cnf(c_0_3487_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_3487]) ).

cnf(c_0_3487_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_3487]) ).

cnf(c_0_3487_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_3487]) ).

cnf(c_0_3488_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_3488]) ).

cnf(c_0_3488_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_3488]) ).

cnf(c_0_3488_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_3488]) ).

cnf(c_0_3488_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_3488]) ).

cnf(c_0_3489_0,axiom,
    ( c_Ring__and__Field_Odvd__class_Odvd(X1,c_Divides_Odiv__class_Omod(X2,X4,X3),X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X4,X3)
    | ~ class_Divides_Osemiring__div(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_3489]) ).

cnf(c_0_3489_1,axiom,
    ( ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
    | c_Ring__and__Field_Odvd__class_Odvd(X1,c_Divides_Odiv__class_Omod(X2,X4,X3),X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X4,X3)
    | ~ class_Divides_Osemiring__div(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_3489]) ).

cnf(c_0_3489_2,axiom,
    ( ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X4,X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
    | c_Ring__and__Field_Odvd__class_Odvd(X1,c_Divides_Odiv__class_Omod(X2,X4,X3),X3)
    | ~ class_Divides_Osemiring__div(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_3489]) ).

cnf(c_0_3489_3,axiom,
    ( ~ class_Divides_Osemiring__div(X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X4,X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
    | c_Ring__and__Field_Odvd__class_Odvd(X1,c_Divides_Odiv__class_Omod(X2,X4,X3),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_3489]) ).

cnf(c_0_3490_0,axiom,
    ( c_Ring__and__Field_Odvd__class_Odvd(X1,c_Divides_Odiv__class_Omod(X4,X2,X3),X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X4,X3)
    | ~ class_Divides_Osemiring__div(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_3490]) ).

cnf(c_0_3490_1,axiom,
    ( ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
    | c_Ring__and__Field_Odvd__class_Odvd(X1,c_Divides_Odiv__class_Omod(X4,X2,X3),X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X4,X3)
    | ~ class_Divides_Osemiring__div(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_3490]) ).

cnf(c_0_3490_2,axiom,
    ( ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X4,X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
    | c_Ring__and__Field_Odvd__class_Odvd(X1,c_Divides_Odiv__class_Omod(X4,X2,X3),X3)
    | ~ class_Divides_Osemiring__div(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_3490]) ).

cnf(c_0_3490_3,axiom,
    ( ~ class_Divides_Osemiring__div(X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X4,X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
    | c_Ring__and__Field_Odvd__class_Odvd(X1,c_Divides_Odiv__class_Omod(X4,X2,X3),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_3490]) ).

cnf(c_0_3491_0,axiom,
    ( c_HOL_Oabs__class_Oabs(c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(X1,X2),c_HOL_Oabs__class_Oabs(X3,X2),X2),X2) = c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(X1,X2),c_HOL_Oabs__class_Oabs(X3,X2),X2)
    | ~ class_OrderedGroup_Opordered__ab__group__add__abs(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_3491]) ).

cnf(c_0_3491_1,axiom,
    ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X2)
    | c_HOL_Oabs__class_Oabs(c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(X1,X2),c_HOL_Oabs__class_Oabs(X3,X2),X2),X2) = c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(X1,X2),c_HOL_Oabs__class_Oabs(X3,X2),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_3491]) ).

cnf(c_0_3492_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_3492]) ).

cnf(c_0_3492_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_3492]) ).

cnf(c_0_3492_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_3492]) ).

cnf(c_0_3493_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_3493]) ).

cnf(c_0_3493_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_3493]) ).

cnf(c_0_3493_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_3493]) ).

cnf(c_0_3493_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_3493]) ).

cnf(c_0_3494_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_3494]) ).

cnf(c_0_3494_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_3494]) ).

cnf(c_0_3494_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_3494]) ).

cnf(c_0_3495_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_3495]) ).

cnf(c_0_3495_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_3495]) ).

cnf(c_0_3495_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_3495]) ).

cnf(c_0_3496_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_3496]) ).

cnf(c_0_3496_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_3496]) ).

cnf(c_0_3496_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_3496]) ).

cnf(c_0_3497_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_3497]) ).

cnf(c_0_3497_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_3497]) ).

cnf(c_0_3497_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_3497]) ).

cnf(c_0_3498_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_3498]) ).

cnf(c_0_3498_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_3498]) ).

cnf(c_0_3498_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_3498]) ).

cnf(c_0_3499_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_3499]) ).

cnf(c_0_3499_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_3499]) ).

cnf(c_0_3499_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_3499]) ).

cnf(c_0_3501_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_3501]) ).

cnf(c_0_3501_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_3501]) ).

cnf(c_0_3502_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_3502]) ).

cnf(c_0_3502_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_3502]) ).

cnf(c_0_3503_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_3503]) ).

cnf(c_0_3503_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_3503]) ).

cnf(c_0_3504_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_3504]) ).

cnf(c_0_3504_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_3504]) ).

cnf(c_0_3505_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_3505]) ).

cnf(c_0_3505_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_3505]) ).

cnf(c_0_3506_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_3506]) ).

cnf(c_0_3506_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_3506]) ).

cnf(c_0_3507_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_3507]) ).

cnf(c_0_3507_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_3507]) ).

cnf(c_0_3508_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_3508]) ).

cnf(c_0_3508_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_3508]) ).

cnf(c_0_3509_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_3509]) ).

cnf(c_0_3509_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_3509]) ).

cnf(c_0_3510_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_3510]) ).

cnf(c_0_3510_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_3510]) ).

cnf(c_0_3511_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_3511]) ).

cnf(c_0_3511_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_3511]) ).

cnf(c_0_3512_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_3512]) ).

cnf(c_0_3512_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_3512]) ).

cnf(c_0_3513_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_3513]) ).

cnf(c_0_3513_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_3513]) ).

cnf(c_0_3514_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_3514]) ).

cnf(c_0_3514_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_3514]) ).

cnf(c_0_3515_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_3515]) ).

cnf(c_0_3515_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_3515]) ).

cnf(c_0_3516_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_3516]) ).

cnf(c_0_3516_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_3516]) ).

cnf(c_0_3517_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_3517]) ).

cnf(c_0_3517_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_3517]) ).

cnf(c_0_3518_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_3518]) ).

cnf(c_0_3518_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_3518]) ).

cnf(c_0_3519_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_3519]) ).

cnf(c_0_3519_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_3519]) ).

cnf(c_0_3520_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_3520]) ).

cnf(c_0_3520_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_3520]) ).

cnf(c_0_3521_0,axiom,
    ( c_Ring__and__Field_Odvd__class_Odvd(X2,X1,tc_nat)
    | c_Ring__and__Field_Odvd__class_Odvd(X3,X2,tc_nat)
    | c_Ring__and__Field_Odvd__class_Odvd(X1,X3,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X3,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_3521]) ).

cnf(c_0_3521_1,axiom,
    ( c_Ring__and__Field_Odvd__class_Odvd(X3,X2,tc_nat)
    | c_Ring__and__Field_Odvd__class_Odvd(X2,X1,tc_nat)
    | c_Ring__and__Field_Odvd__class_Odvd(X1,X3,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X3,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_3521]) ).

cnf(c_0_3521_2,axiom,
    ( c_Ring__and__Field_Odvd__class_Odvd(X1,X3,tc_nat)
    | c_Ring__and__Field_Odvd__class_Odvd(X3,X2,tc_nat)
    | c_Ring__and__Field_Odvd__class_Odvd(X2,X1,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X3,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_3521]) ).

cnf(c_0_3521_3,axiom,
    ( ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
    | c_Ring__and__Field_Odvd__class_Odvd(X1,X3,tc_nat)
    | c_Ring__and__Field_Odvd__class_Odvd(X3,X2,tc_nat)
    | c_Ring__and__Field_Odvd__class_Odvd(X2,X1,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X3,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_3521]) ).

cnf(c_0_3521_4,axiom,
    ( ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X3,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
    | c_Ring__and__Field_Odvd__class_Odvd(X1,X3,tc_nat)
    | c_Ring__and__Field_Odvd__class_Odvd(X3,X2,tc_nat)
    | c_Ring__and__Field_Odvd__class_Odvd(X2,X1,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_3521]) ).

cnf(c_0_3522_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_3522]) ).

cnf(c_0_3522_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_3522]) ).

cnf(c_0_3522_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_3522]) ).

cnf(c_0_3523_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_3523]) ).

cnf(c_0_3523_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_3523]) ).

cnf(c_0_3523_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_3523]) ).

cnf(c_0_3525_0,axiom,
    ( c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Ominus__class_Ominus(X2,X3,tc_nat),tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X3,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_3525]) ).

cnf(c_0_3525_1,axiom,
    ( ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
    | c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Ominus__class_Ominus(X2,X3,tc_nat),tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X3,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_3525]) ).

cnf(c_0_3525_2,axiom,
    ( ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X3,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
    | c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Ominus__class_Ominus(X2,X3,tc_nat),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_3525]) ).

cnf(c_0_3526_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_3526]) ).

cnf(c_0_3526_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_3526]) ).

cnf(c_0_3526_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_3526]) ).

cnf(c_0_3526_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_3526]) ).

cnf(c_0_3527_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_3527]) ).

cnf(c_0_3527_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_3527]) ).

cnf(c_0_3527_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_3527]) ).

cnf(c_0_3527_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_3527]) ).

cnf(c_0_3528_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_3528]) ).

cnf(c_0_3528_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_3528]) ).

cnf(c_0_3528_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_3528]) ).

cnf(c_0_3528_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_3528]) ).

cnf(c_0_3529_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_3529]) ).

cnf(c_0_3529_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_3529]) ).

cnf(c_0_3529_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_3529]) ).

cnf(c_0_3529_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_3529]) ).

cnf(c_0_3530_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_3530]) ).

cnf(c_0_3530_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_3530]) ).

cnf(c_0_3531_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_3531]) ).

cnf(c_0_3531_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_3531]) ).

cnf(c_0_3532_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_3532]) ).

cnf(c_0_3532_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_3532]) ).

cnf(c_0_3532_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_3532]) ).

cnf(c_0_3533_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_3533]) ).

cnf(c_0_3533_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_3533]) ).

cnf(c_0_3533_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_3533]) ).

cnf(c_0_3534_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_3534]) ).

cnf(c_0_3534_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_3534]) ).

cnf(c_0_3534_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_3534]) ).

cnf(c_0_3535_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_3535]) ).

cnf(c_0_3535_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_3535]) ).

cnf(c_0_3535_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_3535]) ).

cnf(c_0_3536_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_3536]) ).

cnf(c_0_3536_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_3536]) ).

cnf(c_0_3536_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_3536]) ).

cnf(c_0_3537_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_3537]) ).

cnf(c_0_3537_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_3537]) ).

cnf(c_0_3537_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_3537]) ).

cnf(c_0_3538_0,axiom,
    ( c_Ring__and__Field_Odvd__class_Odvd(X2,X4,X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_3538]) ).

cnf(c_0_3538_1,axiom,
    ( ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3)
    | c_Ring__and__Field_Odvd__class_Odvd(X2,X4,X3)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_3538]) ).

cnf(c_0_3538_2,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3)
    | c_Ring__and__Field_Odvd__class_Odvd(X2,X4,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_3538]) ).

cnf(c_0_3539_0,axiom,
    ( c_Ring__and__Field_Odvd__class_Odvd(X1,X4,X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_3539]) ).

cnf(c_0_3539_1,axiom,
    ( ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3)
    | c_Ring__and__Field_Odvd__class_Odvd(X1,X4,X3)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_3539]) ).

cnf(c_0_3539_2,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3)
    | c_Ring__and__Field_Odvd__class_Odvd(X1,X4,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_3539]) ).

cnf(c_0_3540_0,axiom,
    ( c_HOL_Ominus__class_Ominus(c_Nat_Osemiring__1__class_Oof__nat(X2,X3),c_Nat_Osemiring__1__class_Oof__nat(X1,X3),X3) = c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),X3)
    | ~ c_lessequals(X1,X2,tc_nat)
    | ~ class_Ring__and__Field_Oring__1(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_3540]) ).

cnf(c_0_3540_1,axiom,
    ( ~ c_lessequals(X1,X2,tc_nat)
    | c_HOL_Ominus__class_Ominus(c_Nat_Osemiring__1__class_Oof__nat(X2,X3),c_Nat_Osemiring__1__class_Oof__nat(X1,X3),X3) = c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),X3)
    | ~ class_Ring__and__Field_Oring__1(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_3540]) ).

cnf(c_0_3540_2,axiom,
    ( ~ class_Ring__and__Field_Oring__1(X3)
    | ~ c_lessequals(X1,X2,tc_nat)
    | c_HOL_Ominus__class_Ominus(c_Nat_Osemiring__1__class_Oof__nat(X2,X3),c_Nat_Osemiring__1__class_Oof__nat(X1,X3),X3) = c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_3540]) ).

cnf(c_0_3548_0,axiom,
    ( c_Divides_Odiv__class_Omod(c_Divides_Odiv__class_Omod(X4,X2,X3),X1,X3) = c_Divides_Odiv__class_Omod(X4,X1,X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
    | ~ class_Divides_Osemiring__div(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_3548]) ).

cnf(c_0_3548_1,axiom,
    ( ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
    | c_Divides_Odiv__class_Omod(c_Divides_Odiv__class_Omod(X4,X2,X3),X1,X3) = c_Divides_Odiv__class_Omod(X4,X1,X3)
    | ~ class_Divides_Osemiring__div(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_3548]) ).

cnf(c_0_3548_2,axiom,
    ( ~ class_Divides_Osemiring__div(X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
    | c_Divides_Odiv__class_Omod(c_Divides_Odiv__class_Omod(X4,X2,X3),X1,X3) = c_Divides_Odiv__class_Omod(X4,X1,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_3548]) ).

cnf(c_0_3549_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_3549]) ).

cnf(c_0_3549_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_3549]) ).

cnf(c_0_3550_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_3550]) ).

cnf(c_0_3550_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_3550]) ).

cnf(c_0_3551_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_3551]) ).

cnf(c_0_3551_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_3551]) ).

cnf(c_0_3552_0,axiom,
    ( c_Ring__and__Field_Odvd__class_Odvd(X2,X1,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X3,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X3,X1,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_3552]) ).

cnf(c_0_3552_1,axiom,
    ( ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
    | c_Ring__and__Field_Odvd__class_Odvd(X2,X1,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X3,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X3,X1,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_3552]) ).

cnf(c_0_3552_2,axiom,
    ( ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X3,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
    | c_Ring__and__Field_Odvd__class_Odvd(X2,X1,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X3,X1,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_3552]) ).

cnf(c_0_3552_3,axiom,
    ( ~ c_Ring__and__Field_Odvd__class_Odvd(X3,X1,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X3,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
    | c_Ring__and__Field_Odvd__class_Odvd(X2,X1,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_3552]) ).

cnf(c_0_3553_0,axiom,
    ( c_Ring__and__Field_Odvd__class_Odvd(X3,X2,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X3,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X3,X1,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_3553]) ).

cnf(c_0_3553_1,axiom,
    ( ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
    | c_Ring__and__Field_Odvd__class_Odvd(X3,X2,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X3,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X3,X1,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_3553]) ).

cnf(c_0_3553_2,axiom,
    ( ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X3,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
    | c_Ring__and__Field_Odvd__class_Odvd(X3,X2,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X3,X1,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_3553]) ).

cnf(c_0_3553_3,axiom,
    ( ~ c_Ring__and__Field_Odvd__class_Odvd(X3,X1,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X3,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
    | c_Ring__and__Field_Odvd__class_Odvd(X3,X2,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_3553]) ).

cnf(c_0_3554_0,axiom,
    ( c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(X3,X1),X2,X1) = c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(X3,X2,X1),X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3554]) ).

cnf(c_0_3554_1,axiom,
    ( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(X3,X1),X2,X1) = c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(X3,X2,X1),X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3554]) ).

cnf(c_0_3554_2,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(X3,X1),X2,X1) = c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(X3,X2,X1),X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3554]) ).

cnf(c_0_3555_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_3555]) ).

cnf(c_0_3555_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_3555]) ).

cnf(c_0_3555_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_3555]) ).

cnf(c_0_3556_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_3556]) ).

cnf(c_0_3556_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_3556]) ).

cnf(c_0_3557_0,axiom,
    ( c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Oplus__class_Oplus(X2,X1,tc_nat),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_3557]) ).

cnf(c_0_3557_1,axiom,
    ( ~ c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Oplus__class_Oplus(X2,X1,tc_nat),tc_nat)
    | c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_3557]) ).

cnf(c_0_3558_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_3558]) ).

cnf(c_0_3558_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_3558]) ).

cnf(c_0_3559_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_3559]) ).

cnf(c_0_3559_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_3559]) ).

cnf(c_0_3560_0,axiom,
    ( c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X1,c_HOL_Ozero__class_Ozero(X2),X2),c_HOL_Otimes__class_Otimes(X3,c_HOL_Ozero__class_Ozero(X2),X2),X2)
    | ~ class_Ring__and__Field_Oidom(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_3560]) ).

cnf(c_0_3560_1,axiom,
    ( ~ class_Ring__and__Field_Oidom(X2)
    | c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X1,c_HOL_Ozero__class_Ozero(X2),X2),c_HOL_Otimes__class_Otimes(X3,c_HOL_Ozero__class_Ozero(X2),X2),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_3560]) ).

cnf(c_0_3561_0,axiom,
    ( c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),X2,X1),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),X3,X1),X1)
    | ~ class_Ring__and__Field_Oidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3561]) ).

cnf(c_0_3561_1,axiom,
    ( ~ class_Ring__and__Field_Oidom(X1)
    | c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),X2,X1),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),X3,X1),X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3561]) ).

cnf(c_0_3562_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_3562]) ).

cnf(c_0_3562_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_3562]) ).

cnf(c_0_3562_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_3562]) ).

cnf(c_0_3562_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_3562]) ).

cnf(c_0_3562_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_3562]) ).

cnf(c_0_3563_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_3563]) ).

cnf(c_0_3563_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_3563]) ).

cnf(c_0_3563_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_3563]) ).

cnf(c_0_3563_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_3563]) ).

cnf(c_0_3563_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_3563]) ).

cnf(c_0_3564_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_3564]) ).

cnf(c_0_3564_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_3564]) ).

cnf(c_0_3565_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_3565]) ).

cnf(c_0_3565_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_3565]) ).

cnf(c_0_3565_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_3565]) ).

cnf(c_0_3565_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_3565]) ).

cnf(c_0_3566_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_3566]) ).

cnf(c_0_3566_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_3566]) ).

cnf(c_0_3567_0,axiom,
    ( c_Ring__and__Field_Odvd__class_Odvd(X3,X2,tc_nat)
    | c_Ring__and__Field_Odvd__class_Odvd(X1,X3,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X3,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_3567]) ).

cnf(c_0_3567_1,axiom,
    ( c_Ring__and__Field_Odvd__class_Odvd(X1,X3,tc_nat)
    | c_Ring__and__Field_Odvd__class_Odvd(X3,X2,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X3,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_3567]) ).

cnf(c_0_3567_2,axiom,
    ( ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
    | c_Ring__and__Field_Odvd__class_Odvd(X1,X3,tc_nat)
    | c_Ring__and__Field_Odvd__class_Odvd(X3,X2,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X3,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_3567]) ).

cnf(c_0_3567_3,axiom,
    ( ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X3,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
    | c_Ring__and__Field_Odvd__class_Odvd(X1,X3,tc_nat)
    | c_Ring__and__Field_Odvd__class_Odvd(X3,X2,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_3567]) ).

cnf(c_0_3568_0,axiom,
    ( c_Ring__and__Field_Odvd__class_Odvd(X2,X1,tc_nat)
    | c_Ring__and__Field_Odvd__class_Odvd(X1,X3,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X3,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_3568]) ).

cnf(c_0_3568_1,axiom,
    ( c_Ring__and__Field_Odvd__class_Odvd(X1,X3,tc_nat)
    | c_Ring__and__Field_Odvd__class_Odvd(X2,X1,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X3,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_3568]) ).

cnf(c_0_3568_2,axiom,
    ( ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
    | c_Ring__and__Field_Odvd__class_Odvd(X1,X3,tc_nat)
    | c_Ring__and__Field_Odvd__class_Odvd(X2,X1,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X3,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_3568]) ).

cnf(c_0_3568_3,axiom,
    ( ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X3,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
    | c_Ring__and__Field_Odvd__class_Odvd(X1,X3,tc_nat)
    | c_Ring__and__Field_Odvd__class_Odvd(X2,X1,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_3568]) ).

cnf(c_0_3570_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_3570]) ).

cnf(c_0_3570_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_3570]) ).

cnf(c_0_3570_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_3570]) ).

cnf(c_0_3571_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_3571]) ).

cnf(c_0_3571_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_3571]) ).

cnf(c_0_3571_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_3571]) ).

cnf(c_0_3572_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_3572]) ).

cnf(c_0_3572_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_3572]) ).

cnf(c_0_3573_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_3573]) ).

cnf(c_0_3573_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_3573]) ).

cnf(c_0_3573_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_3573]) ).

cnf(c_0_3574_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_3574]) ).

cnf(c_0_3574_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_3574]) ).

cnf(c_0_3574_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_3574]) ).

cnf(c_0_3575_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_3575]) ).

cnf(c_0_3575_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_3575]) ).

cnf(c_0_3575_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_3575]) ).

cnf(c_0_3576_0,axiom,
    ( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | c_Parity_Oeven__odd__class_Oeven(X1,tc_nat)
    | ~ c_Parity_Oeven__odd__class_Oeven(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),tc_nat)
    | ~ c_Parity_Oeven__odd__class_Oeven(X2,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_3576]) ).

cnf(c_0_3576_1,axiom,
    ( c_Parity_Oeven__odd__class_Oeven(X1,tc_nat)
    | c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | ~ c_Parity_Oeven__odd__class_Oeven(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),tc_nat)
    | ~ c_Parity_Oeven__odd__class_Oeven(X2,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_3576]) ).

cnf(c_0_3576_2,axiom,
    ( ~ c_Parity_Oeven__odd__class_Oeven(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),tc_nat)
    | c_Parity_Oeven__odd__class_Oeven(X1,tc_nat)
    | c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | ~ c_Parity_Oeven__odd__class_Oeven(X2,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_3576]) ).

cnf(c_0_3576_3,axiom,
    ( ~ c_Parity_Oeven__odd__class_Oeven(X2,tc_nat)
    | ~ c_Parity_Oeven__odd__class_Oeven(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),tc_nat)
    | c_Parity_Oeven__odd__class_Oeven(X1,tc_nat)
    | c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_3576]) ).

cnf(c_0_3577_0,axiom,
    ( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | c_Parity_Oeven__odd__class_Oeven(X2,tc_nat)
    | ~ c_Parity_Oeven__odd__class_Oeven(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),tc_nat)
    | ~ c_Parity_Oeven__odd__class_Oeven(X1,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_3577]) ).

cnf(c_0_3577_1,axiom,
    ( c_Parity_Oeven__odd__class_Oeven(X2,tc_nat)
    | c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | ~ c_Parity_Oeven__odd__class_Oeven(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),tc_nat)
    | ~ c_Parity_Oeven__odd__class_Oeven(X1,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_3577]) ).

cnf(c_0_3577_2,axiom,
    ( ~ c_Parity_Oeven__odd__class_Oeven(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),tc_nat)
    | c_Parity_Oeven__odd__class_Oeven(X2,tc_nat)
    | c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | ~ c_Parity_Oeven__odd__class_Oeven(X1,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_3577]) ).

cnf(c_0_3577_3,axiom,
    ( ~ c_Parity_Oeven__odd__class_Oeven(X1,tc_nat)
    | ~ c_Parity_Oeven__odd__class_Oeven(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),tc_nat)
    | c_Parity_Oeven__odd__class_Oeven(X2,tc_nat)
    | c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_3577]) ).

cnf(c_0_3581_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_3581]) ).

