TSTP Solution File: SET852-1 by iProverMo---2.5-0.1

%------------------------------------------------------------------------------
% File     : iProverMo---2.5-0.1
% Problem  : SET852-1 : TPTP v8.1.0. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : iprover_modulo %s %d

% Computer : n028.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 : Tue Jul 19 02:17:43 EDT 2022

% Result   : Unsatisfiable 151.65s 151.87s
% Output   : CNFRefutation 151.65s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   14
%            Number of leaves      : 1373
% Syntax   : Number of formulae    : 9440 (1329 unt;   0 def)
%            Number of atoms       : 18107 (1342 equ)
%            Maximal formula atoms :    4 (   1 avg)
%            Number of connectives : 17317 (8650   ~;8667   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   12 (   3 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :   83 (  81 usr;   1 prp; 0-3 aty)
%            Number of functors    :  127 ( 127 usr;  21 con; 0-6 aty)
%            Number of variables   : 13587 ( 722 sgn5778   !;   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,
    ! [X46,X38,X14,X47,X7,X3] :
      ( ~ c_in(X46,c_Relation_Orel__comp(X14,X38,X47,X7,X3),tc_prod(X3,X7))
      | c_in(c_Pair(c_Main_Orel__compE__1(X14,X38,X46,X47,X7,X3),c_Main_Orel__compE__2(X14,X38,X46,X47,X7,X3),X3,X47),X38,tc_prod(X3,X47)) ),
    file('<stdin>',cls_Relation_Orel__compE_1) ).

fof(c_0_1,axiom,
    ! [X46,X38,X14,X47,X7,X3] :
      ( ~ c_in(X46,c_Relation_Orel__comp(X14,X38,X47,X7,X3),tc_prod(X3,X7))
      | c_in(c_Pair(c_Main_Orel__compE__2(X14,X38,X46,X47,X7,X3),c_Main_Orel__compE__3(X14,X38,X46,X47,X7,X3),X47,X7),X14,tc_prod(X47,X7)) ),
    file('<stdin>',cls_Relation_Orel__compE_0) ).

fof(c_0_2,axiom,
    ! [X46,X38,X14,X47,X7,X3] :
      ( ~ c_in(X46,c_Relation_Orel__comp(X14,X38,X47,X7,X3),tc_prod(X3,X7))
      | X46 = c_Pair(c_Main_Orel__compE__1(X14,X38,X46,X47,X7,X3),c_Main_Orel__compE__3(X14,X38,X46,X47,X7,X3),X3,X7) ),
    file('<stdin>',cls_Relation_Orel__compE_2) ).

fof(c_0_3,axiom,
    ! [X38,X14,X35,X7,X3] :
      ( ~ c_in(X35,c_Datatype__Universe_Odprod(X14,X38,X3,X7),tc_prod(tc_set(tc_Datatype__Universe_Onode(X3,X7)),tc_set(tc_Datatype__Universe_Onode(X3,X7))))
      | X35 = c_Pair(c_Datatype__Universe_OScons(c_Main_OdprodE__1(X35,X14,X38,X3,X7),c_Main_OdprodE__2(X35,X14,X38,X3,X7),X3,X7),c_Datatype__Universe_OScons(c_Main_OdprodE__3(X35,X14,X38,X3,X7),c_Main_OdprodE__4(X35,X14,X38,X3,X7),X3,X7),tc_set(tc_Datatype__Universe_Onode(X3,X7)),tc_set(tc_Datatype__Universe_Onode(X3,X7))) ),
    file('<stdin>',cls_Datatype__Universe_OdprodE_0) ).

fof(c_0_4,axiom,
    ! [X38,X14,X35,X7,X3] :
      ( ~ c_in(X35,c_Datatype__Universe_Odprod(X14,X38,X3,X7),tc_prod(tc_set(tc_Datatype__Universe_Onode(X3,X7)),tc_set(tc_Datatype__Universe_Onode(X3,X7))))
      | c_in(c_Pair(c_Main_OdprodE__1(X35,X14,X38,X3,X7),c_Main_OdprodE__3(X35,X14,X38,X3,X7),tc_set(tc_Datatype__Universe_Onode(X3,X7)),tc_set(tc_Datatype__Universe_Onode(X3,X7))),X14,tc_prod(tc_set(tc_Datatype__Universe_Onode(X3,X7)),tc_set(tc_Datatype__Universe_Onode(X3,X7)))) ),
    file('<stdin>',cls_Datatype__Universe_OdprodE_2) ).

fof(c_0_5,axiom,
    ! [X38,X14,X35,X7,X3] :
      ( ~ c_in(X35,c_Datatype__Universe_Odprod(X14,X38,X3,X7),tc_prod(tc_set(tc_Datatype__Universe_Onode(X3,X7)),tc_set(tc_Datatype__Universe_Onode(X3,X7))))
      | c_in(c_Pair(c_Main_OdprodE__2(X35,X14,X38,X3,X7),c_Main_OdprodE__4(X35,X14,X38,X3,X7),tc_set(tc_Datatype__Universe_Onode(X3,X7)),tc_set(tc_Datatype__Universe_Onode(X3,X7))),X38,tc_prod(tc_set(tc_Datatype__Universe_Onode(X3,X7)),tc_set(tc_Datatype__Universe_Onode(X3,X7)))) ),
    file('<stdin>',cls_Datatype__Universe_OdprodE_1) ).

fof(c_0_6,axiom,
    ! [X21,X38,X14,X7,X3] :
      ( ~ c_in(X21,c_Datatype__Universe_Odsum(X14,X38,X3,X7),tc_prod(tc_set(tc_Datatype__Universe_Onode(X3,X7)),tc_set(tc_Datatype__Universe_Onode(X3,X7))))
      | c_in(c_Pair(c_Main_OdsumE__1(X14,X21,X3,X7),c_Main_OdsumE__2(X14,X21,X3,X7),tc_set(tc_Datatype__Universe_Onode(X3,X7)),tc_set(tc_Datatype__Universe_Onode(X3,X7))),X14,tc_prod(tc_set(tc_Datatype__Universe_Onode(X3,X7)),tc_set(tc_Datatype__Universe_Onode(X3,X7))))
      | c_in(c_Pair(c_Main_OdsumE__3(X38,X21,X3,X7),c_Main_OdsumE__4(X38,X21,X3,X7),tc_set(tc_Datatype__Universe_Onode(X3,X7)),tc_set(tc_Datatype__Universe_Onode(X3,X7))),X38,tc_prod(tc_set(tc_Datatype__Universe_Onode(X3,X7)),tc_set(tc_Datatype__Universe_Onode(X3,X7)))) ),
    file('<stdin>',cls_Datatype__Universe_OdsumE_3) ).

fof(c_0_7,axiom,
    ! [X21,X38,X14,X7,X3] :
      ( ~ c_in(X21,c_Datatype__Universe_Odsum(X14,X38,X3,X7),tc_prod(tc_set(tc_Datatype__Universe_Onode(X3,X7)),tc_set(tc_Datatype__Universe_Onode(X3,X7))))
      | c_in(c_Pair(c_Main_OdsumE__1(X14,X21,X3,X7),c_Main_OdsumE__2(X14,X21,X3,X7),tc_set(tc_Datatype__Universe_Onode(X3,X7)),tc_set(tc_Datatype__Universe_Onode(X3,X7))),X14,tc_prod(tc_set(tc_Datatype__Universe_Onode(X3,X7)),tc_set(tc_Datatype__Universe_Onode(X3,X7))))
      | X21 = c_Pair(c_Datatype__Universe_OIn1(c_Main_OdsumE__3(X38,X21,X3,X7),X3,X7),c_Datatype__Universe_OIn1(c_Main_OdsumE__4(X38,X21,X3,X7),X3,X7),tc_set(tc_Datatype__Universe_Onode(X3,X7)),tc_set(tc_Datatype__Universe_Onode(X3,X7))) ),
    file('<stdin>',cls_Datatype__Universe_OdsumE_2) ).

fof(c_0_8,axiom,
    ! [X21,X38,X14,X7,X3] :
      ( ~ c_in(X21,c_Datatype__Universe_Odsum(X14,X38,X3,X7),tc_prod(tc_set(tc_Datatype__Universe_Onode(X3,X7)),tc_set(tc_Datatype__Universe_Onode(X3,X7))))
      | c_in(c_Pair(c_Main_OdsumE__3(X38,X21,X3,X7),c_Main_OdsumE__4(X38,X21,X3,X7),tc_set(tc_Datatype__Universe_Onode(X3,X7)),tc_set(tc_Datatype__Universe_Onode(X3,X7))),X38,tc_prod(tc_set(tc_Datatype__Universe_Onode(X3,X7)),tc_set(tc_Datatype__Universe_Onode(X3,X7))))
      | X21 = c_Pair(c_Datatype__Universe_OIn0(c_Main_OdsumE__1(X14,X21,X3,X7),X3,X7),c_Datatype__Universe_OIn0(c_Main_OdsumE__2(X14,X21,X3,X7),X3,X7),tc_set(tc_Datatype__Universe_Onode(X3,X7)),tc_set(tc_Datatype__Universe_Onode(X3,X7))) ),
    file('<stdin>',cls_Datatype__Universe_OdsumE_1) ).

fof(c_0_9,axiom,
    ! [X23,X24,X22,X14,X3] :
      ( ~ c_in(c_Pair(X22,c_List_Olist_OCons(X24,X23,X3),tc_List_Olist(X3),tc_List_Olist(X3)),c_List_Olistrel(X14,X3),tc_prod(tc_List_Olist(X3),tc_List_Olist(X3)))
      | c_in(c_Pair(c_Main_Olistrel__Cons2__2(X14,X22,X24,X23,X3),X23,tc_List_Olist(X3),tc_List_Olist(X3)),c_List_Olistrel(X14,X3),tc_prod(tc_List_Olist(X3),tc_List_Olist(X3))) ),
    file('<stdin>',cls_List_Olistrel__Cons2_1) ).

fof(c_0_10,axiom,
    ! [X23,X24,X22,X14,X3] :
      ( ~ c_in(c_Pair(c_List_Olist_OCons(X24,X23,X3),X22,tc_List_Olist(X3),tc_List_Olist(X3)),c_List_Olistrel(X14,X3),tc_prod(tc_List_Olist(X3),tc_List_Olist(X3)))
      | c_in(c_Pair(X23,c_Main_Olistrel__Cons1__2(X14,X22,X24,X23,X3),tc_List_Olist(X3),tc_List_Olist(X3)),c_List_Olistrel(X14,X3),tc_prod(tc_List_Olist(X3),tc_List_Olist(X3))) ),
    file('<stdin>',cls_List_Olistrel__Cons1_1) ).

fof(c_0_11,axiom,
    ! [X38,X14,X11,X8,X12,X9,X7,X3] :
      ( ~ c_in(c_Pair(X8,X11,tc_set(tc_Datatype__Universe_Onode(X3,X7)),tc_set(tc_Datatype__Universe_Onode(X3,X7))),X38,tc_prod(tc_set(tc_Datatype__Universe_Onode(X3,X7)),tc_set(tc_Datatype__Universe_Onode(X3,X7))))
      | ~ c_in(c_Pair(X9,X12,tc_set(tc_Datatype__Universe_Onode(X3,X7)),tc_set(tc_Datatype__Universe_Onode(X3,X7))),X14,tc_prod(tc_set(tc_Datatype__Universe_Onode(X3,X7)),tc_set(tc_Datatype__Universe_Onode(X3,X7))))
      | c_in(c_Pair(c_Datatype__Universe_OScons(X9,X8,X3,X7),c_Datatype__Universe_OScons(X12,X11,X3,X7),tc_set(tc_Datatype__Universe_Onode(X3,X7)),tc_set(tc_Datatype__Universe_Onode(X3,X7))),c_Datatype__Universe_Odprod(X14,X38,X3,X7),tc_prod(tc_set(tc_Datatype__Universe_Onode(X3,X7)),tc_set(tc_Datatype__Universe_Onode(X3,X7)))) ),
    file('<stdin>',cls_Datatype__Universe_OdprodI_0) ).

fof(c_0_12,axiom,
    ! [X23,X24,X22,X14,X3] :
      ( ~ c_in(c_Pair(X22,c_List_Olist_OCons(X24,X23,X3),tc_List_Olist(X3),tc_List_Olist(X3)),c_List_Olistrel(X14,X3),tc_prod(tc_List_Olist(X3),tc_List_Olist(X3)))
      | c_in(c_Pair(c_Main_Olistrel__Cons2__1(X14,X22,X24,X23,X3),X24,X3,X3),X14,tc_prod(X3,X3)) ),
    file('<stdin>',cls_List_Olistrel__Cons2_2) ).

fof(c_0_13,axiom,
    ! [X23,X24,X22,X14,X3] :
      ( ~ c_in(c_Pair(c_List_Olist_OCons(X24,X23,X3),X22,tc_List_Olist(X3),tc_List_Olist(X3)),c_List_Olistrel(X14,X3),tc_prod(tc_List_Olist(X3),tc_List_Olist(X3)))
      | c_in(c_Pair(X24,c_Main_Olistrel__Cons1__1(X14,X22,X24,X23,X3),X3,X3),X14,tc_prod(X3,X3)) ),
    file('<stdin>',cls_List_Olistrel__Cons1_2) ).

fof(c_0_14,axiom,
    ! [X21,X38,X14,X7,X3] :
      ( ~ c_in(X21,c_Datatype__Universe_Odsum(X14,X38,X3,X7),tc_prod(tc_set(tc_Datatype__Universe_Onode(X3,X7)),tc_set(tc_Datatype__Universe_Onode(X3,X7))))
      | X21 = c_Pair(c_Datatype__Universe_OIn0(c_Main_OdsumE__1(X14,X21,X3,X7),X3,X7),c_Datatype__Universe_OIn0(c_Main_OdsumE__2(X14,X21,X3,X7),X3,X7),tc_set(tc_Datatype__Universe_Onode(X3,X7)),tc_set(tc_Datatype__Universe_Onode(X3,X7)))
      | X21 = c_Pair(c_Datatype__Universe_OIn1(c_Main_OdsumE__3(X38,X21,X3,X7),X3,X7),c_Datatype__Universe_OIn1(c_Main_OdsumE__4(X38,X21,X3,X7),X3,X7),tc_set(tc_Datatype__Universe_Onode(X3,X7)),tc_set(tc_Datatype__Universe_Onode(X3,X7))) ),
    file('<stdin>',cls_Datatype__Universe_OdsumE_0) ).

fof(c_0_15,axiom,
    ! [X14,X6,X15,X7,X3] :
      ( ~ c_in(X6,c_Relation_OImage(X14,X15,X7,X3),X3)
      | c_in(c_Pair(c_Main_OImageE__1(X15,X6,X14,X7,X3),X6,X7,X3),X14,tc_prod(X7,X3)) ),
    file('<stdin>',cls_Relation_OImageE_1) ).

fof(c_0_16,axiom,
    ! [X23,X24,X22,X14,X3] :
      ( ~ c_in(c_Pair(X22,c_List_Olist_OCons(X24,X23,X3),tc_List_Olist(X3),tc_List_Olist(X3)),c_List_Olistrel(X14,X3),tc_prod(tc_List_Olist(X3),tc_List_Olist(X3)))
      | X22 = c_List_Olist_OCons(c_Main_Olistrel__Cons2__1(X14,X22,X24,X23,X3),c_Main_Olistrel__Cons2__2(X14,X22,X24,X23,X3),X3) ),
    file('<stdin>',cls_List_Olistrel__Cons2_0) ).

fof(c_0_17,axiom,
    ! [X23,X24,X22,X14,X3] :
      ( ~ c_in(c_Pair(c_List_Olist_OCons(X24,X23,X3),X22,tc_List_Olist(X3),tc_List_Olist(X3)),c_List_Olistrel(X14,X3),tc_prod(tc_List_Olist(X3),tc_List_Olist(X3)))
      | X22 = c_List_Olist_OCons(c_Main_Olistrel__Cons1__1(X14,X22,X24,X23,X3),c_Main_Olistrel__Cons1__2(X14,X22,X24,X23,X3),X3) ),
    file('<stdin>',cls_List_Olistrel__Cons1_0) ).

fof(c_0_18,axiom,
    ! [X35,X16,X15,X7,X3] :
      ( ~ c_in(X35,c_Datatype__Universe_Ouprod(X15,X16,X3,X7),tc_set(tc_Datatype__Universe_Onode(X3,X7)))
      | X35 = c_Datatype__Universe_OScons(c_Main_OuprodE__1(X15,X16,X35,X3,X7),c_Main_OuprodE__2(X15,X16,X35,X3,X7),X3,X7) ),
    file('<stdin>',cls_Datatype__Universe_OuprodE_0) ).

fof(c_0_19,axiom,
    ! [X38,X14,X35,X6,X5,X47,X7,X3] :
      ( ~ c_in(c_Pair(X6,X35,X7,X47),X14,tc_prod(X7,X47))
      | ~ c_in(c_Pair(X5,X6,X3,X7),X38,tc_prod(X3,X7))
      | c_in(c_Pair(X5,X35,X3,X47),c_Relation_Orel__comp(X14,X38,X7,X47,X3),tc_prod(X3,X47)) ),
    file('<stdin>',cls_Relation_Orel__compI_0) ).

fof(c_0_20,axiom,
    ! [X38,X14,X11,X8,X7,X3] :
      ( ~ c_in(c_Pair(X8,X11,tc_set(tc_Datatype__Universe_Onode(X3,X7)),tc_set(tc_Datatype__Universe_Onode(X3,X7))),X38,tc_prod(tc_set(tc_Datatype__Universe_Onode(X3,X7)),tc_set(tc_Datatype__Universe_Onode(X3,X7))))
      | c_in(c_Pair(c_Datatype__Universe_OIn1(X8,X3,X7),c_Datatype__Universe_OIn1(X11,X3,X7),tc_set(tc_Datatype__Universe_Onode(X3,X7)),tc_set(tc_Datatype__Universe_Onode(X3,X7))),c_Datatype__Universe_Odsum(X14,X38,X3,X7),tc_prod(tc_set(tc_Datatype__Universe_Onode(X3,X7)),tc_set(tc_Datatype__Universe_Onode(X3,X7)))) ),
    file('<stdin>',cls_Datatype__Universe_Odsum__In1I_0) ).

fof(c_0_21,axiom,
    ! [X38,X14,X12,X9,X7,X3] :
      ( ~ c_in(c_Pair(X9,X12,tc_set(tc_Datatype__Universe_Onode(X3,X7)),tc_set(tc_Datatype__Universe_Onode(X3,X7))),X14,tc_prod(tc_set(tc_Datatype__Universe_Onode(X3,X7)),tc_set(tc_Datatype__Universe_Onode(X3,X7))))
      | c_in(c_Pair(c_Datatype__Universe_OIn0(X9,X3,X7),c_Datatype__Universe_OIn0(X12,X3,X7),tc_set(tc_Datatype__Universe_Onode(X3,X7)),tc_set(tc_Datatype__Universe_Onode(X3,X7))),c_Datatype__Universe_Odsum(X14,X38,X3,X7),tc_prod(tc_set(tc_Datatype__Universe_Onode(X3,X7)),tc_set(tc_Datatype__Universe_Onode(X3,X7)))) ),
    file('<stdin>',cls_Datatype__Universe_Odsum__In0I_0) ).

fof(c_0_22,axiom,
    ! [X35,X16,X15,X7,X3] :
      ( ~ c_in(X35,c_Datatype__Universe_Ouprod(X15,X16,X3,X7),tc_set(tc_Datatype__Universe_Onode(X3,X7)))
      | c_in(c_Main_OuprodE__1(X15,X16,X35,X3,X7),X15,tc_set(tc_Datatype__Universe_Onode(X3,X7))) ),
    file('<stdin>',cls_Datatype__Universe_OuprodE_2) ).

fof(c_0_23,axiom,
    ! [X35,X16,X15,X7,X3] :
      ( ~ c_in(X35,c_Datatype__Universe_Ouprod(X15,X16,X3,X7),tc_set(tc_Datatype__Universe_Onode(X3,X7)))
      | c_in(c_Main_OuprodE__2(X15,X16,X35,X3,X7),X16,tc_set(tc_Datatype__Universe_Onode(X3,X7))) ),
    file('<stdin>',cls_Datatype__Universe_OuprodE_1) ).

fof(c_0_24,axiom,
    ! [X14,X6,X15,X7,X3] :
      ( ~ c_in(X6,c_Relation_OImage(X14,X15,X7,X3),X3)
      | c_in(c_Main_OImageE__1(X15,X6,X14,X7,X3),X15,X7) ),
    file('<stdin>',cls_Relation_OImageE_0) ).

fof(c_0_25,axiom,
    ! [X45,X14,X7,X3] :
      ( ~ c_in(X45,c_Relation_Oconverse(X14,X7,X3),tc_prod(X3,X7))
      | c_in(c_Pair(c_Main_OconverseE__1(X14,X45,X7,X3),c_Main_OconverseE__2(X14,X45,X7,X3),X7,X3),X14,tc_prod(X7,X3)) ),
    file('<stdin>',cls_Relation_OconverseE_0) ).

fof(c_0_26,axiom,
    ! [X24,X2,X14,X3] :
      ( ~ c_Wellfounded__Recursion_Owf(c_insert(c_Pair(X24,X2,X3,X3),X14,tc_prod(X3,X3)),X3)
      | ~ c_in(c_Pair(X2,X24,X3,X3),c_Transitive__Closure_Ortrancl(X14,X3),tc_prod(X3,X3)) ),
    file('<stdin>',cls_Wellfounded__Recursion_Owf__insert__iff1_1) ).

fof(c_0_27,axiom,
    ! [X24,X2,X14,X3] :
      ( ~ c_Wellfounded__Recursion_Oacyclic(c_insert(c_Pair(X24,X2,X3,X3),X14,tc_prod(X3,X3)),X3)
      | ~ c_in(c_Pair(X2,X24,X3,X3),c_Transitive__Closure_Ortrancl(X14,X3),tc_prod(X3,X3)) ),
    file('<stdin>',cls_Wellfounded__Recursion_Oacyclic__insert__iff1_1) ).

fof(c_0_28,axiom,
    ! [X39,X16,X15,X7,X3] :
      ( ~ c_in(X39,c_Datatype__Universe_Ousum(X15,X16,X3,X7),tc_set(tc_Datatype__Universe_Onode(X3,X7)))
      | c_in(c_Main_OusumE__1(X15,X39,X3,X7),X15,tc_set(tc_Datatype__Universe_Onode(X3,X7)))
      | c_in(c_Main_OusumE__2(X16,X39,X3,X7),X16,tc_set(tc_Datatype__Universe_Onode(X3,X7))) ),
    file('<stdin>',cls_Datatype__Universe_OusumE_3) ).

fof(c_0_29,axiom,
    ! [X39,X16,X15,X7,X3] :
      ( ~ c_in(X39,c_Datatype__Universe_Ousum(X15,X16,X3,X7),tc_set(tc_Datatype__Universe_Onode(X3,X7)))
      | c_in(c_Main_OusumE__1(X15,X39,X3,X7),X15,tc_set(tc_Datatype__Universe_Onode(X3,X7)))
      | X39 = c_Datatype__Universe_OIn1(c_Main_OusumE__2(X16,X39,X3,X7),X3,X7) ),
    file('<stdin>',cls_Datatype__Universe_OusumE_2) ).

fof(c_0_30,axiom,
    ! [X39,X16,X15,X7,X3] :
      ( ~ c_in(X39,c_Datatype__Universe_Ousum(X15,X16,X3,X7),tc_set(tc_Datatype__Universe_Onode(X3,X7)))
      | c_in(c_Main_OusumE__2(X16,X39,X3,X7),X16,tc_set(tc_Datatype__Universe_Onode(X3,X7)))
      | X39 = c_Datatype__Universe_OIn0(c_Main_OusumE__1(X15,X39,X3,X7),X3,X7) ),
    file('<stdin>',cls_Datatype__Universe_OusumE_1) ).

fof(c_0_31,axiom,
    ! [X39,X16,X15,X7,X3] :
      ( ~ c_in(X39,c_Datatype__Universe_Ousum(X15,X16,X3,X7),tc_set(tc_Datatype__Universe_Onode(X3,X7)))
      | X39 = c_Datatype__Universe_OIn0(c_Main_OusumE__1(X15,X39,X3,X7),X3,X7)
      | X39 = c_Datatype__Universe_OIn1(c_Main_OusumE__2(X16,X39,X3,X7),X3,X7) ),
    file('<stdin>',cls_Datatype__Universe_OusumE_0) ).

fof(c_0_32,axiom,
    ! [X39,X16,X15,X7,X3] :
      ( ~ c_in(X39,c_Sum__Type_OPlus(X15,X16,X3,X7),tc_sum(X3,X7))
      | X39 = c_Sum__Type_OInl(c_Main_OPlusE__1(X15,X39,X3,X7),X3,X7)
      | X39 = c_Sum__Type_OInr(c_Main_OPlusE__2(X16,X39,X7,X3),X7,X3) ),
    file('<stdin>',cls_Sum__Type_OPlusE_0) ).

fof(c_0_33,axiom,
    ! [X39,X16,X15,X7,X3] :
      ( ~ c_in(X39,c_Sum__Type_OPlus(X15,X16,X3,X7),tc_sum(X3,X7))
      | c_in(c_Main_OPlusE__1(X15,X39,X3,X7),X15,X3)
      | X39 = c_Sum__Type_OInr(c_Main_OPlusE__2(X16,X39,X7,X3),X7,X3) ),
    file('<stdin>',cls_Sum__Type_OPlusE_2) ).

fof(c_0_34,axiom,
    ! [X39,X16,X15,X7,X3] :
      ( ~ c_in(X39,c_Sum__Type_OPlus(X15,X16,X3,X7),tc_sum(X3,X7))
      | c_in(c_Main_OPlusE__2(X16,X39,X7,X3),X16,X7)
      | X39 = c_Sum__Type_OInl(c_Main_OPlusE__1(X15,X39,X3,X7),X3,X7) ),
    file('<stdin>',cls_Sum__Type_OPlusE_1) ).

fof(c_0_35,axiom,
    ! [X39,X16,X15,X7,X3] :
      ( ~ c_in(X39,c_Sum__Type_OPlus(X15,X16,X3,X7),tc_sum(X3,X7))
      | c_in(c_Main_OPlusE__1(X15,X39,X3,X7),X15,X3)
      | c_in(c_Main_OPlusE__2(X16,X39,X7,X3),X16,X7) ),
    file('<stdin>',cls_Sum__Type_OPlusE_3) ).