cnf(c_0_3581_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_3581]) ).

cnf(c_0_3582_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_3582]) ).

cnf(c_0_3582_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_3582]) ).

cnf(c_0_3582_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_3582]) ).

cnf(c_0_3583_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_3583]) ).

cnf(c_0_3583_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_3583]) ).

cnf(c_0_3583_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_3583]) ).

cnf(c_0_3584_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_3584]) ).

cnf(c_0_3584_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_3584]) ).

cnf(c_0_3585_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_3585]) ).

cnf(c_0_3585_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_3585]) ).

cnf(c_0_3585_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_3585]) ).

cnf(c_0_3586_0,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
    | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X1,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_3586]) ).

cnf(c_0_3586_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X1,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_3586]) ).

cnf(c_0_3586_2,axiom,
    ( ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X1,tc_nat)
    | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_3586]) ).

cnf(c_0_3587_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_3587]) ).

cnf(c_0_3587_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_3587]) ).

cnf(c_0_3587_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_3587]) ).

cnf(c_0_3588_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_3588]) ).

cnf(c_0_3588_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_3588]) ).

cnf(c_0_3588_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_3588]) ).

cnf(c_0_3589_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_3589]) ).

cnf(c_0_3589_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_3589]) ).

cnf(c_0_3589_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_3589]) ).

cnf(c_0_3590_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_3590]) ).

cnf(c_0_3590_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_3590]) ).

cnf(c_0_3590_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_3590]) ).

cnf(c_0_3591_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_3591]) ).

cnf(c_0_3591_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_3591]) ).

cnf(c_0_3591_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_3591]) ).

cnf(c_0_3592_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_3592]) ).

cnf(c_0_3592_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_3592]) ).

cnf(c_0_3592_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_3592]) ).

cnf(c_0_3593_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_3593]) ).

cnf(c_0_3593_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_3593]) ).

cnf(c_0_3593_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_3593]) ).

cnf(c_0_3594_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_3594]) ).

cnf(c_0_3594_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_3594]) ).

cnf(c_0_3594_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_3594]) ).

cnf(c_0_3595_0,axiom,
    ( c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Otimes__class_Otimes(X2,X4,X3),X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_3595]) ).

cnf(c_0_3595_1,axiom,
    ( ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
    | c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Otimes__class_Otimes(X2,X4,X3),X3)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_3595]) ).

cnf(c_0_3595_2,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
    | c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Otimes__class_Otimes(X2,X4,X3),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_3595]) ).

cnf(c_0_3596_0,axiom,
    ( c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Otimes__class_Otimes(X4,X2,X3),X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_3596]) ).

cnf(c_0_3596_1,axiom,
    ( ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
    | c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Otimes__class_Otimes(X4,X2,X3),X3)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_3596]) ).

cnf(c_0_3596_2,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
    | c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Otimes__class_Otimes(X4,X2,X3),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_3596]) ).

cnf(c_0_3597_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_3597]) ).

cnf(c_0_3597_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_3597]) ).

cnf(c_0_3598_0,axiom,
    ( c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X1,X2,X3),X3) = c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X2,X1,X3),X3)
    | ~ class_OrderedGroup_Opordered__ab__group__add__abs(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_3598]) ).

cnf(c_0_3598_1,axiom,
    ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X3)
    | c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X1,X2,X3),X3) = c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X2,X1,X3),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_3598]) ).

cnf(c_0_3599_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_3599]) ).

cnf(c_0_3599_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_3599]) ).

cnf(c_0_3600_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_3600]) ).

cnf(c_0_3600_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_3600]) ).

cnf(c_0_3603_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_3603]) ).

cnf(c_0_3603_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_3603]) ).

cnf(c_0_3604_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_3604]) ).

cnf(c_0_3604_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_3604]) ).

cnf(c_0_3605_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_3605]) ).

cnf(c_0_3605_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_3605]) ).

cnf(c_0_3606_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_3606]) ).

cnf(c_0_3606_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_3606]) ).

cnf(c_0_3607_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_3607]) ).

cnf(c_0_3607_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_3607]) ).

cnf(c_0_3608_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_3608]) ).

cnf(c_0_3608_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_3608]) ).

cnf(c_0_3609_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_3609]) ).

cnf(c_0_3609_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_3609]) ).

cnf(c_0_3610_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_3610]) ).

cnf(c_0_3610_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_3610]) ).

cnf(c_0_3611_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_3611]) ).

cnf(c_0_3611_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_3611]) ).

cnf(c_0_3612_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_3612]) ).

cnf(c_0_3612_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_3612]) ).

cnf(c_0_3613_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_3613]) ).

cnf(c_0_3613_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_3613]) ).

cnf(c_0_3614_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_3614]) ).

cnf(c_0_3614_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_3614]) ).

cnf(c_0_3615_0,axiom,
    ( c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Oplus__class_Oplus(X2,X1,tc_nat),tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_3615]) ).

cnf(c_0_3615_1,axiom,
    ( ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
    | c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Oplus__class_Oplus(X2,X1,tc_nat),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_3615]) ).

cnf(c_0_3616_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_3616]) ).

cnf(c_0_3616_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_3616]) ).

cnf(c_0_3617_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_3617]) ).

cnf(c_0_3617_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_3617]) ).

cnf(c_0_3618_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_3618]) ).

cnf(c_0_3618_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_3618]) ).

cnf(c_0_3619_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_3619]) ).

cnf(c_0_3619_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_3619]) ).

cnf(c_0_3620_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_3620]) ).

cnf(c_0_3620_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_3620]) ).

cnf(c_0_3620_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_3620]) ).

cnf(c_0_3620_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_3620]) ).

cnf(c_0_3621_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_3621]) ).

cnf(c_0_3621_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_3621]) ).

cnf(c_0_3621_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_3621]) ).

cnf(c_0_3621_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_3621]) ).

cnf(c_0_3622_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_3622]) ).

cnf(c_0_3622_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_3622]) ).

cnf(c_0_3622_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_3622]) ).

cnf(c_0_3622_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_3622]) ).

cnf(c_0_3623_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_3623]) ).

cnf(c_0_3623_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_3623]) ).

cnf(c_0_3623_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_3623]) ).

cnf(c_0_3623_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_3623]) ).

cnf(c_0_3624_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_3624]) ).

cnf(c_0_3624_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_3624]) ).

cnf(c_0_3624_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_3624]) ).

cnf(c_0_3624_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_3624]) ).

cnf(c_0_3625_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_3625]) ).

cnf(c_0_3625_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_3625]) ).

cnf(c_0_3625_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_3625]) ).

cnf(c_0_3625_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_3625]) ).

cnf(c_0_3626_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_3626]) ).

cnf(c_0_3626_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_3626]) ).

cnf(c_0_3626_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_3626]) ).

cnf(c_0_3626_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_3626]) ).

cnf(c_0_3627_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_3627]) ).

cnf(c_0_3627_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_3627]) ).

cnf(c_0_3627_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_3627]) ).

cnf(c_0_3627_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_3627]) ).

cnf(c_0_3628_0,axiom,
    ( c_Ring__and__Field_Odvd__class_Odvd(X1,X4,X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X4,X3)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_3628]) ).

cnf(c_0_3628_1,axiom,
    ( ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
    | c_Ring__and__Field_Odvd__class_Odvd(X1,X4,X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X4,X3)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_3628]) ).

cnf(c_0_3628_2,axiom,
    ( ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X4,X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
    | c_Ring__and__Field_Odvd__class_Odvd(X1,X4,X3)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_3628]) ).

cnf(c_0_3628_3,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X4,X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
    | c_Ring__and__Field_Odvd__class_Odvd(X1,X4,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_3628]) ).

cnf(c_0_3629_0,axiom,
    ( c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(X1,X3),c_HOL_Oabs__class_Oabs(X2,X3),X3) = c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(X1,X2,X3),X3)
    | ~ class_Ring__and__Field_Oordered__idom(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_3629]) ).

cnf(c_0_3629_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(X3)
    | c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(X1,X3),c_HOL_Oabs__class_Oabs(X2,X3),X3) = c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(X1,X2,X3),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_3629]) ).

cnf(c_0_3630_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_3630]) ).

cnf(c_0_3630_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_3630]) ).

cnf(c_0_3631_0,axiom,
    ( c_HOL_Otimes__class_Otimes(c_Nat_Osemiring__1__class_Oof__nat(X1,X3),c_Nat_Osemiring__1__class_Oof__nat(X2,X3),X3) = c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),X3)
    | ~ class_Ring__and__Field_Osemiring__1(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_3631]) ).

cnf(c_0_3631_1,axiom,
    ( ~ class_Ring__and__Field_Osemiring__1(X3)
    | c_HOL_Otimes__class_Otimes(c_Nat_Osemiring__1__class_Oof__nat(X1,X3),c_Nat_Osemiring__1__class_Oof__nat(X2,X3),X3) = c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_3631]) ).

cnf(c_0_3632_0,axiom,
    ( c_HOL_Oplus__class_Oplus(c_Nat_Osemiring__1__class_Oof__nat(X1,X3),c_Nat_Osemiring__1__class_Oof__nat(X2,X3),X3) = c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),X3)
    | ~ class_Ring__and__Field_Osemiring__1(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_3632]) ).

cnf(c_0_3632_1,axiom,
    ( ~ class_Ring__and__Field_Osemiring__1(X3)
    | c_HOL_Oplus__class_Oplus(c_Nat_Osemiring__1__class_Oof__nat(X1,X3),c_Nat_Osemiring__1__class_Oof__nat(X2,X3),X3) = c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_3632]) ).

cnf(c_0_3633_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),X1,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X1,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_3633]) ).

cnf(c_0_3633_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),X2,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X1,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_3633]) ).

cnf(c_0_3633_2,axiom,
    ( ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X1,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_3633]) ).

cnf(c_0_3634_0,axiom,
    ( c_HOL_Oord__class_Oless(X1,X3,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X1,X2),c_Nat_Osemiring__1__class_Oof__nat(X3,X2),X2)
    | ~ class_Ring__and__Field_Oordered__semidom(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_3634]) ).

cnf(c_0_3634_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X1,X2),c_Nat_Osemiring__1__class_Oof__nat(X3,X2),X2)
    | c_HOL_Oord__class_Oless(X1,X3,tc_nat)
    | ~ class_Ring__and__Field_Oordered__semidom(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_3634]) ).

cnf(c_0_3634_2,axiom,
    ( ~ class_Ring__and__Field_Oordered__semidom(X2)
    | ~ c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X1,X2),c_Nat_Osemiring__1__class_Oof__nat(X3,X2),X2)
    | c_HOL_Oord__class_Oless(X1,X3,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_3634]) ).

cnf(c_0_3635_0,axiom,
    ( c_lessequals(X1,X3,tc_nat)
    | ~ c_lessequals(c_Nat_Osemiring__1__class_Oof__nat(X1,X2),c_Nat_Osemiring__1__class_Oof__nat(X3,X2),X2)
    | ~ class_Ring__and__Field_Oordered__semidom(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_3635]) ).

cnf(c_0_3635_1,axiom,
    ( ~ c_lessequals(c_Nat_Osemiring__1__class_Oof__nat(X1,X2),c_Nat_Osemiring__1__class_Oof__nat(X3,X2),X2)
    | c_lessequals(X1,X3,tc_nat)
    | ~ class_Ring__and__Field_Oordered__semidom(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_3635]) ).

cnf(c_0_3635_2,axiom,
    ( ~ class_Ring__and__Field_Oordered__semidom(X2)
    | ~ c_lessequals(c_Nat_Osemiring__1__class_Oof__nat(X1,X2),c_Nat_Osemiring__1__class_Oof__nat(X3,X2),X2)
    | c_lessequals(X1,X3,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_3635]) ).

cnf(c_0_3636_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_3636]) ).

cnf(c_0_3636_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_3636]) ).

cnf(c_0_3636_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_3636]) ).

cnf(c_0_3637_0,axiom,
    ( c_lessequals(X1,X2,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,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_3637]) ).

cnf(c_0_3637_1,axiom,
    ( ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
    | c_lessequals(X1,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_3637]) ).

cnf(c_0_3637_2,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
    | c_lessequals(X1,X2,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_3637]) ).

cnf(c_0_3638_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_3638]) ).

cnf(c_0_3638_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_3638]) ).

cnf(c_0_3639_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_3639]) ).

cnf(c_0_3639_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_3639]) ).

cnf(c_0_3640_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_3640]) ).

cnf(c_0_3640_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_3640]) ).

cnf(c_0_3641_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_3641]) ).

cnf(c_0_3641_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_3641]) ).

cnf(c_0_3642_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_3642]) ).

cnf(c_0_3642_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_3642]) ).

cnf(c_0_3643_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_3643]) ).

cnf(c_0_3643_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_3643]) ).

cnf(c_0_3644_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_3644]) ).

cnf(c_0_3644_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_3644]) ).

cnf(c_0_3644_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_3644]) ).

cnf(c_0_3645_0,axiom,
    ( c_Ring__and__Field_Odvd__class_Odvd(X1,X3,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X3,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_3645]) ).

cnf(c_0_3645_1,axiom,
    ( ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
    | c_Ring__and__Field_Odvd__class_Odvd(X1,X3,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X3,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_3645]) ).

cnf(c_0_3645_2,axiom,
    ( ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X3,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
    | c_Ring__and__Field_Odvd__class_Odvd(X1,X3,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_3645]) ).

cnf(c_0_3646_0,axiom,
    ( c_Parity_Oeven__odd__class_Oeven(X1,tc_nat)
    | ~ c_Parity_Oeven__odd__class_Oeven(X2,tc_nat)
    | ~ c_Parity_Oeven__odd__class_Oeven(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_3646]) ).

cnf(c_0_3646_1,axiom,
    ( ~ c_Parity_Oeven__odd__class_Oeven(X2,tc_nat)
    | c_Parity_Oeven__odd__class_Oeven(X1,tc_nat)
    | ~ c_Parity_Oeven__odd__class_Oeven(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_3646]) ).

cnf(c_0_3646_2,axiom,
    ( ~ c_Parity_Oeven__odd__class_Oeven(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat)
    | ~ c_Parity_Oeven__odd__class_Oeven(X2,tc_nat)
    | c_Parity_Oeven__odd__class_Oeven(X1,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_3646]) ).

cnf(c_0_3647_0,axiom,
    ( c_Parity_Oeven__odd__class_Oeven(X2,tc_nat)
    | ~ c_Parity_Oeven__odd__class_Oeven(X1,tc_nat)
    | ~ c_Parity_Oeven__odd__class_Oeven(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_3647]) ).

cnf(c_0_3647_1,axiom,
    ( ~ c_Parity_Oeven__odd__class_Oeven(X1,tc_nat)
    | c_Parity_Oeven__odd__class_Oeven(X2,tc_nat)
    | ~ c_Parity_Oeven__odd__class_Oeven(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_3647]) ).

cnf(c_0_3647_2,axiom,
    ( ~ c_Parity_Oeven__odd__class_Oeven(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat)
    | ~ c_Parity_Oeven__odd__class_Oeven(X1,tc_nat)
    | c_Parity_Oeven__odd__class_Oeven(X2,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_3647]) ).

cnf(c_0_3648_0,axiom,
    ( c_Parity_Oeven__odd__class_Oeven(X2,tc_nat)
    | ~ c_Parity_Oeven__odd__class_Oeven(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat)
    | ~ c_Parity_Oeven__odd__class_Oeven(X1,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_3648]) ).

cnf(c_0_3648_1,axiom,
    ( ~ c_Parity_Oeven__odd__class_Oeven(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat)
    | c_Parity_Oeven__odd__class_Oeven(X2,tc_nat)
    | ~ c_Parity_Oeven__odd__class_Oeven(X1,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_3648]) ).

cnf(c_0_3648_2,axiom,
    ( ~ c_Parity_Oeven__odd__class_Oeven(X1,tc_nat)
    | ~ c_Parity_Oeven__odd__class_Oeven(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat)
    | c_Parity_Oeven__odd__class_Oeven(X2,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_3648]) ).

cnf(c_0_3649_0,axiom,
    ( c_Parity_Oeven__odd__class_Oeven(X1,tc_nat)
    | ~ c_Parity_Oeven__odd__class_Oeven(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat)
    | ~ c_Parity_Oeven__odd__class_Oeven(X2,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_3649]) ).

cnf(c_0_3649_1,axiom,
    ( ~ c_Parity_Oeven__odd__class_Oeven(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat)
    | c_Parity_Oeven__odd__class_Oeven(X1,tc_nat)
    | ~ c_Parity_Oeven__odd__class_Oeven(X2,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_3649]) ).

cnf(c_0_3649_2,axiom,
    ( ~ c_Parity_Oeven__odd__class_Oeven(X2,tc_nat)
    | ~ c_Parity_Oeven__odd__class_Oeven(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat)
    | c_Parity_Oeven__odd__class_Oeven(X1,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_3649]) ).

cnf(c_0_3650_0,axiom,
    ( c_Parity_Oeven__odd__class_Oeven(X1,tc_nat)
    | ~ c_Parity_Oeven__odd__class_Oeven(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat)
    | ~ c_Parity_Oeven__odd__class_Oeven(X2,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_3650]) ).

cnf(c_0_3650_1,axiom,
    ( ~ c_Parity_Oeven__odd__class_Oeven(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat)
    | c_Parity_Oeven__odd__class_Oeven(X1,tc_nat)
    | ~ c_Parity_Oeven__odd__class_Oeven(X2,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_3650]) ).

cnf(c_0_3650_2,axiom,
    ( ~ c_Parity_Oeven__odd__class_Oeven(X2,tc_nat)
    | ~ c_Parity_Oeven__odd__class_Oeven(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat)
    | c_Parity_Oeven__odd__class_Oeven(X1,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_3650]) ).

cnf(c_0_3651_0,axiom,
    ( c_Parity_Oeven__odd__class_Oeven(X2,tc_nat)
    | ~ c_Parity_Oeven__odd__class_Oeven(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat)
    | ~ c_Parity_Oeven__odd__class_Oeven(X1,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_3651]) ).

cnf(c_0_3651_1,axiom,
    ( ~ c_Parity_Oeven__odd__class_Oeven(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat)
    | c_Parity_Oeven__odd__class_Oeven(X2,tc_nat)
    | ~ c_Parity_Oeven__odd__class_Oeven(X1,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_3651]) ).

cnf(c_0_3651_2,axiom,
    ( ~ c_Parity_Oeven__odd__class_Oeven(X1,tc_nat)
    | ~ c_Parity_Oeven__odd__class_Oeven(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat)
    | c_Parity_Oeven__odd__class_Oeven(X2,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_3651]) ).

cnf(c_0_3654_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_3654]) ).

cnf(c_0_3654_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_3654]) ).

cnf(c_0_3655_0,axiom,
    ( c_Parity_Oeven__odd__class_Oeven(X1,tc_nat)
    | c_Parity_Oeven__odd__class_Oeven(X2,tc_nat)
    | ~ c_Parity_Oeven__odd__class_Oeven(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_3655]) ).

cnf(c_0_3655_1,axiom,
    ( c_Parity_Oeven__odd__class_Oeven(X2,tc_nat)
    | c_Parity_Oeven__odd__class_Oeven(X1,tc_nat)
    | ~ c_Parity_Oeven__odd__class_Oeven(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_3655]) ).

cnf(c_0_3655_2,axiom,
    ( ~ c_Parity_Oeven__odd__class_Oeven(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),tc_nat)
    | c_Parity_Oeven__odd__class_Oeven(X2,tc_nat)
    | c_Parity_Oeven__odd__class_Oeven(X1,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_3655]) ).

cnf(c_0_3656_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_3656]) ).

cnf(c_0_3656_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_3656]) ).

cnf(c_0_3656_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_3656]) ).

cnf(c_0_3656_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_3656]) ).

cnf(c_0_3657_0,axiom,
    ( c_Parity_Oeven__odd__class_Oeven(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),tc_nat)
    | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_3657]) ).

cnf(c_0_3657_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | c_Parity_Oeven__odd__class_Oeven(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_3657]) ).

cnf(c_0_3658_0,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Nat_Osemiring__1__class_Oof__nat(X2,X1),X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3658]) ).

cnf(c_0_3658_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Nat_Osemiring__1__class_Oof__nat(X2,X1),X1)
    | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3658]) ).

cnf(c_0_3658_2,axiom,
    ( ~ class_Ring__and__Field_Oordered__semidom(X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Nat_Osemiring__1__class_Oof__nat(X2,X1),X1)
    | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_3658]) ).

cnf(c_0_3659_0,axiom,
    ( c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X1,X3),c_Nat_Osemiring__1__class_Oof__nat(X2,X3),X3)
    | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | ~ class_Ring__and__Field_Oordered__semidom(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_3659]) ).

cnf(c_0_3659_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X1,X3),c_Nat_Osemiring__1__class_Oof__nat(X2,X3),X3)
    | ~ class_Ring__and__Field_Oordered__semidom(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_3659]) ).

cnf(c_0_3659_2,axiom,
    ( ~ class_Ring__and__Field_Oordered__semidom(X3)
    | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X1,X3),c_Nat_Osemiring__1__class_Oof__nat(X2,X3),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_3659]) ).

cnf(c_0_3660_0,axiom,
    ( c_lessequals(c_Nat_Osemiring__1__class_Oof__nat(X1,X3),c_Nat_Osemiring__1__class_Oof__nat(X2,X3),X3)
    | ~ c_lessequals(X1,X2,tc_nat)
    | ~ class_Ring__and__Field_Oordered__semidom(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_3660]) ).

cnf(c_0_3660_1,axiom,
    ( ~ c_lessequals(X1,X2,tc_nat)
    | c_lessequals(c_Nat_Osemiring__1__class_Oof__nat(X1,X3),c_Nat_Osemiring__1__class_Oof__nat(X2,X3),X3)
    | ~ class_Ring__and__Field_Oordered__semidom(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_3660]) ).

cnf(c_0_3660_2,axiom,
    ( ~ class_Ring__and__Field_Oordered__semidom(X3)
    | ~ c_lessequals(X1,X2,tc_nat)
    | c_lessequals(c_Nat_Osemiring__1__class_Oof__nat(X1,X3),c_Nat_Osemiring__1__class_Oof__nat(X2,X3),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_3660]) ).

cnf(c_0_3661_0,axiom,
    ( c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Oabs__class_Oabs(X2,X3),X3)
    | ~ class_Ring__and__Field_Oordered__idom(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_3661]) ).

cnf(c_0_3661_1,axiom,
    ( ~ c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Oabs__class_Oabs(X2,X3),X3)
    | c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
    | ~ class_Ring__and__Field_Oordered__idom(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_3661]) ).

cnf(c_0_3661_2,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Oabs__class_Oabs(X2,X3),X3)
    | c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_3661]) ).

cnf(c_0_3662_0,axiom,
    ( c_Ring__and__Field_Odvd__class_Odvd(X1,X3,X2)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oabs__class_Oabs(X1,X2),X3,X2)
    | ~ class_Ring__and__Field_Oordered__idom(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_3662]) ).

cnf(c_0_3662_1,axiom,
    ( ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oabs__class_Oabs(X1,X2),X3,X2)
    | c_Ring__and__Field_Odvd__class_Odvd(X1,X3,X2)
    | ~ class_Ring__and__Field_Oordered__idom(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_3662]) ).

cnf(c_0_3662_2,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(X2)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oabs__class_Oabs(X1,X2),X3,X2)
    | c_Ring__and__Field_Odvd__class_Odvd(X1,X3,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_3662]) ).

cnf(c_0_3663_0,axiom,
    ( c_HOL_Oord__class_Oless(X1,X3,X2)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(X1,X2),X3,X2)
    | ~ class_Ring__and__Field_Oordered__idom(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_3663]) ).

cnf(c_0_3663_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(X1,X2),X3,X2)
    | c_HOL_Oord__class_Oless(X1,X3,X2)
    | ~ class_Ring__and__Field_Oordered__idom(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_3663]) ).

cnf(c_0_3663_2,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(X2)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(X1,X2),X3,X2)
    | c_HOL_Oord__class_Oless(X1,X3,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_3663]) ).

cnf(c_0_3664_0,axiom,
    ( c_lessequals(X1,X3,X2)
    | ~ c_lessequals(c_HOL_Oabs__class_Oabs(X1,X2),X3,X2)
    | ~ class_OrderedGroup_Opordered__ab__group__add__abs(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_3664]) ).

cnf(c_0_3664_1,axiom,
    ( ~ c_lessequals(c_HOL_Oabs__class_Oabs(X1,X2),X3,X2)
    | c_lessequals(X1,X3,X2)
    | ~ class_OrderedGroup_Opordered__ab__group__add__abs(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_3664]) ).

cnf(c_0_3664_2,axiom,
    ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X2)
    | ~ c_lessequals(c_HOL_Oabs__class_Oabs(X1,X2),X3,X2)
    | c_lessequals(X1,X3,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_3664]) ).

cnf(c_0_3665_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_3665]) ).

cnf(c_0_3665_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_3665]) ).

cnf(c_0_3665_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_3665]) ).

cnf(c_0_3665_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_3665]) ).

cnf(c_0_3666_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_3666]) ).

cnf(c_0_3666_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_3666]) ).

cnf(c_0_3667_0,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),c_Nat_Osemiring__1__class_Oof__nat(X1,X2),X2)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
    | ~ class_Ring__and__Field_Oordered__semidom(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_3667]) ).

cnf(c_0_3667_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
    | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),c_Nat_Osemiring__1__class_Oof__nat(X1,X2),X2)
    | ~ class_Ring__and__Field_Oordered__semidom(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_3667]) ).

cnf(c_0_3667_2,axiom,
    ( ~ class_Ring__and__Field_Oordered__semidom(X2)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
    | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),c_Nat_Osemiring__1__class_Oof__nat(X1,X2),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_3667]) ).

cnf(c_0_3668_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_3668]) ).

cnf(c_0_3668_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_3668]) ).

cnf(c_0_3668_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_3668]) ).

cnf(c_0_3668_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_3668]) ).

cnf(c_0_3669_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_3669]) ).

cnf(c_0_3669_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_3669]) ).

cnf(c_0_3669_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_3669]) ).

cnf(c_0_3669_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_3669]) ).

cnf(c_0_3670_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_3670]) ).

cnf(c_0_3670_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_3670]) ).

cnf(c_0_3670_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_3670]) ).

cnf(c_0_3670_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_3670]) ).

cnf(c_0_3671_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_3671]) ).

cnf(c_0_3671_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_3671]) ).

cnf(c_0_3671_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_3671]) ).

cnf(c_0_3672_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_3672]) ).

cnf(c_0_3672_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_3672]) ).

cnf(c_0_3672_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_3672]) ).

cnf(c_0_3673_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_3673]) ).

cnf(c_0_3673_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_3673]) ).

cnf(c_0_3673_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_3673]) ).

cnf(c_0_3674_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_3674]) ).

cnf(c_0_3674_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_3674]) ).

cnf(c_0_3674_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_3674]) ).

cnf(c_0_3675_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_3675]) ).

cnf(c_0_3675_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_3675]) ).

cnf(c_0_3675_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_3675]) ).

cnf(c_0_3676_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_3676]) ).

cnf(c_0_3676_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_3676]) ).

cnf(c_0_3676_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_3676]) ).

cnf(c_0_3677_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_3677]) ).

cnf(c_0_3677_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_3677]) ).

cnf(c_0_3677_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_3677]) ).

cnf(c_0_3678_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_3678]) ).

cnf(c_0_3678_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_3678]) ).

cnf(c_0_3678_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_3678]) ).

cnf(c_0_3679_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_3679]) ).

cnf(c_0_3679_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_3679]) ).

cnf(c_0_3679_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_3679]) ).

cnf(c_0_3680_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_3680]) ).

cnf(c_0_3680_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_3680]) ).

cnf(c_0_3680_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_3680]) ).

cnf(c_0_3681_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_3681]) ).

cnf(c_0_3681_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_3681]) ).

cnf(c_0_3681_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_3681]) ).

cnf(c_0_3682_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_3682]) ).

cnf(c_0_3682_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_3682]) ).

cnf(c_0_3682_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_3682]) ).

cnf(c_0_3683_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_3683]) ).

cnf(c_0_3683_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_3683]) ).

cnf(c_0_3683_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_3683]) ).

cnf(c_0_3684_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_3684]) ).

cnf(c_0_3684_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_3684]) ).

cnf(c_0_3684_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_3684]) ).

cnf(c_0_3686_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_3686]) ).

cnf(c_0_3686_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_3686]) ).

cnf(c_0_3687_0,axiom,
    ( ~ c_lessequals(c_Suc(X1),X2,tc_nat)
    | ~ c_lessequals(X2,X1,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_3687]) ).

cnf(c_0_3687_1,axiom,
    ( ~ c_lessequals(X2,X1,tc_nat)
    | ~ c_lessequals(c_Suc(X1),X2,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_3687]) ).

cnf(c_0_3688_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_3688]) ).

cnf(c_0_3688_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_3688]) ).

cnf(c_0_3688_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_3688]) ).

cnf(c_0_3689_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_3689]) ).

cnf(c_0_3689_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_3689]) ).

cnf(c_0_3690_0,axiom,
    ( c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Oabs__class_Oabs(X2,X3),X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
    | ~ class_Ring__and__Field_Oordered__idom(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_3690]) ).

cnf(c_0_3690_1,axiom,
    ( ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
    | c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Oabs__class_Oabs(X2,X3),X3)
    | ~ class_Ring__and__Field_Oordered__idom(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_3690]) ).

cnf(c_0_3690_2,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
    | c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Oabs__class_Oabs(X2,X3),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_3690]) ).

cnf(c_0_3691_0,axiom,
    ( c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oabs__class_Oabs(X1,X3),X2,X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
    | ~ class_Ring__and__Field_Oordered__idom(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_3691]) ).

cnf(c_0_3691_1,axiom,
    ( ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
    | c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oabs__class_Oabs(X1,X3),X2,X3)
    | ~ class_Ring__and__Field_Oordered__idom(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_3691]) ).

cnf(c_0_3691_2,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
    | c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oabs__class_Oabs(X1,X3),X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_3691]) ).

cnf(c_0_3693_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_3693]) ).

cnf(c_0_3693_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_3693]) ).

cnf(c_0_3694_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_3694]) ).

cnf(c_0_3694_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_3694]) ).

cnf(c_0_3695_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_3695]) ).

cnf(c_0_3695_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_3695]) ).

cnf(c_0_3695_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_3695]) ).

cnf(c_0_3696_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_3696]) ).

cnf(c_0_3696_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_3696]) ).

cnf(c_0_3696_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_3696]) ).

cnf(c_0_3697_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_3697]) ).

cnf(c_0_3697_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_3697]) ).

cnf(c_0_3697_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_3697]) ).

cnf(c_0_3698_0,axiom,
    ( X1 = X2
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X1,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_3698]) ).

cnf(c_0_3698_1,axiom,
    ( ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
    | X1 = X2
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X1,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_3698]) ).

cnf(c_0_3698_2,axiom,
    ( ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X1,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
    | X1 = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_3698]) ).

cnf(c_0_3699_0,axiom,
    ( X1 = X2
    | ~ c_lessequals(X1,X2,tc_nat)
    | ~ c_lessequals(X2,X1,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_3699]) ).

cnf(c_0_3699_1,axiom,
    ( ~ c_lessequals(X1,X2,tc_nat)
    | X1 = X2
    | ~ c_lessequals(X2,X1,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_3699]) ).

cnf(c_0_3699_2,axiom,
    ( ~ c_lessequals(X2,X1,tc_nat)
    | ~ c_lessequals(X1,X2,tc_nat)
    | X1 = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_3699]) ).

cnf(c_0_3700_0,axiom,
    ( X1 = X2
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X1,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_3700]) ).

cnf(c_0_3700_1,axiom,
    ( ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
    | X1 = X2
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X1,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_3700]) ).

cnf(c_0_3700_2,axiom,
    ( ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X1,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
    | X1 = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_3700]) ).

cnf(c_0_3701_0,axiom,
    ( X1 = X2
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X1,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_3701]) ).

cnf(c_0_3701_1,axiom,
    ( ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
    | X1 = X2
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X1,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_3701]) ).

cnf(c_0_3701_2,axiom,
    ( ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X1,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
    | X1 = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_3701]) ).

cnf(c_0_3702_0,axiom,
    ( X1 = X2
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X1,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_3702]) ).

cnf(c_0_3702_1,axiom,
    ( ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
    | X1 = X2
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X1,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_3702]) ).

cnf(c_0_3702_2,axiom,
    ( ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X1,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
    | X1 = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_3702]) ).

cnf(c_0_3703_0,axiom,
    ( X2 = X1
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X1,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_3703]) ).

cnf(c_0_3703_1,axiom,
    ( ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
    | X2 = X1
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X1,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_3703]) ).

cnf(c_0_3703_2,axiom,
    ( ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X1,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
    | X2 = X1 ),
    inference(literals_permutation,[status(thm)],[c_0_3703]) ).

cnf(c_0_3704_0,axiom,
    ( X1 = X2
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X1,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_3704]) ).

cnf(c_0_3704_1,axiom,
    ( ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
    | X1 = X2
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X1,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_3704]) ).

cnf(c_0_3704_2,axiom,
    ( ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X1,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
    | X1 = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_3704]) ).

cnf(c_0_3705_0,axiom,
    ( X1 = X2
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X1,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_3705]) ).

cnf(c_0_3705_1,axiom,
    ( ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
    | X1 = X2
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X1,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_3705]) ).

cnf(c_0_3705_2,axiom,
    ( ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X1,tc_nat)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
    | X1 = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_3705]) ).

cnf(c_0_3706_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_3706]) ).

cnf(c_0_3706_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_3706]) ).

cnf(c_0_3707_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_3707]) ).

cnf(c_0_3707_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_3707]) ).

cnf(c_0_3708_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_3708]) ).

cnf(c_0_3708_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_3708]) ).

cnf(c_0_3709_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_3709]) ).

cnf(c_0_3709_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_3709]) ).

cnf(c_0_3710_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_3710]) ).

cnf(c_0_3710_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_3710]) ).

cnf(c_0_3711_0,axiom,
    ( c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Otimes__class_Otimes(X1,X2,X3),X3)
    | ~ class_Ring__and__Field_Odvd(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_3711]) ).

cnf(c_0_3711_1,axiom,
    ( ~ class_Ring__and__Field_Odvd(X3)
    | c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Otimes__class_Otimes(X1,X2,X3),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_3711]) ).

cnf(c_0_3712_0,axiom,
    ( c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Otimes__class_Otimes(X1,X2,X3),X3)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_3712]) ).

cnf(c_0_3712_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
    | c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Otimes__class_Otimes(X1,X2,X3),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_3712]) ).

cnf(c_0_3713_0,axiom,
    ( c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Otimes__class_Otimes(X2,X1,X3),X3)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_3713]) ).

cnf(c_0_3713_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
    | c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Otimes__class_Otimes(X2,X1,X3),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_3713]) ).

cnf(c_0_3714_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_3714]) ).

cnf(c_0_3714_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_3714]) ).

cnf(c_0_3715_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_3715]) ).

cnf(c_0_3715_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_3715]) ).

cnf(c_0_3716_0,axiom,
    ( c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(X1,X2),c_HOL_Oabs__class_Oabs(X1,X2),X2) = c_HOL_Otimes__class_Otimes(X1,X1,X2)
    | ~ class_Ring__and__Field_Oordered__idom(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_3716]) ).

cnf(c_0_3716_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(X2)
    | c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(X1,X2),c_HOL_Oabs__class_Oabs(X1,X2),X2) = c_HOL_Otimes__class_Otimes(X1,X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_3716]) ).

cnf(c_0_3720_0,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oabs__class_Oabs(c_HOL_Ozero__class_Ozero(X1),X1),X1)
    | ~ class_OrderedGroup_Opordered__ab__group__add__abs(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3720]) ).

cnf(c_0_3720_1,axiom,
    ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oabs__class_Oabs(c_HOL_Ozero__class_Ozero(X1),X1),X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3720]) ).

cnf(c_0_3721_0,axiom,
    ( ~ c_Parity_Oeven__odd__class_Oeven(X1,tc_nat)
    | c_Divides_Odiv__class_Omod(X1,c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
    inference(literals_permutation,[status(thm)],[c_0_3721]) ).

cnf(c_0_3721_1,axiom,
    ( c_Divides_Odiv__class_Omod(X1,c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
    | ~ c_Parity_Oeven__odd__class_Oeven(X1,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_3721]) ).

cnf(c_0_3726_0,axiom,
    ( c_Parity_Oeven__odd__class_Oeven(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),tc_nat)
    | ~ c_Parity_Oeven__odd__class_Oeven(X1,tc_nat)
    | ~ c_Parity_Oeven__odd__class_Oeven(X2,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_3726]) ).

cnf(c_0_3726_1,axiom,
    ( ~ c_Parity_Oeven__odd__class_Oeven(X1,tc_nat)
    | c_Parity_Oeven__odd__class_Oeven(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),tc_nat)
    | ~ c_Parity_Oeven__odd__class_Oeven(X2,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_3726]) ).

cnf(c_0_3726_2,axiom,
    ( ~ c_Parity_Oeven__odd__class_Oeven(X2,tc_nat)
    | ~ c_Parity_Oeven__odd__class_Oeven(X1,tc_nat)
    | c_Parity_Oeven__odd__class_Oeven(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_3726]) ).

cnf(c_0_3727_0,axiom,
    ( c_Parity_Oeven__odd__class_Oeven(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat)
    | ~ c_Parity_Oeven__odd__class_Oeven(X1,tc_nat)
    | ~ c_Parity_Oeven__odd__class_Oeven(X2,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_3727]) ).

cnf(c_0_3727_1,axiom,
    ( ~ c_Parity_Oeven__odd__class_Oeven(X1,tc_nat)
    | c_Parity_Oeven__odd__class_Oeven(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat)
    | ~ c_Parity_Oeven__odd__class_Oeven(X2,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_3727]) ).

cnf(c_0_3727_2,axiom,
    ( ~ c_Parity_Oeven__odd__class_Oeven(X2,tc_nat)
    | ~ c_Parity_Oeven__odd__class_Oeven(X1,tc_nat)
    | c_Parity_Oeven__odd__class_Oeven(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_3727]) ).

cnf(c_0_3728_0,axiom,
    ( c_Parity_Oeven__odd__class_Oeven(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat)
    | ~ c_Parity_Oeven__odd__class_Oeven(X1,tc_nat)
    | ~ c_Parity_Oeven__odd__class_Oeven(X2,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_3728]) ).

cnf(c_0_3728_1,axiom,
    ( ~ c_Parity_Oeven__odd__class_Oeven(X1,tc_nat)
    | c_Parity_Oeven__odd__class_Oeven(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat)
    | ~ c_Parity_Oeven__odd__class_Oeven(X2,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_3728]) ).

cnf(c_0_3728_2,axiom,
    ( ~ c_Parity_Oeven__odd__class_Oeven(X2,tc_nat)
    | ~ c_Parity_Oeven__odd__class_Oeven(X1,tc_nat)
    | c_Parity_Oeven__odd__class_Oeven(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_3728]) ).

cnf(c_0_3729_0,axiom,
    ( c_Parity_Oeven__odd__class_Oeven(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat)
    | ~ c_Parity_Oeven__odd__class_Oeven(X1,tc_nat)
    | ~ c_Parity_Oeven__odd__class_Oeven(X2,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_3729]) ).

cnf(c_0_3729_1,axiom,
    ( ~ c_Parity_Oeven__odd__class_Oeven(X1,tc_nat)
    | c_Parity_Oeven__odd__class_Oeven(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat)
    | ~ c_Parity_Oeven__odd__class_Oeven(X2,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_3729]) ).

cnf(c_0_3729_2,axiom,
    ( ~ c_Parity_Oeven__odd__class_Oeven(X2,tc_nat)
    | ~ c_Parity_Oeven__odd__class_Oeven(X1,tc_nat)
    | c_Parity_Oeven__odd__class_Oeven(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_3729]) ).

cnf(c_0_3737_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_3737]) ).

cnf(c_0_3737_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_3737]) ).

cnf(c_0_3738_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_3738]) ).

cnf(c_0_3738_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_3738]) ).

cnf(c_0_3739_0,axiom,
    ( c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
    | c_Divides_Odiv__class_Omod(X2,X1,X3) != c_HOL_Ozero__class_Ozero(X3)
    | ~ class_Divides_Osemiring__div(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_3739]) ).

cnf(c_0_3739_1,axiom,
    ( c_Divides_Odiv__class_Omod(X2,X1,X3) != c_HOL_Ozero__class_Ozero(X3)
    | c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
    | ~ class_Divides_Osemiring__div(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_3739]) ).

cnf(c_0_3739_2,axiom,
    ( ~ class_Divides_Osemiring__div(X3)
    | c_Divides_Odiv__class_Omod(X2,X1,X3) != c_HOL_Ozero__class_Ozero(X3)
    | c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_3739]) ).

cnf(c_0_3740_0,axiom,
    ( c_Divides_Odiv__class_Omod(X2,X1,X3) = c_HOL_Ozero__class_Ozero(X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
    | ~ class_Divides_Osemiring__div(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_3740]) ).

cnf(c_0_3740_1,axiom,
    ( ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
    | c_Divides_Odiv__class_Omod(X2,X1,X3) = c_HOL_Ozero__class_Ozero(X3)
    | ~ class_Divides_Osemiring__div(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_3740]) ).

cnf(c_0_3740_2,axiom,
    ( ~ class_Divides_Osemiring__div(X3)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
    | c_Divides_Odiv__class_Omod(X2,X1,X3) = c_HOL_Ozero__class_Ozero(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_3740]) ).

cnf(c_0_3741_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_3741]) ).

cnf(c_0_3741_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_3741]) ).

cnf(c_0_3741_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_3741]) ).

cnf(c_0_3742_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_3742]) ).

cnf(c_0_3742_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_3742]) ).

cnf(c_0_3742_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_3742]) ).

cnf(c_0_3742_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_3742]) ).

cnf(c_0_3743_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_3743]) ).

cnf(c_0_3743_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_3743]) ).

cnf(c_0_3743_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_3743]) ).

cnf(c_0_3743_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_3743]) ).

cnf(c_0_3744_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_3744]) ).

cnf(c_0_3744_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_3744]) ).

cnf(c_0_3744_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_3744]) ).

cnf(c_0_3744_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_3744]) ).

cnf(c_0_3745_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_3745]) ).

cnf(c_0_3745_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_3745]) ).

cnf(c_0_3745_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_3745]) ).

cnf(c_0_3745_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_3745]) ).

cnf(c_0_3746_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_3746]) ).

cnf(c_0_3746_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_3746]) ).

cnf(c_0_3746_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_3746]) ).

cnf(c_0_3746_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_3746]) ).

cnf(c_0_3747_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_3747]) ).

cnf(c_0_3747_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_3747]) ).

cnf(c_0_3747_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_3747]) ).

cnf(c_0_3747_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_3747]) ).

cnf(c_0_3748_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_3748]) ).

cnf(c_0_3748_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_3748]) ).

cnf(c_0_3748_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_3748]) ).

cnf(c_0_3748_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_3748]) ).

cnf(c_0_3749_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_3749]) ).

cnf(c_0_3749_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_3749]) ).

cnf(c_0_3749_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_3749]) ).

cnf(c_0_3749_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_3749]) ).

cnf(c_0_3750_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_3750]) ).

cnf(c_0_3750_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_3750]) ).

cnf(c_0_3750_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_3750]) ).

cnf(c_0_3751_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_3751]) ).

cnf(c_0_3751_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_3751]) ).

cnf(c_0_3752_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_3752]) ).

cnf(c_0_3752_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_3752]) ).

cnf(c_0_3753_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_3753]) ).

cnf(c_0_3753_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_3753]) ).

cnf(c_0_3754_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_3754]) ).

cnf(c_0_3754_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_3754]) ).

cnf(c_0_3754_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_3754]) ).

cnf(c_0_3755_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_3755]) ).

cnf(c_0_3755_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_3755]) ).

cnf(c_0_3755_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_3755]) ).

cnf(c_0_3756_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_3756]) ).

cnf(c_0_3756_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_3756]) ).

cnf(c_0_3756_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_3756]) ).

cnf(c_0_3757_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_3757]) ).

cnf(c_0_3757_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_3757]) ).

cnf(c_0_3757_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_3757]) ).

cnf(c_0_3758_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_3758]) ).

cnf(c_0_3758_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_3758]) ).

cnf(c_0_3758_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_3758]) ).

cnf(c_0_3759_0,axiom,
    ( X1 = c_HOL_Ozero__class_Ozero(X2)
    | ~ c_lessequals(c_HOL_Oabs__class_Oabs(X1,X2),c_HOL_Ozero__class_Ozero(X2),X2)
    | ~ class_OrderedGroup_Opordered__ab__group__add__abs(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_3759]) ).

cnf(c_0_3759_1,axiom,
    ( ~ c_lessequals(c_HOL_Oabs__class_Oabs(X1,X2),c_HOL_Ozero__class_Ozero(X2),X2)
    | X1 = c_HOL_Ozero__class_Ozero(X2)
    | ~ class_OrderedGroup_Opordered__ab__group__add__abs(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_3759]) ).

cnf(c_0_3759_2,axiom,
    ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X2)
    | ~ c_lessequals(c_HOL_Oabs__class_Oabs(X1,X2),c_HOL_Ozero__class_Ozero(X2),X2)
    | X1 = c_HOL_Ozero__class_Ozero(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_3759]) ).

cnf(c_0_3760_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_3760]) ).

cnf(c_0_3760_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_3760]) ).

cnf(c_0_3760_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_3760]) ).

cnf(c_0_3761_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_3761]) ).

cnf(c_0_3761_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_3761]) ).

cnf(c_0_3761_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_3761]) ).

cnf(c_0_3762_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_3762]) ).

cnf(c_0_3762_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_3762]) ).

cnf(c_0_3762_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_3762]) ).

cnf(c_0_3763_0,axiom,
    ( c_Parity_Oeven__odd__class_Oeven(X1,tc_nat)
    | c_Divides_Odiv__class_Omod(X1,c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_3763]) ).

cnf(c_0_3763_1,axiom,
    ( c_Divides_Odiv__class_Omod(X1,c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)
    | c_Parity_Oeven__odd__class_Oeven(X1,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_3763]) ).

cnf(c_0_3764_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_3764]) ).

cnf(c_0_3764_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_3764]) ).

cnf(c_0_3765_0,axiom,
    ( c_lessequals(X1,X2,tc_nat)
    | ~ c_lessequals(c_Suc(X1),X2,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_3765]) ).

cnf(c_0_3765_1,axiom,
    ( ~ c_lessequals(c_Suc(X1),X2,tc_nat)
    | c_lessequals(X1,X2,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_3765]) ).

cnf(c_0_3766_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_3766]) ).

cnf(c_0_3766_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_3766]) ).

cnf(c_0_3767_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_3767]) ).

cnf(c_0_3767_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_3767]) ).

cnf(c_0_3768_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_3768]) ).

cnf(c_0_3768_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_3768]) ).

cnf(c_0_3769_0,axiom,
    ( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
    | X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
    | ~ c_HOL_Oord__class_Oless(X1,c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_3769]) ).

cnf(c_0_3769_1,axiom,
    ( X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
    | X1 = c_HOL_Ozero__class_Ozero(tc_nat)
    | ~ c_HOL_Oord__class_Oless(X1,c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_3769]) ).

cnf(c_0_3769_2,axiom,
    ( ~ c_HOL_Oord__class_Oless(X1,c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),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_3769]) ).

cnf(c_0_3770_0,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(X1,X2),c_HOL_Ozero__class_Ozero(X2),X2)
    | ~ class_OrderedGroup_Opordered__ab__group__add__abs(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_3770]) ).