fof(c_0_36,axiom,
    ! [X24,X2,X14,X3] :
      ( ~ c_Wellfounded__Recursion_Owf(c_insert(c_Pair(X24,X2,X3,X3),X14,tc_prod(X3,X3)),X3)
      | c_Wellfounded__Recursion_Owf(X14,X3) ),
    file('<stdin>',cls_Wellfounded__Recursion_Owf__insert__iff1_0) ).

fof(c_0_37,axiom,
    ! [X24,X2,X14,X3] :
      ( ~ c_Wellfounded__Recursion_Oacyclic(c_insert(c_Pair(X24,X2,X3,X3),X14,tc_prod(X3,X3)),X3)
      | c_Wellfounded__Recursion_Oacyclic(X14,X3) ),
    file('<stdin>',cls_Wellfounded__Recursion_Oacyclic__insert__iff1_0) ).

fof(c_0_38,axiom,
    ! [X14,X6,X7,X3] :
      ( ~ c_in(X6,c_Relation_ORange(X14,X7,X3),X3)
      | c_in(c_Pair(c_Main_ORangeE__1(X6,X14,X3,X7),X6,X7,X3),X14,tc_prod(X7,X3)) ),
    file('<stdin>',cls_Relation_ORangeE_0) ).

fof(c_0_39,axiom,
    ! [X14,X5,X7,X3] :
      ( ~ c_in(X5,c_Relation_ODomain(X14,X3,X7),X3)
      | c_in(c_Pair(X5,c_Main_ODomainE__1(X5,X14,X3,X7),X3,X7),X14,tc_prod(X3,X7)) ),
    file('<stdin>',cls_Relation_ODomainE_0) ).

fof(c_0_40,axiom,
    ! [X24,X2,X14,X3] :
      ( ~ c_Wellfounded__Recursion_Owf(X14,X3)
      | c_Wellfounded__Recursion_Owf(c_insert(c_Pair(X24,X2,X3,X3),X14,tc_prod(X3,X3)),X3)
      | c_in(c_Pair(X2,X24,X3,X3),c_Transitive__Closure_Ortrancl(X14,X3),tc_prod(X3,X3)) ),
    file('<stdin>',cls_Wellfounded__Recursion_Owf__insert__iff2_0) ).

fof(c_0_41,axiom,
    ! [X24,X2,X14,X3] :
      ( ~ c_Wellfounded__Recursion_Oacyclic(X14,X3)
      | c_Wellfounded__Recursion_Oacyclic(c_insert(c_Pair(X24,X2,X3,X3),X14,tc_prod(X3,X3)),X3)
      | c_in(c_Pair(X2,X24,X3,X3),c_Transitive__Closure_Ortrancl(X14,X3),tc_prod(X3,X3)) ),
    file('<stdin>',cls_Wellfounded__Recursion_Oacyclic__insert__iff2_0) ).

fof(c_0_42,axiom,
    ! [X14,X6,X5,X7,X3] :
      ( ~ c_in(X6,c_Relation_OImage(X14,c_insert(X5,c_emptyset,X7),X7,X3),X3)
      | c_in(c_Pair(X5,X6,X7,X3),X14,tc_prod(X7,X3)) ),
    file('<stdin>',cls_Relation_OImage__singleton__iff__iff1_0) ).

fof(c_0_43,axiom,
    ! [X19,X13,X10] :
      ( ~ c_Divides_Oop_Advd(X10,c_GCD_Ogcd(c_Pair(X13,X19,tc_nat,tc_nat)),tc_nat)
      | c_Divides_Oop_Advd(X10,X19,tc_nat) ),
    file('<stdin>',cls_GCD_Ogcd__greatest__iff__iff1_1) ).

fof(c_0_44,axiom,
    ! [X19,X13,X10] :
      ( ~ c_Divides_Oop_Advd(X10,c_GCD_Ogcd(c_Pair(X13,X19,tc_nat,tc_nat)),tc_nat)
      | c_Divides_Oop_Advd(X10,X13,tc_nat) ),
    file('<stdin>',cls_GCD_Ogcd__greatest__iff__iff1_0) ).

fof(c_0_45,axiom,
    ! [X14,X6,X5,X7,X3] :
      ( ~ c_in(c_Pair(X5,X6,X7,X3),X14,tc_prod(X7,X3))
      | c_in(X6,c_Relation_OImage(X14,c_insert(X5,c_emptyset,X7),X7,X3),X3) ),
    file('<stdin>',cls_Relation_OImage__singleton__iff__iff2_0) ).

fof(c_0_46,axiom,
    ! [X14,X6,X5,X7,X3] :
      ( ~ c_in(c_Pair(X5,X6,X3,X7),c_Relation_Oconverse(X14,X7,X3),tc_prod(X3,X7))
      | c_in(c_Pair(X6,X5,X7,X3),X14,tc_prod(X7,X3)) ),
    file('<stdin>',cls_Relation_Oconverse__iff__iff1_0) ).

fof(c_0_47,axiom,
    ! [X14,X6,X5,X7,X3] :
      ( ~ c_in(c_Pair(X6,X5,X7,X3),X14,tc_prod(X7,X3))
      | c_in(c_Pair(X5,X6,X3,X7),c_Relation_Oconverse(X14,X7,X3),tc_prod(X3,X7)) ),
    file('<stdin>',cls_Relation_Oconverse__iff__iff2_0) ).

fof(c_0_48,axiom,
    ! [X14,X6,X5,X3] :
      ( ~ c_in(c_Pair(X5,X6,X3,X3),c_Transitive__Closure_Otrancl(X14,X3),tc_prod(X3,X3))
      | c_in(c_Pair(X5,X6,X3,X3),c_Transitive__Closure_Ortrancl(X14,X3),tc_prod(X3,X3)) ),
    file('<stdin>',cls_Transitive__Closure_Otrancl__into__rtrancl_0) ).

fof(c_0_49,axiom,
    ! [X14,X6,X5,X15,X7,X3] :
      ( ~ c_in(X5,X15,X3)
      | ~ c_in(c_Pair(X5,X6,X3,X7),X14,tc_prod(X3,X7))
      | c_in(X6,c_Relation_OImage(X14,X15,X3,X7),X7) ),
    file('<stdin>',cls_Relation_OImageI_0) ).

fof(c_0_50,axiom,
    ! [X45,X14,X7,X3] :
      ( ~ c_in(X45,c_Relation_Oconverse(X14,X7,X3),tc_prod(X3,X7))
      | X45 = c_Pair(c_Main_OconverseE__2(X14,X45,X7,X3),c_Main_OconverseE__1(X14,X45,X7,X3),X3,X7) ),
    file('<stdin>',cls_Relation_OconverseE_1) ).

fof(c_0_51,axiom,
    ! [X14,X6,X5,X3] :
      ( ~ c_in(c_Pair(X5,X6,X3,X3),X14,tc_prod(X3,X3))
      | c_in(c_Pair(X5,X6,X3,X3),c_Transitive__Closure_Otrancl(X14,X3),tc_prod(X3,X3)) ),
    file('<stdin>',cls_Transitive__Closure_Otrancl_Or__into__trancl_0) ).

fof(c_0_52,axiom,
    ! [X8,X9,X16,X15,X7,X3] :
      ( ~ c_in(X8,X16,tc_set(tc_Datatype__Universe_Onode(X3,X7)))
      | ~ c_in(X9,X15,tc_set(tc_Datatype__Universe_Onode(X3,X7)))
      | c_in(c_Datatype__Universe_OScons(X9,X8,X3,X7),c_Datatype__Universe_Ouprod(X15,X16,X3,X7),tc_set(tc_Datatype__Universe_Onode(X3,X7))) ),
    file('<stdin>',cls_Datatype__Universe_OuprodI_0) ).

fof(c_0_53,axiom,
    ! [X19,X13,X10] :
      ( ~ c_Divides_Oop_Advd(X10,X19,tc_nat)
      | ~ c_Divides_Oop_Advd(X10,X13,tc_nat)
      | c_Divides_Oop_Advd(X10,c_GCD_Ogcd(c_Pair(X13,X19,tc_nat,tc_nat)),tc_nat) ),
    file('<stdin>',cls_GCD_Ogcd__greatest__iff__iff2_0) ).

fof(c_0_54,axiom,
    ! [X14,X6,X5,X7,X3] :
      ( ~ c_in(c_Pair(X5,X6,X3,X7),X14,tc_prod(X3,X7))
      | c_in(X6,c_Relation_ORange(X14,X3,X7),X7) ),
    file('<stdin>',cls_Relation_ORangeI_0) ).

fof(c_0_55,axiom,
    ! [X14,X6,X5,X7,X3] :
      ( ~ c_in(c_Pair(X5,X6,X3,X7),X14,tc_prod(X3,X7))
      | c_in(X5,c_Relation_ODomain(X14,X3,X7),X3) ),
    file('<stdin>',cls_Relation_ODomainI_0) ).

fof(c_0_56,axiom,
    ! [X37,X16,X15,X3] :
      ( ~ c_lessequals(X16,c_Zorn_OUnion__lemma0__1(X15,X16,X37,X3),tc_set(X3))
      | c_lessequals(X16,c_Union(X37,X3),tc_set(X3))
      | c_lessequals(c_Union(X37,X3),X15,tc_set(X3)) ),
    file('<stdin>',cls_Zorn_OUnion__lemma0_2) ).

fof(c_0_57,axiom,
    ! [X37,X16,X15,X3] :
      ( ~ c_lessequals(c_Zorn_OUnion__lemma0__1(X15,X16,X37,X3),X15,tc_set(X3))
      | c_lessequals(X16,c_Union(X37,X3),tc_set(X3))
      | c_lessequals(c_Union(X37,X3),X15,tc_set(X3)) ),
    file('<stdin>',cls_Zorn_OUnion__lemma0_1) ).

fof(c_0_58,axiom,
    ! [X19,X13] : c_Divides_Oop_Advd(c_GCD_Ogcd(c_Pair(X13,X19,tc_nat,tc_nat)),X19,tc_nat),
    file('<stdin>',cls_GCD_Ogcd__dvd2_0) ).

fof(c_0_59,axiom,
    ! [X19,X13] : c_Divides_Oop_Advd(c_GCD_Ogcd(c_Pair(X13,X19,tc_nat,tc_nat)),X13,tc_nat),
    file('<stdin>',cls_GCD_Ogcd__dvd1_0) ).

fof(c_0_60,axiom,
    ! [X22,X14,X3] :
      ( ~ c_in(c_Pair(X22,c_List_Olist_ONil,tc_List_Olist(X3),tc_List_Olist(X3)),c_List_Olistrel(X14,X3),tc_prod(tc_List_Olist(X3),tc_List_Olist(X3)))
      | X22 = c_List_Olist_ONil ),
    file('<stdin>',cls_List_Olistrel__Nil2_0) ).

fof(c_0_61,axiom,
    ! [X22,X14,X3] :
      ( ~ c_in(c_Pair(c_List_Olist_ONil,X22,tc_List_Olist(X3),tc_List_Olist(X3)),c_List_Olistrel(X14,X3),tc_prod(tc_List_Olist(X3),tc_List_Olist(X3)))
      | X22 = c_List_Olist_ONil ),
    file('<stdin>',cls_List_Olistrel__Nil1_0) ).

fof(c_0_62,axiom,
    ! [X23,X14,X3] : ~ c_in(c_Pair(c_List_Olist_ONil,X23,tc_List_Olist(X3),tc_List_Olist(X3)),c_List_Olex(X14,X3),tc_prod(tc_List_Olist(X3),tc_List_Olist(X3))),
    file('<stdin>',cls_List_ONil__notin__lex__iff1_0) ).

fof(c_0_63,axiom,
    ! [X22,X14,X3] : ~ c_in(c_Pair(X22,c_List_Olist_ONil,tc_List_Olist(X3),tc_List_Olist(X3)),c_List_Olex(X14,X3),tc_prod(tc_List_Olist(X3),tc_List_Olist(X3))),
    file('<stdin>',cls_List_ONil2__notin__lex__iff1_0) ).

fof(c_0_64,axiom,
    ! [X24,X2] :
      ( ~ c_in(c_Pair(X2,X24,tc_nat,tc_nat),c_Wellfounded__Relations_Oless__than,tc_prod(tc_nat,tc_nat))
      | c_less(X2,X24,tc_nat) ),
    file('<stdin>',cls_Wellfounded__Relations_Oless__than__iff__iff1_0) ).

fof(c_0_65,axiom,
    ! [X6,X5,X3] :
      ( ~ c_in(c_Pair(X5,X6,X3,X3),c_Relation_OId,tc_prod(X3,X3))
      | X5 = X6 ),
    file('<stdin>',cls_Relation_Opair__in__Id__conv__iff1_0) ).

fof(c_0_66,axiom,
    ! [X8,X16,X15,X7,X3] :
      ( ~ c_in(X8,X16,tc_set(tc_Datatype__Universe_Onode(X3,X7)))
      | c_in(c_Datatype__Universe_OIn1(X8,X3,X7),c_Datatype__Universe_Ousum(X15,X16,X3,X7),tc_set(tc_Datatype__Universe_Onode(X3,X7))) ),
    file('<stdin>',cls_Datatype__Universe_Ousum__In1I_0) ).

fof(c_0_67,axiom,
    ! [X9,X16,X15,X7,X3] :
      ( ~ c_in(X9,X15,tc_set(tc_Datatype__Universe_Onode(X3,X7)))
      | c_in(c_Datatype__Universe_OIn0(X9,X3,X7),c_Datatype__Universe_Ousum(X15,X16,X3,X7),tc_set(tc_Datatype__Universe_Onode(X3,X7))) ),
    file('<stdin>',cls_Datatype__Universe_Ousum__In0I_0) ).

fof(c_0_68,axiom,
    ! [X5,X16,X15,X3] :
      ( ~ c_in(c_minus(X15,c_insert(X5,X16,X3),tc_set(X3)),c_Finite__Set_OFinites,tc_set(X3))
      | c_in(c_minus(X15,X16,tc_set(X3)),c_Finite__Set_OFinites,tc_set(X3)) ),
    file('<stdin>',cls_Finite__Set_Ofinite__Diff__insert__iff1_0) ).

fof(c_0_69,axiom,
    ! [X34,X6,X4,X5,X7,X3] :
      ( c_Pair(X5,X6,X3,X7) != c_Pair(X4,X34,X3,X7)
      | X6 = X34 ),
    file('<stdin>',cls_Product__Type_OPair__eq__iff1_1) ).

fof(c_0_70,axiom,
    ! [X34,X6,X4,X5,X7,X3] :
      ( c_Pair(X5,X6,X3,X7) != c_Pair(X4,X34,X3,X7)
      | X5 = X4 ),
    file('<stdin>',cls_Product__Type_OPair__eq__iff1_0) ).

fof(c_0_71,axiom,
    ! [X11,X8,X12,X9,X7,X3] :
      ( c_Datatype__Universe_OScons(X9,X8,X3,X7) != c_Datatype__Universe_OScons(X12,X11,X3,X7)
      | X8 = X11 ),
    file('<stdin>',cls_Datatype__Universe_OScons__Scons__eq__iff1_1) ).

fof(c_0_72,axiom,
    ! [X11,X8,X12,X9,X7,X3] :
      ( c_Datatype__Universe_OScons(X9,X8,X3,X7) != c_Datatype__Universe_OScons(X12,X11,X3,X7)
      | X9 = X12 ),
    file('<stdin>',cls_Datatype__Universe_OScons__Scons__eq__iff1_0) ).

fof(c_0_73,axiom,
    ! [X6,X16,X15,X7,X3] :
      ( ~ c_in(X6,X16,X3)
      | c_in(c_Sum__Type_OInr(X6,X3,X7),c_Sum__Type_OPlus(X15,X16,X7,X3),tc_sum(X7,X3)) ),
    file('<stdin>',cls_Sum__Type_OInrI_0) ).

fof(c_0_74,axiom,
    ! [X5,X16,X15,X7,X3] :
      ( ~ c_in(X5,X15,X3)
      | c_in(c_Sum__Type_OInl(X5,X3,X7),c_Sum__Type_OPlus(X15,X16,X3,X7),tc_sum(X3,X7)) ),
    file('<stdin>',cls_Sum__Type_OInlI_0) ).

fof(c_0_75,axiom,
    ! [X37,X16,X15,X3] :
      ( c_in(c_Zorn_OUnion__lemma0__1(X15,X16,X37,X3),X37,tc_set(X3))
      | c_lessequals(X16,c_Union(X37,X3),tc_set(X3))
      | c_lessequals(c_Union(X37,X3),X15,tc_set(X3)) ),
    file('<stdin>',cls_Zorn_OUnion__lemma0_0) ).

fof(c_0_76,axiom,
    ! [X5,X15,X3] :
      ( ~ c_in(X5,X15,X3)
      | c_in(c_Pair(X5,X5,X3,X3),c_Relation_Odiag(X15,X3),tc_prod(X3,X3)) ),
    file('<stdin>',cls_Relation_OdiagI_0) ).

fof(c_0_77,axiom,
    ! [X5,X16,X15,X3] :
      ( ~ c_in(c_minus(X15,X16,tc_set(X3)),c_Finite__Set_OFinites,tc_set(X3))
      | c_in(c_minus(X15,c_insert(X5,X16,X3),tc_set(X3)),c_Finite__Set_OFinites,tc_set(X3)) ),
    file('<stdin>',cls_Finite__Set_Ofinite__Diff__insert__iff2_0) ).

fof(c_0_78,axiom,
    ! [X24,X2] :
      ( ~ c_less(X2,X24,tc_nat)
      | c_in(c_Pair(X2,X24,tc_nat,tc_nat),c_Wellfounded__Relations_Oless__than,tc_prod(tc_nat,tc_nat)) ),
    file('<stdin>',cls_Wellfounded__Relations_Oless__than__iff__iff2_0) ).

fof(c_0_79,axiom,
    ! [X35,X15,X3] :
      ( ~ c_in(X35,c_Relation_Odiag(X15,X3),tc_prod(X3,X3))
      | X35 = c_Pair(c_Main_OdiagE__1(X15,X35,X3),c_Main_OdiagE__1(X15,X35,X3),X3,X3) ),
    file('<stdin>',cls_Relation_OdiagE_0) ).

fof(c_0_80,axiom,
    ! [X14,X5,X3] : c_in(c_Pair(X5,X5,X3,X3),c_Transitive__Closure_Ortrancl(X14,X3),tc_prod(X3,X3)),
    file('<stdin>',cls_Transitive__Closure_Ortrancl_Ortrancl__refl_0) ).

fof(c_0_81,axiom,
    ! [X50,X51,X7,X3] :
      ( ~ c_Wellfounded__Recursion_Owf(X50,X7)
      | ~ c_Wellfounded__Recursion_Owf(X51,X3)
      | c_Wellfounded__Recursion_Owf(c_Wellfounded__Relations_Olex__prod(X51,X50,X3,X7),tc_prod(X3,X7)) ),
    file('<stdin>',cls_Wellfounded__Relations_Owf__lex__prod_0) ).

fof(c_0_82,axiom,
    ! [X48,X49,X7,X3] :
      ( ~ c_Relation_Otrans(X48,X7)
      | ~ c_Relation_Otrans(X49,X3)
      | c_Relation_Otrans(c_Wellfounded__Relations_Olex__prod(X49,X48,X3,X7),tc_prod(X3,X7)) ),
    file('<stdin>',cls_Wellfounded__Relations_Otrans__lex__prod_0) ).

fof(c_0_83,axiom,
    ! [X5,X3] : c_in(c_Pair(X5,X5,X3,X3),c_Relation_OId,tc_prod(X3,X3)),
    file('<stdin>',cls_Relation_OIdI_0) ).

fof(c_0_84,axiom,
    ! [X23,X24,X22,X2,X3] :
      ( c_append(X22,c_List_Olist_OCons(X2,c_List_Olist_ONil,X3),X3) != c_append(X23,c_List_Olist_OCons(X24,c_List_Olist_ONil,X3),X3)
      | X2 = X24 ),
    file('<stdin>',cls_List_Oappend1__eq__conv__iff1_1) ).

fof(c_0_85,axiom,
    ! [X23,X24,X22,X2,X3] :
      ( c_append(X22,c_List_Olist_OCons(X2,c_List_Olist_ONil,X3),X3) != c_append(X23,c_List_Olist_OCons(X24,c_List_Olist_ONil,X3),X3)
      | X22 = X23 ),
    file('<stdin>',cls_List_Oappend1__eq__conv__iff1_0) ).

fof(c_0_86,axiom,
    ! [X10,X8,X9,X7,X3] : c_Datatype__Universe_OScons(X9,X8,X3,X7) != c_Datatype__Universe_ONumb(X10,X3,X7),
    file('<stdin>',cls_Datatype__Universe_OScons__not__Numb__iff1_0) ).

fof(c_0_87,axiom,
    ! [X5,X8,X9,X7,X3] : c_Datatype__Universe_OScons(X9,X8,X3,X7) != c_Datatype__Universe_OLeaf(X5,X3,X7),
    file('<stdin>',cls_Datatype__Universe_OScons__not__Leaf__iff1_0) ).

fof(c_0_88,axiom,
    ! [X5,X8,X9,X7,X3] : c_Datatype__Universe_OScons(X9,X8,X3,X7) != c_Datatype__Universe_OAtom(X5,X3,X7),
    file('<stdin>',cls_Datatype__Universe_OScons__not__Atom__iff1_0) ).

fof(c_0_89,axiom,
    ! [X10,X8,X9,X7,X3] : c_Datatype__Universe_ONumb(X10,X3,X7) != c_Datatype__Universe_OScons(X9,X8,X3,X7),
    file('<stdin>',cls_Datatype__Universe_ONumb__not__Scons__iff1_0) ).

fof(c_0_90,axiom,
    ! [X5,X8,X9,X7,X3] : c_Datatype__Universe_OLeaf(X5,X3,X7) != c_Datatype__Universe_OScons(X9,X8,X3,X7),
    file('<stdin>',cls_Datatype__Universe_OLeaf__not__Scons__iff1_0) ).

fof(c_0_91,axiom,
    ! [X5,X8,X9,X7,X3] : c_Datatype__Universe_OAtom(X5,X3,X7) != c_Datatype__Universe_OScons(X9,X8,X3,X7),
    file('<stdin>',cls_Datatype__Universe_OAtom__not__Scons__iff1_0) ).

fof(c_0_92,axiom,
    ! [X23,X22,X15,X3] :
      ( ~ c_in(X23,c_List_Olists(X15,X3),tc_List_Olist(X3))
      | ~ c_in(X22,c_List_Olists(X15,X3),tc_List_Olist(X3))
      | c_in(c_append(X22,X23,X3),c_List_Olists(X15,X3),tc_List_Olist(X3)) ),
    file('<stdin>',cls_List_Oappend__in__lists__conv__iff2_0) ).

fof(c_0_93,axiom,
    ! [X14,X7,X3] :
      ( ~ c_in(c_Relation_Oconverse(X14,X7,X3),c_Finite__Set_OFinites,tc_set(tc_prod(X3,X7)))
      | c_in(X14,c_Finite__Set_OFinites,tc_set(tc_prod(X7,X3))) ),
    file('<stdin>',cls_Finite__Set_Ofinite__converse__iff1_0) ).

fof(c_0_94,axiom,
    ! [X23,X24,X3] : c_List_Orev(c_append(c_List_Orev(X23,X3),c_List_Olist_OCons(X24,c_List_Olist_ONil,X3),X3),X3) = c_List_Olist_OCons(X24,X23,X3),
    file('<stdin>',cls_List_Orev__eq__Cons__iff__iff2_0) ).

fof(c_0_95,axiom,
    ! [X44,X3] :
      ( ~ c_in(X44,c_Relation_OId,tc_prod(X3,X3))
      | X44 = c_Pair(c_Main_OIdE__1(X44,X3),c_Main_OIdE__1(X44,X3),X3,X3) ),
    file('<stdin>',cls_Relation_OIdE_0) ).

fof(c_0_96,axiom,
    ! [X43,X5,X15,X3] :
      ( ~ c_in(X5,X15,X3)
      | ~ c_in(X43,c_List_Olists(X15,X3),tc_List_Olist(X3))
      | c_in(c_List_Olist_OCons(X5,X43,X3),c_List_Olists(X15,X3),tc_List_Olist(X3)) ),
    file('<stdin>',cls_List_Olists_OCons_0) ).

fof(c_0_97,axiom,
    ! [X14,X7,X3] :
      ( ~ c_in(X14,c_Finite__Set_OFinites,tc_set(tc_prod(X7,X3)))
      | c_in(c_Relation_Oconverse(X14,X7,X3),c_Finite__Set_OFinites,tc_set(tc_prod(X3,X7))) ),
    file('<stdin>',cls_Finite__Set_Ofinite__converse__iff2_0) ).

fof(c_0_98,axiom,
    ! [X2,X43,X15,X3] :
      ( ~ c_in(c_List_Olist_OCons(X2,X43,X3),c_List_Olists(X15,X3),tc_List_Olist(X3))
      | c_in(X43,c_List_Olists(X15,X3),tc_List_Olist(X3)) ),
    file('<stdin>',cls_List_OlistsE_0) ).

fof(c_0_99,axiom,
    ! [X23,X22,X15,X3] :
      ( ~ c_in(c_append(X22,X23,X3),c_List_Olists(X15,X3),tc_List_Olist(X3))
      | c_in(X23,c_List_Olists(X15,X3),tc_List_Olist(X3)) ),
    file('<stdin>',cls_List_Oappend__in__lists__conv__iff1_1) ).

fof(c_0_100,axiom,
    ! [X23,X22,X15,X3] :
      ( ~ c_in(c_append(X22,X23,X3),c_List_Olists(X15,X3),tc_List_Olist(X3))
      | c_in(X22,c_List_Olists(X15,X3),tc_List_Olist(X3)) ),
    file('<stdin>',cls_List_Oappend__in__lists__conv__iff1_0) ).

fof(c_0_101,axiom,
    ! [X2,X15,X3] :
      ( ~ c_lessequals(X15,c_insert(X2,c_emptyset,X3),tc_set(X3))
      | c_insert(X2,c_emptyset,X3) = c_insert(X2,X15,X3) ),
    file('<stdin>',cls_Set_Osingleton__insert__inj__eq__iff2_0) ).

fof(c_0_102,axiom,
    ! [X2,X15,X3] :
      ( ~ c_lessequals(X15,c_insert(X2,c_emptyset,X3),tc_set(X3))
      | c_insert(X2,X15,X3) = c_insert(X2,c_emptyset,X3) ),
    file('<stdin>',cls_Set_Osingleton__insert__inj__eq_H__iff2_0) ).

fof(c_0_103,axiom,
    ! [X35,X16,X15,X3] :
      ( ~ c_in(X35,c_union(X15,X16,X3),X3)
      | c_in(X35,X16,X3)
      | c_in(X35,X15,X3) ),
    file('<stdin>',cls_Set_OUnE_0) ).