cnf(c_0_3770_1,axiom,
    ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X2)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(X1,X2),c_HOL_Ozero__class_Ozero(X2),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_3770]) ).

cnf(c_0_3771_0,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X1,X2),c_HOL_Ozero__class_Ozero(X2),X2)
    | ~ class_Ring__and__Field_Oordered__semidom(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_3771]) ).

cnf(c_0_3771_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__semidom(X2)
    | ~ c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X1,X2),c_HOL_Ozero__class_Ozero(X2),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_3771]) ).

cnf(c_0_3772_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_3772]) ).

cnf(c_0_3772_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_3772]) ).

cnf(c_0_3773_0,axiom,
    ( c_lessequals(X1,c_Suc(X2),tc_nat)
    | ~ c_lessequals(X1,X2,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_3773]) ).

cnf(c_0_3773_1,axiom,
    ( ~ c_lessequals(X1,X2,tc_nat)
    | c_lessequals(X1,c_Suc(X2),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_3773]) ).

cnf(c_0_3774_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_3774]) ).

cnf(c_0_3774_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_3774]) ).

cnf(c_0_3775_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_3775]) ).

cnf(c_0_3775_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_3775]) ).

cnf(c_0_3776_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_3776]) ).

cnf(c_0_3776_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_3776]) ).

cnf(c_0_3777_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_3777]) ).

cnf(c_0_3777_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_3777]) ).

cnf(c_0_3778_0,axiom,
    ( c_Parity_Oeven__odd__class_Oeven(X1,tc_nat)
    | c_Parity_Oeven__odd__class_Oeven(X2,tc_nat)
    | c_Parity_Oeven__odd__class_Oeven(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_3778]) ).

cnf(c_0_3778_1,axiom,
    ( c_Parity_Oeven__odd__class_Oeven(X2,tc_nat)
    | c_Parity_Oeven__odd__class_Oeven(X1,tc_nat)
    | c_Parity_Oeven__odd__class_Oeven(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_3778]) ).

cnf(c_0_3778_2,axiom,
    ( c_Parity_Oeven__odd__class_Oeven(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),tc_nat)
    | c_Parity_Oeven__odd__class_Oeven(X2,tc_nat)
    | c_Parity_Oeven__odd__class_Oeven(X1,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_3778]) ).

cnf(c_0_3779_0,axiom,
    ( c_Parity_Oeven__odd__class_Oeven(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat)
    | c_Parity_Oeven__odd__class_Oeven(X2,tc_nat)
    | c_Parity_Oeven__odd__class_Oeven(X1,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_3779]) ).

cnf(c_0_3779_1,axiom,
    ( c_Parity_Oeven__odd__class_Oeven(X2,tc_nat)
    | c_Parity_Oeven__odd__class_Oeven(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat)
    | c_Parity_Oeven__odd__class_Oeven(X1,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_3779]) ).

cnf(c_0_3779_2,axiom,
    ( c_Parity_Oeven__odd__class_Oeven(X1,tc_nat)
    | c_Parity_Oeven__odd__class_Oeven(X2,tc_nat)
    | c_Parity_Oeven__odd__class_Oeven(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_3779]) ).

cnf(c_0_3780_0,axiom,
    ( c_Parity_Oeven__odd__class_Oeven(X1,tc_nat)
    | c_Parity_Oeven__odd__class_Oeven(X2,tc_nat)
    | c_Parity_Oeven__odd__class_Oeven(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_3780]) ).

cnf(c_0_3780_1,axiom,
    ( c_Parity_Oeven__odd__class_Oeven(X2,tc_nat)
    | c_Parity_Oeven__odd__class_Oeven(X1,tc_nat)
    | c_Parity_Oeven__odd__class_Oeven(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_3780]) ).

cnf(c_0_3780_2,axiom,
    ( c_Parity_Oeven__odd__class_Oeven(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat)
    | c_Parity_Oeven__odd__class_Oeven(X2,tc_nat)
    | c_Parity_Oeven__odd__class_Oeven(X1,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_3780]) ).

cnf(c_0_3781_0,axiom,
    ( c_Parity_Oeven__odd__class_Oeven(X1,tc_nat)
    | c_Parity_Oeven__odd__class_Oeven(X2,tc_nat)
    | c_Parity_Oeven__odd__class_Oeven(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_3781]) ).

cnf(c_0_3781_1,axiom,
    ( c_Parity_Oeven__odd__class_Oeven(X2,tc_nat)
    | c_Parity_Oeven__odd__class_Oeven(X1,tc_nat)
    | c_Parity_Oeven__odd__class_Oeven(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_3781]) ).

cnf(c_0_3781_2,axiom,
    ( c_Parity_Oeven__odd__class_Oeven(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat)
    | c_Parity_Oeven__odd__class_Oeven(X2,tc_nat)
    | c_Parity_Oeven__odd__class_Oeven(X1,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_3781]) ).

cnf(c_0_3782_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_3782]) ).

cnf(c_0_3782_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_3782]) ).

cnf(c_0_3783_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_3783]) ).

cnf(c_0_3783_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_3783]) ).

cnf(c_0_3783_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_3783]) ).

cnf(c_0_3784_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_3784]) ).

cnf(c_0_3784_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_3784]) ).

cnf(c_0_3784_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_3784]) ).

cnf(c_0_3785_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_3785]) ).

cnf(c_0_3785_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_3785]) ).

cnf(c_0_3785_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_3785]) ).

cnf(c_0_3786_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_3786]) ).

cnf(c_0_3786_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_3786]) ).

cnf(c_0_3787_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_3787]) ).

cnf(c_0_3787_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_3787]) ).

cnf(c_0_3788_0,axiom,
    ( c_lessequals(X1,X2,tc_nat)
    | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_3788]) ).

cnf(c_0_3788_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | c_lessequals(X1,X2,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_3788]) ).

cnf(c_0_3789_0,axiom,
    ( c_lessequals(X1,X2,tc_nat)
    | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_3789]) ).

cnf(c_0_3789_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | c_lessequals(X1,X2,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_3789]) ).

cnf(c_0_3790_0,axiom,
    ( c_Parity_Oeven__odd__class_Oeven(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),tc_nat)
    | ~ c_Parity_Oeven__odd__class_Oeven(X1,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_3790]) ).

cnf(c_0_3790_1,axiom,
    ( ~ c_Parity_Oeven__odd__class_Oeven(X1,tc_nat)
    | c_Parity_Oeven__odd__class_Oeven(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_3790]) ).

cnf(c_0_3791_0,axiom,
    ( c_Parity_Oeven__odd__class_Oeven(c_HOL_Otimes__class_Otimes(X2,X1,tc_nat),tc_nat)
    | ~ c_Parity_Oeven__odd__class_Oeven(X1,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_3791]) ).

cnf(c_0_3791_1,axiom,
    ( ~ c_Parity_Oeven__odd__class_Oeven(X1,tc_nat)
    | c_Parity_Oeven__odd__class_Oeven(c_HOL_Otimes__class_Otimes(X2,X1,tc_nat),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_3791]) ).

cnf(c_0_3792_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_3792]) ).

cnf(c_0_3792_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_3792]) ).

cnf(c_0_3792_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_3792]) ).

cnf(c_0_3792_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_3792]) ).

cnf(c_0_3793_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_3793]) ).

cnf(c_0_3793_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_3793]) ).

cnf(c_0_3793_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_3793]) ).

cnf(c_0_3793_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_3793]) ).

cnf(c_0_3794_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_3794]) ).

cnf(c_0_3794_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_3794]) ).

cnf(c_0_3794_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_3794]) ).

cnf(c_0_3794_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_3794]) ).

cnf(c_0_3795_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_3795]) ).

cnf(c_0_3795_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_3795]) ).

cnf(c_0_3795_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_3795]) ).

cnf(c_0_3795_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_3795]) ).

cnf(c_0_3796_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_3796]) ).

cnf(c_0_3796_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_3796]) ).

cnf(c_0_3796_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_3796]) ).

cnf(c_0_3796_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_3796]) ).

cnf(c_0_3797_0,axiom,
    ( c_HOL_Oabs__class_Oabs(X2,X1) = X2
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | ~ class_OrderedGroup_Opordered__ab__group__add__abs(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3797]) ).

cnf(c_0_3797_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | c_HOL_Oabs__class_Oabs(X2,X1) = X2
    | ~ class_OrderedGroup_Opordered__ab__group__add__abs(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3797]) ).

cnf(c_0_3797_2,axiom,
    ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | c_HOL_Oabs__class_Oabs(X2,X1) = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_3797]) ).

cnf(c_0_3798_0,axiom,
    ( c_HOL_Oabs__class_Oabs(X2,X1) = X2
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | ~ class_OrderedGroup_Opordered__ab__group__add__abs(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3798]) ).

cnf(c_0_3798_1,axiom,
    ( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | c_HOL_Oabs__class_Oabs(X2,X1) = X2
    | ~ class_OrderedGroup_Opordered__ab__group__add__abs(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3798]) ).

cnf(c_0_3798_2,axiom,
    ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X1)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | c_HOL_Oabs__class_Oabs(X2,X1) = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_3798]) ).

cnf(c_0_3801_0,axiom,
    ( c_lessequals(X1,X2,X3)
    | c_lessequals(X2,X1,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_3801]) ).

cnf(c_0_3801_1,axiom,
    ( c_lessequals(X2,X1,X3)
    | c_lessequals(X1,X2,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_3801]) ).

cnf(c_0_3801_2,axiom,
    ( ~ class_Orderings_Olinorder(X3)
    | c_lessequals(X2,X1,X3)
    | c_lessequals(X1,X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_3801]) ).

cnf(c_0_3802_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_3802]) ).

cnf(c_0_3802_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_3802]) ).

cnf(c_0_3802_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_3802]) ).

cnf(c_0_3803_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_3803]) ).

cnf(c_0_3803_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_3803]) ).

cnf(c_0_3803_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_3803]) ).

cnf(c_0_3804_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_3804]) ).

cnf(c_0_3804_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_3804]) ).

cnf(c_0_3804_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_3804]) ).

cnf(c_0_3805_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_3805]) ).

cnf(c_0_3805_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_3805]) ).

cnf(c_0_3805_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_3805]) ).

cnf(c_0_3806_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_3806]) ).

cnf(c_0_3806_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_3806]) ).

cnf(c_0_3807_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_3807]) ).

cnf(c_0_3807_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_3807]) ).

cnf(c_0_3808_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_3808]) ).

cnf(c_0_3808_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_3808]) ).

cnf(c_0_3809_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_3809]) ).

cnf(c_0_3809_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_3809]) ).

cnf(c_0_3810_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_3810]) ).

cnf(c_0_3810_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_3810]) ).

cnf(c_0_3811_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_3811]) ).

cnf(c_0_3811_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_3811]) ).

cnf(c_0_3812_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_3812]) ).

cnf(c_0_3812_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_3812]) ).

cnf(c_0_3813_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_3813]) ).

cnf(c_0_3813_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_3813]) ).

cnf(c_0_3814_0,axiom,
    ( c_lessequals(X1,X2,tc_nat)
    | c_lessequals(c_Suc(X2),X1,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_3814]) ).

cnf(c_0_3814_1,axiom,
    ( c_lessequals(c_Suc(X2),X1,tc_nat)
    | c_lessequals(X1,X2,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_3814]) ).

cnf(c_0_3817_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_3817]) ).

cnf(c_0_3817_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_3817]) ).

cnf(c_0_3817_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_3817]) ).

cnf(c_0_3818_0,axiom,
    ( X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
    | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_3818]) ).

cnf(c_0_3818_1,axiom,
    ( ~ c_Ring__and__Field_Odvd__class_Odvd(X1,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat)
    | X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
    inference(literals_permutation,[status(thm)],[c_0_3818]) ).

cnf(c_0_3819_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_3819]) ).

cnf(c_0_3819_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_3819]) ).

cnf(c_0_3819_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_3819]) ).

cnf(c_0_3820_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_3820]) ).

cnf(c_0_3820_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_3820]) ).

cnf(c_0_3820_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_3820]) ).

cnf(c_0_3820_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_3820]) ).

cnf(c_0_3821_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_3821]) ).

cnf(c_0_3821_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_3821]) ).

cnf(c_0_3821_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_3821]) ).

cnf(c_0_3821_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_3821]) ).

cnf(c_0_3822_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_3822]) ).

cnf(c_0_3822_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_3822]) ).

cnf(c_0_3822_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_3822]) ).

cnf(c_0_3822_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_3822]) ).

cnf(c_0_3823_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_3823]) ).

cnf(c_0_3823_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_3823]) ).

cnf(c_0_3823_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_3823]) ).

cnf(c_0_3824_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_3824]) ).

cnf(c_0_3824_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_3824]) ).

cnf(c_0_3824_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_3824]) ).

cnf(c_0_3825_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_3825]) ).

cnf(c_0_3825_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_3825]) ).

cnf(c_0_3825_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_3825]) ).

cnf(c_0_3825_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_3825]) ).

cnf(c_0_3826_0,axiom,
    ( X2 = c_HOL_Ozero__class_Ozero(X1)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3826]) ).

cnf(c_0_3826_1,axiom,
    ( ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | X2 = c_HOL_Ozero__class_Ozero(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3826]) ).

cnf(c_0_3826_2,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | X2 = c_HOL_Ozero__class_Ozero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3826]) ).

cnf(c_0_3827_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_3827]) ).

cnf(c_0_3827_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_3827]) ).

cnf(c_0_3827_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_3827]) ).

cnf(c_0_3827_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_3827]) ).

cnf(c_0_3828_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_3828]) ).

cnf(c_0_3828_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_3828]) ).

cnf(c_0_3828_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_3828]) ).

cnf(c_0_3829_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_3829]) ).

cnf(c_0_3829_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_3829]) ).

cnf(c_0_3829_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_3829]) ).

cnf(c_0_3830_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_3830]) ).

cnf(c_0_3830_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_3830]) ).

cnf(c_0_3830_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_3830]) ).

cnf(c_0_3831_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_3831]) ).

cnf(c_0_3831_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_3831]) ).

cnf(c_0_3831_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_3831]) ).

cnf(c_0_3832_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_3832]) ).

cnf(c_0_3832_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_3832]) ).

cnf(c_0_3833_0,axiom,
    ( c_lessequals(X1,X2,tc_nat)
    | c_lessequals(X2,X1,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_3833]) ).

cnf(c_0_3833_1,axiom,
    ( c_lessequals(X2,X1,tc_nat)
    | c_lessequals(X1,X2,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_3833]) ).

cnf(c_0_3834_0,axiom,
    ( c_Divides_Odiv__class_Omod(X1,c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat)
    | ~ c_Parity_Oeven__odd__class_Oeven(X1,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_3834]) ).

cnf(c_0_3834_1,axiom,
    ( ~ c_Parity_Oeven__odd__class_Oeven(X1,tc_nat)
    | c_Divides_Odiv__class_Omod(X1,c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_3834]) ).

cnf(c_0_3835_0,axiom,
    ( c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
    | c_HOL_Oabs__class_Oabs(X1,X3) != c_HOL_Oabs__class_Oabs(X2,X3)
    | ~ class_Ring__and__Field_Oordered__idom(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_3835]) ).

cnf(c_0_3835_1,axiom,
    ( c_HOL_Oabs__class_Oabs(X1,X3) != c_HOL_Oabs__class_Oabs(X2,X3)
    | c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3)
    | ~ class_Ring__and__Field_Oordered__idom(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_3835]) ).

cnf(c_0_3835_2,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(X3)
    | c_HOL_Oabs__class_Oabs(X1,X3) != c_HOL_Oabs__class_Oabs(X2,X3)
    | c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_3835]) ).

cnf(c_0_3836_0,axiom,
    ( c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Ozero__class_Ozero(X1),X1),c_HOL_Ozero__class_Ozero(X1),X1)
    | ~ class_OrderedGroup_Opordered__ab__group__add__abs(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3836]) ).

cnf(c_0_3836_1,axiom,
    ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X1)
    | c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Ozero__class_Ozero(X1),X1),c_HOL_Ozero__class_Ozero(X1),X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3836]) ).

cnf(c_0_3839_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_3839]) ).

cnf(c_0_3839_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_3839]) ).

cnf(c_0_3839_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_3839]) ).

cnf(c_0_3840_0,axiom,
    ( c_Parity_Oeven__odd__class_Oeven(X1,tc_nat)
    | c_Divides_Odiv__class_Omod(X1,c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),tc_nat) = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
    inference(literals_permutation,[status(thm)],[c_0_3840]) ).

cnf(c_0_3840_1,axiom,
    ( c_Divides_Odiv__class_Omod(X1,c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),tc_nat) = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
    | c_Parity_Oeven__odd__class_Oeven(X1,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_3840]) ).

cnf(c_0_3841_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_3841]) ).

cnf(c_0_3841_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_3841]) ).

cnf(c_0_3842_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_3842]) ).

cnf(c_0_3842_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_3842]) ).

cnf(c_0_3843_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_3843]) ).

cnf(c_0_3843_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_3843]) ).

cnf(c_0_3843_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_3843]) ).

cnf(c_0_3844_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_3844]) ).

cnf(c_0_3844_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_3844]) ).

cnf(c_0_3844_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_3844]) ).

cnf(c_0_3845_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_3845]) ).

cnf(c_0_3845_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_3845]) ).

cnf(c_0_3845_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_3845]) ).

cnf(c_0_3846_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_3846]) ).

cnf(c_0_3846_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_3846]) ).

cnf(c_0_3846_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_3846]) ).

cnf(c_0_3847_0,axiom,
    ( X1 = c_HOL_Ozero__class_Ozero(X2)
    | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),c_HOL_Oabs__class_Oabs(X1,X2),X2)
    | ~ class_OrderedGroup_Opordered__ab__group__add__abs(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_3847]) ).

cnf(c_0_3847_1,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),c_HOL_Oabs__class_Oabs(X1,X2),X2)
    | X1 = c_HOL_Ozero__class_Ozero(X2)
    | ~ class_OrderedGroup_Opordered__ab__group__add__abs(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_3847]) ).

cnf(c_0_3847_2,axiom,
    ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X2)
    | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),c_HOL_Oabs__class_Oabs(X1,X2),X2)
    | X1 = c_HOL_Ozero__class_Ozero(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_3847]) ).

cnf(c_0_3848_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_3848]) ).

cnf(c_0_3848_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_3848]) ).

cnf(c_0_3848_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_3848]) ).

cnf(c_0_3849_0,axiom,
    ( c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oabs__class_Oabs(X2,X1),X1)
    | ~ class_OrderedGroup_Opordered__ab__group__add__abs(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3849]) ).

cnf(c_0_3849_1,axiom,
    ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X1)
    | c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oabs__class_Oabs(X2,X1),X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3849]) ).

cnf(c_0_3850_0,axiom,
    ( c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_Nat_Osemiring__1__class_Oof__nat(X2,X1),X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3850]) ).

cnf(c_0_3850_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__semidom(X1)
    | c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_Nat_Osemiring__1__class_Oof__nat(X2,X1),X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3850]) ).

cnf(c_0_3851_0,axiom,
    ( c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_Nat_Osemiring__1__class_Oof__nat(X2,X1),X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3851]) ).

cnf(c_0_3851_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__semidom(X1)
    | c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_Nat_Osemiring__1__class_Oof__nat(X2,X1),X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3851]) ).

cnf(c_0_3852_0,axiom,
    ( ~ c_HOL_Oord__class_Oless(X1,X1,X2)
    | ~ class_Orderings_Oorder(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_3852]) ).

cnf(c_0_3852_1,axiom,
    ( ~ class_Orderings_Oorder(X2)
    | ~ c_HOL_Oord__class_Oless(X1,X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_3852]) ).

cnf(c_0_3853_0,axiom,
    ( ~ c_HOL_Oord__class_Oless(X1,X1,X2)
    | ~ class_Orderings_Olinorder(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_3853]) ).

cnf(c_0_3853_1,axiom,
    ( ~ class_Orderings_Olinorder(X2)
    | ~ c_HOL_Oord__class_Oless(X1,X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_3853]) ).

cnf(c_0_3854_0,axiom,
    ( ~ c_HOL_Oord__class_Oless(X1,X1,X2)
    | ~ class_Orderings_Opreorder(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_3854]) ).

cnf(c_0_3854_1,axiom,
    ( ~ class_Orderings_Opreorder(X2)
    | ~ c_HOL_Oord__class_Oless(X1,X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_3854]) ).

cnf(c_0_3857_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_3857]) ).

cnf(c_0_3857_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_3857]) ).

cnf(c_0_3858_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_3858]) ).

cnf(c_0_3858_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_3858]) ).

cnf(c_0_3859_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_3859]) ).

cnf(c_0_3859_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_3859]) ).

cnf(c_0_3860_0,axiom,
    ( c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
    | c_HOL_Oabs__class_Oabs(X1,X2) = X1
    | ~ class_OrderedGroup_Olordered__ab__group__add__abs(X2)
    | ~ class_Orderings_Olinorder(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_3860]) ).

cnf(c_0_3860_1,axiom,
    ( c_HOL_Oabs__class_Oabs(X1,X2) = X1
    | c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
    | ~ class_OrderedGroup_Olordered__ab__group__add__abs(X2)
    | ~ class_Orderings_Olinorder(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_3860]) ).

cnf(c_0_3860_2,axiom,
    ( ~ class_OrderedGroup_Olordered__ab__group__add__abs(X2)
    | c_HOL_Oabs__class_Oabs(X1,X2) = X1
    | c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
    | ~ class_Orderings_Olinorder(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_3860]) ).

cnf(c_0_3860_3,axiom,
    ( ~ class_Orderings_Olinorder(X2)
    | ~ class_OrderedGroup_Olordered__ab__group__add__abs(X2)
    | c_HOL_Oabs__class_Oabs(X1,X2) = X1
    | c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_3860]) ).

cnf(c_0_3861_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_3861]) ).

cnf(c_0_3861_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_3861]) ).

cnf(c_0_3862_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_3862]) ).

cnf(c_0_3862_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_3862]) ).

cnf(c_0_3865_0,axiom,
    ( c_lessequals(X1,c_HOL_Oabs__class_Oabs(X1,X2),X2)
    | ~ class_OrderedGroup_Opordered__ab__group__add__abs(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_3865]) ).

cnf(c_0_3865_1,axiom,
    ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X2)
    | c_lessequals(X1,c_HOL_Oabs__class_Oabs(X1,X2),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_3865]) ).

cnf(c_0_3869_0,axiom,
    ( c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
    | c_HOL_Oabs__class_Oabs(X1,X2) = X1
    | ~ class_Ring__and__Field_Oabs__if(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_3869]) ).

cnf(c_0_3869_1,axiom,
    ( c_HOL_Oabs__class_Oabs(X1,X2) = X1
    | c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2)
    | ~ class_Ring__and__Field_Oabs__if(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_3869]) ).

cnf(c_0_3869_2,axiom,
    ( ~ class_Ring__and__Field_Oabs__if(X2)
    | c_HOL_Oabs__class_Oabs(X1,X2) = X1
    | c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X2),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_3869]) ).

cnf(c_0_3870_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_3870]) ).

cnf(c_0_3870_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_3870]) ).

cnf(c_0_3872_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_3872]) ).

cnf(c_0_3872_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_3872]) ).

cnf(c_0_3872_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_3872]) ).

cnf(c_0_3877_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_3877]) ).

cnf(c_0_3877_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_3877]) ).

cnf(c_0_3877_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_3877]) ).

cnf(c_0_3878_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_3878]) ).

cnf(c_0_3878_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_3878]) ).

cnf(c_0_3879_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_3879]) ).

cnf(c_0_3879_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_3879]) ).

cnf(c_0_3880_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_3880]) ).

cnf(c_0_3880_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_3880]) ).

cnf(c_0_3881_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_3881]) ).

cnf(c_0_3881_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_3881]) ).

cnf(c_0_3882_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_3882]) ).

cnf(c_0_3882_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_3882]) ).

cnf(c_0_3883_0,axiom,
    ( c_HOL_Otimes__class_Otimes(X1,c_HOL_Ozero__class_Ozero(X2),X2) = c_HOL_Ozero__class_Ozero(X2)
    | ~ class_RealVector_Oreal__normed__algebra(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_3883]) ).

cnf(c_0_3883_1,axiom,
    ( ~ class_RealVector_Oreal__normed__algebra(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_3883]) ).

cnf(c_0_3884_0,axiom,
    ( c_HOL_Otimes__class_Otimes(X1,c_HOL_Ozero__class_Ozero(X2),X2) = c_HOL_Ozero__class_Ozero(X2)
    | ~ class_RealVector_Oreal__normed__algebra(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_3884]) ).

cnf(c_0_3884_1,axiom,
    ( ~ class_RealVector_Oreal__normed__algebra(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_3884]) ).

cnf(c_0_3885_0,axiom,
    ( c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),X2,X1) = c_HOL_Ozero__class_Ozero(X1)
    | ~ class_RealVector_Oreal__normed__algebra(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3885]) ).

cnf(c_0_3885_1,axiom,
    ( ~ class_RealVector_Oreal__normed__algebra(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_3885]) ).

cnf(c_0_3886_0,axiom,
    ( c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),X2,X1) = c_HOL_Ozero__class_Ozero(X1)
    | ~ class_RealVector_Oreal__normed__algebra(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3886]) ).

cnf(c_0_3886_1,axiom,
    ( ~ class_RealVector_Oreal__normed__algebra(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_3886]) ).

cnf(c_0_3887_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_3887]) ).

cnf(c_0_3887_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_3887]) ).

cnf(c_0_3888_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_3888]) ).

cnf(c_0_3888_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_3888]) ).

cnf(c_0_3889_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_3889]) ).

cnf(c_0_3889_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_3889]) ).

cnf(c_0_3890_0,axiom,
    ( c_Parity_Oeven__odd__class_Oeven(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_3890]) ).

cnf(c_0_3890_1,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
    | c_Parity_Oeven__odd__class_Oeven(X1,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_3890]) ).

cnf(c_0_3891_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_3891]) ).

cnf(c_0_3891_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_3891]) ).

cnf(c_0_3892_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_3892]) ).

cnf(c_0_3892_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_3892]) ).

cnf(c_0_3893_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_3893]) ).

cnf(c_0_3893_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_3893]) ).

cnf(c_0_3894_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_3894]) ).

cnf(c_0_3894_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_3894]) ).

cnf(c_0_3895_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_3895]) ).

cnf(c_0_3895_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_3895]) ).

cnf(c_0_3896_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_3896]) ).

cnf(c_0_3896_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_3896]) ).

cnf(c_0_3897_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_3897]) ).

cnf(c_0_3897_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_3897]) ).

cnf(c_0_3898_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_3898]) ).

cnf(c_0_3898_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_3898]) ).

cnf(c_0_3899_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_3899]) ).

cnf(c_0_3899_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_3899]) ).

cnf(c_0_3901_0,axiom,
    ( c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Ozero__class_Ozero(X2),X2)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_3901]) ).

cnf(c_0_3901_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__1(X2)
    | c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Ozero__class_Ozero(X2),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_3901]) ).

cnf(c_0_3903_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_3903]) ).

cnf(c_0_3903_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_3903]) ).

cnf(c_0_3904_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_3904]) ).

cnf(c_0_3904_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_3904]) ).

cnf(c_0_3905_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_3905]) ).

cnf(c_0_3905_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_3905]) ).

cnf(c_0_3906_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_3906]) ).

cnf(c_0_3906_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_3906]) ).

cnf(c_0_3909_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_3909]) ).

cnf(c_0_3909_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_3909]) ).

cnf(c_0_3910_0,axiom,
    ( c_Orderings_Oord__class_Omin(X1,X1,X2) = X1
    | ~ class_Orderings_Olinorder(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_3910]) ).

cnf(c_0_3910_1,axiom,
    ( ~ class_Orderings_Olinorder(X2)
    | c_Orderings_Oord__class_Omin(X1,X1,X2) = X1 ),
    inference(literals_permutation,[status(thm)],[c_0_3910]) ).

cnf(c_0_3913_0,axiom,
    ( c_lessequals(X1,X1,X2)
    | ~ class_Orderings_Oorder(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_3913]) ).

cnf(c_0_3913_1,axiom,
    ( ~ class_Orderings_Oorder(X2)
    | c_lessequals(X1,X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_3913]) ).

cnf(c_0_3914_0,axiom,
    ( c_lessequals(X1,X1,X2)
    | ~ class_Orderings_Opreorder(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_3914]) ).

cnf(c_0_3914_1,axiom,
    ( ~ class_Orderings_Opreorder(X2)
    | c_lessequals(X1,X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_3914]) ).

cnf(c_0_3915_0,axiom,
    ( c_Ring__and__Field_Odvd__class_Odvd(X1,X1,X2)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_3915]) ).

cnf(c_0_3915_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__1(X2)
    | c_Ring__and__Field_Odvd__class_Odvd(X1,X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_3915]) ).

cnf(c_0_3917_0,axiom,
    ( c_HOL_Oabs__class_Oabs(c_HOL_Oabs__class_Oabs(X1,X2),X2) = c_HOL_Oabs__class_Oabs(X1,X2)
    | ~ class_OrderedGroup_Opordered__ab__group__add__abs(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_3917]) ).

cnf(c_0_3917_1,axiom,
    ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X2)
    | c_HOL_Oabs__class_Oabs(c_HOL_Oabs__class_Oabs(X1,X2),X2) = c_HOL_Oabs__class_Oabs(X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_3917]) ).

cnf(c_0_3918_0,axiom,
    ( c_HOL_Oabs__class_Oabs(c_Nat_Osemiring__1__class_Oof__nat(X1,X2),X2) = c_Nat_Osemiring__1__class_Oof__nat(X1,X2)
    | ~ class_Ring__and__Field_Oordered__idom(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_3918]) ).

cnf(c_0_3918_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(X2)
    | c_HOL_Oabs__class_Oabs(c_Nat_Osemiring__1__class_Oof__nat(X1,X2),X2) = c_Nat_Osemiring__1__class_Oof__nat(X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_3918]) ).

cnf(c_0_3919_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_3919]) ).

cnf(c_0_3919_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_3919]) ).

cnf(c_0_3935_0,axiom,
    ( X1 = X2
    | c_Nat_Osemiring__1__class_Oof__nat(X1,X3) != c_Nat_Osemiring__1__class_Oof__nat(X2,X3)
    | ~ class_Nat_Osemiring__char__0(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_3935]) ).

cnf(c_0_3935_1,axiom,
    ( c_Nat_Osemiring__1__class_Oof__nat(X1,X3) != c_Nat_Osemiring__1__class_Oof__nat(X2,X3)
    | X1 = X2
    | ~ class_Nat_Osemiring__char__0(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_3935]) ).

cnf(c_0_3935_2,axiom,
    ( ~ class_Nat_Osemiring__char__0(X3)
    | c_Nat_Osemiring__1__class_Oof__nat(X1,X3) != c_Nat_Osemiring__1__class_Oof__nat(X2,X3)
    | X1 = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_3935]) ).

cnf(c_0_3941_0,axiom,
    ( ~ c_Parity_Oeven__odd__class_Oeven(c_Suc(X1),tc_nat)
    | ~ c_Parity_Oeven__odd__class_Oeven(X1,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_3941]) ).

cnf(c_0_3941_1,axiom,
    ( ~ c_Parity_Oeven__odd__class_Oeven(X1,tc_nat)
    | ~ c_Parity_Oeven__odd__class_Oeven(c_Suc(X1),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_3941]) ).

cnf(c_0_3942_0,axiom,
    ( X1 = c_HOL_Ozero__class_Ozero(X2)
    | c_HOL_Oabs__class_Oabs(X1,X2) != c_HOL_Ozero__class_Ozero(X2)
    | ~ class_OrderedGroup_Opordered__ab__group__add__abs(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_3942]) ).

cnf(c_0_3942_1,axiom,
    ( c_HOL_Oabs__class_Oabs(X1,X2) != c_HOL_Ozero__class_Ozero(X2)
    | X1 = c_HOL_Ozero__class_Ozero(X2)
    | ~ class_OrderedGroup_Opordered__ab__group__add__abs(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_3942]) ).

cnf(c_0_3942_2,axiom,
    ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X2)
    | c_HOL_Oabs__class_Oabs(X1,X2) != c_HOL_Ozero__class_Ozero(X2)
    | X1 = c_HOL_Ozero__class_Ozero(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_3942]) ).

cnf(c_0_3943_0,axiom,
    ( c_Parity_Oeven__odd__class_Oeven(X1,tc_nat)
    | c_Parity_Oeven__odd__class_Oeven(c_Suc(X1),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_3943]) ).

cnf(c_0_3943_1,axiom,
    ( c_Parity_Oeven__odd__class_Oeven(c_Suc(X1),tc_nat)
    | c_Parity_Oeven__odd__class_Oeven(X1,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_3943]) ).

cnf(c_0_3944_0,axiom,
    ( c_HOL_Oabs__class_Oabs(c_HOL_Ozero__class_Ozero(X1),X1) = c_HOL_Ozero__class_Ozero(X1)
    | ~ class_OrderedGroup_Opordered__ab__group__add__abs(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3944]) ).

cnf(c_0_3944_1,axiom,
    ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X1)
    | c_HOL_Oabs__class_Oabs(c_HOL_Ozero__class_Ozero(X1),X1) = c_HOL_Ozero__class_Ozero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3944]) ).

cnf(c_0_3945_0,axiom,
    ( c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Ozero__class_Ozero(tc_nat),X1) = c_HOL_Ozero__class_Ozero(X1)
    | ~ class_Ring__and__Field_Osemiring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3945]) ).

cnf(c_0_3945_1,axiom,
    ( ~ class_Ring__and__Field_Osemiring__1(X1)
    | c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Ozero__class_Ozero(tc_nat),X1) = c_HOL_Ozero__class_Ozero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3945]) ).

cnf(c_0_3947_0,axiom,
    ( X1 = X2
    | c_Suc(X1) != c_Suc(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_3947]) ).

cnf(c_0_3947_1,axiom,
    ( c_Suc(X1) != c_Suc(X2)
    | X1 = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_3947]) ).

cnf(c_0_3948_0,axiom,
    ( X1 = X2
    | c_Suc(X1) != c_Suc(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_3948]) ).

cnf(c_0_3948_1,axiom,
    ( c_Suc(X1) != c_Suc(X2)
    | X1 = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_3948]) ).

cnf(c_0_3276_0,axiom,
    ~ c_Parity_Oeven__odd__class_Oeven(c_Suc(c_HOL_Otimes__class_Otimes(c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),X1,tc_nat)),tc_nat),
    inference(literals_permutation,[status(thm)],[c_0_3276]) ).

cnf(c_0_3601_0,axiom,
    ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),X2,tc_nat),
    inference(literals_permutation,[status(thm)],[c_0_3601]) ).

cnf(c_0_3602_0,axiom,
    ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),X1,tc_nat),
    inference(literals_permutation,[status(thm)],[c_0_3602]) ).

cnf(c_0_3855_0,axiom,
    ~ c_lessequals(c_Suc(X1),X1,tc_nat),
    inference(literals_permutation,[status(thm)],[c_0_3855]) ).

cnf(c_0_3856_0,axiom,
    ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
    inference(literals_permutation,[status(thm)],[c_0_3856]) ).

cnf(c_0_3863_0,axiom,
    ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
    inference(literals_permutation,[status(thm)],[c_0_3863]) ).

cnf(c_0_3864_0,axiom,
    ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
    inference(literals_permutation,[status(thm)],[c_0_3864]) ).

cnf(c_0_3867_0,axiom,
    ~ c_HOL_Oord__class_Oless(X1,X1,tc_nat),
    inference(literals_permutation,[status(thm)],[c_0_3867]) ).

cnf(c_0_3868_0,axiom,
    ~ c_HOL_Oord__class_Oless(X1,X1,tc_nat),
    inference(literals_permutation,[status(thm)],[c_0_3868]) ).

cnf(c_0_3949_0,axiom,
    c_Suc(X1) != c_HOL_Ozero__class_Ozero(tc_nat),
    inference(literals_permutation,[status(thm)],[c_0_3949]) ).

cnf(c_0_3950_0,axiom,
    c_Suc(X1) != c_HOL_Ozero__class_Ozero(tc_nat),
    inference(literals_permutation,[status(thm)],[c_0_3950]) ).

cnf(c_0_3951_0,axiom,
    c_Suc(X1) != c_HOL_Ozero__class_Ozero(tc_nat),
    inference(literals_permutation,[status(thm)],[c_0_3951]) ).

cnf(c_0_3952_0,axiom,
    c_Suc(X1) != c_HOL_Ozero__class_Ozero(tc_nat),
    inference(literals_permutation,[status(thm)],[c_0_3952]) ).

cnf(c_0_3953_0,axiom,
    c_Suc(X1) != X1,
    inference(literals_permutation,[status(thm)],[c_0_3953]) ).

cnf(c_0_3954_0,axiom,
    c_Suc(X1) != X1,
    inference(literals_permutation,[status(thm)],[c_0_3954]) ).

cnf(c_0_3226_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(X3,X2,tc_nat),X4,tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X1,X3,tc_nat),X2,tc_nat),X4,tc_nat),
    inference(literals_permutation,[status(thm)],[c_0_3226]) ).

cnf(c_0_3234_0,axiom,
    c_Divides_Odiv__class_Omod(c_Suc(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),X3,tc_nat)),X2,tc_nat) = c_Divides_Odiv__class_Omod(c_Suc(X3),X2,tc_nat),
    inference(literals_permutation,[status(thm)],[c_0_3234]) ).

cnf(c_0_3296_0,axiom,
    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) = 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),
    inference(literals_permutation,[status(thm)],[c_0_3296]) ).

cnf(c_0_3297_0,axiom,
    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) = 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),
    inference(literals_permutation,[status(thm)],[c_0_3297]) ).

cnf(c_0_3391_0,axiom,
    c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Ominus__class_Ominus(X2,X3,tc_nat),tc_nat),
    inference(literals_permutation,[status(thm)],[c_0_3391]) ).

cnf(c_0_3392_0,axiom,
    c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),c_HOL_Otimes__class_Otimes(X2,X3,tc_nat),tc_nat) = c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),X3,tc_nat),
    inference(literals_permutation,[status(thm)],[c_0_3392]) ).

cnf(c_0_3393_0,axiom,
    c_Orderings_Oord__class_Omin(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),c_HOL_Ominus__class_Ominus(X3,X2,tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(c_Orderings_Oord__class_Omin(X1,X3,tc_nat),X2,tc_nat),
    inference(literals_permutation,[status(thm)],[c_0_3393]) ).

cnf(c_0_3394_0,axiom,
    c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),X3,tc_nat),X2,tc_nat) = c_Divides_Odiv__class_Omod(X3,X2,tc_nat),
    inference(literals_permutation,[status(thm)],[c_0_3394]) ).

cnf(c_0_3395_0,axiom,
    c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat) = c_HOL_Otimes__class_Otimes(X1,c_Divides_Odiv__class_Omod(X2,X3,tc_nat),tc_nat),
    inference(literals_permutation,[status(thm)],[c_0_3395]) ).

cnf(c_0_3396_0,axiom,
    c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),c_HOL_Otimes__class_Otimes(X2,X3,tc_nat),tc_nat) = c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(X1,X2,tc_nat),X3,tc_nat),
    inference(literals_permutation,[status(thm)],[c_0_3396]) ).

cnf(c_0_3397_0,axiom,
    c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),c_HOL_Otimes__class_Otimes(X2,X3,tc_nat),tc_nat) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),X3,tc_nat),
    inference(literals_permutation,[status(thm)],[c_0_3397]) ).

cnf(c_0_3398_0,axiom,
    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) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Oplus__class_Oplus(X2,X3,tc_nat),tc_nat),
    inference(literals_permutation,[status(thm)],[c_0_3398]) ).

cnf(c_0_3453_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(literals_permutation,[status(thm)],[c_0_3453]) ).

cnf(c_0_3500_0,axiom,
    c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(c_Suc(X1),X2,tc_nat),c_Suc(X3),tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),X3,tc_nat),
    inference(literals_permutation,[status(thm)],[c_0_3500]) ).

cnf(c_0_3524_0,axiom,
    c_Divides_Odiv__class_Omod(c_Suc(c_Divides_Odiv__class_Omod(X1,X2,tc_nat)),X2,tc_nat) = c_Divides_Odiv__class_Omod(c_Suc(X1),X2,tc_nat),
    inference(literals_permutation,[status(thm)],[c_0_3524]) ).

cnf(c_0_3541_0,axiom,
    c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),X3,tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X1,X3,tc_nat),X2,tc_nat),
    inference(literals_permutation,[status(thm)],[c_0_3541]) ).

cnf(c_0_3542_0,axiom,
    c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),X3,tc_nat) = c_HOL_Ominus__class_Ominus(X1,c_HOL_Oplus__class_Oplus(X2,X3,tc_nat),tc_nat),
    inference(literals_permutation,[status(thm)],[c_0_3542]) ).

cnf(c_0_3543_0,axiom,
    c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),c_HOL_Oplus__class_Oplus(X3,X2,tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(X1,X3,tc_nat),
    inference(literals_permutation,[status(thm)],[c_0_3543]) ).

cnf(c_0_3544_0,axiom,
    c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),c_HOL_Oplus__class_Oplus(X1,X3,tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(X2,X3,tc_nat),
    inference(literals_permutation,[status(thm)],[c_0_3544]) ).

cnf(c_0_3545_0,axiom,
    c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X2,X3,tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(X2,c_HOL_Oplus__class_Oplus(X1,X3,tc_nat),tc_nat),
    inference(literals_permutation,[status(thm)],[c_0_3545]) ).

cnf(c_0_3546_0,axiom,
    c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),X3,tc_nat) = c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X2,X3,tc_nat),tc_nat),
    inference(literals_permutation,[status(thm)],[c_0_3546]) ).

cnf(c_0_3547_0,axiom,
    c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),X3,tc_nat) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Otimes__class_Otimes(X2,X3,tc_nat),tc_nat),
    inference(literals_permutation,[status(thm)],[c_0_3547]) ).

cnf(c_0_3569_0,axiom,
    c_Ring__and__Field_Odvd__class_Odvd(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),tc_nat),
    inference(literals_permutation,[status(thm)],[c_0_3569]) ).

cnf(c_0_3578_0,axiom,
    c_HOL_Oord__class_Oless(X1,c_Suc(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat)),tc_nat),
    inference(literals_permutation,[status(thm)],[c_0_3578]) ).

cnf(c_0_3579_0,axiom,
    c_HOL_Oord__class_Oless(X1,c_Suc(c_HOL_Oplus__class_Oplus(X2,X1,tc_nat)),tc_nat),
    inference(literals_permutation,[status(thm)],[c_0_3579]) ).

cnf(c_0_3580_0,axiom,
    c_HOL_Oord__class_Oless(X1,c_Suc(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat)),tc_nat),
    inference(literals_permutation,[status(thm)],[c_0_3580]) ).

cnf(c_0_3652_0,axiom,
    c_HOL_Oplus__class_Oplus(X1,c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),tc_nat) = c_HOL_Otimes__class_Otimes(X1,c_Suc(X2),tc_nat),
    inference(literals_permutation,[status(thm)],[c_0_3652]) ).

cnf(c_0_3653_0,axiom,
    c_HOL_Oplus__class_Oplus(X2,c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),tc_nat) = c_HOL_Otimes__class_Otimes(c_Suc(X1),X2,tc_nat),
    inference(literals_permutation,[status(thm)],[c_0_3653]) ).

cnf(c_0_3685_0,axiom,
    c_Parity_Oeven__odd__class_Oeven(c_HOL_Otimes__class_Otimes(c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),X1,tc_nat),tc_nat),
    inference(literals_permutation,[status(thm)],[c_0_3685]) ).

cnf(c_0_3692_0,axiom,
    c_Orderings_Oord__class_Omin(c_Suc(X1),c_Suc(X2),tc_nat) = c_Suc(c_Orderings_Oord__class_Omin(X1,X2,tc_nat)),
    inference(literals_permutation,[status(thm)],[c_0_3692]) ).

cnf(c_0_3717_0,axiom,
    c_Suc(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat)) = c_HOL_Oplus__class_Oplus(X1,c_Suc(X2),tc_nat),
    inference(literals_permutation,[status(thm)],[c_0_3717]) ).

cnf(c_0_3718_0,axiom,
    c_Suc(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat)) = c_HOL_Oplus__class_Oplus(c_Suc(X1),X2,tc_nat),
    inference(literals_permutation,[status(thm)],[c_0_3718]) ).

cnf(c_0_3719_0,axiom,
    c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),c_Suc(X1),tc_nat),
    inference(literals_permutation,[status(thm)],[c_0_3719]) ).

cnf(c_0_3722_0,axiom,
    c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),X1,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
    inference(literals_permutation,[status(thm)],[c_0_3722]) ).

cnf(c_0_3723_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(literals_permutation,[status(thm)],[c_0_3723]) ).

cnf(c_0_3724_0,axiom,
    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_3724]) ).

cnf(c_0_3725_0,axiom,
    c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),X1,tc_nat) = X2,
    inference(literals_permutation,[status(thm)],[c_0_3725]) ).

cnf(c_0_3730_0,axiom,
    c_lessequals(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),X1,tc_nat),
    inference(literals_permutation,[status(thm)],[c_0_3730]) ).

cnf(c_0_3731_0,axiom,
    c_lessequals(X1,c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat),
    inference(literals_permutation,[status(thm)],[c_0_3731]) ).

cnf(c_0_3732_0,axiom,
    c_lessequals(X1,c_HOL_Oplus__class_Oplus(X2,X1,tc_nat),tc_nat),
    inference(literals_permutation,[status(thm)],[c_0_3732]) ).

cnf(c_0_3733_0,axiom,
    c_lessequals(X1,c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat),
    inference(literals_permutation,[status(thm)],[c_0_3733]) ).

cnf(c_0_3734_0,axiom,
    c_lessequals(X1,c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat),
    inference(literals_permutation,[status(thm)],[c_0_3734]) ).

cnf(c_0_3735_0,axiom,
    c_lessequals(X1,c_HOL_Otimes__class_Otimes(X1,X1,tc_nat),tc_nat),
    inference(literals_permutation,[status(thm)],[c_0_3735]) ).

cnf(c_0_3736_0,axiom,
    c_lessequals(c_Divides_Odiv__class_Omod(X1,X2,tc_nat),X1,tc_nat),
    inference(literals_permutation,[status(thm)],[c_0_3736]) ).

cnf(c_0_3799_0,axiom,
    c_HOL_Ominus__class_Ominus(c_Suc(X1),c_Suc(X2),tc_nat) = c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),
    inference(literals_permutation,[status(thm)],[c_0_3799]) ).

cnf(c_0_3800_0,axiom,
    c_HOL_Oplus__class_Oplus(c_Suc(X1),X2,tc_nat) = c_HOL_Oplus__class_Oplus(X1,c_Suc(X2),tc_nat),
    inference(literals_permutation,[status(thm)],[c_0_3800]) ).

cnf(c_0_3815_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),
    inference(literals_permutation,[status(thm)],[c_0_3815]) ).

cnf(c_0_3816_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),
    inference(literals_permutation,[status(thm)],[c_0_3816]) ).

cnf(c_0_3837_0,axiom,
    c_HOL_Oplus__class_Oplus(X1,X2,tc_nat) = c_HOL_Oplus__class_Oplus(X2,X1,tc_nat),
    inference(literals_permutation,[status(thm)],[c_0_3837]) ).

cnf(c_0_3838_0,axiom,
    c_HOL_Otimes__class_Otimes(X1,X2,tc_nat) = c_HOL_Otimes__class_Otimes(X2,X1,tc_nat),
    inference(literals_permutation,[status(thm)],[c_0_3838]) ).