fof(c_0_104,axiom,
    ! [X35,X16,X15,X3] :
      ( ~ c_in(X35,X16,X3)
      | ~ c_in(X35,c_minus(X15,X16,tc_set(X3)),X3) ),
    file('<stdin>',cls_Set_ODiffE_0) ).

fof(c_0_105,axiom,
    ! [X2,X43,X15,X3] :
      ( ~ c_in(c_List_Olist_OCons(X2,X43,X3),c_List_Olists(X15,X3),tc_List_Olist(X3))
      | c_in(X2,X15,X3) ),
    file('<stdin>',cls_List_OlistsE_1) ).

fof(c_0_106,axiom,
    ! [X17,X18,X3] :
      ( ~ c_in(X17,c_Finite__Set_OFinites,tc_set(X3))
      | ~ c_in(X18,c_Finite__Set_OFinites,tc_set(X3))
      | c_in(c_union(X18,X17,X3),c_Finite__Set_OFinites,tc_set(X3)) ),
    file('<stdin>',cls_Finite__Set_Ofinite__Un__iff2_0) ).

fof(c_0_107,axiom,
    ! [X19,X13] :
      ( ~ c_less(c_0,c_plus(X13,X19,tc_nat),tc_nat)
      | c_less(c_0,X19,tc_nat)
      | c_less(c_0,X13,tc_nat) ),
    file('<stdin>',cls_Nat_Oadd__gr__0__iff1_0) ).

fof(c_0_108,axiom,
    ! [X22,X15,X3] :
      ( ~ c_in(c_Main_Oin__listsI__1(X15,X22,X3),X15,X3)
      | c_in(X22,c_List_Olists(X15,X3),tc_List_Olist(X3)) ),
    file('<stdin>',cls_List_Oin__listsI_1) ).

fof(c_0_109,axiom,
    ! [X37,X15,X3] :
      ( ~ c_in(X15,c_Main_OInterI__1(X15,X37,X3),X3)
      | c_in(X15,c_Inter(X37,X3),X3) ),
    file('<stdin>',cls_Set_OInterI_1) ).

fof(c_0_110,axiom,
    ! [X35,X16,X15,X3] :
      ( ~ c_in(X35,X16,X3)
      | ~ c_in(X35,X15,X3)
      | c_in(X35,c_inter(X15,X16,X3),X3) ),
    file('<stdin>',cls_Set_OIntI_0) ).

fof(c_0_111,axiom,
    ! [X6,X5,X15,X3] :
      ( c_insert(X6,c_emptyset,X3) != c_insert(X5,X15,X3)
      | c_lessequals(X15,c_insert(X6,c_emptyset,X3),tc_set(X3)) ),
    file('<stdin>',cls_Set_Osingleton__insert__inj__eq__iff1_1) ).

fof(c_0_112,axiom,
    ! [X6,X5,X15,X3] :
      ( c_insert(X5,X15,X3) != c_insert(X6,c_emptyset,X3)
      | c_lessequals(X15,c_insert(X6,c_emptyset,X3),tc_set(X3)) ),
    file('<stdin>',cls_Set_Osingleton__insert__inj__eq_H__iff1_1) ).

fof(c_0_113,axiom,
    ! [X15,X3] :
      ( ~ c_in(X15,c_Finite__Set_OFinites,tc_set(tc_set(X3)))
      | ~ c_in(c_Main_Ofinite__Union__1(X15,X3),c_Finite__Set_OFinites,tc_set(X3))
      | c_in(c_Union(X15,X3),c_Finite__Set_OFinites,tc_set(X3)) ),
    file('<stdin>',cls_Finite__Set_Ofinite__Union_1) ).

fof(c_0_114,axiom,
    ! [X35,X15,X3] :
      ( ~ c_in(X35,c_Relation_Odiag(X15,X3),tc_prod(X3,X3))
      | c_in(c_Main_OdiagE__1(X15,X35,X3),X15,X3) ),
    file('<stdin>',cls_Relation_OdiagE_1) ).

fof(c_0_115,axiom,
    ! [X35,X16,X15,X3] :
      ( ~ c_in(X35,c_minus(X15,X16,tc_set(X3)),X3)
      | c_in(X35,X15,X3) ),
    file('<stdin>',cls_Set_ODiffE_1) ).

fof(c_0_116,axiom,
    ! [X17,X18,X3] :
      ( ~ c_in(c_union(X18,X17,X3),c_Finite__Set_OFinites,tc_set(X3))
      | c_in(X17,c_Finite__Set_OFinites,tc_set(X3)) ),
    file('<stdin>',cls_Finite__Set_Ofinite__Un__iff1_1) ).

fof(c_0_117,axiom,
    ! [X17,X18,X3] :
      ( ~ c_in(c_union(X18,X17,X3),c_Finite__Set_OFinites,tc_set(X3))
      | c_in(X18,c_Finite__Set_OFinites,tc_set(X3)) ),
    file('<stdin>',cls_Finite__Set_Ofinite__Un__iff1_0) ).

fof(c_0_118,axiom,
    ! [X22,X42,X15,X3] :
      ( ~ c_in(X22,c_List_Olists(X15,X3),tc_List_Olist(X3))
      | ~ c_in(X42,c_List_Oset(X22,X3),X3)
      | c_in(X42,X15,X3) ),
    file('<stdin>',cls_List_Oin__listsD__dest_0) ).

fof(c_0_119,axiom,
    ! [X16,X15,X3] :
      ( ~ c_in(c_Main_OsubsetI__1(X15,X16,X3),X16,X3)
      | c_lessequals(X15,X16,tc_set(X3)) ),
    file('<stdin>',cls_Set_OsubsetI_1) ).

fof(c_0_120,axiom,
    ! [X35,X16,X15,X3] :
      ( ~ c_in(X35,X15,X3)
      | c_in(X35,X16,X3)
      | c_in(X35,c_minus(X15,X16,tc_set(X3)),X3) ),
    file('<stdin>',cls_Set_ODiffI_0) ).

fof(c_0_121,axiom,
    ! [X6,X5,X15,X3] :
      ( ~ c_in(X5,c_insert(X6,X15,X3),X3)
      | c_in(X5,X15,X3)
      | X5 = X6 ),
    file('<stdin>',cls_Set_OinsertE_0) ).

fof(c_0_122,axiom,
    ! [X35,X16,X15,X3] :
      ( ~ c_in(X35,c_inter(X15,X16,X3),X3)
      | c_in(X35,X15,X3) ),
    file('<stdin>',cls_Set_OIntE_1) ).

fof(c_0_123,axiom,
    ! [X35,X16,X15,X3] :
      ( ~ c_in(X35,c_inter(X15,X16,X3),X3)
      | c_in(X35,X16,X3) ),
    file('<stdin>',cls_Set_OIntE_0) ).

fof(c_0_124,axiom,
    ! [X24,X2,X41,X3] :
      ( ~ c_lessequals(X2,X24,tc_set(tc_set(X3)))
      | c_lessequals(X2,c_Zorn_Osucc(X41,X24,X3),tc_set(tc_set(X3))) ),
    file('<stdin>',cls_Zorn_Osucc__trans_0) ).

fof(c_0_125,axiom,
    ! [X37,X15,X3] :
      ( ~ c_in(X15,c_Union(X37,X3),X3)
      | c_in(c_Main_OUnionE__1(X15,X37,X3),X37,tc_set(X3)) ),
    file('<stdin>',cls_Set_OUnionE_0) ).

fof(c_0_126,axiom,
    ! [X23,X24,X22,X3] :
      ( c_List_Orev(X22,X3) != c_List_Olist_OCons(X24,X23,X3)
      | X22 = c_append(c_List_Orev(X23,X3),c_List_Olist_OCons(X24,c_List_Olist_ONil,X3),X3) ),
    file('<stdin>',cls_List_Orev__eq__Cons__iff__iff1_0) ).

fof(c_0_127,axiom,
    ! [X37,X15,X3] :
      ( ~ c_in(X15,c_Union(X37,X3),X3)
      | c_in(X15,c_Main_OUnionE__1(X15,X37,X3),X3) ),
    file('<stdin>',cls_Set_OUnionE_1) ).

fof(c_0_128,axiom,
    ! [X15,X3] :
      ( ~ c_in(X15,c_Finite__Set_OFinites,tc_set(tc_set(X3)))
      | c_in(c_Main_Ofinite__Union__1(X15,X3),X15,tc_set(X3))
      | c_in(c_Union(X15,X3),c_Finite__Set_OFinites,tc_set(X3)) ),
    file('<stdin>',cls_Finite__Set_Ofinite__Union_0) ).

fof(c_0_129,axiom,
    ! [X36,X37,X15,X3] :
      ( ~ c_in(X36,X37,tc_set(X3))
      | ~ c_in(X15,c_Inter(X37,X3),X3)
      | c_in(X15,X36,X3) ),
    file('<stdin>',cls_Set_OInterD_0) ).

fof(c_0_130,axiom,
    ! [X16,X15,X3] :
      ( ~ c_lessequals(c_uminus(X15,tc_set(X3)),c_uminus(X16,tc_set(X3)),tc_set(X3))
      | c_lessequals(X16,X15,tc_set(X3)) ),
    file('<stdin>',cls_Set_OCompl__subset__Compl__iff__iff1_0) ).

fof(c_0_131,axiom,
    ! [X22,X15,X3] :
      ( c_in(X22,c_List_Olists(X15,X3),tc_List_Olist(X3))
      | c_in(c_Main_Oin__listsI__1(X15,X22,X3),c_List_Oset(X22,X3),X3) ),
    file('<stdin>',cls_List_Oin__listsI_0) ).

fof(c_0_132,axiom,
    ! [X36,X37,X15,X3] :
      ( ~ c_in(X15,X36,X3)
      | ~ c_in(X36,X37,tc_set(X3))
      | c_in(X15,c_Union(X37,X3),X3) ),
    file('<stdin>',cls_Set_OUnionI_0) ).

fof(c_0_133,axiom,
    ! [X17,X18,X3] :
      ( ~ c_in(X17,c_Finite__Set_OFinites,tc_set(X3))
      | c_in(c_inter(X18,X17,X3),c_Finite__Set_OFinites,tc_set(X3)) ),
    file('<stdin>',cls_Finite__Set_Ofinite__Int_1) ).

fof(c_0_134,axiom,
    ! [X17,X18,X3] :
      ( ~ c_in(X18,c_Finite__Set_OFinites,tc_set(X3))
      | c_in(c_inter(X18,X17,X3),c_Finite__Set_OFinites,tc_set(X3)) ),
    file('<stdin>',cls_Finite__Set_Ofinite__Int_0) ).

fof(c_0_135,axiom,
    ! [X5,X15,X3] :
      ( ~ c_in(X15,c_Finite__Set_OFinites,tc_set(X3))
      | c_in(c_insert(X5,X15,X3),c_Finite__Set_OFinites,tc_set(X3)) ),
    file('<stdin>',cls_Finite__Set_OFinites_OinsertI_0) ).

fof(c_0_136,axiom,
    ! [X6,X5,X3] :
      ( ~ c_in(X6,c_insert(X5,c_emptyset,X3),X3)
      | X6 = X5 ),
    file('<stdin>',cls_Set_OsingletonD__dest_0) ).

fof(c_0_137,axiom,
    ! [X37,X15,X3] :
      ( c_in(X15,c_Inter(X37,X3),X3)
      | c_in(c_Main_OInterI__1(X15,X37,X3),X37,tc_set(X3)) ),
    file('<stdin>',cls_Set_OInterI_0) ).

fof(c_0_138,axiom,
    ! [X6,X5,X16,X3] :
      ( ~ c_in(X5,X16,X3)
      | c_in(X5,c_insert(X6,X16,X3),X3) ),
    file('<stdin>',cls_Set_OinsertCI_0) ).

fof(c_0_139,axiom,
    ! [X35,X16,X15,X3] :
      ( ~ c_in(X35,X15,X3)
      | c_in(X35,c_union(X15,X16,X3),X3) ),
    file('<stdin>',cls_Set_OUnCI_1) ).

fof(c_0_140,axiom,
    ! [X35,X16,X15,X3] :
      ( ~ c_in(X35,X16,X3)
      | c_in(X35,c_union(X15,X16,X3),X3) ),
    file('<stdin>',cls_Set_OUnCI_0) ).

fof(c_0_141,axiom,
    ! [X33,X32] : ~ c_less(c_plus(X33,X32,tc_nat),X32,tc_nat),
    file('<stdin>',cls_Nat_Onot__add__less2__iff1_0) ).

fof(c_0_142,axiom,
    ! [X33,X32] : ~ c_less(c_plus(X32,X33,tc_nat),X32,tc_nat),
    file('<stdin>',cls_Nat_Onot__add__less1__iff1_0) ).

fof(c_0_143,axiom,
    ! [X24,X2,X3] :
      ( ~ class_Orderings_Olinorder(X3)
      | ~ c_lessequals(c_SetInterval_OlessThan(X2,X3),c_SetInterval_OlessThan(X24,X3),tc_set(X3))
      | c_lessequals(X2,X24,X3) ),
    file('<stdin>',cls_SetInterval_OlessThan__subset__iff__iff1_0) ).

fof(c_0_144,axiom,
    ! [X24,X2,X3] :
      ( ~ class_Orderings_Olinorder(X3)
      | ~ c_lessequals(c_SetInterval_OgreaterThan(X2,X3),c_SetInterval_OgreaterThan(X24,X3),tc_set(X3))
      | c_lessequals(X24,X2,X3) ),
    file('<stdin>',cls_SetInterval_OgreaterThan__subset__iff__iff1_0) ).

fof(c_0_145,axiom,
    ! [X24,X2,X3] :
      ( ~ class_Orderings_Oorder(X3)
      | ~ c_lessequals(c_SetInterval_OatMost(X2,X3),c_SetInterval_OatMost(X24,X3),tc_set(X3))
      | c_lessequals(X2,X24,X3) ),
    file('<stdin>',cls_SetInterval_OatMost__subset__iff__iff1_0) ).

fof(c_0_146,axiom,
    ! [X24,X2,X3] :
      ( ~ class_Orderings_Oorder(X3)
      | ~ c_lessequals(c_SetInterval_OatLeast(X2,X3),c_SetInterval_OatLeast(X24,X3),tc_set(X3))
      | c_lessequals(X24,X2,X3) ),
    file('<stdin>',cls_SetInterval_OatLeast__subset__iff__iff1_0) ).

fof(c_0_147,axiom,
    ! [X35,X16,X15,X3] :
      ( ~ c_in(X35,X15,X3)
      | ~ c_lessequals(X15,X16,tc_set(X3))
      | c_in(X35,X16,X3) ),
    file('<stdin>',cls_Set_OsubsetD_0) ).

fof(c_0_148,axiom,
    ! [X19,X13] :
      ( ~ c_less(c_0,X19,tc_nat)
      | c_less(c_0,c_plus(X13,X19,tc_nat),tc_nat) ),
    file('<stdin>',cls_Nat_Oadd__gr__0__iff2_1) ).

fof(c_0_149,axiom,
    ! [X19,X13] :
      ( ~ c_less(c_0,X13,tc_nat)
      | c_less(c_0,c_plus(X13,X19,tc_nat),tc_nat) ),
    file('<stdin>',cls_Nat_Oadd__gr__0__iff2_0) ).

fof(c_0_150,axiom,
    ! [X14,X44,X3] :
      ( ~ c_in(X44,X14,tc_prod(X3,X3))
      | c_in(X44,c_Transitive__Closure_Ortrancl(X14,X3),tc_prod(X3,X3)) ),
    file('<stdin>',cls_Transitive__Closure_Or__into__rtrancl_0) ).

fof(c_0_151,axiom,
    ! [X16,X15,X3] :
      ( ~ c_lessequals(X16,X15,tc_set(X3))
      | c_lessequals(c_uminus(X15,tc_set(X3)),c_uminus(X16,tc_set(X3)),tc_set(X3)) ),
    file('<stdin>',cls_Set_OCompl__subset__Compl__iff__iff2_0) ).

fof(c_0_152,axiom,
    ! [X35,X15,X3] :
      ( ~ c_in(X35,X15,X3)
      | ~ c_in(X35,c_uminus(X15,tc_set(X3)),X3) ),
    file('<stdin>',cls_Set_OComplD__dest_0) ).

fof(c_0_153,axiom,
    ! [X16,X15,X3] :
      ( c_in(c_Main_OsubsetI__1(X15,X16,X3),X15,X3)
      | c_lessequals(X15,X16,tc_set(X3)) ),
    file('<stdin>',cls_Set_OsubsetI_0) ).

fof(c_0_154,axiom,
    ! [X15,X3] :
      ( ~ c_in(c_Pow(X15,X3),c_Finite__Set_OFinites,tc_set(tc_set(X3)))
      | c_in(X15,c_Finite__Set_OFinites,tc_set(X3)) ),
    file('<stdin>',cls_Finite__Set_Ofinite__Pow__iff__iff1_0) ).

fof(c_0_155,axiom,
    ! [X24,X2,X3] :
      ( ~ class_Orderings_Olinorder(X3)
      | ~ c_lessequals(X2,X24,X3)
      | c_lessequals(c_SetInterval_OlessThan(X2,X3),c_SetInterval_OlessThan(X24,X3),tc_set(X3)) ),
    file('<stdin>',cls_SetInterval_OlessThan__subset__iff__iff2_0) ).

fof(c_0_156,axiom,
    ! [X24,X2,X3] :
      ( ~ class_Orderings_Olinorder(X3)
      | ~ c_lessequals(X24,X2,X3)
      | c_lessequals(c_SetInterval_OgreaterThan(X2,X3),c_SetInterval_OgreaterThan(X24,X3),tc_set(X3)) ),
    file('<stdin>',cls_SetInterval_OgreaterThan__subset__iff__iff2_0) ).

fof(c_0_157,axiom,
    ! [X24,X2,X3] :
      ( ~ class_Orderings_Oorder(X3)
      | ~ c_lessequals(X2,X24,X3)
      | c_lessequals(c_SetInterval_OatMost(X2,X3),c_SetInterval_OatMost(X24,X3),tc_set(X3)) ),
    file('<stdin>',cls_SetInterval_OatMost__subset__iff__iff2_0) ).

fof(c_0_158,axiom,
    ! [X24,X2,X3] :
      ( ~ class_Orderings_Oorder(X3)
      | ~ c_lessequals(X24,X2,X3)
      | c_lessequals(c_SetInterval_OatLeast(X2,X3),c_SetInterval_OatLeast(X24,X3),tc_set(X3)) ),
    file('<stdin>',cls_SetInterval_OatLeast__subset__iff__iff2_0) ).

fof(c_0_159,axiom,
    ! [X14,X3] :
      ( ~ c_Wellfounded__Recursion_Oacyclic(c_Relation_Oconverse(X14,X3,X3),X3)
      | c_Wellfounded__Recursion_Oacyclic(X14,X3) ),
    file('<stdin>',cls_Wellfounded__Recursion_Oacyclic__converse__iff1_0) ).

fof(c_0_160,axiom,
    ! [X24,X2,X41,X3] :
      ( ~ c_Infinite__Set_Oatmost__one(X41,X3)
      | ~ c_in(X24,X41,X3)
      | ~ c_in(X2,X41,X3)
      | X24 = X2 ),
    file('<stdin>',cls_Infinite__Set_Oatmost__one__unique_0) ).

fof(c_0_161,axiom,
    ! [X16,X15,X3] :
      ( ~ c_in(X15,c_Pow(X16,X3),tc_set(X3))
      | c_lessequals(X15,X16,tc_set(X3)) ),
    file('<stdin>',cls_Set_OPow__iff__iff1_0) ).

fof(c_0_162,axiom,
    ! [X16,X15,X3] :
      ( ~ c_lessequals(X16,X15,tc_set(X3))
      | ~ c_lessequals(X15,X16,tc_set(X3))
      | X15 = X16 ),
    file('<stdin>',cls_Set_Osubset__antisym_0) ).

fof(c_0_163,axiom,
    ! [X16,X15,X3] :
      ( ~ c_less(X15,X16,tc_set(X3))
      | ~ c_lessequals(X16,X15,tc_set(X3)) ),
    file('<stdin>',cls_Set_OpsubsetE_0) ).

fof(c_0_164,axiom,
    ! [X15,X3] :
      ( ~ c_in(X15,c_Finite__Set_OFinites,tc_set(X3))
      | c_in(c_Pow(X15,X3),c_Finite__Set_OFinites,tc_set(tc_set(X3))) ),
    file('<stdin>',cls_Finite__Set_Ofinite__Pow__iff__iff2_0) ).

fof(c_0_165,axiom,
    ! [X10,X32,X3] :
      ( ~ class_Orderings_Oord(X3)
      | ~ c_in(X32,c_SetInterval_OlessThan(X10,X3),X3)
      | c_less(X32,X10,X3) ),
    file('<stdin>',cls_SetInterval_OlessThan__iff__iff1_0) ).

fof(c_0_166,axiom,
    ! [X10,X32,X3] :
      ( ~ class_Orderings_Oord(X3)
      | ~ c_in(X32,c_SetInterval_OgreaterThan(X10,X3),X3)
      | c_less(X10,X32,X3) ),
    file('<stdin>',cls_SetInterval_OgreaterThan__iff__iff1_0) ).

fof(c_0_167,axiom,
    ! [X10,X32,X3] :
      ( ~ class_Orderings_Oord(X3)
      | ~ c_in(X32,c_SetInterval_OatMost(X10,X3),X3)
      | c_lessequals(X32,X10,X3) ),
    file('<stdin>',cls_SetInterval_OatMost__iff__iff1_0) ).

fof(c_0_168,axiom,
    ! [X10,X32,X3] :
      ( ~ class_Orderings_Oord(X3)
      | ~ c_in(X32,c_SetInterval_OatLeast(X10,X3),X3)
      | c_lessequals(X10,X32,X3) ),
    file('<stdin>',cls_SetInterval_OatLeast__iff__iff1_0) ).

fof(c_0_169,axiom,
    ! [X16,X15,X3] :
      ( ~ c_lessequals(X15,X16,tc_set(X3))
      | c_in(X15,c_Pow(X16,X3),tc_set(X3)) ),
    file('<stdin>',cls_Set_OPow__iff__iff2_0) ).

fof(c_0_170,axiom,
    ! [X22,X3] : c_lessequals(c_Nat_Osize(c_List_Oremdups(X22,X3),tc_List_Olist(X3)),c_Nat_Osize(X22,tc_List_Olist(X3)),tc_nat),
    file('<stdin>',cls_List_Olength__remdups__leq_0) ).

fof(c_0_171,axiom,
    ! [X10,X32,X3] :
      ( ~ class_Orderings_Oord(X3)
      | ~ c_less(X32,X10,X3)
      | c_in(X32,c_SetInterval_OlessThan(X10,X3),X3) ),
    file('<stdin>',cls_SetInterval_OlessThan__iff__iff2_0) ).

fof(c_0_172,axiom,
    ! [X10,X32,X3] :
      ( ~ class_Orderings_Oord(X3)
      | ~ c_less(X10,X32,X3)
      | c_in(X32,c_SetInterval_OgreaterThan(X10,X3),X3) ),
    file('<stdin>',cls_SetInterval_OgreaterThan__iff__iff2_0) ).

fof(c_0_173,axiom,
    ! [X10,X32,X3] :
      ( ~ class_Orderings_Oord(X3)
      | ~ c_lessequals(X32,X10,X3)
      | c_in(X32,c_SetInterval_OatMost(X10,X3),X3) ),
    file('<stdin>',cls_SetInterval_OatMost__iff__iff2_0) ).

fof(c_0_174,axiom,
    ! [X10,X32,X3] :
      ( ~ class_Orderings_Oord(X3)
      | ~ c_lessequals(X10,X32,X3)
      | c_in(X32,c_SetInterval_OatLeast(X10,X3),X3) ),
    file('<stdin>',cls_SetInterval_OatLeast__iff__iff2_0) ).

fof(c_0_175,axiom,
    ! [X24,X2,X7,X3] :
      ( c_Datatype__Universe_ONumb(X2,X3,X7) != c_Datatype__Universe_ONumb(X24,X3,X7)
      | X2 = X24 ),
    file('<stdin>',cls_Datatype__Universe_ONumb__inject__dest_0) ).

fof(c_0_176,axiom,
    ! [X24,X2,X7,X3] :
      ( c_Datatype__Universe_OLeaf(X2,X3,X7) != c_Datatype__Universe_OLeaf(X24,X3,X7)
      | X2 = X24 ),
    file('<stdin>',cls_Datatype__Universe_OLeaf__inject__dest_0) ).

fof(c_0_177,axiom,
    ! [X24,X2,X7,X3] :
      ( c_Sum__Type_OInr(X2,X7,X3) != c_Sum__Type_OInr(X24,X7,X3)
      | X2 = X24 ),
    file('<stdin>',cls_Sum__Type_OInr__eq__iff1_0) ).

fof(c_0_178,axiom,
    ! [X24,X2,X7,X3] :
      ( c_Sum__Type_OInl(X2,X3,X7) != c_Sum__Type_OInl(X24,X3,X7)
      | X2 = X24 ),
    file('<stdin>',cls_Sum__Type_OInl__eq__iff1_0) ).

fof(c_0_179,axiom,
    ! [X25,X23,X22,X3] :
      ( c_append(X22,X23,X3) != c_append(X22,X25,X3)
      | X23 = X25 ),
    file('<stdin>',cls_List_Osame__append__eq__iff1_0) ).

fof(c_0_180,axiom,
    ! [X30,X31,X4,X5,X3] :
      ( c_List_Olist_OCons(X5,X31,X3) != c_List_Olist_OCons(X4,X30,X3)
      | X31 = X30 ),
    file('<stdin>',cls_List_Olist_Oinject__iff1_1) ).

fof(c_0_181,axiom,
    ! [X30,X31,X4,X5,X3] :
      ( c_List_Olist_OCons(X5,X31,X3) != c_List_Olist_OCons(X4,X30,X3)
      | X5 = X4 ),
    file('<stdin>',cls_List_Olist_Oinject__iff1_0) ).

fof(c_0_182,axiom,
    ! [X25,X23,X22,X3] :
      ( c_append(X23,X22,X3) != c_append(X25,X22,X3)
      | X23 = X25 ),
    file('<stdin>',cls_List_Oappend__same__eq__iff1_0) ).

fof(c_0_183,axiom,
    ! [X8,X9,X7,X3] :
      ( c_Datatype__Universe_OIn1(X9,X3,X7) != c_Datatype__Universe_OIn1(X8,X3,X7)
      | X9 = X8 ),
    file('<stdin>',cls_Datatype__Universe_OIn1__eq__iff1_0) ).