cnf(c_0_3866_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(literals_permutation,[status(thm)],[c_0_3866]) ).

cnf(c_0_3871_0,axiom,
    c_Ring__and__Field_Odvd__class_Odvd(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),
    inference(literals_permutation,[status(thm)],[c_0_3871]) ).

cnf(c_0_3873_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(literals_permutation,[status(thm)],[c_0_3873]) ).

cnf(c_0_3874_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(literals_permutation,[status(thm)],[c_0_3874]) ).

cnf(c_0_3875_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(literals_permutation,[status(thm)],[c_0_3875]) ).

cnf(c_0_3876_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(literals_permutation,[status(thm)],[c_0_3876]) ).

cnf(c_0_3900_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(literals_permutation,[status(thm)],[c_0_3900]) ).

cnf(c_0_3902_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(literals_permutation,[status(thm)],[c_0_3902]) ).

cnf(c_0_3907_0,axiom,
    c_lessequals(c_Suc(X1),c_Suc(X1),tc_nat),
    inference(literals_permutation,[status(thm)],[c_0_3907]) ).

cnf(c_0_3908_0,axiom,
    c_Ring__and__Field_Odvd__class_Odvd(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X1,tc_nat),
    inference(literals_permutation,[status(thm)],[c_0_3908]) ).

cnf(c_0_3911_0,axiom,
    c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(X1),tc_nat),
    inference(literals_permutation,[status(thm)],[c_0_3911]) ).

cnf(c_0_3912_0,axiom,
    c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(X1),tc_nat),
    inference(literals_permutation,[status(thm)],[c_0_3912]) ).

cnf(c_0_3916_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(literals_permutation,[status(thm)],[c_0_3916]) ).

cnf(c_0_3920_0,axiom,
    c_HOL_Oord__class_Oless(X1,c_Suc(X1),tc_nat),
    inference(literals_permutation,[status(thm)],[c_0_3920]) ).

cnf(c_0_3921_0,axiom,
    c_HOL_Oord__class_Oless(X1,c_Suc(X1),tc_nat),
    inference(literals_permutation,[status(thm)],[c_0_3921]) ).

cnf(c_0_3922_0,axiom,
    c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
    inference(literals_permutation,[status(thm)],[c_0_3922]) ).

cnf(c_0_3923_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(literals_permutation,[status(thm)],[c_0_3923]) ).

cnf(c_0_3924_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(literals_permutation,[status(thm)],[c_0_3924]) ).

cnf(c_0_3925_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(literals_permutation,[status(thm)],[c_0_3925]) ).

cnf(c_0_3926_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(literals_permutation,[status(thm)],[c_0_3926]) ).

cnf(c_0_3927_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(literals_permutation,[status(thm)],[c_0_3927]) ).

cnf(c_0_3928_0,axiom,
    c_HOL_Ominus__class_Ominus(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = X1,
    inference(literals_permutation,[status(thm)],[c_0_3928]) ).

cnf(c_0_3929_0,axiom,
    c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) = X1,
    inference(literals_permutation,[status(thm)],[c_0_3929]) ).

cnf(c_0_3930_0,axiom,
    c_HOL_Oplus__class_Oplus(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = X1,
    inference(literals_permutation,[status(thm)],[c_0_3930]) ).

cnf(c_0_3931_0,axiom,
    c_HOL_Oplus__class_Oplus(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = X1,
    inference(literals_permutation,[status(thm)],[c_0_3931]) ).

cnf(c_0_3932_0,axiom,
    c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
    inference(literals_permutation,[status(thm)],[c_0_3932]) ).

cnf(c_0_3933_0,axiom,
    c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat),
    inference(literals_permutation,[status(thm)],[c_0_3933]) ).

cnf(c_0_3934_0,axiom,
    c_HOL_Ominus__class_Ominus(X1,X1,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
    inference(literals_permutation,[status(thm)],[c_0_3934]) ).

cnf(c_0_3936_0,axiom,
    c_lessequals(X1,X1,tc_nat),
    inference(literals_permutation,[status(thm)],[c_0_3936]) ).

cnf(c_0_3937_0,axiom,
    c_lessequals(X1,X1,tc_nat),
    inference(literals_permutation,[status(thm)],[c_0_3937]) ).

cnf(c_0_3938_0,axiom,
    c_Ring__and__Field_Odvd__class_Odvd(X1,X1,tc_nat),
    inference(literals_permutation,[status(thm)],[c_0_3938]) ).

cnf(c_0_3939_0,axiom,
    c_HOL_Oord__class_Oless(v_i,v_n,tc_nat),
    inference(literals_permutation,[status(thm)],[c_0_3939]) ).

cnf(c_0_3940_0,axiom,
    c_HOL_Oord__class_Oless(v_i,v_n,tc_nat),
    inference(literals_permutation,[status(thm)],[c_0_3940]) ).

cnf(c_0_3946_0,axiom,
    c_Parity_Oeven__odd__class_Oeven(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
    inference(literals_permutation,[status(thm)],[c_0_3946]) ).

cnf(c_0_3955_0,axiom,
    class_Orderings_Oorder(tc_nat),
    inference(literals_permutation,[status(thm)],[c_0_3955]) ).

cnf(c_0_3956_0,axiom,
    class_Orderings_Olinorder(tc_nat),
    inference(literals_permutation,[status(thm)],[c_0_3956]) ).

cnf(c_0_3957_0,axiom,
    class_Orderings_Opreorder(tc_nat),
    inference(literals_permutation,[status(thm)],[c_0_3957]) ).

cnf(c_0_3958_0,axiom,
    class_Ring__and__Field_Odvd(tc_nat),
    inference(literals_permutation,[status(thm)],[c_0_3958]) ).

cnf(c_0_3959_0,axiom,
    class_Nat_Osemiring__char__0(tc_nat),
    inference(literals_permutation,[status(thm)],[c_0_3959]) ).

cnf(c_0_3960_0,axiom,
    class_Divides_Osemiring__div(tc_nat),
    inference(literals_permutation,[status(thm)],[c_0_3960]) ).

cnf(c_0_3961_0,axiom,
    class_OrderedGroup_Omonoid__add(tc_nat),
    inference(literals_permutation,[status(thm)],[c_0_3961]) ).

cnf(c_0_3962_0,axiom,
    class_Ring__and__Field_Osemiring(tc_nat),
    inference(literals_permutation,[status(thm)],[c_0_3962]) ).

cnf(c_0_3963_0,axiom,
    class_Ring__and__Field_Omult__mono(tc_nat),
    inference(literals_permutation,[status(thm)],[c_0_3963]) ).

cnf(c_0_3964_0,axiom,
    class_Ring__and__Field_Omult__zero(tc_nat),
    inference(literals_permutation,[status(thm)],[c_0_3964]) ).

cnf(c_0_3965_0,axiom,
    class_Ring__and__Field_Omult__mono1(tc_nat),
    inference(literals_permutation,[status(thm)],[c_0_3965]) ).

cnf(c_0_3966_0,axiom,
    class_Ring__and__Field_Osemiring__1(tc_nat),
    inference(literals_permutation,[status(thm)],[c_0_3966]) ).

cnf(c_0_3967_0,axiom,
    class_OrderedGroup_Ocomm__monoid__add(tc_nat),
    inference(literals_permutation,[status(thm)],[c_0_3967]) ).

cnf(c_0_3968_0,axiom,
    class_Ring__and__Field_Ocomm__semiring(tc_nat),
    inference(literals_permutation,[status(thm)],[c_0_3968]) ).

cnf(c_0_3969_0,axiom,
    class_OrderedGroup_Oab__semigroup__add(tc_nat),
    inference(literals_permutation,[status(thm)],[c_0_3969]) ).

cnf(c_0_3970_0,axiom,
    class_OrderedGroup_Oab__semigroup__mult(tc_nat),
    inference(literals_permutation,[status(thm)],[c_0_3970]) ).

cnf(c_0_3971_0,axiom,
    class_Ring__and__Field_Ocomm__semiring__1(tc_nat),
    inference(literals_permutation,[status(thm)],[c_0_3971]) ).

cnf(c_0_3972_0,axiom,
    class_Ring__and__Field_Oordered__semidom(tc_nat),
    inference(literals_permutation,[status(thm)],[c_0_3972]) ).

cnf(c_0_3973_0,axiom,
    class_Ring__and__Field_Ono__zero__divisors(tc_nat),
    inference(literals_permutation,[status(thm)],[c_0_3973]) ).

cnf(c_0_3974_0,axiom,
    class_Ring__and__Field_Oordered__semiring(tc_nat),
    inference(literals_permutation,[status(thm)],[c_0_3974]) ).

cnf(c_0_3975_0,axiom,
    class_Ring__and__Field_Opordered__semiring(tc_nat),
    inference(literals_permutation,[status(thm)],[c_0_3975]) ).

cnf(c_0_3976_0,axiom,
    class_OrderedGroup_Ocancel__semigroup__add(tc_nat),
    inference(literals_permutation,[status(thm)],[c_0_3976]) ).

cnf(c_0_3977_0,axiom,
    class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat),
    inference(literals_permutation,[status(thm)],[c_0_3977]) ).

cnf(c_0_3978_0,axiom,
    class_OrderedGroup_Opordered__comm__monoid__add(tc_nat),
    inference(literals_permutation,[status(thm)],[c_0_3978]) ).

cnf(c_0_3979_0,axiom,
    class_OrderedGroup_Opordered__ab__semigroup__add(tc_nat),
    inference(literals_permutation,[status(thm)],[c_0_3979]) ).

cnf(c_0_3980_0,axiom,
    class_Ring__and__Field_Oordered__semiring__strict(tc_nat),
    inference(literals_permutation,[status(thm)],[c_0_3980]) ).

cnf(c_0_3981_0,axiom,
    class_Ring__and__Field_Opordered__cancel__semiring(tc_nat),
    inference(literals_permutation,[status(thm)],[c_0_3981]) ).

cnf(c_0_3982_0,axiom,
    class_Ring__and__Field_Oordered__comm__semiring__strict(tc_nat),
    inference(literals_permutation,[status(thm)],[c_0_3982]) ).

cnf(c_0_3983_0,axiom,
    class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat),
    inference(literals_permutation,[status(thm)],[c_0_3983]) ).

cnf(c_0_3984_0,axiom,
    class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat),
    inference(literals_permutation,[status(thm)],[c_0_3984]) ).

% CNF of non-axioms
% Start CNF derivation
fof(c_0_0_001,negated_conjecture,
    ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(v_i,v_k,tc_nat),v_n,tc_nat),
    file('<stdin>',cls_conjecture_0) ).

fof(c_0_1_002,negated_conjecture,
    ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(v_i,v_k,tc_nat),v_n,tc_nat),
    inference(fof_simplification,[status(thm)],[c_0_0]) ).

fof(c_0_2_003,negated_conjecture,
    ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(v_i,v_k,tc_nat),v_n,tc_nat),
    c_0_1 ).

cnf(c_0_3_004,negated_conjecture,
    ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(v_i,v_k,tc_nat),v_n,tc_nat),
    inference(split_conjunct,[status(thm)],[c_0_2]) ).

cnf(c_0_4_005,negated_conjecture,
    ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(v_i,v_k,tc_nat),v_n,tc_nat),
    c_0_3,
    [final] ).

% End CNF derivation

%-------------------------------------------------------------
% Proof by iprover

cnf(c_2056,negated_conjecture,
    ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(v_i,v_k,tc_nat),v_n,tc_nat),
    file('/export/starexec/sandbox2/tmp/iprover_modulo_8967c6.p',c_0_4) ).

cnf(c_2552,negated_conjecture,
    ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(v_i,v_k,tc_nat),v_n,tc_nat),
    inference(copy,[status(esa)],[c_2056]) ).

cnf(c_2556,negated_conjecture,
    ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(v_i,v_k,tc_nat),v_n,tc_nat),
    inference(copy,[status(esa)],[c_2552]) ).

cnf(c_2557,negated_conjecture,
    ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(v_i,v_k,tc_nat),v_n,tc_nat),
    inference(copy,[status(esa)],[c_2556]) ).

cnf(c_2558,negated_conjecture,
    ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(v_i,v_k,tc_nat),v_n,tc_nat),
    inference(copy,[status(esa)],[c_2557]) ).

cnf(c_8683,plain,
    ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(v_i,v_k,tc_nat),v_n,tc_nat),
    inference(copy,[status(esa)],[c_2558]) ).

cnf(c_727,plain,
    ( ~ class_Orderings_Opreorder(X0)
    | ~ c_lessequals(X1,X2,X0)
    | c_lessequals(X2,X1,X0)
    | c_HOL_Oord__class_Oless(X1,X2,X0) ),
    file('/export/starexec/sandbox2/tmp/iprover_modulo_8967c6.p',c_0_3656_1) ).

cnf(c_6025,plain,
    ( ~ class_Orderings_Opreorder(X0)
    | ~ c_lessequals(X1,X2,X0)
    | c_lessequals(X2,X1,X0)
    | c_HOL_Oord__class_Oless(X1,X2,X0) ),
    inference(copy,[status(esa)],[c_727]) ).

cnf(c_6026,plain,
    ( ~ class_Orderings_Opreorder(X0)
    | c_HOL_Oord__class_Oless(X1,X2,X0)
    | ~ c_lessequals(X1,X2,X0)
    | c_lessequals(X2,X1,X0) ),
    inference(rewriting,[status(thm)],[c_6025]) ).

cnf(c_8694,plain,
    ( ~ class_Orderings_Opreorder(tc_nat)
    | c_lessequals(v_n,c_HOL_Ominus__class_Ominus(v_i,v_k,tc_nat),tc_nat)
    | ~ c_lessequals(c_HOL_Ominus__class_Ominus(v_i,v_k,tc_nat),v_n,tc_nat) ),
    inference(resolution,[status(thm)],[c_8683,c_6026]) ).

cnf(c_8697,plain,
    ( ~ class_Orderings_Opreorder(tc_nat)
    | c_lessequals(v_n,c_HOL_Ominus__class_Ominus(v_i,v_k,tc_nat),tc_nat)
    | ~ c_lessequals(c_HOL_Ominus__class_Ominus(v_i,v_k,tc_nat),v_n,tc_nat) ),
    inference(rewriting,[status(thm)],[c_8694]) ).

cnf(c_290,plain,
    ( c_lessequals(X0,X1,tc_nat)
    | c_lessequals(X1,X0,tc_nat) ),
    file('/export/starexec/sandbox2/tmp/iprover_modulo_8967c6.p',c_0_3833_1) ).

cnf(c_5151,plain,
    ( c_lessequals(X0,X1,tc_nat)
    | c_lessequals(X1,X0,tc_nat) ),
    inference(copy,[status(esa)],[c_290]) ).

cnf(c_27,plain,
    class_Orderings_Opreorder(tc_nat),
    file('/export/starexec/sandbox2/tmp/iprover_modulo_8967c6.p',c_0_3957_0) ).

cnf(c_4670,plain,
    class_Orderings_Opreorder(tc_nat),
    inference(copy,[status(esa)],[c_27]) ).

cnf(c_8895,plain,
    c_lessequals(v_n,c_HOL_Ominus__class_Ominus(v_i,v_k,tc_nat),tc_nat),
    inference(forward_subsumption_resolution,[status(thm)],[c_8697,c_5151,c_4670]) ).

cnf(c_8896,plain,
    c_lessequals(v_n,c_HOL_Ominus__class_Ominus(v_i,v_k,tc_nat),tc_nat),
    inference(rewriting,[status(thm)],[c_8895]) ).

cnf(c_811,plain,
    ( ~ class_Orderings_Opreorder(X0)
    | ~ c_HOL_Oord__class_Oless(X1,X2,X0)
    | c_HOL_Oord__class_Oless(X3,X2,X0)
    | ~ c_lessequals(X3,X1,X0) ),
    file('/export/starexec/sandbox2/tmp/iprover_modulo_8967c6.p',c_0_3624_1) ).

cnf(c_6193,plain,
    ( ~ class_Orderings_Opreorder(X0)
    | ~ c_HOL_Oord__class_Oless(X1,X2,X0)
    | c_HOL_Oord__class_Oless(X3,X2,X0)
    | ~ c_lessequals(X3,X1,X0) ),
    inference(copy,[status(esa)],[c_811]) ).

cnf(c_8989,plain,
    ( ~ class_Orderings_Opreorder(tc_nat)
    | c_HOL_Oord__class_Oless(v_n,X0,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(v_i,v_k,tc_nat),X0,tc_nat) ),
    inference(resolution,[status(thm)],[c_8896,c_6193]) ).

cnf(c_8990,plain,
    ( ~ class_Orderings_Opreorder(tc_nat)
    | c_HOL_Oord__class_Oless(v_n,X0,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(v_i,v_k,tc_nat),X0,tc_nat) ),
    inference(rewriting,[status(thm)],[c_8989]) ).

cnf(c_10025,plain,
    ( c_HOL_Oord__class_Oless(v_n,X0,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(v_i,v_k,tc_nat),X0,tc_nat) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_8990,c_4670]) ).

cnf(c_10026,plain,
    ( c_HOL_Oord__class_Oless(v_n,X0,tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(v_i,v_k,tc_nat),X0,tc_nat) ),
    inference(rewriting,[status(thm)],[c_10025]) ).

cnf(c_10046,plain,
    ( ~ class_Orderings_Opreorder(tc_nat)
    | c_HOL_Oord__class_Oless(v_n,X0,tc_nat)
    | ~ c_lessequals(c_HOL_Ominus__class_Ominus(v_i,v_k,tc_nat),X0,tc_nat)
    | c_lessequals(X0,c_HOL_Ominus__class_Ominus(v_i,v_k,tc_nat),tc_nat) ),
    inference(resolution,[status(thm)],[c_10026,c_6026]) ).

cnf(c_10049,plain,
    ( ~ class_Orderings_Opreorder(tc_nat)
    | c_HOL_Oord__class_Oless(v_n,X0,tc_nat)
    | ~ c_lessequals(c_HOL_Ominus__class_Ominus(v_i,v_k,tc_nat),X0,tc_nat)
    | c_lessequals(X0,c_HOL_Ominus__class_Ominus(v_i,v_k,tc_nat),tc_nat) ),
    inference(rewriting,[status(thm)],[c_10046]) ).

cnf(c_84992,plain,
    ( c_HOL_Oord__class_Oless(v_n,X0,tc_nat)
    | c_lessequals(X0,c_HOL_Ominus__class_Ominus(v_i,v_k,tc_nat),tc_nat) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_10049,c_5151,c_4670]) ).

cnf(c_84993,plain,
    ( c_HOL_Oord__class_Oless(v_n,X0,tc_nat)
    | c_lessequals(X0,c_HOL_Ominus__class_Ominus(v_i,v_k,tc_nat),tc_nat) ),
    inference(rewriting,[status(thm)],[c_84992]) ).

cnf(c_803,plain,
    ( ~ class_Orderings_Oorder(X0)
    | ~ c_HOL_Oord__class_Oless(X1,X2,X0)
    | c_HOL_Oord__class_Oless(X1,X3,X0)
    | ~ c_lessequals(X2,X3,X0) ),
    file('/export/starexec/sandbox2/tmp/iprover_modulo_8967c6.p',c_0_3626_1) ).

cnf(c_6177,plain,
    ( ~ class_Orderings_Oorder(X0)
    | ~ c_HOL_Oord__class_Oless(X1,X2,X0)
    | c_HOL_Oord__class_Oless(X1,X3,X0)
    | ~ c_lessequals(X2,X3,X0) ),
    inference(copy,[status(esa)],[c_803]) ).

cnf(c_85093,plain,
    ( ~ class_Orderings_Oorder(tc_nat)
    | c_HOL_Oord__class_Oless(v_n,X0,tc_nat)
    | c_HOL_Oord__class_Oless(X1,c_HOL_Ominus__class_Ominus(v_i,v_k,tc_nat),tc_nat)
    | ~ c_HOL_Oord__class_Oless(X1,X0,tc_nat) ),
    inference(resolution,[status(thm)],[c_84993,c_6177]) ).

cnf(c_85094,plain,
    ( ~ class_Orderings_Oorder(tc_nat)
    | c_HOL_Oord__class_Oless(v_n,X0,tc_nat)
    | c_HOL_Oord__class_Oless(X1,c_HOL_Ominus__class_Ominus(v_i,v_k,tc_nat),tc_nat)
    | ~ c_HOL_Oord__class_Oless(X1,X0,tc_nat) ),
    inference(rewriting,[status(thm)],[c_85093]) ).

cnf(c_29,plain,
    class_Orderings_Oorder(tc_nat),
    file('/export/starexec/sandbox2/tmp/iprover_modulo_8967c6.p',c_0_3955_0) ).

cnf(c_4674,plain,
    class_Orderings_Oorder(tc_nat),
    inference(copy,[status(esa)],[c_29]) ).

cnf(c_94943,plain,
    ( c_HOL_Oord__class_Oless(v_n,X0,tc_nat)
    | c_HOL_Oord__class_Oless(X1,c_HOL_Ominus__class_Ominus(v_i,v_k,tc_nat),tc_nat)
    | ~ c_HOL_Oord__class_Oless(X1,X0,tc_nat) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_85094,c_4674]) ).

cnf(c_94944,plain,
    ( c_HOL_Oord__class_Oless(v_n,X0,tc_nat)
    | c_HOL_Oord__class_Oless(X1,c_HOL_Ominus__class_Ominus(v_i,v_k,tc_nat),tc_nat)
    | ~ c_HOL_Oord__class_Oless(X1,X0,tc_nat) ),
    inference(rewriting,[status(thm)],[c_94943]) ).

cnf(c_31,plain,
    c_HOL_Oord__class_Oless(v_i,v_n,tc_nat),
    file('/export/starexec/sandbox2/tmp/iprover_modulo_8967c6.p',c_0_3940_0) ).

cnf(c_4678,plain,
    c_HOL_Oord__class_Oless(v_i,v_n,tc_nat),
    inference(copy,[status(esa)],[c_31]) ).

cnf(c_94948,plain,
    ( c_HOL_Oord__class_Oless(v_i,c_HOL_Ominus__class_Ominus(v_i,v_k,tc_nat),tc_nat)
    | c_HOL_Oord__class_Oless(v_n,v_n,tc_nat) ),
    inference(resolution,[status(thm)],[c_94944,c_4678]) ).

cnf(c_94949,plain,
    ( c_HOL_Oord__class_Oless(v_i,c_HOL_Ominus__class_Ominus(v_i,v_k,tc_nat),tc_nat)
    | c_HOL_Oord__class_Oless(v_n,v_n,tc_nat) ),
    inference(rewriting,[status(thm)],[c_94948]) ).

cnf(c_120,plain,
    ~ c_HOL_Oord__class_Oless(X0,X0,tc_nat),
    file('/export/starexec/sandbox2/tmp/iprover_modulo_8967c6.p',c_0_3868_0) ).

cnf(c_4811,plain,
    ~ c_HOL_Oord__class_Oless(X0,X0,tc_nat),
    inference(copy,[status(esa)],[c_120]) ).

cnf(c_95948,plain,
    c_HOL_Oord__class_Oless(v_i,c_HOL_Ominus__class_Ominus(v_i,v_k,tc_nat),tc_nat),
    inference(forward_subsumption_resolution,[status(thm)],[c_94949,c_4811]) ).

cnf(c_95949,plain,
    c_HOL_Oord__class_Oless(v_i,c_HOL_Ominus__class_Ominus(v_i,v_k,tc_nat),tc_nat),
    inference(rewriting,[status(thm)],[c_95948]) ).

cnf(c_1432,plain,
    ( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),X2,tc_nat)
    | ~ c_HOL_Oord__class_Oless(X0,c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),tc_nat) ),
    file('/export/starexec/sandbox2/tmp/iprover_modulo_8967c6.p',c_0_3401_1) ).

cnf(c_7435,plain,
    ( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),X2,tc_nat)
    | ~ c_HOL_Oord__class_Oless(X0,c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),tc_nat) ),
    inference(copy,[status(esa)],[c_1432]) ).

cnf(c_96029,plain,
    c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(v_i,v_k,tc_nat),v_i,tc_nat),
    inference(resolution,[status(thm)],[c_95949,c_7435]) ).

cnf(c_96030,plain,
    c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(v_i,v_k,tc_nat),v_i,tc_nat),
    inference(rewriting,[status(thm)],[c_96029]) ).

cnf(c_126,plain,
    ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),X0,tc_nat),
    file('/export/starexec/sandbox2/tmp/iprover_modulo_8967c6.p',c_0_3602_0) ).

cnf(c_4823,plain,
    ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),X0,tc_nat),
    inference(copy,[status(esa)],[c_126]) ).

cnf(c_96040,plain,
    $false,
    inference(forward_subsumption_resolution,[status(thm)],[c_96030,c_4823]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12  % Problem  : SWV689-1 : TPTP v8.1.0. Released v4.1.0.
% 0.04/0.13  % Command  : iprover_modulo %s %d
% 0.13/0.34  % Computer : n010.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 600
% 0.13/0.34  % DateTime : Thu Jun 16 02:21:09 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 0.13/0.35  % Running in mono-core mode
% 0.20/0.55  % Orienting using strategy Equiv(ClausalAll)
% 0.20/0.55  % Orientation found
% 0.20/0.55  % Executing iprover_moduloopt --modulo true --schedule none --sub_typing false --res_to_prop_solver none --res_prop_simpl_given false --res_lit_sel kbo_max --large_theory_mode false --res_time_limit 1000 --res_orphan_elimination false --prep_sem_filter none --prep_unflatten false --comb_res_mult 1000 --comb_inst_mult 300 --clausifier .//eprover --clausifier_options "--tstp-format  " --proof_out_file /export/starexec/sandbox2/tmp/iprover_proof_698159.s --tptp_safe_out true --time_out_real 150 /export/starexec/sandbox2/tmp/iprover_modulo_8967c6.p | tee /export/starexec/sandbox2/tmp/iprover_modulo_out_570083 | grep -v "SZS"
% 0.40/0.57  
% 0.40/0.57  %---------------- iProver v2.5 (CASC-J8 2016) ----------------%
% 0.40/0.57  
% 0.40/0.57  % 
% 0.40/0.57  % ------  iProver source info 
% 0.40/0.57  
% 0.40/0.57  % git: sha1: 57accf6c58032223c7708532cf852a99fa48c1b3
% 0.40/0.57  % git: non_committed_changes: true
% 0.40/0.57  % git: last_make_outside_of_git: true
% 0.40/0.57  
% 0.40/0.57  % 
% 0.40/0.57  % ------ Input Options
% 0.40/0.57  
% 0.40/0.57  % --out_options                         all
% 0.40/0.57  % --tptp_safe_out                       true
% 0.40/0.57  % --problem_path                        ""
% 0.40/0.57  % --include_path                        ""
% 0.40/0.57  % --clausifier                          .//eprover
% 0.40/0.57  % --clausifier_options                  --tstp-format  
% 0.40/0.57  % --stdin                               false
% 0.40/0.57  % --dbg_backtrace                       false
% 0.40/0.57  % --dbg_dump_prop_clauses               false
% 0.40/0.57  % --dbg_dump_prop_clauses_file          -
% 0.40/0.57  % --dbg_out_stat                        false
% 0.40/0.57  
% 0.40/0.57  % ------ General Options
% 0.40/0.57  
% 0.40/0.57  % --fof                                 false
% 0.40/0.57  % --time_out_real                       150.
% 0.40/0.57  % --time_out_prep_mult                  0.2
% 0.40/0.57  % --time_out_virtual                    -1.
% 0.40/0.57  % --schedule                            none
% 0.40/0.57  % --ground_splitting                    input
% 0.40/0.57  % --splitting_nvd                       16
% 0.40/0.57  % --non_eq_to_eq                        false
% 0.40/0.57  % --prep_gs_sim                         true
% 0.40/0.57  % --prep_unflatten                      false
% 0.40/0.57  % --prep_res_sim                        true
% 0.40/0.57  % --prep_upred                          true
% 0.40/0.57  % --res_sim_input                       true
% 0.40/0.57  % --clause_weak_htbl                    true
% 0.40/0.57  % --gc_record_bc_elim                   false
% 0.40/0.57  % --symbol_type_check                   false
% 0.40/0.57  % --clausify_out                        false
% 0.40/0.57  % --large_theory_mode                   false
% 0.40/0.57  % --prep_sem_filter                     none
% 0.40/0.57  % --prep_sem_filter_out                 false
% 0.40/0.57  % --preprocessed_out                    false
% 0.40/0.57  % --sub_typing                          false
% 0.40/0.57  % --brand_transform                     false
% 0.40/0.57  % --pure_diseq_elim                     true
% 0.40/0.57  % --min_unsat_core                      false
% 0.40/0.57  % --pred_elim                           true
% 0.40/0.57  % --add_important_lit                   false
% 0.40/0.57  % --soft_assumptions                    false
% 0.40/0.57  % --reset_solvers                       false
% 0.40/0.57  % --bc_imp_inh                          []
% 0.40/0.57  % --conj_cone_tolerance                 1.5
% 0.40/0.57  % --prolific_symb_bound                 500
% 0.40/0.57  % --lt_threshold                        2000
% 0.40/0.57  
% 0.40/0.57  % ------ SAT Options
% 0.40/0.57  
% 0.40/0.57  % --sat_mode                            false
% 0.40/0.57  % --sat_fm_restart_options              ""
% 0.40/0.57  % --sat_gr_def                          false
% 0.40/0.57  % --sat_epr_types                       true
% 0.40/0.57  % --sat_non_cyclic_types                false
% 0.40/0.57  % --sat_finite_models                   false
% 0.40/0.57  % --sat_fm_lemmas                       false
% 0.40/0.57  % --sat_fm_prep                         false
% 0.40/0.57  % --sat_fm_uc_incr                      true
% 0.40/0.57  % --sat_out_model                       small
% 0.40/0.57  % --sat_out_clauses                     false
% 0.40/0.57  
% 0.40/0.57  % ------ QBF Options
% 0.40/0.57  
% 0.40/0.57  % --qbf_mode                            false
% 0.40/0.57  % --qbf_elim_univ                       true
% 0.40/0.57  % --qbf_sk_in                           true
% 0.40/0.57  % --qbf_pred_elim                       true
% 0.40/0.57  % --qbf_split                           32
% 0.40/0.57  
% 0.40/0.57  % ------ BMC1 Options
% 0.40/0.57  
% 0.40/0.57  % --bmc1_incremental                    false
% 0.40/0.57  % --bmc1_axioms                         reachable_all
% 0.40/0.57  % --bmc1_min_bound                      0
% 0.40/0.57  % --bmc1_max_bound                      -1
% 0.40/0.57  % --bmc1_max_bound_default              -1
% 0.40/0.57  % --bmc1_symbol_reachability            true
% 0.40/0.57  % --bmc1_property_lemmas                false
% 0.40/0.57  % --bmc1_k_induction                    false
% 0.40/0.57  % --bmc1_non_equiv_states               false
% 0.40/0.57  % --bmc1_deadlock                       false
% 0.40/0.57  % --bmc1_ucm                            false
% 0.40/0.57  % --bmc1_add_unsat_core                 none
% 0.40/0.57  % --bmc1_unsat_core_children            false
% 0.40/0.57  % --bmc1_unsat_core_extrapolate_axioms  false
% 0.40/0.57  % --bmc1_out_stat                       full
% 0.40/0.57  % --bmc1_ground_init                    false
% 0.40/0.57  % --bmc1_pre_inst_next_state            false
% 0.40/0.57  % --bmc1_pre_inst_state                 false
% 0.40/0.57  % --bmc1_pre_inst_reach_state           false
% 0.40/0.57  % --bmc1_out_unsat_core                 false
% 0.40/0.57  % --bmc1_aig_witness_out                false
% 0.40/0.57  % --bmc1_verbose                        false
% 0.40/0.57  % --bmc1_dump_clauses_tptp              false
% 150.39/150.57  % --bmc1_dump_unsat_core_tptp           false
% 150.39/150.57  % --bmc1_dump_file                      -
% 150.39/150.57  % --bmc1_ucm_expand_uc_limit            128
% 150.39/150.57  % --bmc1_ucm_n_expand_iterations        6
% 150.39/150.57  % --bmc1_ucm_extend_mode                1
% 150.39/150.57  % --bmc1_ucm_init_mode                  2
% 150.39/150.57  % --bmc1_ucm_cone_mode                  none
% 150.39/150.57  % --bmc1_ucm_reduced_relation_type      0
% 150.39/150.57  % --bmc1_ucm_relax_model                4
% 150.39/150.57  % --bmc1_ucm_full_tr_after_sat          true
% 150.39/150.57  % --bmc1_ucm_expand_neg_assumptions     false
% 150.39/150.57  % --bmc1_ucm_layered_model              none
% 150.39/150.57  % --bmc1_ucm_max_lemma_size             10
% 150.39/150.57  
% 150.39/150.57  % ------ AIG Options
% 150.39/150.57  
% 150.39/150.57  % --aig_mode                            false
% 150.39/150.57  
% 150.39/150.57  % ------ Instantiation Options
% 150.39/150.57  
% 150.39/150.57  % --instantiation_flag                  true
% 150.39/150.57  % --inst_lit_sel                        [+prop;+sign;+ground;-num_var;-num_symb]
% 150.39/150.57  % --inst_solver_per_active              750
% 150.39/150.57  % --inst_solver_calls_frac              0.5
% 150.39/150.57  % --inst_passive_queue_type             priority_queues
% 150.39/150.57  % --inst_passive_queues                 [[-conj_dist;+conj_symb;-num_var];[+age;-num_symb]]
% 150.39/150.57  % --inst_passive_queues_freq            [25;2]
% 150.39/150.57  % --inst_dismatching                    true
% 150.39/150.57  % --inst_eager_unprocessed_to_passive   true
% 150.39/150.57  % --inst_prop_sim_given                 true
% 150.39/150.57  % --inst_prop_sim_new                   false
% 150.39/150.57  % --inst_orphan_elimination             true
% 150.39/150.57  % --inst_learning_loop_flag             true
% 150.39/150.57  % --inst_learning_start                 3000
% 150.39/150.57  % --inst_learning_factor                2
% 150.39/150.57  % --inst_start_prop_sim_after_learn     3
% 150.39/150.57  % --inst_sel_renew                      solver
% 150.39/150.57  % --inst_lit_activity_flag              true
% 150.39/150.57  % --inst_out_proof                      true
% 150.39/150.57  
% 150.39/150.57  % ------ Resolution Options
% 150.39/150.57  
% 150.39/150.57  % --resolution_flag                     true
% 150.39/150.57  % --res_lit_sel                         kbo_max
% 150.39/150.57  % --res_to_prop_solver                  none
% 150.39/150.57  % --res_prop_simpl_new                  false
% 150.39/150.57  % --res_prop_simpl_given                false
% 150.39/150.57  % --res_passive_queue_type              priority_queues
% 150.39/150.57  % --res_passive_queues                  [[-conj_dist;+conj_symb;-num_symb];[+age;-num_symb]]
% 150.39/150.57  % --res_passive_queues_freq             [15;5]
% 150.39/150.57  % --res_forward_subs                    full
% 150.39/150.57  % --res_backward_subs                   full
% 150.39/150.57  % --res_forward_subs_resolution         true
% 150.39/150.57  % --res_backward_subs_resolution        true
% 150.39/150.57  % --res_orphan_elimination              false
% 150.39/150.57  % --res_time_limit                      1000.
% 150.39/150.57  % --res_out_proof                       true
% 150.39/150.57  % --proof_out_file                      /export/starexec/sandbox2/tmp/iprover_proof_698159.s
% 150.39/150.57  % --modulo                              true
% 150.39/150.57  
% 150.39/150.57  % ------ Combination Options
% 150.39/150.57  
% 150.39/150.57  % --comb_res_mult                       1000
% 150.39/150.57  % --comb_inst_mult                      300
% 150.39/150.57  % ------ 
% 150.39/150.57  
% 150.39/150.57  % ------ Parsing...% successful
% 150.39/150.57  
% 150.39/150.57  % ------ 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 % 
% 150.39/150.57  
% 150.39/150.57  % ------ Proving...
% 150.39/150.57  % ------ Problem Properties 
% 150.39/150.57  
% 150.39/150.57  % 
% 150.39/150.57  % EPR                                   false
% 150.39/150.57  % Horn                                  false
% 150.39/150.57  % Has equality                          true
% 150.39/150.57  
% 150.39/150.57  % % ------ Input Options Time Limit: Unbounded
% 150.39/150.57  
% 150.39/150.57  
% 150.39/150.57  Compiling...
% 150.39/150.57  Loading plugin: done.
% 150.39/150.57  % 
% 150.39/150.57  
% 150.39/150.57  
% 150.39/150.57  % Time Out Real
% 150.39/150.57  
% 150.39/150.57  % ------                             Statistics
% 150.39/150.57  
% 150.39/150.57  % ------ General
% 150.39/150.57  
% 150.39/150.57  % num_of_input_clauses:                 2057
% 150.39/150.57  % num_of_input_neg_conjectures:         1
% 150.39/150.57  % num_of_splits:                        0
% 150.39/150.57  % num_of_split_atoms:                   0
% 150.39/150.57  % num_of_sem_filtered_clauses:          0
% 150.39/150.57  % num_of_subtypes:                      0
% 150.39/150.57  % monotx_restored_types:                0
% 150.39/150.57  % sat_num_of_epr_types:                 0
% 150.39/150.57  % sat_num_of_non_cyclic_types:          0
% 150.39/150.57  % sat_guarded_non_collapsed_types:      0
% 150.39/150.57  % is_epr:                               0
% 150.39/150.57  % is_horn:                              0
% 150.39/150.57  % has_eq:                               1
% 150.39/150.57  % num_pure_diseq_elim:                  0
% 150.39/150.57  % simp_replaced_by:                     0
% 150.39/150.57  % res_preprocessed:                     2
% 150.39/150.57  % prep_upred:                           0
% 150.39/150.57  % prep_unflattend:                      0
% 150.39/150.57  % pred_elim_cands:                      0
% 150.39/150.57  % pred_elim:                            0
% 150.39/150.57  % pred_elim_cl:                         0
% 150.39/150.57  % pred_elim_cycles:                     0
% 150.39/150.57  % forced_gc_time:                       0
% 150.39/150.57  % gc_basic_clause_elim:                 0
% 150.39/150.57  % parsing_time:                         0.081
% 150.39/150.57  % sem_filter_time:                      0.
% 150.39/150.57  % pred_elim_time:                       0.
% 150.39/150.57  % out_proof_time:                       0.
% 150.39/150.57  % monotx_time:                          0.
% 150.39/150.57  % subtype_inf_time:                     0.
% 150.39/150.57  % unif_index_cands_time:                0.
% 150.39/150.57  % unif_index_add_time:                  0.
% 150.39/150.57  % total_time:                           150.018
% 150.39/150.57  % num_of_symbols:                       94
% 150.39/150.57  % num_of_terms:                         3956
% 150.39/150.57  
% 150.39/150.57  % ------ Propositional Solver
% 150.39/150.57  
% 150.39/150.57  % prop_solver_calls:                    1
% 150.39/150.57  % prop_fast_solver_calls:               3
% 150.39/150.57  % prop_num_of_clauses:                  1636
% 150.39/150.57  % prop_preprocess_simplified:           6512
% 150.39/150.57  % prop_fo_subsumed:                     0
% 150.39/150.57  % prop_solver_time:                     0.
% 150.39/150.57  % prop_fast_solver_time:                0.
% 150.39/150.57  % prop_unsat_core_time:                 0.
% 150.39/150.57  
% 150.39/150.57  % ------ QBF 
% 150.39/150.57  
% 150.39/150.57  % qbf_q_res:                            0
% 150.39/150.57  % qbf_num_tautologies:                  0
% 150.39/150.57  % qbf_prep_cycles:                      0
% 150.39/150.57  
% 150.39/150.57  % ------ BMC1
% 150.39/150.57  
% 150.39/150.57  % bmc1_current_bound:                   -1
% 150.39/150.57  % bmc1_last_solved_bound:               -1
% 150.39/150.57  % bmc1_unsat_core_size:                 -1
% 150.39/150.57  % bmc1_unsat_core_parents_size:         -1
% 150.39/150.57  % bmc1_merge_next_fun:                  0
% 150.39/150.57  % bmc1_unsat_core_clauses_time:         0.
% 150.39/150.57  
% 150.39/150.57  % ------ Instantiation
% 150.39/150.57  
% 150.39/150.57  % inst_num_of_clauses:                  1806
% 150.39/150.57  % inst_num_in_passive:                  0
% 150.39/150.57  % inst_num_in_active:                   0
% 150.39/150.57  % inst_num_in_unprocessed:              2057
% 150.39/150.57  % inst_num_of_loops:                    0
% 150.39/150.57  % inst_num_of_learning_restarts:        0
% 150.39/150.57  % inst_num_moves_active_passive:        0
% 150.39/150.57  % inst_lit_activity:                    0
% 150.39/150.57  % inst_lit_activity_moves:              0
% 150.39/150.57  % inst_num_tautologies:                 0
% 150.39/150.57  % inst_num_prop_implied:                0
% 150.39/150.57  % inst_num_existing_simplified:         0
% 150.39/150.57  % inst_num_eq_res_simplified:           0
% 150.39/150.57  % inst_num_child_elim:                  0
% 150.39/150.57  % inst_num_of_dismatching_blockings:    0
% 150.39/150.57  % inst_num_of_non_proper_insts:         0
% 150.39/150.57  % inst_num_of_duplicates:               0
% 150.39/150.57  % inst_inst_num_from_inst_to_res:       0
% 150.39/150.57  % inst_dismatching_checking_time:       0.
% 150.39/150.57  
% 150.39/150.57  % ------ Resolution
% 150.39/150.57  
% 150.39/150.57  % res_num_of_clauses:                   1944
% 150.39/150.57  % res_num_in_passive:                   0
% 150.39/150.57  % res_num_in_active:                    690
% 150.39/150.57  % res_num_of_loops:                     0
% 150.39/150.57  % res_forward_subset_subsumed:          1227
% 150.39/150.57  % res_backward_subset_subsumed:         11
% 150.39/150.57  % res_forward_subsumed:                 0
% 150.39/150.57  % res_backward_subsumed:                0
% 150.39/150.57  % res_forward_subsumption_resolution:   0
% 150.39/150.57  % res_backward_subsumption_resolution:  0
% 150.39/150.57  % res_clause_to_clause_subsumption:     0
% 150.39/150.57  % res_orphan_elimination:               0
% 150.39/150.57  % res_tautology_del:                    0
% 150.39/150.57  % res_num_eq_res_simplified:            0
% 150.39/150.57  % res_num_sel_changes:                  0
% 150.39/150.57  % res_moves_from_active_to_pass:        0
% 150.39/150.57  
% 150.39/150.57  % Status Unknown
% 150.43/150.70  % Orienting using strategy ClausalAll
% 150.43/150.70  % Orientation found
% 150.43/150.70  % Executing iprover_moduloopt --modulo true --schedule none --sub_typing false --res_to_prop_solver none --res_prop_simpl_given false --res_lit_sel kbo_max --large_theory_mode false --res_time_limit 1000 --res_orphan_elimination false --prep_sem_filter none --prep_unflatten false --comb_res_mult 1000 --comb_inst_mult 300 --clausifier .//eprover --clausifier_options "--tstp-format  " --proof_out_file /export/starexec/sandbox2/tmp/iprover_proof_698159.s --tptp_safe_out true --time_out_real 150 /export/starexec/sandbox2/tmp/iprover_modulo_8967c6.p | tee /export/starexec/sandbox2/tmp/iprover_modulo_out_6956a5 | grep -v "SZS"
% 150.43/150.72  
% 150.43/150.72  %---------------- iProver v2.5 (CASC-J8 2016) ----------------%
% 150.43/150.72  
% 150.43/150.72  % 
% 150.43/150.72  % ------  iProver source info 
% 150.43/150.72  
% 150.43/150.72  % git: sha1: 57accf6c58032223c7708532cf852a99fa48c1b3
% 150.43/150.72  % git: non_committed_changes: true
% 150.43/150.72  % git: last_make_outside_of_git: true
% 150.43/150.72  
% 150.43/150.72  % 
% 150.43/150.72  % ------ Input Options
% 150.43/150.72  
% 150.43/150.72  % --out_options                         all
% 150.43/150.72  % --tptp_safe_out                       true
% 150.43/150.72  % --problem_path                        ""
% 150.43/150.72  % --include_path                        ""
% 150.43/150.72  % --clausifier                          .//eprover
% 150.43/150.72  % --clausifier_options                  --tstp-format  
% 150.43/150.72  % --stdin                               false
% 150.43/150.72  % --dbg_backtrace                       false
% 150.43/150.72  % --dbg_dump_prop_clauses               false
% 150.43/150.72  % --dbg_dump_prop_clauses_file          -
% 150.43/150.72  % --dbg_out_stat                        false
% 150.43/150.72  
% 150.43/150.72  % ------ General Options
% 150.43/150.72  
% 150.43/150.72  % --fof                                 false
% 150.43/150.72  % --time_out_real                       150.
% 150.43/150.72  % --time_out_prep_mult                  0.2
% 150.43/150.72  % --time_out_virtual                    -1.
% 150.43/150.72  % --schedule                            none
% 150.43/150.72  % --ground_splitting                    input
% 150.43/150.72  % --splitting_nvd                       16
% 150.43/150.72  % --non_eq_to_eq                        false
% 150.43/150.72  % --prep_gs_sim                         true
% 150.43/150.72  % --prep_unflatten                      false
% 150.43/150.72  % --prep_res_sim                        true
% 150.43/150.72  % --prep_upred                          true
% 150.43/150.72  % --res_sim_input                       true
% 150.43/150.72  % --clause_weak_htbl                    true
% 150.43/150.72  % --gc_record_bc_elim                   false
% 150.43/150.72  % --symbol_type_check                   false
% 150.43/150.72  % --clausify_out                        false
% 150.43/150.72  % --large_theory_mode                   false
% 150.43/150.72  % --prep_sem_filter                     none
% 150.43/150.72  % --prep_sem_filter_out                 false
% 150.43/150.72  % --preprocessed_out                    false
% 150.43/150.72  % --sub_typing                          false
% 150.43/150.72  % --brand_transform                     false
% 150.43/150.72  % --pure_diseq_elim                     true
% 150.43/150.72  % --min_unsat_core                      false
% 150.43/150.72  % --pred_elim                           true
% 150.43/150.72  % --add_important_lit                   false
% 150.43/150.72  % --soft_assumptions                    false
% 150.43/150.72  % --reset_solvers                       false
% 150.43/150.72  % --bc_imp_inh                          []
% 150.43/150.72  % --conj_cone_tolerance                 1.5
% 150.43/150.72  % --prolific_symb_bound                 500
% 150.43/150.72  % --lt_threshold                        2000
% 150.43/150.72  
% 150.43/150.72  % ------ SAT Options
% 150.43/150.72  
% 150.43/150.72  % --sat_mode                            false
% 150.43/150.72  % --sat_fm_restart_options              ""
% 150.43/150.72  % --sat_gr_def                          false
% 150.43/150.72  % --sat_epr_types                       true
% 150.43/150.72  % --sat_non_cyclic_types                false
% 150.43/150.72  % --sat_finite_models                   false
% 150.43/150.72  % --sat_fm_lemmas                       false
% 150.43/150.72  % --sat_fm_prep                         false
% 150.43/150.72  % --sat_fm_uc_incr                      true
% 150.43/150.72  % --sat_out_model                       small
% 150.43/150.72  % --sat_out_clauses                     false
% 150.43/150.72  
% 150.43/150.72  % ------ QBF Options
% 150.43/150.72  
% 150.43/150.72  % --qbf_mode                            false