fof(c_0_184,axiom,
    ! [X8,X9,X7,X3] :
      ( c_Datatype__Universe_OIn0(X9,X3,X7) != c_Datatype__Universe_OIn0(X8,X3,X7)
      | X9 = X8 ),
    file('<stdin>',cls_Datatype__Universe_OIn0__eq__iff1_0) ).

fof(c_0_185,axiom,
    ! [X6,X5,X7,X3] :
      ( c_Datatype__Universe_OAtom(X5,X3,X7) != c_Datatype__Universe_OAtom(X6,X3,X7)
      | X5 = X6 ),
    file('<stdin>',cls_Datatype__Universe_OAtom__Atom__eq__iff1_0) ).

fof(c_0_186,axiom,
    ! [X20,X21] :
      ( ~ c_Divides_Oop_Advd(c_uminus(X20,tc_IntDef_Oint),X21,tc_IntDef_Oint)
      | c_Divides_Oop_Advd(X20,X21,tc_IntDef_Oint) ),
    file('<stdin>',cls_IntDiv_Ozminus__dvd__iff__iff1_0) ).

fof(c_0_187,axiom,
    ! [X20,X21] :
      ( ~ c_Divides_Oop_Advd(X20,c_uminus(X21,tc_IntDef_Oint),tc_IntDef_Oint)
      | c_Divides_Oop_Advd(X20,X21,tc_IntDef_Oint) ),
    file('<stdin>',cls_IntDiv_Odvd__zminus__iff__iff1_0) ).

fof(c_0_188,axiom,
    ! [X6,X5,X7,X3] : c_Sum__Type_OInr(X6,X7,X3) != c_Sum__Type_OInl(X5,X3,X7),
    file('<stdin>',cls_Sum__Type_OInr__not__Inl__iff1_0) ).

fof(c_0_189,axiom,
    ! [X6,X5,X7,X3] : c_Sum__Type_OInl(X5,X3,X7) != c_Sum__Type_OInr(X6,X7,X3),
    file('<stdin>',cls_Sum__Type_OInl__not__Inr__iff1_0) ).

fof(c_0_190,axiom,
    ! [X10,X5,X7,X3] : c_Datatype__Universe_ONumb(X10,X3,X7) != c_Datatype__Universe_OLeaf(X5,X3,X7),
    file('<stdin>',cls_Datatype__Universe_ONumb__not__Leaf__iff1_0) ).

fof(c_0_191,axiom,
    ! [X10,X5,X7,X3] : c_Datatype__Universe_OLeaf(X5,X3,X7) != c_Datatype__Universe_ONumb(X10,X3,X7),
    file('<stdin>',cls_Datatype__Universe_OLeaf__not__Numb__iff1_0) ).

fof(c_0_192,axiom,
    ! [X8,X9,X7,X3] : c_Datatype__Universe_OIn1(X8,X3,X7) != c_Datatype__Universe_OIn0(X9,X3,X7),
    file('<stdin>',cls_Datatype__Universe_OIn1__not__In0__iff1_0) ).

fof(c_0_193,axiom,
    ! [X8,X9,X7,X3] : c_Datatype__Universe_OIn0(X9,X3,X7) != c_Datatype__Universe_OIn1(X8,X3,X7),
    file('<stdin>',cls_Datatype__Universe_OIn0__not__In1__iff1_0) ).

fof(c_0_194,axiom,
    ! [X6,X5,X15,X3] :
      ( c_insert(X6,c_emptyset,X3) != c_insert(X5,X15,X3)
      | X5 = X6 ),
    file('<stdin>',cls_Set_Osingleton__insert__inj__eq__iff1_0) ).

fof(c_0_195,axiom,
    ! [X6,X5,X15,X3] :
      ( c_insert(X5,X15,X3) != c_insert(X6,c_emptyset,X3)
      | X5 = X6 ),
    file('<stdin>',cls_Set_Osingleton__insert__inj__eq_H__iff1_0) ).

fof(c_0_196,axiom,
    ! [X6,X5,X3] :
      ( c_insert(X5,c_emptyset,X3) != c_insert(X6,c_emptyset,X3)
      | X5 = X6 ),
    file('<stdin>',cls_Set_Osingleton__inject__dest_0) ).

fof(c_0_197,axiom,
    ! [X13,X40] :
      ( c_Divides_Oop_Amod(X13,X40,tc_IntDef_Oint) != c_0
      | X13 = c_times(X40,c_Main_Ozmod__eq__0D__dest__1(X40,X13),tc_IntDef_Oint) ),
    file('<stdin>',cls_IntDiv_Ozmod__eq__0D__dest_0) ).

fof(c_0_198,axiom,
    ! [X13,X40] :
      ( c_Divides_Oop_Amod(X13,X40,tc_nat) != c_0
      | X13 = c_times(X40,c_Main_Omod__eq__0D__dest__1(X40,X13),tc_nat) ),
    file('<stdin>',cls_Divides_Omod__eq__0D__dest_0) ).

fof(c_0_199,axiom,
    ! [X2,X16,X3] : c_in(X2,c_insert(X2,X16,X3),X3),
    file('<stdin>',cls_Set_OinsertCI_1) ).

fof(c_0_200,axiom,
    ! [X39,X43] : c_in(c_SetInterval_OgreaterThanLessThan(X43,X39,tc_IntDef_Oint),c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)),
    file('<stdin>',cls_SetInterval_Ofinite__greaterThanLessThan__int_0) ).

fof(c_0_201,axiom,
    ! [X39,X43] : c_in(c_SetInterval_OgreaterThanLessThan(X43,X39,tc_nat),c_Finite__Set_OFinites,tc_set(tc_nat)),
    file('<stdin>',cls_SetInterval_Ofinite__greaterThanLessThan_0) ).

fof(c_0_202,axiom,
    ! [X39,X43] : c_in(c_SetInterval_OgreaterThanAtMost(X43,X39,tc_IntDef_Oint),c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)),
    file('<stdin>',cls_SetInterval_Ofinite__greaterThanAtMost__int_0) ).

fof(c_0_203,axiom,
    ! [X39,X43] : c_in(c_SetInterval_OgreaterThanAtMost(X43,X39,tc_nat),c_Finite__Set_OFinites,tc_set(tc_nat)),
    file('<stdin>',cls_SetInterval_Ofinite__greaterThanAtMost_0) ).

fof(c_0_204,axiom,
    ! [X39,X43] : c_in(c_SetInterval_OatLeastLessThan(X43,X39,tc_IntDef_Oint),c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)),
    file('<stdin>',cls_SetInterval_Ofinite__atLeastLessThan__int_0) ).

fof(c_0_205,axiom,
    ! [X39,X43] : c_in(c_SetInterval_OatLeastLessThan(X43,X39,tc_nat),c_Finite__Set_OFinites,tc_set(tc_nat)),
    file('<stdin>',cls_SetInterval_Ofinite__atLeastLessThan_0) ).

fof(c_0_206,axiom,
    ! [X39,X43] : c_in(c_SetInterval_OatLeastAtMost(X43,X39,tc_IntDef_Oint),c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)),
    file('<stdin>',cls_SetInterval_Ofinite__atLeastAtMost__int_0) ).

fof(c_0_207,axiom,
    ! [X39,X43] : c_in(c_SetInterval_OatLeastAtMost(X43,X39,tc_nat),c_Finite__Set_OFinites,tc_set(tc_nat)),
    file('<stdin>',cls_SetInterval_Ofinite__atLeastAtMost_0) ).

fof(c_0_208,axiom,
    ! [X20,X21] :
      ( ~ c_Divides_Oop_Advd(X20,X21,tc_IntDef_Oint)
      | c_Divides_Oop_Advd(c_uminus(X20,tc_IntDef_Oint),X21,tc_IntDef_Oint) ),
    file('<stdin>',cls_IntDiv_Ozminus__dvd__iff__iff2_0) ).

fof(c_0_209,axiom,
    ! [X20,X21] :
      ( ~ c_Divides_Oop_Advd(X20,X21,tc_IntDef_Oint)
      | c_Divides_Oop_Advd(X20,c_uminus(X21,tc_IntDef_Oint),tc_IntDef_Oint) ),
    file('<stdin>',cls_IntDiv_Odvd__zminus__iff__iff2_0) ).

fof(c_0_210,axiom,
    ! [X16,X15,X3] :
      ( ~ c_lessequals(X15,X16,tc_set(X3))
      | c_less(X15,X16,tc_set(X3))
      | X15 = X16 ),
    file('<stdin>',cls_Set_OpsubsetI_0) ).

fof(c_0_211,axiom,
    ! [X5,X3] : c_in(X5,c_insert(X5,c_emptyset,X3),X3),
    file('<stdin>',cls_Set_OsingletonI_0) ).

fof(c_0_212,axiom,
    ! [X13,X10] : c_Divides_Oop_Advd(X10,c_times(X13,X10,tc_IntDef_Oint),tc_IntDef_Oint),
    file('<stdin>',cls_IntDiv_Ozdvd__triv__right_0) ).

fof(c_0_213,axiom,
    ! [X13,X10] : c_Divides_Oop_Advd(X10,c_times(X10,X13,tc_IntDef_Oint),tc_IntDef_Oint),
    file('<stdin>',cls_IntDiv_Ozdvd__triv__left_0) ).

fof(c_0_214,axiom,
    ! [X13,X10] : c_Divides_Oop_Advd(X10,c_times(X13,X10,tc_nat),tc_nat),
    file('<stdin>',cls_Divides_Odvd__triv__right_0) ).

fof(c_0_215,axiom,
    ! [X13,X10] : c_Divides_Oop_Advd(X10,c_times(X10,X13,tc_nat),tc_nat),
    file('<stdin>',cls_Divides_Odvd__triv__left_0) ).

fof(c_0_216,axiom,
    ! [X16,X15,X3] :
      ( ~ c_less(X15,X16,tc_set(X3))
      | c_lessequals(X15,X16,tc_set(X3)) ),
    file('<stdin>',cls_Set_OpsubsetE_1) ).

fof(c_0_217,axiom,
    ! [X19,X13] :
      ( ~ c_less(c_Suc(X13),c_Suc(X19),tc_nat)
      | c_less(X13,X19,tc_nat) ),
    file('<stdin>',cls_Nat_OSuc__less__eq__iff1_0) ).

fof(c_0_218,axiom,
    ! [X19,X13] :
      ( ~ c_lessequals(c_Suc(X19),c_Suc(X13),tc_nat)
      | c_lessequals(X19,X13,tc_nat) ),
    file('<stdin>',cls_Nat_OSuc__le__mono__iff1_0) ).

fof(c_0_219,axiom,
    ! [X19,X13] :
      ( ~ c_less(X13,X19,tc_nat)
      | c_less(c_Suc(X13),c_Suc(X19),tc_nat) ),
    file('<stdin>',cls_Nat_OSuc__less__eq__iff2_0) ).

fof(c_0_220,axiom,
    ! [X19,X13] :
      ( ~ c_lessequals(X19,X13,tc_nat)
      | c_lessequals(c_Suc(X19),c_Suc(X13),tc_nat) ),
    file('<stdin>',cls_Nat_OSuc__le__mono__iff2_0) ).

fof(c_0_221,axiom,
    ! [X35,X15,X3] :
      ( c_in(X35,X15,X3)
      | c_in(X35,c_uminus(X15,tc_set(X3)),X3) ),
    file('<stdin>',cls_Set_OComplI_0) ).

fof(c_0_222,axiom,
    ! [X14,X3] :
      ( ~ c_Wellfounded__Recursion_Oacyclic(X14,X3)
      | c_Wellfounded__Recursion_Oacyclic(c_Relation_Oconverse(X14,X3,X3),X3) ),
    file('<stdin>',cls_Wellfounded__Recursion_Oacyclic__converse__iff2_0) ).

fof(c_0_223,axiom,
    ! [X1,X2,X3] :
      ( ~ c_in(X2,c_Datatype_Oo2s(X1,X3),X3)
      | X1 = c_Datatype_Ooption_OSome(X2,X3) ),
    file('<stdin>',cls_Datatype_Oelem__o2s__iff1_0) ).

fof(c_0_224,axiom,
    ! [X3] : ~ c_less(c_0,c_Nat_Osize(c_List_Olist_ONil,tc_List_Olist(X3)),tc_nat),
    file('<stdin>',cls_List_Olength__greater__0__conv__iff1_0) ).

fof(c_0_225,axiom,
    ! [X2,X3] : c_in(X2,c_Datatype_Oo2s(c_Datatype_Ooption_OSome(X2,X3),X3),X3),
    file('<stdin>',cls_Datatype_Oelem__o2s__iff2_0) ).

fof(c_0_226,axiom,
    ! [X22,X3] :
      ( c_Nat_Osize(c_List_Oremdups(X22,X3),tc_List_Olist(X3)) != c_Nat_Osize(X22,tc_List_Olist(X3))
      | c_List_Oremdups(X22,X3) = X22 ),
    file('<stdin>',cls_List_Olength__remdups__eq__iff1_0) ).

fof(c_0_227,axiom,
    ! [X19,X13] : c_less(c_uminus(c_IntDef_Oint(c_Suc(X19)),tc_IntDef_Oint),c_IntDef_Oint(X13),tc_IntDef_Oint),
    file('<stdin>',cls_IntDef_Onegative__zless_0) ).

fof(c_0_228,axiom,
    ! [X19,X13] : c_lessequals(c_uminus(c_IntDef_Oint(X19),tc_IntDef_Oint),c_IntDef_Oint(X13),tc_IntDef_Oint),
    file('<stdin>',cls_IntDef_Onegative__zle_0) ).

fof(c_0_229,axiom,
    ! [X15,X3] : ~ c_less(X15,c_emptyset,tc_set(X3)),
    file('<stdin>',cls_Set_Onot__psubset__empty__iff1_0) ).

fof(c_0_230,axiom,
    ! [X2,X3] :
      ( ~ class_Orderings_Oorder(X3)
      | ~ c_less(X2,X2,X3) ),
    file('<stdin>',cls_Orderings_Oorder__less__irrefl__iff1_0) ).

fof(c_0_231,axiom,
    ! [X22,X3] :
      ( c_less(c_0,c_Nat_Osize(X22,tc_List_Olist(X3)),tc_nat)
      | X22 = c_List_Olist_ONil ),
    file('<stdin>',cls_List_Olength__greater__0__conv__iff2_0) ).

fof(c_0_232,axiom,
    ! [X22,X3] :
      ( c_List_Oremdups(X22,X3) != X22
      | c_Nat_Osize(c_List_Oremdups(X22,X3),tc_List_Olist(X3)) = c_Nat_Osize(X22,tc_List_Olist(X3)) ),
    file('<stdin>',cls_List_Olength__remdups__eq__iff2_0) ).

fof(c_0_233,axiom,
    ! [X19] :
      ( ~ c_less(X19,c_Suc(c_0),tc_nat)
      | X19 = c_0 ),
    file('<stdin>',cls_Nat_Oless__Suc0__iff1_0) ).

fof(c_0_234,axiom,
    ! [X23,X22,X3] :
      ( X22 != c_append(X22,X23,X3)
      | X23 = c_List_Olist_ONil ),
    file('<stdin>',cls_List_Oself__append__conv__iff1_0) ).

fof(c_0_235,axiom,
    ! [X23,X22,X3] :
      ( X23 != c_append(X22,X23,X3)
      | X22 = c_List_Olist_ONil ),
    file('<stdin>',cls_List_Oself__append__conv2__iff1_0) ).

fof(c_0_236,axiom,
    ! [X23,X22,X3] :
      ( c_append(X22,X23,X3) != X22
      | X23 = c_List_Olist_ONil ),
    file('<stdin>',cls_List_Oappend__self__conv__iff1_0) ).

fof(c_0_237,axiom,
    ! [X23,X22,X3] :
      ( c_append(X22,X23,X3) != X23
      | X22 = c_List_Olist_ONil ),
    file('<stdin>',cls_List_Oappend__self__conv2__iff1_0) ).

fof(c_0_238,axiom,
    ! [X16,X15,X3] :
      ( c_union(X15,X16,X3) != c_emptyset
      | X16 = c_emptyset ),
    file('<stdin>',cls_Set_OUn__empty__iff1_1) ).

fof(c_0_239,axiom,
    ! [X16,X15,X3] :
      ( c_union(X15,X16,X3) != c_emptyset
      | X15 = c_emptyset ),
    file('<stdin>',cls_Set_OUn__empty__iff1_0) ).

fof(c_0_240,axiom,
    ! [X23,X22,X3] :
      ( c_append(X22,X23,X3) != c_List_Olist_ONil
      | X23 = c_List_Olist_ONil ),
    file('<stdin>',cls_List_Oappend__is__Nil__conv__iff1_1) ).

fof(c_0_241,axiom,
    ! [X23,X22,X3] :
      ( c_append(X22,X23,X3) != c_List_Olist_ONil
      | X22 = c_List_Olist_ONil ),
    file('<stdin>',cls_List_Oappend__is__Nil__conv__iff1_0) ).

fof(c_0_242,axiom,
    ! [X23,X22,X3] :
      ( c_List_Olist_ONil != c_append(X22,X23,X3)
      | X23 = c_List_Olist_ONil ),
    file('<stdin>',cls_List_ONil__is__append__conv__iff1_1) ).

fof(c_0_243,axiom,
    ! [X23,X22,X3] :
      ( c_List_Olist_ONil != c_append(X22,X23,X3)
      | X22 = c_List_Olist_ONil ),
    file('<stdin>',cls_List_ONil__is__append__conv__iff1_0) ).

fof(c_0_244,axiom,
    ! [X14,X15,X3] :
      ( c_Equiv__Relations_Oquotient(X15,X14,X3) != c_emptyset
      | X15 = c_emptyset ),
    file('<stdin>',cls_Equiv__Relations_Oquotient__is__empty__iff1_0) ).

fof(c_0_245,axiom,
    ! [X14,X15,X3] :
      ( c_emptyset != c_Equiv__Relations_Oquotient(X15,X14,X3)
      | X15 = c_emptyset ),
    file('<stdin>',cls_Equiv__Relations_Oquotient__is__empty2__iff1_0) ).

fof(c_0_246,axiom,
    ! [X30,X4,X3] : c_List_Olist_OCons(X4,X30,X3) != c_List_Olist_ONil,
    file('<stdin>',cls_List_Olist_Odistinct__2__iff1_0) ).

fof(c_0_247,axiom,
    ! [X30,X4,X3] : c_List_Olist_ONil != c_List_Olist_OCons(X4,X30,X3),
    file('<stdin>',cls_List_Olist_Odistinct__1__iff1_0) ).

fof(c_0_248,axiom,
    ~ c_in(c_UNIV,c_Finite__Set_OFinites,tc_set(tc_nat)),
    file('<stdin>',cls_Infinite__Set_Onat__not__finite_0) ).

fof(c_0_249,axiom,
    ! [X15,X3] : c_in(c_List_Olist_ONil,c_List_Olists(X15,X3),tc_List_Olist(X3)),
    file('<stdin>',cls_List_Olists_ONil_0) ).

fof(c_0_250,axiom,
    ! [X22,X3] : c_in(c_List_Oset(X22,X3),c_Finite__Set_OFinites,tc_set(X3)),
    file('<stdin>',cls_List_Ofinite__set_0) ).

fof(c_0_251,axiom,
    ! [X19,X13] :
      ( c_plus(X13,X19,tc_nat) != c_0
      | X19 = c_0 ),
    file('<stdin>',cls_Nat_Oadd__is__0__iff1_1) ).

fof(c_0_252,axiom,
    ! [X19,X13] :
      ( c_plus(X13,X19,tc_nat) != c_0
      | X13 = c_0 ),
    file('<stdin>',cls_Nat_Oadd__is__0__iff1_0) ).

fof(c_0_253,axiom,
    ! [X19] : ~ c_less(X19,X19,tc_nat),
    file('<stdin>',cls_Nat_Oless__irrefl_0) ).

fof(c_0_254,axiom,
    ! [X5,X3] : ~ c_in(X5,c_emptyset,X3),
    file('<stdin>',cls_Set_OemptyE_0) ).

fof(c_0_255,axiom,
    ! [X19] :
      ( ~ c_less(X19,c_1,tc_nat)
      | X19 = c_0 ),
    file('<stdin>',cls_Nat_Oless__one__iff1_0) ).

fof(c_0_256,axiom,
    ! [X32] :
      ( ~ c_lessequals(X32,c_0,tc_nat)
      | X32 = c_0 ),
    file('<stdin>',cls_Nat_Ole__0__eq__iff1_0) ).

fof(c_0_257,axiom,
    ! [X13] :
      ( ~ c_Divides_Oop_Advd(c_0,X13,tc_IntDef_Oint)
      | X13 = c_0 ),
    file('<stdin>',cls_IntDiv_Ozdvd__0__left__iff1_0) ).

fof(c_0_258,axiom,
    ! [X13] :
      ( ~ c_Divides_Oop_Advd(c_0,X13,tc_nat)
      | X13 = c_0 ),
    file('<stdin>',cls_Divides_Odvd__0__left__iff__iff1_0) ).

fof(c_0_259,axiom,
    ! [X19] : ~ c_less(X19,c_0,tc_nat),
    file('<stdin>',cls_Nat_Onot__less0__iff1_0) ).

fof(c_0_260,axiom,
    ! [X10] : c_in(c_SetInterval_OlessThan(X10,tc_nat),c_Finite__Set_OFinites,tc_set(tc_nat)),
    file('<stdin>',cls_SetInterval_Ofinite__lessThan_0) ).

fof(c_0_261,axiom,
    ! [X10] : c_in(c_SetInterval_OatMost(X10,tc_nat),c_Finite__Set_OFinites,tc_set(tc_nat)),
    file('<stdin>',cls_SetInterval_Ofinite__atMost_0) ).

fof(c_0_262,axiom,
    ~ c_less(c_0,c_0,tc_nat),
    file('<stdin>',cls_Nat_Oneq0__conv__iff2_0) ).

fof(c_0_263,axiom,
    ! [X14,X3] :
      ( ~ c_Wellfounded__Recursion_Owf(X14,X3)
      | c_Wellfounded__Recursion_Owf(c_List_Olex(X14,X3),tc_List_Olist(X3)) ),
    file('<stdin>',cls_List_Owf__lex_0) ).

fof(c_0_264,axiom,
    ! [X14,X3] :
      ( ~ c_Wellfounded__Recursion_Owf(X14,X3)
      | c_Wellfounded__Recursion_Owf(c_List_Olenlex(X14,X3),tc_List_Olist(X3)) ),
    file('<stdin>',cls_List_Owf__lenlex_0) ).

fof(c_0_265,axiom,
    ! [X16,X15,X3] :
      ( c_uminus(X15,tc_set(X3)) != c_uminus(X16,tc_set(X3))
      | X15 = X16 ),
    file('<stdin>',cls_Set_OCompl__eq__Compl__iff__iff1_0) ).

fof(c_0_266,axiom,
    ! [X2,X3] :
      ( ~ class_Orderings_Oorder(X3)
      | c_lessequals(X2,X2,X3) ),
    file('<stdin>',cls_Orderings_Oorder__class_Oaxioms__1_0) ).

fof(c_0_267,axiom,
    ! [X15,X3] : c_lessequals(X15,X15,tc_set(X3)),
    file('<stdin>',cls_Set_Osubset__refl_0) ).

fof(c_0_268,axiom,
    ! [X15,X3] : c_lessequals(c_emptyset,X15,tc_set(X3)),
    file('<stdin>',cls_Set_Oempty__subsetI_0) ).

fof(c_0_269,axiom,
    ! [X19] : c_less(X19,c_Suc(X19),tc_nat),
    file('<stdin>',cls_Nat_OlessI_0) ).

fof(c_0_270,axiom,
    ! [X19] : c_less(c_0,c_Suc(X19),tc_nat),
    file('<stdin>',cls_Nat_Ozero__less__Suc_0) ).

fof(c_0_271,axiom,
    ! [X3] : c_in(c_emptyset,c_Finite__Set_OFinites,tc_set(X3)),
    file('<stdin>',cls_Finite__Set_OFinites_OemptyI_0) ).

fof(c_0_272,axiom,
    ! [X10] : c_Divides_Oop_Advd(c_Suc(c_0),X10,tc_nat),
    file('<stdin>',cls_Divides_Odvd__1__left_0) ).

fof(c_0_273,axiom,
    c_less(c_0,c_Suc(c_0),tc_nat),
    file('<stdin>',cls_Nat_Oless__Suc0__iff2_0) ).

fof(c_0_274,axiom,
    ! [X22,X3] : X22 = c_append(X22,c_List_Olist_ONil,X3),
    file('<stdin>',cls_List_Oself__append__conv__iff2_0) ).

fof(c_0_275,axiom,
    ! [X23,X3] : X23 = c_append(c_List_Olist_ONil,X23,X3),
    file('<stdin>',cls_List_Oself__append__conv2__iff2_0) ).

fof(c_0_276,axiom,
    ! [X22,X3] : c_append(X22,c_List_Olist_ONil,X3) = X22,
    file('<stdin>',cls_List_Oappend__self__conv__iff2_0) ).

fof(c_0_277,axiom,
    ! [X23,X3] : c_append(c_List_Olist_ONil,X23,X3) = X23,
    file('<stdin>',cls_List_Oappend__self__conv2__iff2_0) ).

fof(c_0_278,axiom,
    ! [X24,X2,X3] :
      ( ~ class_Orderings_Olinorder(X3)
      | c_SetInterval_OlessThan(X2,X3) != c_SetInterval_OlessThan(X24,X3)
      | X2 = X24 ),
    file('<stdin>',cls_SetInterval_OlessThan__eq__iff__iff1_0) ).

fof(c_0_279,axiom,
    ! [X24,X2,X3] :
      ( ~ class_Orderings_Olinorder(X3)
      | c_SetInterval_OgreaterThan(X2,X3) != c_SetInterval_OgreaterThan(X24,X3)
      | X2 = X24 ),
    file('<stdin>',cls_SetInterval_OgreaterThan__eq__iff__iff1_0) ).

fof(c_0_280,axiom,
    ! [X24,X2,X3] :
      ( ~ class_Orderings_Olinorder(X3)
      | c_SetInterval_OatMost(X2,X3) != c_SetInterval_OatMost(X24,X3)
      | X2 = X24 ),
    file('<stdin>',cls_SetInterval_OatMost__eq__iff__iff1_0) ).

fof(c_0_281,axiom,
    ! [X24,X2,X3] :
      ( ~ class_Orderings_Olinorder(X3)
      | c_SetInterval_OatLeast(X2,X3) != c_SetInterval_OatLeast(X24,X3)
      | X2 = X24 ),
    file('<stdin>',cls_SetInterval_OatLeast__eq__iff__iff1_0) ).

fof(c_0_282,axiom,
    ! [X2,X3] : c_in(X2,c_UNIV,X3),
    file('<stdin>',cls_Set_OUNIV__I_0) ).

fof(c_0_283,axiom,
    ! [X19] :
      ( c_less(c_0,X19,tc_nat)
      | X19 = c_0 ),
    file('<stdin>',cls_Nat_Oneq0__conv__iff1_0) ).

fof(c_0_284,axiom,
    ! [X14,X3] : c_Equiv__Relations_Oquotient(c_emptyset,X14,X3) = c_emptyset,
    file('<stdin>',cls_Equiv__Relations_Oquotient__is__empty__iff2_0) ).

fof(c_0_285,axiom,
    ! [X14,X3] : c_emptyset = c_Equiv__Relations_Oquotient(c_emptyset,X14,X3),
    file('<stdin>',cls_Equiv__Relations_Oquotient__is__empty2__iff2_0) ).

fof(c_0_286,axiom,
    ! [X19] : c_lessequals(c_0,X19,tc_nat),
    file('<stdin>',cls_Nat_Ole0_0) ).

fof(c_0_287,axiom,
    ! [X13] : c_Divides_Oop_Advd(c_1,X13,tc_IntDef_Oint),
    file('<stdin>',cls_IntDiv_Ozdvd__1__left_0) ).

fof(c_0_288,axiom,
    ! [X13] : c_Divides_Oop_Advd(X13,c_0,tc_IntDef_Oint),
    file('<stdin>',cls_IntDiv_Ozdvd__0__right_0) ).

fof(c_0_289,axiom,
    ! [X13] : c_Divides_Oop_Advd(X13,c_0,tc_nat),
    file('<stdin>',cls_Divides_Odvd__0__right_0) ).

fof(c_0_290,axiom,
    ! [X3] : c_union(c_emptyset,c_emptyset,X3) = c_emptyset,
    file('<stdin>',cls_Set_OUn__empty__iff2_0) ).

fof(c_0_291,axiom,
    ! [X3] : c_append(c_List_Olist_ONil,c_List_Olist_ONil,X3) = c_List_Olist_ONil,
    file('<stdin>',cls_List_Oappend__is__Nil__conv__iff2_0) ).

fof(c_0_292,axiom,
    ! [X3] : c_List_Olist_ONil = c_append(c_List_Olist_ONil,c_List_Olist_ONil,X3),
    file('<stdin>',cls_List_ONil__is__append__conv__iff2_0) ).

fof(c_0_293,axiom,
    c_less(c_0,c_1,tc_nat),
    file('<stdin>',cls_Nat_Oless__one__iff2_0) ).

fof(c_0_294,axiom,
    c_lessequals(c_0,c_0,tc_nat),
    file('<stdin>',cls_Nat_Ole__0__eq__iff2_0) ).

fof(c_0_295,axiom,
    c_plus(c_0,c_0,tc_nat) = c_0,
    file('<stdin>',cls_Nat_Oadd__is__0__iff2_0) ).

fof(c_0_296,axiom,
    c_Divides_Oop_Advd(c_0,c_0,tc_IntDef_Oint),
    file('<stdin>',cls_IntDiv_Ozdvd__0__left__iff2_0) ).

fof(c_0_297,axiom,
    c_Divides_Oop_Advd(c_0,c_0,tc_nat),
    file('<stdin>',cls_Divides_Odvd__0__left__iff__iff2_0) ).

fof(c_0_298,axiom,
    ! [X23,X22,X3] :
      ( c_List_Orev(X22,X3) != c_List_Orev(X23,X3)
      | X22 = X23 ),
    file('<stdin>',cls_List_Orev__is__rev__conv__iff1_0) ).

fof(c_0_299,axiom,
    ! [X26,X27,X28,X29] :
      ( c_List_Ochar_OChar(X29,X27) != c_List_Ochar_OChar(X28,X26)
      | X27 = X26 ),
    file('<stdin>',cls_List_Ochar_Oinject__iff1_1) ).

fof(c_0_300,axiom,
    ! [X26,X27,X28,X29] :
      ( c_List_Ochar_OChar(X29,X27) != c_List_Ochar_OChar(X28,X26)
      | X29 = X28 ),
    file('<stdin>',cls_List_Ochar_Oinject__iff1_0) ).

fof(c_0_301,axiom,
    ! [X4,X5,X3] :
      ( c_Datatype_Ooption_OSome(X5,X3) != c_Datatype_Ooption_OSome(X4,X3)
      | X5 = X4 ),
    file('<stdin>',cls_Datatype_Ooption_Oinject__iff1_0) ).

fof(c_0_302,axiom,
    ! [X53,X52] :
      ( class_Finite__Set_Ofinite(tc_sum(X53,X52))
      | ~ class_Finite__Set_Ofinite(X52)
      | ~ class_Finite__Set_Ofinite(X53) ),
    file('<stdin>',clsarity_sum_0) ).

fof(c_0_303,axiom,
    ! [X53,X52] :
      ( class_Finite__Set_Ofinite(tc_prod(X53,X52))
      | ~ class_Finite__Set_Ofinite(X52)
      | ~ class_Finite__Set_Ofinite(X53) ),
    file('<stdin>',clsarity_prod_0) ).

fof(c_0_304,axiom,
    ! [X53,X52] :
      ( class_Finite__Set_Ofinite(tc_fun(X53,X52))
      | ~ class_Finite__Set_Ofinite(X52)
      | ~ class_Finite__Set_Ofinite(X53) ),
    file('<stdin>',clsarity_fun_0) ).

fof(c_0_305,axiom,
    ! [X2,X3] :
      ( X2 = c_Datatype_Ooption_ONone
      | X2 = c_Datatype_Ooption_OSome(c_Main_Onot__Some__eq__iff1__1(X2,X3),X3) ),
    file('<stdin>',cls_Datatype_Onot__Some__eq__iff1_0) ).

fof(c_0_306,axiom,
    ! [X2,X3] :
      ( X2 = c_Datatype_Ooption_ONone
      | X2 = c_Datatype_Ooption_OSome(c_Main_Onot__None__eq__iff1__1(X2,X3),X3) ),
    file('<stdin>',cls_Datatype_Onot__None__eq__iff1_0) ).

fof(c_0_307,axiom,
    ! [X22,X3] : c_List_Odistinct(c_List_Oremdups(X22,X3),X3),
    file('<stdin>',cls_List_Odistinct__remdups_0) ).

fof(c_0_308,axiom,
    ! [X22,X3] :
      ( c_Nat_Osize(X22,tc_List_Olist(X3)) != c_0
      | X22 = c_List_Olist_ONil ),
    file('<stdin>',cls_List_Olength__0__conv__iff1_0) ).

fof(c_0_309,axiom,
    ! [X53,X52] : class_Nat_Opower(tc_fun(X53,X52)),
    file('<stdin>',clsarity_fun_1) ).

fof(c_0_310,axiom,
    ! [X22,X3] :
      ( c_List_Oset(X22,X3) != c_emptyset
      | X22 = c_List_Olist_ONil ),
    file('<stdin>',cls_List_Oset__empty__iff1_0) ).

fof(c_0_311,axiom,
    ! [X22,X3] :
      ( c_emptyset != c_List_Oset(X22,X3)
      | X22 = c_List_Olist_ONil ),
    file('<stdin>',cls_List_Oset__empty2__iff1_0) ).

fof(c_0_312,axiom,
    ! [X22,X3] :
      ( c_List_Orev(X22,X3) != c_List_Olist_ONil
      | X22 = c_List_Olist_ONil ),
    file('<stdin>',cls_List_Orev__is__Nil__conv__iff1_0) ).

fof(c_0_313,axiom,
    ! [X22,X3] :
      ( c_List_Olist_ONil != c_List_Orev(X22,X3)
      | X22 = c_List_Olist_ONil ),
    file('<stdin>',cls_List_ONil__is__rev__conv__iff1_0) ).

fof(c_0_314,axiom,
    ! [X4,X3] : c_Datatype_Ooption_OSome(X4,X3) != c_Datatype_Ooption_ONone,
    file('<stdin>',cls_Datatype_Ooption_Odistinct__2__iff1_0) ).

fof(c_0_315,axiom,
    ! [X4,X3] : c_Datatype_Ooption_ONone != c_Datatype_Ooption_OSome(X4,X3),
    file('<stdin>',cls_Datatype_Ooption_Odistinct__1__iff1_0) ).

fof(c_0_316,axiom,
    ! [X3] : c_Nat_Osize(c_List_Olist_ONil,tc_List_Olist(X3)) = c_0,
    file('<stdin>',cls_List_Olength__0__conv__iff2_0) ).

fof(c_0_317,axiom,
    ! [X52] :
      ( class_Finite__Set_Ofinite(tc_set(X52))
      | ~ class_Finite__Set_Ofinite(X52) ),
    file('<stdin>',clsarity_set_3) ).

fof(c_0_318,axiom,
    ! [X52] :
      ( class_Finite__Set_Ofinite(tc_Datatype_Ooption(X52))
      | ~ class_Finite__Set_Ofinite(X52) ),
    file('<stdin>',clsarity_Datatype__Ooption_0) ).

fof(c_0_319,axiom,
    ! [X19,X13] :
      ( c_Suc(X13) != c_Suc(X19)
      | X13 = X19 ),
    file('<stdin>',cls_Nat_OSuc__Suc__eq__iff1_0) ).

fof(c_0_320,axiom,
    ! [X19,X13] :
      ( c_IntDef_Oint(X13) != c_IntDef_Oint(X19)
      | X13 = X19 ),
    file('<stdin>',cls_IntDef_Oint__int__eq__iff1_0) ).

fof(c_0_321,axiom,
    ! [X3] : c_Wellfounded__Recursion_Owf(c_emptyset,X3),
    file('<stdin>',cls_Wellfounded__Recursion_Owf__empty_0) ).

fof(c_0_322,axiom,
    ! [X3] : c_List_Oset(c_List_Olist_ONil,X3) = c_emptyset,
    file('<stdin>',cls_List_Oset__empty__iff2_0) ).

fof(c_0_323,axiom,
    ! [X3] : c_emptyset = c_List_Oset(c_List_Olist_ONil,X3),
    file('<stdin>',cls_List_Oset__empty2__iff2_0) ).

fof(c_0_324,axiom,
    ! [X3] : c_List_Orev(c_List_Olist_ONil,X3) = c_List_Olist_ONil,
    file('<stdin>',cls_List_Orev__is__Nil__conv__iff2_0) ).

fof(c_0_325,axiom,
    ! [X3] : c_List_Olist_ONil = c_List_Orev(c_List_Olist_ONil,X3),
    file('<stdin>',cls_List_ONil__is__rev__conv__iff2_0) ).

fof(c_0_326,axiom,
    ! [X54] :
      ( ~ class_Wellfounded__Recursion_Owellorder(X54)
      | class_Orderings_Olinorder(X54) ),
    file('<stdin>',clsrel_Wellfounded__Recursion_Owellorder_5) ).

fof(c_0_327,axiom,
    ! [X54] :
      ( ~ class_Wellfounded__Recursion_Owellorder(X54)
      | class_LOrder_Olorder(X54) ),
    file('<stdin>',clsrel_Wellfounded__Recursion_Owellorder_4) ).

fof(c_0_328,axiom,
    ! [X54] :
      ( ~ class_Wellfounded__Recursion_Owellorder(X54)
      | class_LOrder_Ojoin__semilorder(X54) ),
    file('<stdin>',clsrel_Wellfounded__Recursion_Owellorder_3) ).

fof(c_0_329,axiom,
    ! [X54] :
      ( ~ class_Wellfounded__Recursion_Owellorder(X54)
      | class_LOrder_Omeet__semilorder(X54) ),
    file('<stdin>',clsrel_Wellfounded__Recursion_Owellorder_2) ).

fof(c_0_330,axiom,
    ! [X54] :
      ( ~ class_Wellfounded__Recursion_Owellorder(X54)
      | class_Orderings_Oorder(X54) ),
    file('<stdin>',clsrel_Wellfounded__Recursion_Owellorder_1) ).

fof(c_0_331,axiom,
    ! [X54] :
      ( ~ class_Wellfounded__Recursion_Owellorder(X54)
      | class_Orderings_Oord(X54) ),
    file('<stdin>',clsrel_Wellfounded__Recursion_Owellorder_0) ).

fof(c_0_332,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Osemiring__1__cancel(X54)
      | class_OrderedGroup_Omonoid__mult(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Osemiring__1__cancel_9) ).

fof(c_0_333,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Osemiring__1__cancel(X54)
      | class_HOL_Oplus(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Osemiring__1__cancel_8) ).

fof(c_0_334,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Osemiring__1__cancel(X54)
      | class_OrderedGroup_Osemigroup__add(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Osemiring__1__cancel_7) ).

fof(c_0_335,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Osemiring__1__cancel(X54)
      | class_OrderedGroup_Oab__semigroup__add(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Osemiring__1__cancel_6) ).

fof(c_0_336,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Osemiring__1__cancel(X54)
      | class_HOL_Ozero(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Osemiring__1__cancel_5) ).

fof(c_0_337,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Osemiring__1__cancel(X54)
      | class_OrderedGroup_Ocomm__monoid__add(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Osemiring__1__cancel_4) ).

fof(c_0_338,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Osemiring__1__cancel(X54)
      | class_Ring__and__Field_Osemiring(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Osemiring__1__cancel_3) ).

fof(c_0_339,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Osemiring__1__cancel(X54)
      | class_Ring__and__Field_Osemiring__0(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Osemiring__1__cancel_2) ).

fof(c_0_340,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Osemiring__1__cancel(X54)
      | class_Ring__and__Field_Osemiring__0__cancel(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Osemiring__1__cancel_15) ).

fof(c_0_341,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Osemiring__1__cancel(X54)
      | class_OrderedGroup_Ocancel__semigroup__add(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Osemiring__1__cancel_14) ).

fof(c_0_342,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Osemiring__1__cancel(X54)
      | class_OrderedGroup_Ocancel__ab__semigroup__add(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Osemiring__1__cancel_13) ).

fof(c_0_343,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Osemiring__1__cancel(X54)
      | class_HOL_Otimes(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Osemiring__1__cancel_12) ).

fof(c_0_344,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Osemiring__1__cancel(X54)
      | class_OrderedGroup_Osemigroup__mult(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Osemiring__1__cancel_11) ).

fof(c_0_345,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Osemiring__1__cancel(X54)
      | class_HOL_Oone(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Osemiring__1__cancel_10) ).

fof(c_0_346,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Osemiring__1__cancel(X54)
      | class_Ring__and__Field_Oaxclass__0__neq__1(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Osemiring__1__cancel_1) ).

fof(c_0_347,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Osemiring__1__cancel(X54)
      | class_Ring__and__Field_Osemiring__1(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Osemiring__1__cancel_0) ).

fof(c_0_348,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Osemiring__1(X54)
      | class_OrderedGroup_Osemigroup__add(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Osemiring__1_9) ).

fof(c_0_349,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Osemiring__1(X54)
      | class_OrderedGroup_Oab__semigroup__add(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Osemiring__1_8) ).

fof(c_0_350,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Osemiring__1(X54)
      | class_OrderedGroup_Ocomm__monoid__add(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Osemiring__1_7) ).

fof(c_0_351,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Osemiring__1(X54)
      | class_HOL_Otimes(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Osemiring__1_6) ).

fof(c_0_352,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Osemiring__1(X54)
      | class_OrderedGroup_Osemigroup__mult(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Osemiring__1_5) ).

fof(c_0_353,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Osemiring__1(X54)
      | class_Ring__and__Field_Osemiring(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Osemiring__1_4) ).

fof(c_0_354,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Osemiring__1(X54)
      | class_Ring__and__Field_Osemiring__0(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Osemiring__1_3) ).

fof(c_0_355,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Osemiring__1(X54)
      | class_HOL_Oone(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Osemiring__1_2) ).

fof(c_0_356,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Osemiring__1(X54)
      | class_OrderedGroup_Omonoid__mult(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Osemiring__1_11) ).

fof(c_0_357,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Osemiring__1(X54)
      | class_HOL_Oplus(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Osemiring__1_10) ).

fof(c_0_358,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Osemiring__1(X54)
      | class_HOL_Ozero(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Osemiring__1_1) ).

fof(c_0_359,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Osemiring__1(X54)
      | class_Ring__and__Field_Oaxclass__0__neq__1(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Osemiring__1_0) ).

fof(c_0_360,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Osemiring__0__cancel(X54)
      | class_OrderedGroup_Ocancel__ab__semigroup__add(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Osemiring__0__cancel_9) ).

fof(c_0_361,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Osemiring__0__cancel(X54)
      | class_HOL_Ozero(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Osemiring__0__cancel_8) ).

fof(c_0_362,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Osemiring__0__cancel(X54)
      | class_HOL_Oplus(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Osemiring__0__cancel_7) ).

fof(c_0_363,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Osemiring__0__cancel(X54)
      | class_OrderedGroup_Osemigroup__add(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Osemiring__0__cancel_6) ).

fof(c_0_364,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Osemiring__0__cancel(X54)
      | class_OrderedGroup_Oab__semigroup__add(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Osemiring__0__cancel_5) ).

fof(c_0_365,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Osemiring__0__cancel(X54)
      | class_OrderedGroup_Ocomm__monoid__add(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Osemiring__0__cancel_4) ).

fof(c_0_366,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Osemiring__0__cancel(X54)
      | class_HOL_Otimes(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Osemiring__0__cancel_3) ).

fof(c_0_367,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Osemiring__0__cancel(X54)
      | class_OrderedGroup_Osemigroup__mult(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Osemiring__0__cancel_2) ).

fof(c_0_368,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Osemiring__0__cancel(X54)
      | class_OrderedGroup_Ocancel__semigroup__add(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Osemiring__0__cancel_10) ).

fof(c_0_369,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Osemiring__0__cancel(X54)
      | class_Ring__and__Field_Osemiring(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Osemiring__0__cancel_1) ).

fof(c_0_370,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Osemiring__0__cancel(X54)
      | class_Ring__and__Field_Osemiring__0(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Osemiring__0__cancel_0) ).

fof(c_0_371,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Osemiring__0(X54)
      | class_HOL_Ozero(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Osemiring__0_7) ).

fof(c_0_372,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Osemiring__0(X54)
      | class_OrderedGroup_Ocomm__monoid__add(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Osemiring__0_6) ).

fof(c_0_373,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Osemiring__0(X54)
      | class_HOL_Otimes(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Osemiring__0_5) ).

fof(c_0_374,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Osemiring__0(X54)
      | class_OrderedGroup_Osemigroup__mult(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Osemiring__0_4) ).

fof(c_0_375,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Osemiring__0(X54)
      | class_HOL_Oplus(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Osemiring__0_3) ).

fof(c_0_376,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Osemiring__0(X54)
      | class_OrderedGroup_Osemigroup__add(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Osemiring__0_2) ).

fof(c_0_377,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Osemiring__0(X54)
      | class_OrderedGroup_Oab__semigroup__add(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Osemiring__0_1) ).

fof(c_0_378,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Osemiring__0(X54)
      | class_Ring__and__Field_Osemiring(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Osemiring__0_0) ).

fof(c_0_379,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Osemiring(X54)
      | class_HOL_Otimes(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Osemiring_4) ).

fof(c_0_380,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Osemiring(X54)
      | class_OrderedGroup_Osemigroup__mult(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Osemiring_3) ).

fof(c_0_381,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Osemiring(X54)
      | class_HOL_Oplus(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Osemiring_2) ).

fof(c_0_382,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Osemiring(X54)
      | class_OrderedGroup_Osemigroup__add(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Osemiring_1) ).

fof(c_0_383,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Osemiring(X54)
      | class_OrderedGroup_Oab__semigroup__add(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Osemiring_0) ).

fof(c_0_384,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oring__1(X54)
      | class_HOL_Otimes(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oring__1_9) ).

fof(c_0_385,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oring__1(X54)
      | class_OrderedGroup_Osemigroup__mult(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oring__1_8) ).

fof(c_0_386,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oring__1(X54)
      | class_Ring__and__Field_Osemiring(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oring__1_7) ).

fof(c_0_387,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oring__1(X54)
      | class_Ring__and__Field_Osemiring__0(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oring__1_6) ).

fof(c_0_388,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oring__1(X54)
      | class_OrderedGroup_Ocancel__semigroup__add(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oring__1_5) ).

fof(c_0_389,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oring__1(X54)
      | class_OrderedGroup_Ocancel__ab__semigroup__add(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oring__1_4) ).

fof(c_0_390,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oring__1(X54)
      | class_Ring__and__Field_Osemiring__0__cancel(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oring__1_3) ).

fof(c_0_391,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oring__1(X54)
      | class_HOL_Ominus(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oring__1_2) ).

fof(c_0_392,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oring__1(X54)
      | class_Ring__and__Field_Osemiring__1__cancel(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oring__1_19) ).

fof(c_0_393,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oring__1(X54)
      | class_HOL_Oone(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oring__1_18) ).

fof(c_0_394,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oring__1(X54)
      | class_OrderedGroup_Omonoid__mult(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oring__1_17) ).

fof(c_0_395,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oring__1(X54)
      | class_Ring__and__Field_Oaxclass__0__neq__1(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oring__1_16) ).

fof(c_0_396,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oring__1(X54)
      | class_Ring__and__Field_Osemiring__1(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oring__1_15) ).

fof(c_0_397,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oring__1(X54)
      | class_HOL_Ozero(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oring__1_14) ).

fof(c_0_398,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oring__1(X54)
      | class_HOL_Oplus(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oring__1_13) ).

fof(c_0_399,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oring__1(X54)
      | class_OrderedGroup_Osemigroup__add(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oring__1_12) ).

fof(c_0_400,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oring__1(X54)
      | class_OrderedGroup_Oab__semigroup__add(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oring__1_11) ).

fof(c_0_401,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oring__1(X54)
      | class_OrderedGroup_Ocomm__monoid__add(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oring__1_10) ).

fof(c_0_402,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oring__1(X54)
      | class_OrderedGroup_Oab__group__add(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oring__1_1) ).

fof(c_0_403,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oring__1(X54)
      | class_Ring__and__Field_Oring(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oring__1_0) ).

fof(c_0_404,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oring(X54)
      | class_HOL_Ozero(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oring_9) ).

fof(c_0_405,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oring(X54)
      | class_OrderedGroup_Ocomm__monoid__add(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oring_8) ).

fof(c_0_406,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oring(X54)
      | class_HOL_Ominus(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oring_7) ).

fof(c_0_407,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oring(X54)
      | class_OrderedGroup_Oab__group__add(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oring_6) ).

fof(c_0_408,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oring(X54)
      | class_HOL_Otimes(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oring_5) ).

fof(c_0_409,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oring(X54)
      | class_OrderedGroup_Osemigroup__mult(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oring_4) ).

fof(c_0_410,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oring(X54)
      | class_HOL_Oplus(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oring_3) ).

fof(c_0_411,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oring(X54)
      | class_OrderedGroup_Osemigroup__add(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oring_2) ).

fof(c_0_412,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oring(X54)
      | class_Ring__and__Field_Osemiring__0(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oring_13) ).

fof(c_0_413,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oring(X54)
      | class_Ring__and__Field_Osemiring__0__cancel(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oring_12) ).

fof(c_0_414,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oring(X54)
      | class_OrderedGroup_Ocancel__semigroup__add(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oring_11) ).

fof(c_0_415,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oring(X54)
      | class_OrderedGroup_Ocancel__ab__semigroup__add(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oring_10) ).

fof(c_0_416,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oring(X54)
      | class_OrderedGroup_Oab__semigroup__add(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oring_1) ).

fof(c_0_417,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oring(X54)
      | class_Ring__and__Field_Osemiring(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oring_0) ).

fof(c_0_418,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Opordered__semiring(X54)
      | class_OrderedGroup_Opordered__ab__semigroup__add(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Opordered__semiring_9) ).

fof(c_0_419,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Opordered__semiring(X54)
      | class_HOL_Ozero(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Opordered__semiring_8) ).

fof(c_0_420,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Opordered__semiring(X54)
      | class_HOL_Oplus(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Opordered__semiring_7) ).

fof(c_0_421,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Opordered__semiring(X54)
      | class_OrderedGroup_Osemigroup__add(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Opordered__semiring_6) ).

fof(c_0_422,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Opordered__semiring(X54)
      | class_OrderedGroup_Oab__semigroup__add(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Opordered__semiring_5) ).

fof(c_0_423,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Opordered__semiring(X54)
      | class_OrderedGroup_Ocomm__monoid__add(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Opordered__semiring_4) ).

fof(c_0_424,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Opordered__semiring(X54)
      | class_HOL_Otimes(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Opordered__semiring_3) ).

fof(c_0_425,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Opordered__semiring(X54)
      | class_OrderedGroup_Osemigroup__mult(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Opordered__semiring_2) ).

fof(c_0_426,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Opordered__semiring(X54)
      | class_Orderings_Oord(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Opordered__semiring_11) ).

fof(c_0_427,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Opordered__semiring(X54)
      | class_Orderings_Oorder(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Opordered__semiring_10) ).

fof(c_0_428,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Opordered__semiring(X54)
      | class_Ring__and__Field_Osemiring(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Opordered__semiring_1) ).

fof(c_0_429,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Opordered__semiring(X54)
      | class_Ring__and__Field_Osemiring__0(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Opordered__semiring_0) ).

fof(c_0_430,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Opordered__ring(X54)
      | class_HOL_Otimes(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Opordered__ring_9) ).

fof(c_0_431,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Opordered__ring(X54)
      | class_OrderedGroup_Osemigroup__mult(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Opordered__ring_8) ).

fof(c_0_432,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Opordered__ring(X54)
      | class_Ring__and__Field_Osemiring(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Opordered__ring_7) ).

fof(c_0_433,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Opordered__ring(X54)
      | class_Ring__and__Field_Osemiring__0(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Opordered__ring_6) ).

fof(c_0_434,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Opordered__ring(X54)
      | class_OrderedGroup_Ocancel__semigroup__add(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Opordered__ring_5) ).

fof(c_0_435,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Opordered__ring(X54)
      | class_OrderedGroup_Ocancel__ab__semigroup__add(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Opordered__ring_4) ).

fof(c_0_436,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Opordered__ring(X54)
      | class_Ring__and__Field_Osemiring__0__cancel(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Opordered__ring_3) ).

fof(c_0_437,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Opordered__ring(X54)
      | class_Ring__and__Field_Opordered__cancel__semiring(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Opordered__ring_22) ).

fof(c_0_438,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Opordered__ring(X54)
      | class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Opordered__ring_21) ).