% 150.43/150.72  % --qbf_elim_univ                       true
% 150.43/150.72  % --qbf_sk_in                           true
% 150.43/150.72  % --qbf_pred_elim                       true
% 150.43/150.72  % --qbf_split                           32
% 150.43/150.72  
% 150.43/150.72  % ------ BMC1 Options
% 150.43/150.72  
% 150.43/150.72  % --bmc1_incremental                    false
% 150.43/150.72  % --bmc1_axioms                         reachable_all
% 150.43/150.72  % --bmc1_min_bound                      0
% 150.43/150.72  % --bmc1_max_bound                      -1
% 150.43/150.72  % --bmc1_max_bound_default              -1
% 150.43/150.72  % --bmc1_symbol_reachability            true
% 150.43/150.72  % --bmc1_property_lemmas                false
% 150.43/150.72  % --bmc1_k_induction                    false
% 150.43/150.72  % --bmc1_non_equiv_states               false
% 150.43/150.72  % --bmc1_deadlock                       false
% 150.43/150.72  % --bmc1_ucm                            false
% 150.43/150.72  % --bmc1_add_unsat_core                 none
% 150.43/150.72  % --bmc1_unsat_core_children            false
% 150.43/150.72  % --bmc1_unsat_core_extrapolate_axioms  false
% 150.43/150.72  % --bmc1_out_stat                       full
% 150.43/150.72  % --bmc1_ground_init                    false
% 150.43/150.72  % --bmc1_pre_inst_next_state            false
% 150.43/150.72  % --bmc1_pre_inst_state                 false
% 150.43/150.72  % --bmc1_pre_inst_reach_state           false
% 150.43/150.72  % --bmc1_out_unsat_core                 false
% 150.43/150.72  % --bmc1_aig_witness_out                false
% 150.43/150.72  % --bmc1_verbose                        false
% 150.43/150.72  % --bmc1_dump_clauses_tptp              false
% 152.67/152.90  % --bmc1_dump_unsat_core_tptp           false
% 152.67/152.90  % --bmc1_dump_file                      -
% 152.67/152.90  % --bmc1_ucm_expand_uc_limit            128
% 152.67/152.90  % --bmc1_ucm_n_expand_iterations        6
% 152.67/152.90  % --bmc1_ucm_extend_mode                1
% 152.67/152.90  % --bmc1_ucm_init_mode                  2
% 152.67/152.90  % --bmc1_ucm_cone_mode                  none
% 152.67/152.90  % --bmc1_ucm_reduced_relation_type      0
% 152.67/152.90  % --bmc1_ucm_relax_model                4
% 152.67/152.90  % --bmc1_ucm_full_tr_after_sat          true
% 152.67/152.90  % --bmc1_ucm_expand_neg_assumptions     false
% 152.67/152.90  % --bmc1_ucm_layered_model              none
% 152.67/152.90  % --bmc1_ucm_max_lemma_size             10
% 152.67/152.90  
% 152.67/152.90  % ------ AIG Options
% 152.67/152.90  
% 152.67/152.90  % --aig_mode                            false
% 152.67/152.90  
% 152.67/152.90  % ------ Instantiation Options
% 152.67/152.90  
% 152.67/152.90  % --instantiation_flag                  true
% 152.67/152.90  % --inst_lit_sel                        [+prop;+sign;+ground;-num_var;-num_symb]
% 152.67/152.90  % --inst_solver_per_active              750
% 152.67/152.90  % --inst_solver_calls_frac              0.5
% 152.67/152.90  % --inst_passive_queue_type             priority_queues
% 152.67/152.90  % --inst_passive_queues                 [[-conj_dist;+conj_symb;-num_var];[+age;-num_symb]]
% 152.67/152.90  % --inst_passive_queues_freq            [25;2]
% 152.67/152.90  % --inst_dismatching                    true
% 152.67/152.90  % --inst_eager_unprocessed_to_passive   true
% 152.67/152.90  % --inst_prop_sim_given                 true
% 152.67/152.90  % --inst_prop_sim_new                   false
% 152.67/152.90  % --inst_orphan_elimination             true
% 152.67/152.90  % --inst_learning_loop_flag             true
% 152.67/152.90  % --inst_learning_start                 3000
% 152.67/152.90  % --inst_learning_factor                2
% 152.67/152.90  % --inst_start_prop_sim_after_learn     3
% 152.67/152.90  % --inst_sel_renew                      solver
% 152.67/152.90  % --inst_lit_activity_flag              true
% 152.67/152.90  % --inst_out_proof                      true
% 152.67/152.90  
% 152.67/152.90  % ------ Resolution Options
% 152.67/152.90  
% 152.67/152.90  % --resolution_flag                     true
% 152.67/152.90  % --res_lit_sel                         kbo_max
% 152.67/152.90  % --res_to_prop_solver                  none
% 152.67/152.90  % --res_prop_simpl_new                  false
% 152.67/152.90  % --res_prop_simpl_given                false
% 152.67/152.90  % --res_passive_queue_type              priority_queues
% 152.67/152.90  % --res_passive_queues                  [[-conj_dist;+conj_symb;-num_symb];[+age;-num_symb]]
% 152.67/152.90  % --res_passive_queues_freq             [15;5]
% 152.67/152.90  % --res_forward_subs                    full
% 152.67/152.90  % --res_backward_subs                   full
% 152.67/152.90  % --res_forward_subs_resolution         true
% 152.67/152.90  % --res_backward_subs_resolution        true
% 152.67/152.90  % --res_orphan_elimination              false
% 152.67/152.90  % --res_time_limit                      1000.
% 152.67/152.90  % --res_out_proof                       true
% 152.67/152.90  % --proof_out_file                      /export/starexec/sandbox2/tmp/iprover_proof_698159.s
% 152.67/152.90  % --modulo                              true
% 152.67/152.90  
% 152.67/152.90  % ------ Combination Options
% 152.67/152.90  
% 152.67/152.90  % --comb_res_mult                       1000
% 152.67/152.90  % --comb_inst_mult                      300
% 152.67/152.90  % ------ 
% 152.67/152.90  
% 152.67/152.90  % ------ Parsing...% successful
% 152.67/152.90  
% 152.67/152.90  % ------ 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 % 
% 152.67/152.90  
% 152.67/152.90  % ------ Proving...
% 152.67/152.90  % ------ Problem Properties 
% 152.67/152.90  
% 152.67/152.90  % 
% 152.67/152.90  % EPR                                   false
% 152.67/152.90  % Horn                                  false
% 152.67/152.90  % Has equality                          true
% 152.67/152.90  
% 152.67/152.90  % % ------ Input Options Time Limit: Unbounded
% 152.67/152.90  
% 152.67/152.90  
% 152.67/152.90  Compiling...
% 152.67/152.90  Loading plugin: done.
% 152.67/152.90  Compiling...
% 152.67/152.90  Loading plugin: done.
% 152.67/152.90  Compiling...
% 152.67/152.90  Loading plugin: done.
% 152.67/152.90  Compiling...
% 152.67/152.90  Loading plugin: done.
% 152.67/152.90  Compiling...
% 152.67/152.90  Loading plugin: done.
% 152.67/152.90  Compiling...
% 152.67/152.90  Loading plugin: done.
% 152.67/152.90  Compiling...
% 152.67/152.90  Loading plugin: done.
% 152.67/152.90  Compiling...
% 152.67/152.90  Loading plugin: done.
% 152.67/152.90  Compiling...
% 152.67/152.90  Loading plugin: done.
% 152.67/152.90  Compiling...
% 152.67/152.90  Loading plugin: done.
% 152.67/152.90  Compiling...
% 152.67/152.90  Loading plugin: done.
% 152.67/152.90  Compiling...
% 152.67/152.90  Loading plugin: done.
% 152.67/152.90  Compiling...
% 152.67/152.90  Loading plugin: done.
% 152.67/152.90  Compiling...
% 152.67/152.90  Loading plugin: done.
% 152.67/152.90  Compiling...
% 152.67/152.90  Loading plugin: done.
% 152.67/152.90  % % ------ Current options:
% 152.67/152.90  
% 152.67/152.90  % ------ Input Options
% 152.67/152.90  
% 152.67/152.90  % --out_options                         all
% 152.67/152.90  % --tptp_safe_out                       true
% 152.67/152.90  % --problem_path                        ""
% 152.67/152.90  % --include_path                        ""
% 152.67/152.90  % --clausifier                          .//eprover
% 152.67/152.90  % --clausifier_options                  --tstp-format  
% 152.67/152.90  % --stdin                               false
% 152.67/152.90  % --dbg_backtrace                       false
% 152.67/152.90  % --dbg_dump_prop_clauses               false
% 152.67/152.90  % --dbg_dump_prop_clauses_file          -
% 152.67/152.90  % --dbg_out_stat                        false
% 152.67/152.90  
% 152.67/152.90  % ------ General Options
% 152.67/152.90  
% 152.67/152.90  % --fof                                 false
% 152.67/152.90  % --time_out_real                       150.
% 152.67/152.90  % --time_out_prep_mult                  0.2
% 152.67/152.90  % --time_out_virtual                    -1.
% 152.67/152.90  % --schedule                            none
% 152.67/152.90  % --ground_splitting                    input
% 152.67/152.90  % --splitting_nvd                       16
% 152.67/152.90  % --non_eq_to_eq                        false
% 152.67/152.90  % --prep_gs_sim                         true
% 152.67/152.90  % --prep_unflatten                      false
% 152.67/152.90  % --prep_res_sim                        true
% 152.67/152.90  % --prep_upred                          true
% 152.67/152.90  % --res_sim_input                       true
% 152.67/152.90  % --clause_weak_htbl                    true
% 152.67/152.90  % --gc_record_bc_elim                   false
% 152.67/152.90  % --symbol_type_check                   false
% 152.67/152.90  % --clausify_out                        false
% 152.67/152.90  % --large_theory_mode                   false
% 152.67/152.90  % --prep_sem_filter                     none
% 152.67/152.90  % --prep_sem_filter_out                 false
% 152.67/152.90  % --preprocessed_out                    false
% 152.67/152.90  % --sub_typing                          false
% 152.67/152.90  % --brand_transform                     false
% 152.67/152.90  % --pure_diseq_elim                     true
% 152.67/152.90  % --min_unsat_core                      false
% 152.67/152.90  % --pred_elim                           true
% 152.67/152.90  % --add_important_lit                   false
% 152.67/152.90  % --soft_assumptions                    false
% 152.67/152.90  % --reset_solvers                       false
% 152.67/152.90  % --bc_imp_inh                          []
% 152.67/152.90  % --conj_cone_tolerance                 1.5
% 152.67/152.90  % --prolific_symb_bound                 500
% 152.67/152.90  % --lt_threshold                        2000
% 152.67/152.90  
% 152.67/152.90  % ------ SAT Options
% 152.67/152.90  
% 152.67/152.90  % --sat_mode                            false
% 152.67/152.90  % --sat_fm_restart_options              ""
% 152.67/152.90  % --sat_gr_def                          false
% 152.67/152.90  % --sat_epr_types                       true
% 152.67/152.90  % --sat_non_cyclic_types                false
% 152.67/152.90  % --sat_finite_models                   false
% 152.67/152.90  % --sat_fm_lemmas                       false
% 152.67/152.90  % --sat_fm_prep                         false
% 152.67/152.90  % --sat_fm_uc_incr                      true
% 152.67/152.90  % --sat_out_model                       small
% 152.67/152.90  % --sat_out_clauses                     false
% 152.67/152.90  
% 152.67/152.90  % ------ QBF Options
% 152.67/152.90  
% 152.67/152.90  % --qbf_mode                            false
% 152.67/152.90  % --qbf_elim_univ                       true
% 152.67/152.90  % --qbf_sk_in                           true
% 152.67/152.90  % --qbf_pred_elim                       true
% 152.67/152.90  % --qbf_split                           32
% 152.67/152.90  
% 152.67/152.90  % ------ BMC1 Options
% 152.67/152.90  
% 152.67/152.90  % --bmc1_incremental                    false
% 152.67/152.90  % --bmc1_axioms                         reachable_all
% 152.67/152.90  % --bmc1_min_bound                      0
% 152.67/152.90  % --bmc1_max_bound                      -1
% 152.67/152.90  % --bmc1_max_bound_default              -1
% 152.67/152.90  % --bmc1_symbol_reachability            true
% 152.67/152.90  % --bmc1_property_lemmas                false
% 152.67/152.90  % --bmc1_k_induction                    false
% 152.67/152.90  % --bmc1_non_equiv_states               false
% 152.67/152.90  % --bmc1_deadlock                       false
% 152.67/152.90  % --bmc1_ucm                            false
% 152.67/152.90  % --bmc1_add_unsat_core                 none
% 152.67/152.90  % --bmc1_unsat_core_children            false
% 152.67/152.90  % --bmc1_unsat_core_extrapolate_axioms  false
% 152.67/152.90  % --bmc1_out_stat                       full
% 152.67/152.90  % --bmc1_ground_init                    false
% 152.67/152.90  % --bmc1_pre_inst_next_state            false
% 152.67/152.90  % --bmc1_pre_inst_state                 false
% 152.67/152.90  % --bmc1_pre_inst_reach_state           false
% 152.67/152.90  % --bmc1_out_unsat_core                 false
% 152.67/152.90  % --bmc1_aig_witness_out                false
% 152.67/152.90  % --bmc1_verbose                        false
% 152.67/152.90  % --bmc1_dump_clauses_tptp              false
% 152.67/152.90  % --bmc1_dump_unsat_core_tptp           false
% 152.67/152.90  % --bmc1_dump_file                      -
% 152.67/152.90  % --bmc1_ucm_expand_uc_limit            128
% 152.67/152.90  % --bmc1_ucm_n_expand_iterations        6
% 152.67/152.90  % --bmc1_ucm_extend_mode                1
% 152.67/152.90  % --bmc1_ucm_init_mode                  2
% 152.67/152.90  % --bmc1_ucm_cone_mode                  none
% 152.67/152.90  % --bmc1_ucm_reduced_relation_type      0
% 152.67/152.90  % --bmc1_ucm_relax_model                4
% 152.67/152.90  % --bmc1_ucm_full_tr_after_sat          true
% 152.67/152.90  % --bmc1_ucm_expand_neg_assumptions     false
% 152.67/152.90  % --bmc1_ucm_layered_model              none
% 152.67/152.90  % --bmc1_ucm_max_lemma_size             10
% 152.67/152.90  
% 152.67/152.90  % ------ AIG Options
% 152.67/152.90  
% 152.67/152.90  % --aig_mode                            false
% 152.67/152.90  
% 152.67/152.90  % ------ Instantiation Options
% 155.01/155.24  
% 155.01/155.24  % --instantiation_flag                  true
% 155.01/155.24  % --inst_lit_sel                        [+prop;+sign;+ground;-num_var;-num_symb]
% 155.01/155.24  % --inst_solver_per_active              750
% 155.01/155.24  % --inst_solver_calls_frac              0.5
% 155.01/155.24  % --inst_passive_queue_type             priority_queues
% 155.01/155.24  % --inst_passive_queues                 [[-conj_dist;+conj_symb;-num_var];[+age;-num_symb]]
% 155.01/155.24  % --inst_passive_queues_freq            [25;2]
% 155.01/155.24  % --inst_dismatching                    true
% 155.01/155.24  % --inst_eager_unprocessed_to_passive   true
% 155.01/155.24  % --inst_prop_sim_given                 true
% 155.01/155.24  % --inst_prop_sim_new                   false
% 155.01/155.24  % --inst_orphan_elimination             true
% 155.01/155.24  % --inst_learning_loop_flag             true
% 155.01/155.24  % --inst_learning_start                 3000
% 155.01/155.24  % --inst_learning_factor                2
% 155.01/155.24  % --inst_start_prop_sim_after_learn     3
% 155.01/155.24  % --inst_sel_renew                      solver
% 155.01/155.24  % --inst_lit_activity_flag              true
% 155.01/155.24  % --inst_out_proof                      true
% 155.01/155.24  
% 155.01/155.24  % ------ Resolution Options
% 155.01/155.24  
% 155.01/155.24  % --resolution_flag                     true
% 155.01/155.24  % --res_lit_sel                         kbo_max
% 155.01/155.24  % --res_to_prop_solver                  none
% 155.01/155.24  % --res_prop_simpl_new                  false
% 155.01/155.24  % --res_prop_simpl_given                false
% 155.01/155.24  % --res_passive_queue_type              priority_queues
% 155.01/155.24  % --res_passive_queues                  [[-conj_dist;+conj_symb;-num_symb];[+age;-num_symb]]
% 155.01/155.24  % --res_passive_queues_freq             [15;5]
% 155.01/155.24  % --res_forward_subs                    full
% 155.01/155.24  % --res_backward_subs                   full
% 155.01/155.24  % --res_forward_subs_resolution         true
% 155.01/155.24  % --res_backward_subs_resolution        true
% 155.01/155.24  % --res_orphan_elimination              false
% 155.01/155.24  % --res_time_limit                      1000.
% 155.01/155.24  % --res_out_proof                       true
% 155.01/155.24  % --proof_out_file                      /export/starexec/sandbox2/tmp/iprover_proof_698159.s
% 155.01/155.24  % --modulo                              true
% 155.01/155.24  
% 155.01/155.24  % ------ Combination Options
% 155.01/155.24  
% 155.01/155.24  % --comb_res_mult                       1000
% 155.01/155.24  % --comb_inst_mult                      300
% 155.01/155.24  % ------ 
% 155.01/155.24  
% 155.01/155.24  
% 155.01/155.24  
% 155.01/155.24  % ------ Proving...
% 155.01/155.24  % 
% 155.01/155.24  
% 155.01/155.24  
% 155.01/155.24  %  Resolution empty clause
% 155.01/155.24  
% 155.01/155.24  % ------                             Statistics
% 155.01/155.24  
% 155.01/155.24  % ------ General
% 155.01/155.24  
% 155.01/155.24  % num_of_input_clauses:                 2057
% 155.01/155.24  % num_of_input_neg_conjectures:         1
% 155.01/155.24  % num_of_splits:                        0
% 155.01/155.24  % num_of_split_atoms:                   0
% 155.01/155.24  % num_of_sem_filtered_clauses:          0
% 155.01/155.24  % num_of_subtypes:                      0
% 155.01/155.24  % monotx_restored_types:                0
% 155.01/155.24  % sat_num_of_epr_types:                 0
% 155.01/155.24  % sat_num_of_non_cyclic_types:          0
% 155.01/155.24  % sat_guarded_non_collapsed_types:      0
% 155.01/155.24  % is_epr:                               0
% 155.01/155.24  % is_horn:                              0
% 155.01/155.24  % has_eq:                               1
% 155.01/155.24  % num_pure_diseq_elim:                  0
% 155.01/155.24  % simp_replaced_by:                     0
% 155.01/155.24  % res_preprocessed:                     2
% 155.01/155.24  % prep_upred:                           0
% 155.01/155.24  % prep_unflattend:                      0
% 155.01/155.24  % pred_elim_cands:                      0
% 155.01/155.24  % pred_elim:                            0
% 155.01/155.24  % pred_elim_cl:                         0
% 155.01/155.24  % pred_elim_cycles:                     0
% 155.01/155.24  % forced_gc_time:                       0
% 155.01/155.24  % gc_basic_clause_elim:                 0
% 155.01/155.24  % parsing_time:                         0.051
% 155.01/155.24  % sem_filter_time:                      0.
% 155.01/155.24  % pred_elim_time:                       0.
% 155.01/155.24  % out_proof_time:                       0.001
% 155.01/155.24  % monotx_time:                          0.
% 155.01/155.24  % subtype_inf_time:                     0.
% 155.01/155.24  % unif_index_cands_time:                0.011
% 155.01/155.24  % unif_index_add_time:                  0.005
% 155.01/155.24  % total_time:                           4.526
% 155.01/155.24  % num_of_symbols:                       94
% 155.01/155.24  % num_of_terms:                         58015
% 155.01/155.24  
% 155.01/155.24  % ------ Propositional Solver
% 155.01/155.24  
% 155.01/155.24  % prop_solver_calls:                    2
% 155.01/155.24  % prop_fast_solver_calls:               3
% 155.01/155.24  % prop_num_of_clauses:                  2097
% 155.01/155.24  % prop_preprocess_simplified:           10487
% 155.01/155.24  % prop_fo_subsumed:                     0
% 155.01/155.24  % prop_solver_time:                     0.
% 155.01/155.24  % prop_fast_solver_time:                0.
% 155.01/155.24  % prop_unsat_core_time:                 0.
% 155.01/155.24  
% 155.01/155.24  % ------ QBF 
% 155.01/155.24  
% 155.01/155.24  % qbf_q_res:                            0
% 155.01/155.24  % qbf_num_tautologies:                  0
% 155.01/155.24  % qbf_prep_cycles:                      0
% 155.01/155.24  
% 155.01/155.24  % ------ BMC1
% 155.01/155.24  
% 155.01/155.24  % bmc1_current_bound:                   -1
% 155.01/155.24  % bmc1_last_solved_bound:               -1
% 155.01/155.24  % bmc1_unsat_core_size:                 -1
% 155.01/155.24  % bmc1_unsat_core_parents_size:         -1
% 155.01/155.24  % bmc1_merge_next_fun:                  0
% 155.01/155.24  % bmc1_unsat_core_clauses_time:         0.
% 155.01/155.24  
% 155.01/155.24  % ------ Instantiation
% 155.01/155.24  
% 155.01/155.24  % inst_num_of_clauses:                  1994
% 155.01/155.24  % inst_num_in_passive:                  1502
% 155.01/155.24  % inst_num_in_active:                   299
% 155.01/155.24  % inst_num_in_unprocessed:              193
% 155.01/155.24  % inst_num_of_loops:                    300
% 155.01/155.24  % inst_num_of_learning_restarts:        0
% 155.01/155.24  % inst_num_moves_active_passive:        0
% 155.01/155.24  % inst_lit_activity:                    40
% 155.01/155.24  % inst_lit_activity_moves:              0
% 155.01/155.24  % inst_num_tautologies:                 0
% 155.01/155.24  % inst_num_prop_implied:                0
% 155.01/155.24  % inst_num_existing_simplified:         0
% 155.01/155.24  % inst_num_eq_res_simplified:           0
% 155.01/155.24  % inst_num_child_elim:                  0
% 155.01/155.24  % inst_num_of_dismatching_blockings:    107
% 155.01/155.24  % inst_num_of_non_proper_insts:         195
% 155.01/155.24  % inst_num_of_duplicates:               335
% 155.01/155.24  % inst_inst_num_from_inst_to_res:       0
% 155.01/155.24  % inst_dismatching_checking_time:       0.
% 155.01/155.24  
% 155.01/155.24  % ------ Resolution
% 155.01/155.24  
% 155.01/155.24  % res_num_of_clauses:                   35890
% 155.01/155.24  % res_num_in_passive:                   33131
% 155.01/155.24  % res_num_in_active:                    1713
% 155.01/155.24  % res_num_of_loops:                     1275
% 155.01/155.24  % res_forward_subset_subsumed:          7132
% 155.01/155.24  % res_backward_subset_subsumed:         216
% 155.01/155.24  % res_forward_subsumed:                 310
% 155.01/155.24  % res_backward_subsumed:                2
% 155.01/155.24  % res_forward_subsumption_resolution:   142
% 155.01/155.24  % res_backward_subsumption_resolution:  0
% 155.01/155.24  % res_clause_to_clause_subsumption:     24180
% 155.01/155.24  % res_orphan_elimination:               0
% 155.01/155.24  % res_tautology_del:                    69
% 155.01/155.24  % res_num_eq_res_simplified:            0
% 155.01/155.24  % res_num_sel_changes:                  0
% 155.01/155.24  % res_moves_from_active_to_pass:        0
% 155.01/155.24  
% 155.01/155.24  % Status Unsatisfiable
% 155.01/155.24  % SZS status Unsatisfiable
% 155.01/155.24  % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------