fof(c_0_439,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Opordered__ring(X54)
      | class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Opordered__ring_20) ).

fof(c_0_440,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Opordered__ring(X54)
      | class_HOL_Ominus(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Opordered__ring_2) ).

fof(c_0_441,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Opordered__ring(X54)
      | class_OrderedGroup_Opordered__ab__group__add(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Opordered__ring_19) ).

fof(c_0_442,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Opordered__ring(X54)
      | class_Orderings_Oord(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Opordered__ring_18) ).

fof(c_0_443,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Opordered__ring(X54)
      | class_Orderings_Oorder(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Opordered__ring_17) ).

fof(c_0_444,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Opordered__ring(X54)
      | class_OrderedGroup_Opordered__ab__semigroup__add(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Opordered__ring_16) ).

fof(c_0_445,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Opordered__ring(X54)
      | class_Ring__and__Field_Opordered__semiring(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Opordered__ring_15) ).

fof(c_0_446,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Opordered__ring(X54)
      | class_HOL_Ozero(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Opordered__ring_14) ).

fof(c_0_447,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Opordered__ring(X54)
      | class_HOL_Oplus(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Opordered__ring_13) ).

fof(c_0_448,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Opordered__ring(X54)
      | class_OrderedGroup_Osemigroup__add(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Opordered__ring_12) ).

fof(c_0_449,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Opordered__ring(X54)
      | class_OrderedGroup_Oab__semigroup__add(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Opordered__ring_11) ).

fof(c_0_450,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Opordered__ring(X54)
      | class_OrderedGroup_Ocomm__monoid__add(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Opordered__ring_10) ).

fof(c_0_451,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Opordered__ring(X54)
      | class_OrderedGroup_Oab__group__add(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Opordered__ring_1) ).

fof(c_0_452,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Opordered__ring(X54)
      | class_Ring__and__Field_Oring(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Opordered__ring_0) ).

fof(c_0_453,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Opordered__comm__semiring(X54)
      | class_OrderedGroup_Osemigroup__add(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Opordered__comm__semiring_9) ).

fof(c_0_454,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Opordered__comm__semiring(X54)
      | class_OrderedGroup_Oab__semigroup__add(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Opordered__comm__semiring_8) ).

fof(c_0_455,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Opordered__comm__semiring(X54)
      | class_OrderedGroup_Ocomm__monoid__add(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Opordered__comm__semiring_7) ).

fof(c_0_456,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Opordered__comm__semiring(X54)
      | class_HOL_Otimes(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Opordered__comm__semiring_6) ).

fof(c_0_457,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Opordered__comm__semiring(X54)
      | class_OrderedGroup_Osemigroup__mult(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Opordered__comm__semiring_5) ).

fof(c_0_458,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Opordered__comm__semiring(X54)
      | class_Ring__and__Field_Osemiring(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Opordered__comm__semiring_4) ).

fof(c_0_459,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Opordered__comm__semiring(X54)
      | class_Ring__and__Field_Osemiring__0(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Opordered__comm__semiring_3) ).

fof(c_0_460,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Opordered__comm__semiring(X54)
      | class_OrderedGroup_Oab__semigroup__mult(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Opordered__comm__semiring_2) ).

fof(c_0_461,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Opordered__comm__semiring(X54)
      | class_Ring__and__Field_Opordered__semiring(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Opordered__comm__semiring_15) ).

fof(c_0_462,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Opordered__comm__semiring(X54)
      | class_Orderings_Oord(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Opordered__comm__semiring_14) ).

fof(c_0_463,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Opordered__comm__semiring(X54)
      | class_Orderings_Oorder(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Opordered__comm__semiring_13) ).

fof(c_0_464,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Opordered__comm__semiring(X54)
      | class_OrderedGroup_Opordered__ab__semigroup__add(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Opordered__comm__semiring_12) ).

fof(c_0_465,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Opordered__comm__semiring(X54)
      | class_HOL_Ozero(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Opordered__comm__semiring_11) ).

fof(c_0_466,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Opordered__comm__semiring(X54)
      | class_HOL_Oplus(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Opordered__comm__semiring_10) ).

fof(c_0_467,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Opordered__comm__semiring(X54)
      | class_Ring__and__Field_Ocomm__semiring(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Opordered__comm__semiring_1) ).

fof(c_0_468,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Opordered__comm__semiring(X54)
      | class_Ring__and__Field_Ocomm__semiring__0(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Opordered__comm__semiring_0) ).

fof(c_0_469,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Opordered__comm__ring(X54)
      | class_Ring__and__Field_Osemiring__0(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Opordered__comm__ring_9) ).

fof(c_0_470,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Opordered__comm__ring(X54)
      | class_Ring__and__Field_Osemiring__0__cancel(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Opordered__comm__ring_8) ).

fof(c_0_471,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Opordered__comm__ring(X54)
      | class_OrderedGroup_Oab__semigroup__mult(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Opordered__comm__ring_7) ).

fof(c_0_472,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Opordered__comm__ring(X54)
      | class_Ring__and__Field_Ocomm__semiring(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Opordered__comm__ring_6) ).

fof(c_0_473,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Opordered__comm__ring(X54)
      | class_Ring__and__Field_Ocomm__semiring__0(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Opordered__comm__ring_5) ).

fof(c_0_474,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Opordered__comm__ring(X54)
      | class_Ring__and__Field_Ocomm__semiring__0__cancel(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Opordered__comm__ring_4) ).

fof(c_0_475,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Opordered__comm__ring(X54)
      | class_HOL_Ominus(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Opordered__comm__ring_3) ).

fof(c_0_476,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Opordered__comm__ring(X54)
      | class_Orderings_Oord(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Opordered__comm__ring_24) ).

fof(c_0_477,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Opordered__comm__ring(X54)
      | class_Orderings_Oorder(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Opordered__comm__ring_23) ).

fof(c_0_478,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Opordered__comm__ring(X54)
      | class_OrderedGroup_Opordered__ab__semigroup__add(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Opordered__comm__ring_22) ).

fof(c_0_479,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Opordered__comm__ring(X54)
      | class_Ring__and__Field_Opordered__semiring(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Opordered__comm__ring_21) ).

fof(c_0_480,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Opordered__comm__ring(X54)
      | class_Ring__and__Field_Opordered__comm__semiring(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Opordered__comm__ring_20) ).

fof(c_0_481,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Opordered__comm__ring(X54)
      | class_OrderedGroup_Oab__group__add(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Opordered__comm__ring_2) ).

fof(c_0_482,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Opordered__comm__ring(X54)
      | class_HOL_Oplus(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Opordered__comm__ring_19) ).

fof(c_0_483,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Opordered__comm__ring(X54)
      | class_OrderedGroup_Osemigroup__add(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Opordered__comm__ring_18) ).

fof(c_0_484,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Opordered__comm__ring(X54)
      | class_OrderedGroup_Ocancel__semigroup__add(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Opordered__comm__ring_17) ).

fof(c_0_485,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Opordered__comm__ring(X54)
      | class_OrderedGroup_Oab__semigroup__add(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Opordered__comm__ring_16) ).

fof(c_0_486,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Opordered__comm__ring(X54)
      | class_OrderedGroup_Ocancel__ab__semigroup__add(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Opordered__comm__ring_15) ).

fof(c_0_487,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Opordered__comm__ring(X54)
      | class_HOL_Ozero(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Opordered__comm__ring_14) ).

fof(c_0_488,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Opordered__comm__ring(X54)
      | class_OrderedGroup_Ocomm__monoid__add(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Opordered__comm__ring_13) ).

fof(c_0_489,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Opordered__comm__ring(X54)
      | class_HOL_Otimes(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Opordered__comm__ring_12) ).

fof(c_0_490,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Opordered__comm__ring(X54)
      | class_OrderedGroup_Osemigroup__mult(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Opordered__comm__ring_11) ).

fof(c_0_491,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Opordered__comm__ring(X54)
      | class_Ring__and__Field_Osemiring(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Opordered__comm__ring_10) ).

fof(c_0_492,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Opordered__comm__ring(X54)
      | class_Ring__and__Field_Oring(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Opordered__comm__ring_1) ).

fof(c_0_493,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Opordered__comm__ring(X54)
      | class_Ring__and__Field_Ocomm__ring(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Opordered__comm__ring_0) ).

fof(c_0_494,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Opordered__cancel__semiring(X54)
      | class_OrderedGroup_Osemigroup__add(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Opordered__cancel__semiring_9) ).

fof(c_0_495,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Opordered__cancel__semiring(X54)
      | class_OrderedGroup_Oab__semigroup__add(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Opordered__cancel__semiring_8) ).

fof(c_0_496,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Opordered__cancel__semiring(X54)
      | class_OrderedGroup_Opordered__ab__semigroup__add(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Opordered__cancel__semiring_7) ).

fof(c_0_497,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Opordered__cancel__semiring(X54)
      | class_HOL_Ozero(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Opordered__cancel__semiring_6) ).

fof(c_0_498,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Opordered__cancel__semiring(X54)
      | class_OrderedGroup_Ocomm__monoid__add(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Opordered__cancel__semiring_5) ).

fof(c_0_499,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Opordered__cancel__semiring(X54)
      | class_HOL_Otimes(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Opordered__cancel__semiring_4) ).

fof(c_0_500,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Opordered__cancel__semiring(X54)
      | class_OrderedGroup_Osemigroup__mult(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Opordered__cancel__semiring_3) ).

fof(c_0_501,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Opordered__cancel__semiring(X54)
      | class_Ring__and__Field_Osemiring(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Opordered__cancel__semiring_2) ).

fof(c_0_502,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Opordered__cancel__semiring(X54)
      | class_Ring__and__Field_Osemiring__0__cancel(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Opordered__cancel__semiring_15) ).

fof(c_0_503,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Opordered__cancel__semiring(X54)
      | class_OrderedGroup_Ocancel__semigroup__add(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Opordered__cancel__semiring_14) ).

fof(c_0_504,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Opordered__cancel__semiring(X54)
      | class_OrderedGroup_Ocancel__ab__semigroup__add(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Opordered__cancel__semiring_13) ).

fof(c_0_505,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Opordered__cancel__semiring(X54)
      | class_Orderings_Oord(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Opordered__cancel__semiring_12) ).

fof(c_0_506,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Opordered__cancel__semiring(X54)
      | class_Orderings_Oorder(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Opordered__cancel__semiring_11) ).

fof(c_0_507,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Opordered__cancel__semiring(X54)
      | class_HOL_Oplus(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Opordered__cancel__semiring_10) ).

fof(c_0_508,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Opordered__cancel__semiring(X54)
      | class_Ring__and__Field_Osemiring__0(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Opordered__cancel__semiring_1) ).

fof(c_0_509,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Opordered__cancel__semiring(X54)
      | class_Ring__and__Field_Opordered__semiring(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Opordered__cancel__semiring_0) ).

fof(c_0_510,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X54)
      | class_HOL_Ozero(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_9) ).

fof(c_0_511,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X54)
      | class_OrderedGroup_Ocomm__monoid__add(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_8) ).

fof(c_0_512,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X54)
      | class_HOL_Otimes(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_7) ).

fof(c_0_513,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X54)
      | class_OrderedGroup_Osemigroup__mult(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_6) ).

fof(c_0_514,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X54)
      | class_Ring__and__Field_Osemiring(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_5) ).

fof(c_0_515,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X54)
      | class_Ring__and__Field_Osemiring__0(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_4) ).

fof(c_0_516,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X54)
      | class_OrderedGroup_Oab__semigroup__mult(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_3) ).

fof(c_0_517,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X54)
      | class_Ring__and__Field_Osemiring__0__cancel(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_20) ).

fof(c_0_518,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X54)
      | class_Ring__and__Field_Ocomm__semiring(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_2) ).

fof(c_0_519,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X54)
      | class_Ring__and__Field_Opordered__cancel__semiring(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_19) ).

fof(c_0_520,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X54)
      | class_Ring__and__Field_Opordered__semiring(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_18) ).

fof(c_0_521,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X54)
      | class_OrderedGroup_Ocancel__semigroup__add(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_17) ).

fof(c_0_522,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X54)
      | class_OrderedGroup_Ocancel__ab__semigroup__add(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_16) ).

fof(c_0_523,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X54)
      | class_Orderings_Oord(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_15) ).

fof(c_0_524,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X54)
      | class_Orderings_Oorder(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_14) ).

fof(c_0_525,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X54)
      | class_HOL_Oplus(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_13) ).

fof(c_0_526,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X54)
      | class_OrderedGroup_Osemigroup__add(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_12) ).

fof(c_0_527,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X54)
      | class_OrderedGroup_Oab__semigroup__add(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_11) ).

fof(c_0_528,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X54)
      | class_OrderedGroup_Opordered__ab__semigroup__add(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_10) ).

fof(c_0_529,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X54)
      | class_Ring__and__Field_Ocomm__semiring__0(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_1) ).

fof(c_0_530,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X54)
      | class_Ring__and__Field_Opordered__comm__semiring(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_0) ).

fof(c_0_531,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X54)
      | class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__semiring__strict_9) ).

fof(c_0_532,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X54)
      | class_HOL_Ozero(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__semiring__strict_8) ).

fof(c_0_533,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X54)
      | class_HOL_Oplus(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__semiring__strict_7) ).

fof(c_0_534,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X54)
      | class_OrderedGroup_Osemigroup__add(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__semiring__strict_6) ).

fof(c_0_535,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X54)
      | class_OrderedGroup_Oab__semigroup__add(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__semiring__strict_5) ).

fof(c_0_536,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X54)
      | class_OrderedGroup_Ocomm__monoid__add(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__semiring__strict_4) ).

fof(c_0_537,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X54)
      | class_HOL_Otimes(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__semiring__strict_3) ).

fof(c_0_538,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X54)
      | class_Ring__and__Field_Opordered__semiring(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__semiring__strict_23) ).

fof(c_0_539,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X54)
      | class_Ring__and__Field_Opordered__cancel__semiring(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__semiring__strict_22) ).

fof(c_0_540,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X54)
      | class_Ring__and__Field_Osemiring__0__cancel(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__semiring__strict_21) ).

fof(c_0_541,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X54)
      | class_OrderedGroup_Ocancel__semigroup__add(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__semiring__strict_20) ).

fof(c_0_542,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X54)
      | class_OrderedGroup_Osemigroup__mult(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__semiring__strict_2) ).

fof(c_0_543,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X54)
      | class_OrderedGroup_Ocancel__ab__semigroup__add(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__semiring__strict_19) ).

fof(c_0_544,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X54)
      | class_Orderings_Oord(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__semiring__strict_18) ).

fof(c_0_545,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X54)
      | class_Orderings_Oorder(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__semiring__strict_17) ).

fof(c_0_546,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X54)
      | class_OrderedGroup_Opordered__ab__semigroup__add(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__semiring__strict_16) ).

fof(c_0_547,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X54)
      | class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__semiring__strict_15) ).

fof(c_0_548,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X54)
      | class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__semiring__strict_14) ).

fof(c_0_549,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X54)
      | class_LOrder_Omeet__semilorder(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__semiring__strict_13) ).

fof(c_0_550,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X54)
      | class_LOrder_Ojoin__semilorder(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__semiring__strict_12) ).

fof(c_0_551,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X54)
      | class_LOrder_Olorder(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__semiring__strict_11) ).

fof(c_0_552,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X54)
      | class_Orderings_Olinorder(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__semiring__strict_10) ).

fof(c_0_553,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X54)
      | class_Ring__and__Field_Osemiring(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__semiring__strict_1) ).

fof(c_0_554,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X54)
      | class_Ring__and__Field_Osemiring__0(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__semiring__strict_0) ).

fof(c_0_555,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X54)
      | class_Ring__and__Field_Ocomm__semiring__0(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__semidom_9) ).

fof(c_0_556,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X54)
      | class_Ring__and__Field_Ocomm__semiring__0__cancel(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__semidom_8) ).

fof(c_0_557,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X54)
      | class_HOL_Oone(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__semidom_7) ).

fof(c_0_558,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X54)
      | class_OrderedGroup_Omonoid__mult(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__semidom_6) ).

fof(c_0_559,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X54)
      | class_Ring__and__Field_Oaxclass__0__neq__1(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__semidom_5) ).

fof(c_0_560,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X54)
      | class_Ring__and__Field_Osemiring__1(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__semidom_4) ).

fof(c_0_561,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X54)
      | class_Orderings_Oord(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__semidom_39) ).

fof(c_0_562,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X54)
      | class_Orderings_Oorder(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__semidom_38) ).

fof(c_0_563,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X54)
      | class_OrderedGroup_Opordered__ab__semigroup__add(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__semidom_37) ).

fof(c_0_564,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X54)
      | class_Ring__and__Field_Opordered__semiring(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__semidom_36) ).

fof(c_0_565,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X54)
      | class_Ring__and__Field_Opordered__comm__semiring(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__semidom_35) ).

fof(c_0_566,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X54)
      | class_Ring__and__Field_Opordered__cancel__semiring(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__semidom_34) ).

fof(c_0_567,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X54)
      | class_Ring__and__Field_Opordered__cancel__comm__semiring(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__semidom_33) ).

fof(c_0_568,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X54)
      | class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__semidom_32) ).

fof(c_0_569,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X54)
      | class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__semidom_31) ).

fof(c_0_570,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X54)
      | class_LOrder_Omeet__semilorder(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__semidom_30) ).

fof(c_0_571,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X54)
      | class_Ring__and__Field_Osemiring__1__cancel(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__semidom_3) ).

fof(c_0_572,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X54)
      | class_LOrder_Ojoin__semilorder(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__semidom_29) ).

fof(c_0_573,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X54)
      | class_LOrder_Olorder(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__semidom_28) ).

fof(c_0_574,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X54)
      | class_Orderings_Olinorder(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__semidom_27) ).

fof(c_0_575,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X54)
      | class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__semidom_26) ).

fof(c_0_576,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X54)
      | class_Ring__and__Field_Oordered__semiring__strict(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__semidom_25) ).

fof(c_0_577,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X54)
      | class_Ring__and__Field_Oordered__comm__semiring__strict(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__semidom_24) ).

fof(c_0_578,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X54)
      | class_HOL_Oplus(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__semidom_23) ).

fof(c_0_579,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X54)
      | class_OrderedGroup_Osemigroup__add(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__semidom_22) ).

fof(c_0_580,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X54)
      | class_OrderedGroup_Ocancel__semigroup__add(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__semidom_21) ).

fof(c_0_581,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X54)
      | class_OrderedGroup_Oab__semigroup__add(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__semidom_20) ).

fof(c_0_582,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X54)
      | class_OrderedGroup_Ocomm__monoid__mult(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__semidom_2) ).

fof(c_0_583,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X54)
      | class_OrderedGroup_Ocancel__ab__semigroup__add(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__semidom_19) ).

fof(c_0_584,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X54)
      | class_HOL_Ozero(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__semidom_18) ).

fof(c_0_585,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X54)
      | class_OrderedGroup_Ocomm__monoid__add(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__semidom_17) ).

fof(c_0_586,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X54)
      | class_HOL_Otimes(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__semidom_16) ).

fof(c_0_587,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X54)
      | class_OrderedGroup_Osemigroup__mult(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__semidom_15) ).

fof(c_0_588,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X54)
      | class_Ring__and__Field_Osemiring(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__semidom_14) ).

fof(c_0_589,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X54)
      | class_Ring__and__Field_Osemiring__0(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__semidom_13) ).

fof(c_0_590,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X54)
      | class_Ring__and__Field_Osemiring__0__cancel(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__semidom_12) ).

fof(c_0_591,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X54)
      | class_OrderedGroup_Oab__semigroup__mult(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__semidom_11) ).

fof(c_0_592,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X54)
      | class_Ring__and__Field_Ocomm__semiring(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__semidom_10) ).

fof(c_0_593,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X54)
      | class_Ring__and__Field_Ocomm__semiring__1(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__semidom_1) ).

fof(c_0_594,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X54)
      | class_Ring__and__Field_Ocomm__semiring__1__cancel(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__semidom_0) ).

fof(c_0_595,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X54)
      | class_HOL_Otimes(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__ring__strict_9) ).

fof(c_0_596,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X54)
      | class_OrderedGroup_Osemigroup__mult(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__ring__strict_8) ).

fof(c_0_597,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X54)
      | class_Ring__and__Field_Osemiring(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__ring__strict_7) ).

fof(c_0_598,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X54)
      | class_Ring__and__Field_Osemiring__0(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__ring__strict_6) ).

fof(c_0_599,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X54)
      | class_OrderedGroup_Ocancel__semigroup__add(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__ring__strict_5) ).

fof(c_0_600,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X54)
      | class_OrderedGroup_Ocancel__ab__semigroup__add(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__ring__strict_4) ).

fof(c_0_601,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X54)
      | class_Ring__and__Field_Oaxclass__no__zero__divisors(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__ring__strict_36) ).

fof(c_0_602,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X54)
      | class_OrderedGroup_Olordered__ab__group__join(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__ring__strict_35) ).

fof(c_0_603,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X54)
      | class_OrderedGroup_Olordered__ab__group__meet(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__ring__strict_34) ).

fof(c_0_604,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X54)
      | class_OrderedGroup_Olordered__ab__group__abs(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__ring__strict_33) ).

fof(c_0_605,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X54)
      | class_Ring__and__Field_Opordered__ring(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__ring__strict_32) ).

fof(c_0_606,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X54)
      | class_Ring__and__Field_Olordered__ring(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__ring__strict_31) ).

fof(c_0_607,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X54)
      | class_OrderedGroup_Opordered__ab__group__add(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__ring__strict_30) ).

fof(c_0_608,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X54)
      | class_Ring__and__Field_Osemiring__0__cancel(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__ring__strict_3) ).

fof(c_0_609,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X54)
      | class_OrderedGroup_Olordered__ab__group(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__ring__strict_29) ).

fof(c_0_610,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X54)
      | class_Ring__and__Field_Oaxclass__abs__if(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__ring__strict_28) ).

fof(c_0_611,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X54)
      | class_Orderings_Oord(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__ring__strict_27) ).

fof(c_0_612,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X54)
      | class_Orderings_Oorder(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__ring__strict_26) ).

fof(c_0_613,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X54)
      | class_OrderedGroup_Opordered__ab__semigroup__add(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__ring__strict_25) ).

fof(c_0_614,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X54)
      | class_Ring__and__Field_Opordered__semiring(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__ring__strict_24) ).

fof(c_0_615,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X54)
      | class_Ring__and__Field_Opordered__cancel__semiring(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__ring__strict_23) ).

fof(c_0_616,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X54)
      | class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__ring__strict_22) ).

fof(c_0_617,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X54)
      | class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__ring__strict_21) ).

fof(c_0_618,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X54)
      | class_LOrder_Omeet__semilorder(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__ring__strict_20) ).

fof(c_0_619,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X54)
      | class_HOL_Ominus(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__ring__strict_2) ).

fof(c_0_620,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X54)
      | class_LOrder_Ojoin__semilorder(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__ring__strict_19) ).

fof(c_0_621,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X54)
      | class_LOrder_Olorder(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__ring__strict_18) ).

fof(c_0_622,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X54)
      | class_Orderings_Olinorder(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__ring__strict_17) ).

fof(c_0_623,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X54)
      | class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__ring__strict_16) ).

fof(c_0_624,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X54)
      | class_Ring__and__Field_Oordered__semiring__strict(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__ring__strict_15) ).

fof(c_0_625,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X54)
      | class_HOL_Ozero(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__ring__strict_14) ).

fof(c_0_626,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X54)
      | class_HOL_Oplus(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__ring__strict_13) ).

fof(c_0_627,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X54)
      | class_OrderedGroup_Osemigroup__add(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__ring__strict_12) ).

fof(c_0_628,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X54)
      | class_OrderedGroup_Oab__semigroup__add(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__ring__strict_11) ).

fof(c_0_629,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X54)
      | class_OrderedGroup_Ocomm__monoid__add(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__ring__strict_10) ).

fof(c_0_630,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X54)
      | class_OrderedGroup_Oab__group__add(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__ring__strict_1) ).

fof(c_0_631,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X54)
      | class_Ring__and__Field_Oring(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__ring__strict_0) ).

fof(c_0_632,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__idom(X54)
      | class_Ring__and__Field_Osemiring__1__cancel(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__idom_9) ).

fof(c_0_633,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__idom(X54)
      | class_OrderedGroup_Ocomm__monoid__mult(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__idom_8) ).

fof(c_0_634,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__idom(X54)
      | class_Ring__and__Field_Ocomm__semiring__1(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__idom_7) ).

fof(c_0_635,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__idom(X54)
      | class_Ring__and__Field_Ocomm__semiring__1__cancel(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__idom_6) ).

fof(c_0_636,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__idom(X54)
      | class_Ring__and__Field_Oidom(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__idom_57) ).

fof(c_0_637,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__idom(X54)
      | class_Ring__and__Field_Oaxclass__no__zero__divisors(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__idom_56) ).

fof(c_0_638,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__idom(X54)
      | class_Ring__and__Field_Oordered__semidom(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__idom_55) ).

fof(c_0_639,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__idom(X54)
      | class_OrderedGroup_Opordered__ab__group__add(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__idom_54) ).

fof(c_0_640,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__idom(X54)
      | class_OrderedGroup_Olordered__ab__group(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__idom_53) ).

fof(c_0_641,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__idom(X54)
      | class_OrderedGroup_Olordered__ab__group__join(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__idom_52) ).

fof(c_0_642,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__idom(X54)
      | class_OrderedGroup_Olordered__ab__group__meet(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__idom_51) ).

fof(c_0_643,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__idom(X54)
      | class_OrderedGroup_Olordered__ab__group__abs(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__idom_50) ).

fof(c_0_644,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__idom(X54)
      | class_HOL_Ominus(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__idom_5) ).

fof(c_0_645,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__idom(X54)
      | class_Ring__and__Field_Opordered__ring(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__idom_49) ).

fof(c_0_646,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__idom(X54)
      | class_Ring__and__Field_Olordered__ring(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__idom_48) ).

fof(c_0_647,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__idom(X54)
      | class_Ring__and__Field_Oordered__ring__strict(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__idom_47) ).

fof(c_0_648,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__idom(X54)
      | class_Ring__and__Field_Oaxclass__abs__if(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__idom_46) ).

fof(c_0_649,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__idom(X54)
      | class_Orderings_Oord(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__idom_45) ).

fof(c_0_650,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__idom(X54)
      | class_Orderings_Oorder(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__idom_44) ).

fof(c_0_651,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__idom(X54)
      | class_OrderedGroup_Opordered__ab__semigroup__add(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__idom_43) ).

fof(c_0_652,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__idom(X54)
      | class_Ring__and__Field_Opordered__semiring(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__idom_42) ).

fof(c_0_653,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__idom(X54)
      | class_Ring__and__Field_Opordered__comm__semiring(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__idom_41) ).

fof(c_0_654,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__idom(X54)
      | class_Ring__and__Field_Opordered__cancel__semiring(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__idom_40) ).

fof(c_0_655,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__idom(X54)
      | class_OrderedGroup_Oab__group__add(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__idom_4) ).

fof(c_0_656,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__idom(X54)
      | class_Ring__and__Field_Opordered__cancel__comm__semiring(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__idom_39) ).

fof(c_0_657,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__idom(X54)
      | class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__idom_38) ).

fof(c_0_658,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__idom(X54)
      | class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__idom_37) ).

fof(c_0_659,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__idom(X54)
      | class_LOrder_Omeet__semilorder(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__idom_36) ).

fof(c_0_660,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__idom(X54)
      | class_LOrder_Ojoin__semilorder(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__idom_35) ).

fof(c_0_661,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__idom(X54)
      | class_LOrder_Olorder(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__idom_34) ).

fof(c_0_662,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__idom(X54)
      | class_Orderings_Olinorder(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__idom_33) ).

fof(c_0_663,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__idom(X54)
      | class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__idom_32) ).

fof(c_0_664,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__idom(X54)
      | class_Ring__and__Field_Oordered__semiring__strict(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__idom_31) ).

fof(c_0_665,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__idom(X54)
      | class_Ring__and__Field_Oordered__comm__semiring__strict(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__idom_30) ).

fof(c_0_666,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__idom(X54)
      | class_Ring__and__Field_Oring(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__idom_3) ).

fof(c_0_667,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__idom(X54)
      | class_HOL_Oplus(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__idom_29) ).

fof(c_0_668,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__idom(X54)
      | class_OrderedGroup_Osemigroup__add(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__idom_28) ).

fof(c_0_669,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__idom(X54)
      | class_OrderedGroup_Ocancel__semigroup__add(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__idom_27) ).

fof(c_0_670,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__idom(X54)
      | class_OrderedGroup_Oab__semigroup__add(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__idom_26) ).

fof(c_0_671,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__idom(X54)
      | class_OrderedGroup_Ocancel__ab__semigroup__add(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__idom_25) ).

fof(c_0_672,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__idom(X54)
      | class_HOL_Ozero(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__idom_24) ).

fof(c_0_673,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__idom(X54)
      | class_OrderedGroup_Ocomm__monoid__add(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__idom_23) ).

fof(c_0_674,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__idom(X54)
      | class_HOL_Otimes(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__idom_22) ).

fof(c_0_675,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__idom(X54)
      | class_OrderedGroup_Osemigroup__mult(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__idom_21) ).

fof(c_0_676,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__idom(X54)
      | class_Ring__and__Field_Osemiring(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__idom_20) ).

fof(c_0_677,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__idom(X54)
      | class_Ring__and__Field_Oring__1(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__idom_2) ).

fof(c_0_678,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__idom(X54)
      | class_Ring__and__Field_Osemiring__0(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__idom_19) ).

fof(c_0_679,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__idom(X54)
      | class_Ring__and__Field_Osemiring__0__cancel(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__idom_18) ).

fof(c_0_680,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__idom(X54)
      | class_OrderedGroup_Oab__semigroup__mult(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__idom_17) ).

fof(c_0_681,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__idom(X54)
      | class_Ring__and__Field_Ocomm__semiring(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__idom_16) ).

fof(c_0_682,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__idom(X54)
      | class_Ring__and__Field_Ocomm__semiring__0(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__idom_15) ).

fof(c_0_683,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__idom(X54)
      | class_Ring__and__Field_Ocomm__semiring__0__cancel(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__idom_14) ).

fof(c_0_684,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__idom(X54)
      | class_HOL_Oone(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__idom_13) ).

fof(c_0_685,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__idom(X54)
      | class_OrderedGroup_Omonoid__mult(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__idom_12) ).

fof(c_0_686,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__idom(X54)
      | class_Ring__and__Field_Oaxclass__0__neq__1(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__idom_11) ).

fof(c_0_687,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__idom(X54)
      | class_Ring__and__Field_Osemiring__1(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__idom_10) ).

fof(c_0_688,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__idom(X54)
      | class_Ring__and__Field_Ocomm__ring(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__idom_1) ).

fof(c_0_689,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__idom(X54)
      | class_Ring__and__Field_Ocomm__ring__1(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__idom_0) ).

fof(c_0_690,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__field(X54)
      | class_Ring__and__Field_Ocomm__semiring__1__cancel(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__field_9) ).

fof(c_0_691,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__field(X54)
      | class_HOL_Ominus(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__field_8) ).

fof(c_0_692,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__field(X54)
      | class_OrderedGroup_Oab__group__add(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__field_7) ).

fof(c_0_693,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__field(X54)
      | class_Ring__and__Field_Oordered__semidom(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__field_60) ).

fof(c_0_694,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__field(X54)
      | class_Ring__and__Field_Oring(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__field_6) ).

fof(c_0_695,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__field(X54)
      | class_Orderings_Oord(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__field_59) ).

fof(c_0_696,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__field(X54)
      | class_Orderings_Oorder(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__field_58) ).

fof(c_0_697,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__field(X54)
      | class_OrderedGroup_Opordered__ab__semigroup__add(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__field_57) ).

fof(c_0_698,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__field(X54)
      | class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__field_56) ).

fof(c_0_699,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__field(X54)
      | class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__field_55) ).

fof(c_0_700,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__field(X54)
      | class_OrderedGroup_Opordered__ab__group__add(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__field_54) ).

fof(c_0_701,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__field(X54)
      | class_LOrder_Omeet__semilorder(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__field_53) ).

fof(c_0_702,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__field(X54)
      | class_LOrder_Ojoin__semilorder(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__field_52) ).

fof(c_0_703,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__field(X54)
      | class_LOrder_Olorder(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__field_51) ).

fof(c_0_704,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__field(X54)
      | class_OrderedGroup_Olordered__ab__group(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__field_50) ).

fof(c_0_705,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__field(X54)
      | class_Ring__and__Field_Oring__1(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__field_5) ).

fof(c_0_706,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__field(X54)
      | class_OrderedGroup_Olordered__ab__group__join(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__field_49) ).

fof(c_0_707,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__field(X54)
      | class_OrderedGroup_Olordered__ab__group__meet(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__field_48) ).

fof(c_0_708,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__field(X54)
      | class_OrderedGroup_Olordered__ab__group__abs(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__field_47) ).

fof(c_0_709,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__field(X54)
      | class_Ring__and__Field_Opordered__semiring(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__field_46) ).

fof(c_0_710,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__field(X54)
      | class_Ring__and__Field_Opordered__cancel__semiring(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__field_45) ).

fof(c_0_711,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__field(X54)
      | class_Ring__and__Field_Opordered__ring(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__field_44) ).

fof(c_0_712,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__field(X54)
      | class_Ring__and__Field_Olordered__ring(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__field_43) ).

fof(c_0_713,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__field(X54)
      | class_Ring__and__Field_Oaxclass__abs__if(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__field_42) ).

fof(c_0_714,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__field(X54)
      | class_Orderings_Olinorder(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__field_41) ).

fof(c_0_715,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__field(X54)
      | class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__field_40) ).

fof(c_0_716,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__field(X54)
      | class_Ring__and__Field_Ocomm__ring(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__field_4) ).

fof(c_0_717,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__field(X54)
      | class_Ring__and__Field_Oordered__semiring__strict(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__field_39) ).

fof(c_0_718,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__field(X54)
      | class_Ring__and__Field_Oordered__ring__strict(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__field_38) ).

fof(c_0_719,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__field(X54)
      | class_Ring__and__Field_Opordered__comm__semiring(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__field_37) ).

fof(c_0_720,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__field(X54)
      | class_Ring__and__Field_Opordered__cancel__comm__semiring(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__field_36) ).

fof(c_0_721,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__field(X54)
      | class_Ring__and__Field_Oordered__comm__semiring__strict(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__field_35) ).

fof(c_0_722,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__field(X54)
      | class_Ring__and__Field_Oordered__idom(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__field_34) ).

fof(c_0_723,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__field(X54)
      | class_HOL_Otimes(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__field_33) ).

fof(c_0_724,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__field(X54)
      | class_HOL_Ozero(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__field_32) ).

fof(c_0_725,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__field(X54)
      | class_Ring__and__Field_Oaxclass__no__zero__divisors(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__field_31) ).

fof(c_0_726,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__field(X54)
      | class_HOL_Oplus(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__field_30) ).

fof(c_0_727,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__field(X54)
      | class_Ring__and__Field_Ocomm__ring__1(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__field_3) ).

fof(c_0_728,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__field(X54)
      | class_OrderedGroup_Osemigroup__add(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__field_29) ).

fof(c_0_729,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__field(X54)
      | class_OrderedGroup_Ocancel__semigroup__add(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__field_28) ).

fof(c_0_730,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__field(X54)
      | class_OrderedGroup_Oab__semigroup__add(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__field_27) ).

fof(c_0_731,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__field(X54)
      | class_OrderedGroup_Ocancel__ab__semigroup__add(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__field_26) ).

fof(c_0_732,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__field(X54)
      | class_OrderedGroup_Ocomm__monoid__add(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__field_25) ).

fof(c_0_733,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__field(X54)
      | class_OrderedGroup_Osemigroup__mult(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__field_24) ).

fof(c_0_734,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__field(X54)
      | class_Ring__and__Field_Osemiring(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__field_23) ).

fof(c_0_735,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__field(X54)
      | class_Ring__and__Field_Osemiring__0(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__field_22) ).

fof(c_0_736,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__field(X54)
      | class_Ring__and__Field_Osemiring__0__cancel(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__field_21) ).

fof(c_0_737,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__field(X54)
      | class_OrderedGroup_Oab__semigroup__mult(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__field_20) ).

fof(c_0_738,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__field(X54)
      | class_Ring__and__Field_Oidom(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__field_2) ).

fof(c_0_739,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__field(X54)
      | class_Ring__and__Field_Ocomm__semiring(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__field_19) ).

fof(c_0_740,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__field(X54)
      | class_Ring__and__Field_Ocomm__semiring__0(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__field_18) ).

fof(c_0_741,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__field(X54)
      | class_Ring__and__Field_Ocomm__semiring__0__cancel(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__field_17) ).

fof(c_0_742,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__field(X54)
      | class_HOL_Oone(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__field_16) ).

fof(c_0_743,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__field(X54)
      | class_OrderedGroup_Omonoid__mult(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__field_15) ).

fof(c_0_744,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__field(X54)
      | class_Ring__and__Field_Oaxclass__0__neq__1(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__field_14) ).

fof(c_0_745,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__field(X54)
      | class_Ring__and__Field_Osemiring__1(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__field_13) ).

fof(c_0_746,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__field(X54)
      | class_Ring__and__Field_Osemiring__1__cancel(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__field_12) ).

fof(c_0_747,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__field(X54)
      | class_OrderedGroup_Ocomm__monoid__mult(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__field_11) ).

fof(c_0_748,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__field(X54)
      | class_Ring__and__Field_Ocomm__semiring__1(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__field_10) ).

fof(c_0_749,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__field(X54)
      | class_HOL_Oinverse(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__field_1) ).

fof(c_0_750,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__field(X54)
      | class_Ring__and__Field_Ofield(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__field_0) ).

fof(c_0_751,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X54)
      | class_OrderedGroup_Osemigroup__add(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_9) ).

fof(c_0_752,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X54)
      | class_OrderedGroup_Oab__semigroup__add(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_8) ).

fof(c_0_753,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X54)
      | class_OrderedGroup_Ocomm__monoid__add(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_7) ).

fof(c_0_754,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X54)
      | class_HOL_Otimes(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_6) ).

fof(c_0_755,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X54)
      | class_OrderedGroup_Osemigroup__mult(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_5) ).

fof(c_0_756,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X54)
      | class_Ring__and__Field_Osemiring(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_4) ).

fof(c_0_757,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X54)
      | class_Ring__and__Field_Osemiring__0(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_3) ).

fof(c_0_758,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X54)
      | class_Ring__and__Field_Opordered__comm__semiring(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_29) ).

fof(c_0_759,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X54)
      | class_Ring__and__Field_Opordered__cancel__comm__semiring(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_28) ).

fof(c_0_760,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X54)
      | class_Ring__and__Field_Opordered__semiring(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_27) ).

fof(c_0_761,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X54)
      | class_Ring__and__Field_Osemiring__0__cancel(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_26) ).

fof(c_0_762,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X54)
      | class_Ring__and__Field_Opordered__cancel__semiring(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_25) ).

fof(c_0_763,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X54)
      | class_Ring__and__Field_Oordered__semiring__strict(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_24) ).

fof(c_0_764,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X54)
      | class_OrderedGroup_Ocancel__semigroup__add(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_23) ).

fof(c_0_765,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X54)
      | class_OrderedGroup_Ocancel__ab__semigroup__add(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_22) ).

fof(c_0_766,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X54)
      | class_Orderings_Oord(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_21) ).

fof(c_0_767,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X54)
      | class_Orderings_Oorder(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_20) ).

fof(c_0_768,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X54)
      | class_OrderedGroup_Oab__semigroup__mult(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_2) ).

fof(c_0_769,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X54)
      | class_OrderedGroup_Opordered__ab__semigroup__add(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_19) ).

fof(c_0_770,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X54)
      | class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_18) ).

fof(c_0_771,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X54)
      | class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_17) ).

fof(c_0_772,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X54)
      | class_LOrder_Omeet__semilorder(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_16) ).

fof(c_0_773,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X54)
      | class_LOrder_Ojoin__semilorder(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_15) ).

fof(c_0_774,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X54)
      | class_LOrder_Olorder(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_14) ).

fof(c_0_775,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X54)
      | class_Orderings_Olinorder(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_13) ).

fof(c_0_776,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X54)
      | class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_12) ).

fof(c_0_777,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X54)
      | class_HOL_Ozero(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_11) ).

fof(c_0_778,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X54)
      | class_HOL_Oplus(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_10) ).

fof(c_0_779,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X54)
      | class_Ring__and__Field_Ocomm__semiring(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_1) ).

fof(c_0_780,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X54)
      | class_Ring__and__Field_Ocomm__semiring__0(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_0) ).

fof(c_0_781,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Olordered__ring(X54)
      | class_OrderedGroup_Opordered__ab__semigroup__add(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Olordered__ring_9) ).

fof(c_0_782,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Olordered__ring(X54)
      | class_Ring__and__Field_Opordered__semiring(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Olordered__ring_8) ).

fof(c_0_783,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Olordered__ring(X54)
      | class_Ring__and__Field_Opordered__cancel__semiring(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Olordered__ring_7) ).

fof(c_0_784,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Olordered__ring(X54)
      | class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Olordered__ring_6) ).

fof(c_0_785,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Olordered__ring(X54)
      | class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Olordered__ring_5) ).

fof(c_0_786,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Olordered__ring(X54)
      | class_HOL_Ominus(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Olordered__ring_4) ).

fof(c_0_787,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Olordered__ring(X54)
      | class_OrderedGroup_Olordered__ab__group__join(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Olordered__ring_30) ).

fof(c_0_788,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Olordered__ring(X54)
      | class_OrderedGroup_Oab__group__add(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Olordered__ring_3) ).

fof(c_0_789,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Olordered__ring(X54)
      | class_OrderedGroup_Olordered__ab__group__meet(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Olordered__ring_29) ).

fof(c_0_790,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Olordered__ring(X54)
      | class_LOrder_Omeet__semilorder(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Olordered__ring_28) ).

fof(c_0_791,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Olordered__ring(X54)
      | class_LOrder_Ojoin__semilorder(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Olordered__ring_27) ).

fof(c_0_792,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Olordered__ring(X54)
      | class_LOrder_Olorder(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Olordered__ring_26) ).

fof(c_0_793,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Olordered__ring(X54)
      | class_OrderedGroup_Olordered__ab__group(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Olordered__ring_25) ).

fof(c_0_794,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Olordered__ring(X54)
      | class_OrderedGroup_Olordered__ab__group__abs(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Olordered__ring_24) ).

fof(c_0_795,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Olordered__ring(X54)
      | class_HOL_Oplus(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Olordered__ring_23) ).

fof(c_0_796,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Olordered__ring(X54)
      | class_OrderedGroup_Osemigroup__add(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Olordered__ring_22) ).

fof(c_0_797,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Olordered__ring(X54)
      | class_OrderedGroup_Ocancel__semigroup__add(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Olordered__ring_21) ).

fof(c_0_798,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Olordered__ring(X54)
      | class_OrderedGroup_Oab__semigroup__add(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Olordered__ring_20) ).

fof(c_0_799,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Olordered__ring(X54)
      | class_OrderedGroup_Opordered__ab__group__add(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Olordered__ring_2) ).

fof(c_0_800,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Olordered__ring(X54)
      | class_OrderedGroup_Ocancel__ab__semigroup__add(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Olordered__ring_19) ).

fof(c_0_801,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Olordered__ring(X54)
      | class_HOL_Ozero(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Olordered__ring_18) ).

fof(c_0_802,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Olordered__ring(X54)
      | class_OrderedGroup_Ocomm__monoid__add(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Olordered__ring_17) ).

fof(c_0_803,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Olordered__ring(X54)
      | class_HOL_Otimes(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Olordered__ring_16) ).

fof(c_0_804,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Olordered__ring(X54)
      | class_OrderedGroup_Osemigroup__mult(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Olordered__ring_15) ).

fof(c_0_805,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Olordered__ring(X54)
      | class_Ring__and__Field_Osemiring(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Olordered__ring_14) ).

fof(c_0_806,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Olordered__ring(X54)
      | class_Ring__and__Field_Osemiring__0(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Olordered__ring_13) ).

fof(c_0_807,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Olordered__ring(X54)
      | class_Ring__and__Field_Osemiring__0__cancel(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Olordered__ring_12) ).

fof(c_0_808,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Olordered__ring(X54)
      | class_Orderings_Oord(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Olordered__ring_11) ).

fof(c_0_809,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Olordered__ring(X54)
      | class_Orderings_Oorder(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Olordered__ring_10) ).

fof(c_0_810,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Olordered__ring(X54)
      | class_Ring__and__Field_Oring(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Olordered__ring_1) ).

fof(c_0_811,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Olordered__ring(X54)
      | class_Ring__and__Field_Opordered__ring(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Olordered__ring_0) ).

fof(c_0_812,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oidom(X54)
      | class_Ring__and__Field_Osemiring__1__cancel(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oidom_9) ).

fof(c_0_813,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oidom(X54)
      | class_OrderedGroup_Ocomm__monoid__mult(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oidom_8) ).

fof(c_0_814,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oidom(X54)
      | class_Ring__and__Field_Ocomm__semiring__1(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oidom_7) ).

fof(c_0_815,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oidom(X54)
      | class_Ring__and__Field_Ocomm__semiring__1__cancel(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oidom_6) ).

fof(c_0_816,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oidom(X54)
      | class_HOL_Ominus(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oidom_5) ).

fof(c_0_817,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oidom(X54)
      | class_OrderedGroup_Oab__group__add(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oidom_4) ).

fof(c_0_818,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oidom(X54)
      | class_Ring__and__Field_Oaxclass__no__zero__divisors(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oidom_30) ).

fof(c_0_819,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oidom(X54)
      | class_Ring__and__Field_Oring(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oidom_3) ).

fof(c_0_820,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oidom(X54)
      | class_HOL_Oplus(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oidom_29) ).

fof(c_0_821,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oidom(X54)
      | class_OrderedGroup_Osemigroup__add(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oidom_28) ).

fof(c_0_822,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oidom(X54)
      | class_OrderedGroup_Ocancel__semigroup__add(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oidom_27) ).

fof(c_0_823,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oidom(X54)
      | class_OrderedGroup_Oab__semigroup__add(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oidom_26) ).

fof(c_0_824,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oidom(X54)
      | class_OrderedGroup_Ocancel__ab__semigroup__add(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oidom_25) ).

fof(c_0_825,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oidom(X54)
      | class_HOL_Ozero(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oidom_24) ).

fof(c_0_826,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oidom(X54)
      | class_OrderedGroup_Ocomm__monoid__add(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oidom_23) ).

fof(c_0_827,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oidom(X54)
      | class_HOL_Otimes(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oidom_22) ).

fof(c_0_828,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oidom(X54)
      | class_OrderedGroup_Osemigroup__mult(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oidom_21) ).

fof(c_0_829,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oidom(X54)
      | class_Ring__and__Field_Osemiring(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oidom_20) ).

fof(c_0_830,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oidom(X54)
      | class_Ring__and__Field_Oring__1(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oidom_2) ).

fof(c_0_831,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oidom(X54)
      | class_Ring__and__Field_Osemiring__0(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oidom_19) ).

fof(c_0_832,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oidom(X54)
      | class_Ring__and__Field_Osemiring__0__cancel(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oidom_18) ).

fof(c_0_833,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oidom(X54)
      | class_OrderedGroup_Oab__semigroup__mult(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oidom_17) ).

fof(c_0_834,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oidom(X54)
      | class_Ring__and__Field_Ocomm__semiring(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oidom_16) ).

fof(c_0_835,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oidom(X54)
      | class_Ring__and__Field_Ocomm__semiring__0(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oidom_15) ).

fof(c_0_836,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oidom(X54)
      | class_Ring__and__Field_Ocomm__semiring__0__cancel(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oidom_14) ).

fof(c_0_837,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oidom(X54)
      | class_HOL_Oone(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oidom_13) ).

fof(c_0_838,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oidom(X54)
      | class_OrderedGroup_Omonoid__mult(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oidom_12) ).

fof(c_0_839,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oidom(X54)
      | class_Ring__and__Field_Oaxclass__0__neq__1(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oidom_11) ).

fof(c_0_840,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oidom(X54)
      | class_Ring__and__Field_Osemiring__1(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oidom_10) ).

fof(c_0_841,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oidom(X54)
      | class_Ring__and__Field_Ocomm__ring(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oidom_1) ).

fof(c_0_842,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oidom(X54)
      | class_Ring__and__Field_Ocomm__ring__1(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oidom_0) ).

fof(c_0_843,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Ofield(X54)
      | class_Ring__and__Field_Osemiring__1__cancel(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Ofield_9) ).

fof(c_0_844,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Ofield(X54)
      | class_OrderedGroup_Ocomm__monoid__mult(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Ofield_8) ).

fof(c_0_845,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Ofield(X54)
      | class_Ring__and__Field_Ocomm__semiring__1(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Ofield_7) ).

fof(c_0_846,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Ofield(X54)
      | class_Ring__and__Field_Ocomm__semiring__1__cancel(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Ofield_6) ).

fof(c_0_847,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Ofield(X54)
      | class_HOL_Ominus(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Ofield_5) ).

fof(c_0_848,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Ofield(X54)
      | class_OrderedGroup_Oab__group__add(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Ofield_4) ).

fof(c_0_849,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Ofield(X54)
      | class_Ring__and__Field_Oaxclass__no__zero__divisors(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Ofield_32) ).

fof(c_0_850,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Ofield(X54)
      | class_Ring__and__Field_Oidom(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Ofield_31) ).

fof(c_0_851,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Ofield(X54)
      | class_HOL_Oinverse(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Ofield_30) ).

fof(c_0_852,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Ofield(X54)
      | class_Ring__and__Field_Oring(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Ofield_3) ).

fof(c_0_853,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Ofield(X54)
      | class_HOL_Oplus(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Ofield_29) ).

fof(c_0_854,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Ofield(X54)
      | class_OrderedGroup_Osemigroup__add(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Ofield_28) ).

fof(c_0_855,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Ofield(X54)
      | class_OrderedGroup_Ocancel__semigroup__add(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Ofield_27) ).

fof(c_0_856,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Ofield(X54)
      | class_OrderedGroup_Oab__semigroup__add(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Ofield_26) ).

fof(c_0_857,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Ofield(X54)
      | class_OrderedGroup_Ocancel__ab__semigroup__add(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Ofield_25) ).

fof(c_0_858,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Ofield(X54)
      | class_HOL_Ozero(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Ofield_24) ).

fof(c_0_859,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Ofield(X54)
      | class_OrderedGroup_Ocomm__monoid__add(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Ofield_23) ).

fof(c_0_860,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Ofield(X54)
      | class_HOL_Otimes(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Ofield_22) ).

fof(c_0_861,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Ofield(X54)
      | class_OrderedGroup_Osemigroup__mult(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Ofield_21) ).

fof(c_0_862,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Ofield(X54)
      | class_Ring__and__Field_Osemiring(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Ofield_20) ).

fof(c_0_863,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Ofield(X54)
      | class_Ring__and__Field_Oring__1(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Ofield_2) ).

fof(c_0_864,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Ofield(X54)
      | class_Ring__and__Field_Osemiring__0(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Ofield_19) ).

fof(c_0_865,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Ofield(X54)
      | class_Ring__and__Field_Osemiring__0__cancel(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Ofield_18) ).

fof(c_0_866,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Ofield(X54)
      | class_OrderedGroup_Oab__semigroup__mult(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Ofield_17) ).

fof(c_0_867,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Ofield(X54)
      | class_Ring__and__Field_Ocomm__semiring(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Ofield_16) ).

fof(c_0_868,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Ofield(X54)
      | class_Ring__and__Field_Ocomm__semiring__0(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Ofield_15) ).

fof(c_0_869,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Ofield(X54)
      | class_Ring__and__Field_Ocomm__semiring__0__cancel(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Ofield_14) ).

fof(c_0_870,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Ofield(X54)
      | class_HOL_Oone(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Ofield_13) ).

fof(c_0_871,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Ofield(X54)
      | class_OrderedGroup_Omonoid__mult(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Ofield_12) ).

fof(c_0_872,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Ofield(X54)
      | class_Ring__and__Field_Oaxclass__0__neq__1(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Ofield_11) ).

fof(c_0_873,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Ofield(X54)
      | class_Ring__and__Field_Osemiring__1(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Ofield_10) ).

fof(c_0_874,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Ofield(X54)
      | class_Ring__and__Field_Ocomm__ring(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Ofield_1) ).

fof(c_0_875,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Ofield(X54)
      | class_Ring__and__Field_Ocomm__ring__1(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Ofield_0) ).

fof(c_0_876,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Odivision__by__zero(X54)
      | class_HOL_Oinverse(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Odivision__by__zero_1) ).

fof(c_0_877,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Odivision__by__zero(X54)
      | class_HOL_Ozero(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Odivision__by__zero_0) ).

fof(c_0_878,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X54)
      | class_OrderedGroup_Ocomm__monoid__add(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_9) ).

fof(c_0_879,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X54)
      | class_Ring__and__Field_Osemiring(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_8) ).

fof(c_0_880,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X54)
      | class_Ring__and__Field_Osemiring__0(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_7) ).

fof(c_0_881,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X54)
      | class_Ring__and__Field_Oaxclass__0__neq__1(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_6) ).

fof(c_0_882,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X54)
      | class_Ring__and__Field_Osemiring__1(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_5) ).

fof(c_0_883,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X54)
      | class_OrderedGroup_Oab__semigroup__mult(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_4) ).

fof(c_0_884,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X54)
      | class_OrderedGroup_Ocomm__monoid__mult(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_3) ).

fof(c_0_885,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X54)
      | class_Ring__and__Field_Ocomm__semiring__0__cancel(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_22) ).

fof(c_0_886,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X54)
      | class_Ring__and__Field_Osemiring__0__cancel(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_21) ).

fof(c_0_887,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X54)
      | class_Ring__and__Field_Osemiring__1__cancel(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_20) ).

fof(c_0_888,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X54)
      | class_Ring__and__Field_Ocomm__semiring(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_2) ).

fof(c_0_889,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X54)
      | class_OrderedGroup_Ocancel__semigroup__add(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_19) ).

fof(c_0_890,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X54)
      | class_OrderedGroup_Ocancel__ab__semigroup__add(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_18) ).

fof(c_0_891,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X54)
      | class_HOL_Otimes(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_17) ).

fof(c_0_892,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X54)
      | class_OrderedGroup_Osemigroup__mult(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_16) ).

fof(c_0_893,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X54)
      | class_HOL_Oone(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_15) ).

fof(c_0_894,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X54)
      | class_OrderedGroup_Omonoid__mult(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_14) ).

fof(c_0_895,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X54)
      | class_HOL_Oplus(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_13) ).

fof(c_0_896,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X54)
      | class_OrderedGroup_Osemigroup__add(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_12) ).

fof(c_0_897,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X54)
      | class_OrderedGroup_Oab__semigroup__add(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_11) ).

fof(c_0_898,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X54)
      | class_HOL_Ozero(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_10) ).

fof(c_0_899,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X54)
      | class_Ring__and__Field_Ocomm__semiring__0(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_1) ).

fof(c_0_900,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X54)
      | class_Ring__and__Field_Ocomm__semiring__1(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_0) ).

fof(c_0_901,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X54)
      | class_HOL_Otimes(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Ocomm__semiring__1_9) ).

fof(c_0_902,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X54)
      | class_OrderedGroup_Osemigroup__mult(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Ocomm__semiring__1_8) ).

fof(c_0_903,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X54)
      | class_Ring__and__Field_Osemiring(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Ocomm__semiring__1_7) ).

fof(c_0_904,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X54)
      | class_Ring__and__Field_Osemiring__0(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Ocomm__semiring__1_6) ).

fof(c_0_905,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X54)
      | class_OrderedGroup_Oab__semigroup__mult(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Ocomm__semiring__1_5) ).

fof(c_0_906,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X54)
      | class_Ring__and__Field_Ocomm__semiring(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Ocomm__semiring__1_4) ).

fof(c_0_907,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X54)
      | class_Ring__and__Field_Ocomm__semiring__0(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Ocomm__semiring__1_3) ).

fof(c_0_908,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X54)
      | class_HOL_Oone(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Ocomm__semiring__1_2) ).

fof(c_0_909,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X54)
      | class_Ring__and__Field_Osemiring__1(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Ocomm__semiring__1_16) ).

fof(c_0_910,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X54)
      | class_OrderedGroup_Omonoid__mult(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Ocomm__semiring__1_15) ).

fof(c_0_911,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X54)
      | class_OrderedGroup_Ocomm__monoid__mult(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Ocomm__semiring__1_14) ).

fof(c_0_912,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X54)
      | class_HOL_Oplus(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Ocomm__semiring__1_13) ).

fof(c_0_913,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X54)
      | class_OrderedGroup_Osemigroup__add(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Ocomm__semiring__1_12) ).

fof(c_0_914,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X54)
      | class_OrderedGroup_Oab__semigroup__add(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Ocomm__semiring__1_11) ).

fof(c_0_915,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X54)
      | class_OrderedGroup_Ocomm__monoid__add(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Ocomm__semiring__1_10) ).

fof(c_0_916,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X54)
      | class_HOL_Ozero(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Ocomm__semiring__1_1) ).

fof(c_0_917,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X54)
      | class_Ring__and__Field_Oaxclass__0__neq__1(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Ocomm__semiring__1_0) ).

fof(c_0_918,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X54)
      | class_OrderedGroup_Osemigroup__add(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_9) ).

fof(c_0_919,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X54)
      | class_OrderedGroup_Oab__semigroup__add(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_8) ).

fof(c_0_920,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X54)
      | class_OrderedGroup_Ocomm__monoid__add(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_7) ).

fof(c_0_921,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X54)
      | class_HOL_Otimes(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_6) ).

fof(c_0_922,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X54)
      | class_OrderedGroup_Osemigroup__mult(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_5) ).

fof(c_0_923,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X54)
      | class_Ring__and__Field_Osemiring(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_4) ).

fof(c_0_924,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X54)
      | class_Ring__and__Field_Osemiring__0(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_3) ).

fof(c_0_925,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X54)
      | class_OrderedGroup_Oab__semigroup__mult(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_2) ).

fof(c_0_926,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X54)
      | class_Ring__and__Field_Osemiring__0__cancel(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_14) ).

fof(c_0_927,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X54)
      | class_OrderedGroup_Ocancel__semigroup__add(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_13) ).

fof(c_0_928,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X54)
      | class_OrderedGroup_Ocancel__ab__semigroup__add(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_12) ).

fof(c_0_929,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X54)
      | class_HOL_Ozero(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_11) ).

fof(c_0_930,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X54)
      | class_HOL_Oplus(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_10) ).

fof(c_0_931,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X54)
      | class_Ring__and__Field_Ocomm__semiring(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_1) ).

fof(c_0_932,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X54)
      | class_Ring__and__Field_Ocomm__semiring__0(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_0) ).

fof(c_0_933,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__0(X54)
      | class_HOL_Ozero(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Ocomm__semiring__0_9) ).

fof(c_0_934,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__0(X54)
      | class_OrderedGroup_Ocomm__monoid__add(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Ocomm__semiring__0_8) ).

fof(c_0_935,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__0(X54)
      | class_HOL_Otimes(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Ocomm__semiring__0_7) ).

fof(c_0_936,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__0(X54)
      | class_OrderedGroup_Osemigroup__mult(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Ocomm__semiring__0_6) ).

fof(c_0_937,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__0(X54)
      | class_HOL_Oplus(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Ocomm__semiring__0_5) ).

fof(c_0_938,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__0(X54)
      | class_OrderedGroup_Osemigroup__add(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Ocomm__semiring__0_4) ).

fof(c_0_939,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__0(X54)
      | class_OrderedGroup_Oab__semigroup__add(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Ocomm__semiring__0_3) ).

fof(c_0_940,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__0(X54)
      | class_Ring__and__Field_Osemiring(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Ocomm__semiring__0_2) ).

fof(c_0_941,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__0(X54)
      | class_Ring__and__Field_Osemiring__0(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Ocomm__semiring__0_10) ).

fof(c_0_942,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__0(X54)
      | class_OrderedGroup_Oab__semigroup__mult(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Ocomm__semiring__0_1) ).

fof(c_0_943,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__0(X54)
      | class_Ring__and__Field_Ocomm__semiring(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Ocomm__semiring__0_0) ).

fof(c_0_944,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Ocomm__semiring(X54)
      | class_Ring__and__Field_Osemiring(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Ocomm__semiring_6) ).

fof(c_0_945,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Ocomm__semiring(X54)
      | class_HOL_Otimes(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Ocomm__semiring_5) ).

fof(c_0_946,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Ocomm__semiring(X54)
      | class_OrderedGroup_Osemigroup__mult(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Ocomm__semiring_4) ).

fof(c_0_947,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Ocomm__semiring(X54)
      | class_OrderedGroup_Oab__semigroup__mult(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Ocomm__semiring_3) ).

fof(c_0_948,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Ocomm__semiring(X54)
      | class_HOL_Oplus(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Ocomm__semiring_2) ).

fof(c_0_949,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Ocomm__semiring(X54)
      | class_OrderedGroup_Osemigroup__add(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Ocomm__semiring_1) ).

fof(c_0_950,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Ocomm__semiring(X54)
      | class_OrderedGroup_Oab__semigroup__add(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Ocomm__semiring_0) ).

fof(c_0_951,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Ocomm__ring__1(X54)
      | class_Ring__and__Field_Osemiring__0(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Ocomm__ring__1_9) ).

fof(c_0_952,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Ocomm__ring__1(X54)
      | class_Ring__and__Field_Osemiring__0__cancel(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Ocomm__ring__1_8) ).

fof(c_0_953,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Ocomm__ring__1(X54)
      | class_OrderedGroup_Oab__semigroup__mult(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Ocomm__ring__1_7) ).

fof(c_0_954,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Ocomm__ring__1(X54)
      | class_Ring__and__Field_Ocomm__semiring(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Ocomm__ring__1_6) ).

fof(c_0_955,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Ocomm__ring__1(X54)
      | class_Ring__and__Field_Ocomm__semiring__0(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Ocomm__ring__1_5) ).

fof(c_0_956,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Ocomm__ring__1(X54)
      | class_Ring__and__Field_Ocomm__semiring__0__cancel(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Ocomm__ring__1_4) ).

fof(c_0_957,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Ocomm__ring__1(X54)
      | class_HOL_Ominus(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Ocomm__ring__1_3) ).

fof(c_0_958,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Ocomm__ring__1(X54)
      | class_Ring__and__Field_Ocomm__semiring__1__cancel(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Ocomm__ring__1_28) ).

fof(c_0_959,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Ocomm__ring__1(X54)
      | class_Ring__and__Field_Osemiring__1__cancel(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Ocomm__ring__1_27) ).

fof(c_0_960,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Ocomm__ring__1(X54)
      | class_Ring__and__Field_Oring__1(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Ocomm__ring__1_26) ).

fof(c_0_961,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Ocomm__ring__1(X54)
      | class_HOL_Oone(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Ocomm__ring__1_25) ).

fof(c_0_962,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Ocomm__ring__1(X54)
      | class_OrderedGroup_Omonoid__mult(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Ocomm__ring__1_24) ).

fof(c_0_963,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Ocomm__ring__1(X54)
      | class_Ring__and__Field_Oaxclass__0__neq__1(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Ocomm__ring__1_23) ).

fof(c_0_964,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Ocomm__ring__1(X54)
      | class_Ring__and__Field_Osemiring__1(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Ocomm__ring__1_22) ).

fof(c_0_965,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Ocomm__ring__1(X54)
      | class_OrderedGroup_Ocomm__monoid__mult(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Ocomm__ring__1_21) ).

fof(c_0_966,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Ocomm__ring__1(X54)
      | class_Ring__and__Field_Ocomm__semiring__1(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Ocomm__ring__1_20) ).

fof(c_0_967,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Ocomm__ring__1(X54)
      | class_OrderedGroup_Oab__group__add(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Ocomm__ring__1_2) ).

fof(c_0_968,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Ocomm__ring__1(X54)
      | class_HOL_Oplus(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Ocomm__ring__1_19) ).

fof(c_0_969,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Ocomm__ring__1(X54)
      | class_OrderedGroup_Osemigroup__add(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Ocomm__ring__1_18) ).

fof(c_0_970,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Ocomm__ring__1(X54)
      | class_OrderedGroup_Ocancel__semigroup__add(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Ocomm__ring__1_17) ).

fof(c_0_971,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Ocomm__ring__1(X54)
      | class_OrderedGroup_Oab__semigroup__add(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Ocomm__ring__1_16) ).

fof(c_0_972,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Ocomm__ring__1(X54)
      | class_OrderedGroup_Ocancel__ab__semigroup__add(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Ocomm__ring__1_15) ).

fof(c_0_973,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Ocomm__ring__1(X54)
      | class_HOL_Ozero(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Ocomm__ring__1_14) ).

fof(c_0_974,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Ocomm__ring__1(X54)
      | class_OrderedGroup_Ocomm__monoid__add(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Ocomm__ring__1_13) ).

fof(c_0_975,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Ocomm__ring__1(X54)
      | class_HOL_Otimes(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Ocomm__ring__1_12) ).

fof(c_0_976,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Ocomm__ring__1(X54)
      | class_OrderedGroup_Osemigroup__mult(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Ocomm__ring__1_11) ).

fof(c_0_977,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Ocomm__ring__1(X54)
      | class_Ring__and__Field_Osemiring(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Ocomm__ring__1_10) ).

fof(c_0_978,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Ocomm__ring__1(X54)
      | class_Ring__and__Field_Oring(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Ocomm__ring__1_1) ).

fof(c_0_979,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Ocomm__ring__1(X54)
      | class_Ring__and__Field_Ocomm__ring(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Ocomm__ring__1_0) ).

fof(c_0_980,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Ocomm__ring(X54)
      | class_OrderedGroup_Osemigroup__add(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Ocomm__ring_9) ).

fof(c_0_981,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Ocomm__ring(X54)
      | class_OrderedGroup_Oab__semigroup__add(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Ocomm__ring_8) ).

fof(c_0_982,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Ocomm__ring(X54)
      | class_OrderedGroup_Ocomm__monoid__add(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Ocomm__ring_7) ).

fof(c_0_983,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Ocomm__ring(X54)
      | class_HOL_Otimes(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Ocomm__ring_6) ).

fof(c_0_984,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Ocomm__ring(X54)
      | class_OrderedGroup_Osemigroup__mult(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Ocomm__ring_5) ).

fof(c_0_985,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Ocomm__ring(X54)
      | class_Ring__and__Field_Osemiring(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Ocomm__ring_4) ).

fof(c_0_986,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Ocomm__ring(X54)
      | class_Ring__and__Field_Osemiring__0(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Ocomm__ring_3) ).

fof(c_0_987,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Ocomm__ring(X54)
      | class_OrderedGroup_Oab__semigroup__mult(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Ocomm__ring_2) ).

fof(c_0_988,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Ocomm__ring(X54)
      | class_Ring__and__Field_Ocomm__semiring__0__cancel(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Ocomm__ring_18) ).

fof(c_0_989,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Ocomm__ring(X54)
      | class_Ring__and__Field_Osemiring__0__cancel(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Ocomm__ring_17) ).

fof(c_0_990,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Ocomm__ring(X54)
      | class_Ring__and__Field_Oring(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Ocomm__ring_16) ).

fof(c_0_991,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Ocomm__ring(X54)
      | class_OrderedGroup_Ocancel__semigroup__add(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Ocomm__ring_15) ).

fof(c_0_992,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Ocomm__ring(X54)
      | class_OrderedGroup_Ocancel__ab__semigroup__add(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Ocomm__ring_14) ).

fof(c_0_993,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Ocomm__ring(X54)
      | class_HOL_Ominus(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Ocomm__ring_13) ).

fof(c_0_994,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Ocomm__ring(X54)
      | class_OrderedGroup_Oab__group__add(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Ocomm__ring_12) ).

fof(c_0_995,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Ocomm__ring(X54)
      | class_HOL_Ozero(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Ocomm__ring_11) ).

fof(c_0_996,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Ocomm__ring(X54)
      | class_HOL_Oplus(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Ocomm__ring_10) ).

fof(c_0_997,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Ocomm__ring(X54)
      | class_Ring__and__Field_Ocomm__semiring(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Ocomm__ring_1) ).

fof(c_0_998,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Ocomm__ring(X54)
      | class_Ring__and__Field_Ocomm__semiring__0(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Ocomm__ring_0) ).

fof(c_0_999,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oaxclass__no__zero__divisors(X54)
      | class_HOL_Otimes(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oaxclass__no__zero__divisors_1) ).

fof(c_0_1000,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oaxclass__no__zero__divisors(X54)
      | class_HOL_Ozero(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oaxclass__no__zero__divisors_0) ).

fof(c_0_1001,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oaxclass__abs__if(X54)
      | class_HOL_Ozero(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oaxclass__abs__if_2) ).

fof(c_0_1002,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oaxclass__abs__if(X54)
      | class_Orderings_Oord(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oaxclass__abs__if_1) ).

fof(c_0_1003,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oaxclass__abs__if(X54)
      | class_HOL_Ominus(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oaxclass__abs__if_0) ).

fof(c_0_1004,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oaxclass__0__neq__1(X54)
      | class_HOL_Oone(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oaxclass__0__neq__1_1) ).

fof(c_0_1005,axiom,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oaxclass__0__neq__1(X54)
      | class_HOL_Ozero(X54) ),
    file('<stdin>',clsrel_Ring__and__Field_Oaxclass__0__neq__1_0) ).

fof(c_0_1006,axiom,
    ! [X54] :
      ( ~ class_Power_Orecpower(X54)
      | class_OrderedGroup_Oab__semigroup__mult(X54) ),
    file('<stdin>',clsrel_Power_Orecpower_9) ).

fof(c_0_1007,axiom,
    ! [X54] :
      ( ~ class_Power_Orecpower(X54)
      | class_OrderedGroup_Osemigroup__mult(X54) ),
    file('<stdin>',clsrel_Power_Orecpower_8) ).

fof(c_0_1008,axiom,
    ! [X54] :
      ( ~ class_Power_Orecpower(X54)
      | class_HOL_Otimes(X54) ),
    file('<stdin>',clsrel_Power_Orecpower_7) ).

fof(c_0_1009,axiom,
    ! [X54] :
      ( ~ class_Power_Orecpower(X54)
      | class_OrderedGroup_Oab__semigroup__add(X54) ),
    file('<stdin>',clsrel_Power_Orecpower_6) ).

fof(c_0_1010,axiom,
    ! [X54] :
      ( ~ class_Power_Orecpower(X54)
      | class_OrderedGroup_Osemigroup__add(X54) ),
    file('<stdin>',clsrel_Power_Orecpower_5) ).

fof(c_0_1011,axiom,
    ! [X54] :
      ( ~ class_Power_Orecpower(X54)
      | class_HOL_Oplus(X54) ),
    file('<stdin>',clsrel_Power_Orecpower_4) ).

fof(c_0_1012,axiom,
    ! [X54] :
      ( ~ class_Power_Orecpower(X54)
      | class_Ring__and__Field_Oaxclass__0__neq__1(X54) ),
    file('<stdin>',clsrel_Power_Orecpower_3) ).

fof(c_0_1013,axiom,
    ! [X54] :
      ( ~ class_Power_Orecpower(X54)
      | class_Ring__and__Field_Ocomm__semiring__1__cancel(X54) ),
    file('<stdin>',clsrel_Power_Orecpower_24) ).

fof(c_0_1014,axiom,
    ! [X54] :
      ( ~ class_Power_Orecpower(X54)
      | class_Ring__and__Field_Ocomm__semiring__0__cancel(X54) ),
    file('<stdin>',clsrel_Power_Orecpower_23) ).

fof(c_0_1015,axiom,
    ! [X54] :
      ( ~ class_Power_Orecpower(X54)
      | class_Ring__and__Field_Osemiring__1__cancel(X54) ),
    file('<stdin>',clsrel_Power_Orecpower_22) ).

fof(c_0_1016,axiom,
    ! [X54] :
      ( ~ class_Power_Orecpower(X54)
      | class_Ring__and__Field_Osemiring__0__cancel(X54) ),
    file('<stdin>',clsrel_Power_Orecpower_21) ).

fof(c_0_1017,axiom,
    ! [X54] :
      ( ~ class_Power_Orecpower(X54)
      | class_OrderedGroup_Ocancel__ab__semigroup__add(X54) ),
    file('<stdin>',clsrel_Power_Orecpower_20) ).

fof(c_0_1018,axiom,
    ! [X54] :
      ( ~ class_Power_Orecpower(X54)
      | class_HOL_Oone(X54) ),
    file('<stdin>',clsrel_Power_Orecpower_2) ).

fof(c_0_1019,axiom,
    ! [X54] :
      ( ~ class_Power_Orecpower(X54)
      | class_OrderedGroup_Ocancel__semigroup__add(X54) ),
    file('<stdin>',clsrel_Power_Orecpower_19) ).

fof(c_0_1020,axiom,
    ! [X54] :
      ( ~ class_Power_Orecpower(X54)
      | class_Ring__and__Field_Ocomm__semiring__1(X54) ),
    file('<stdin>',clsrel_Power_Orecpower_18) ).

fof(c_0_1021,axiom,
    ! [X54] :
      ( ~ class_Power_Orecpower(X54)
      | class_Ring__and__Field_Osemiring__1(X54) ),
    file('<stdin>',clsrel_Power_Orecpower_17) ).

fof(c_0_1022,axiom,
    ! [X54] :
      ( ~ class_Power_Orecpower(X54)
      | class_OrderedGroup_Ocomm__monoid__mult(X54) ),
    file('<stdin>',clsrel_Power_Orecpower_16) ).

fof(c_0_1023,axiom,
    ! [X54] :
      ( ~ class_Power_Orecpower(X54)
      | class_OrderedGroup_Omonoid__mult(X54) ),
    file('<stdin>',clsrel_Power_Orecpower_15) ).

fof(c_0_1024,axiom,
    ! [X54] :
      ( ~ class_Power_Orecpower(X54)
      | class_Ring__and__Field_Ocomm__semiring__0(X54) ),
    file('<stdin>',clsrel_Power_Orecpower_14) ).

fof(c_0_1025,axiom,
    ! [X54] :
      ( ~ class_Power_Orecpower(X54)
      | class_Ring__and__Field_Osemiring__0(X54) ),
    file('<stdin>',clsrel_Power_Orecpower_13) ).

fof(c_0_1026,axiom,
    ! [X54] :
      ( ~ class_Power_Orecpower(X54)
      | class_OrderedGroup_Ocomm__monoid__add(X54) ),
    file('<stdin>',clsrel_Power_Orecpower_12) ).

fof(c_0_1027,axiom,
    ! [X54] :
      ( ~ class_Power_Orecpower(X54)
      | class_Ring__and__Field_Ocomm__semiring(X54) ),
    file('<stdin>',clsrel_Power_Orecpower_11) ).

fof(c_0_1028,axiom,
    ! [X54] :
      ( ~ class_Power_Orecpower(X54)
      | class_Ring__and__Field_Osemiring(X54) ),
    file('<stdin>',clsrel_Power_Orecpower_10) ).

fof(c_0_1029,axiom,
    ! [X54] :
      ( ~ class_Power_Orecpower(X54)
      | class_HOL_Ozero(X54) ),
    file('<stdin>',clsrel_Power_Orecpower_1) ).

fof(c_0_1030,axiom,
    ! [X54] :
      ( ~ class_Power_Orecpower(X54)
      | class_Nat_Opower(X54) ),
    file('<stdin>',clsrel_Power_Orecpower_0) ).

fof(c_0_1031,axiom,
    ! [X54] :
      ( ~ class_Orderings_Oorder(X54)
      | class_Orderings_Oord(X54) ),
    file('<stdin>',clsrel_Orderings_Oorder_0) ).

fof(c_0_1032,axiom,
    ! [X54] :
      ( ~ class_Orderings_Olinorder(X54)
      | class_Orderings_Oorder(X54) ),
    file('<stdin>',clsrel_Orderings_Olinorder_4) ).

fof(c_0_1033,axiom,
    ! [X54] :
      ( ~ class_Orderings_Olinorder(X54)
      | class_Orderings_Oord(X54) ),
    file('<stdin>',clsrel_Orderings_Olinorder_3) ).

fof(c_0_1034,axiom,
    ! [X54] :
      ( ~ class_Orderings_Olinorder(X54)
      | class_LOrder_Omeet__semilorder(X54) ),
    file('<stdin>',clsrel_Orderings_Olinorder_2) ).

fof(c_0_1035,axiom,
    ! [X54] :
      ( ~ class_Orderings_Olinorder(X54)
      | class_LOrder_Ojoin__semilorder(X54) ),
    file('<stdin>',clsrel_Orderings_Olinorder_1) ).

fof(c_0_1036,axiom,
    ! [X54] :
      ( ~ class_Orderings_Olinorder(X54)
      | class_LOrder_Olorder(X54) ),
    file('<stdin>',clsrel_Orderings_Olinorder_0) ).

fof(c_0_1037,axiom,
    ! [X54] :
      ( ~ class_OrderedGroup_Osemigroup__mult(X54)
      | class_HOL_Otimes(X54) ),
    file('<stdin>',clsrel_OrderedGroup_Osemigroup__mult_0) ).

fof(c_0_1038,axiom,
    ! [X54] :
      ( ~ class_OrderedGroup_Osemigroup__add(X54)
      | class_HOL_Oplus(X54) ),
    file('<stdin>',clsrel_OrderedGroup_Osemigroup__add_0) ).

fof(c_0_1039,axiom,
    ! [X54] :
      ( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X54)
      | class_OrderedGroup_Ocancel__semigroup__add(X54) ),
    file('<stdin>',clsrel_OrderedGroup_Opordered__cancel__ab__semigroup__add_7) ).

fof(c_0_1040,axiom,
    ! [X54] :
      ( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X54)
      | class_OrderedGroup_Ocancel__ab__semigroup__add(X54) ),
    file('<stdin>',clsrel_OrderedGroup_Opordered__cancel__ab__semigroup__add_6) ).

fof(c_0_1041,axiom,
    ! [X54] :
      ( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X54)
      | class_HOL_Oplus(X54) ),
    file('<stdin>',clsrel_OrderedGroup_Opordered__cancel__ab__semigroup__add_5) ).

fof(c_0_1042,axiom,
    ! [X54] :
      ( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X54)
      | class_OrderedGroup_Osemigroup__add(X54) ),
    file('<stdin>',clsrel_OrderedGroup_Opordered__cancel__ab__semigroup__add_4) ).

fof(c_0_1043,axiom,
    ! [X54] :
      ( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X54)
      | class_OrderedGroup_Oab__semigroup__add(X54) ),
    file('<stdin>',clsrel_OrderedGroup_Opordered__cancel__ab__semigroup__add_3) ).

fof(c_0_1044,axiom,
    ! [X54] :
      ( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X54)
      | class_Orderings_Oord(X54) ),
    file('<stdin>',clsrel_OrderedGroup_Opordered__cancel__ab__semigroup__add_2) ).

fof(c_0_1045,axiom,
    ! [X54] :
      ( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X54)
      | class_Orderings_Oorder(X54) ),
    file('<stdin>',clsrel_OrderedGroup_Opordered__cancel__ab__semigroup__add_1) ).

fof(c_0_1046,axiom,
    ! [X54] :
      ( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X54)
      | class_OrderedGroup_Opordered__ab__semigroup__add(X54) ),
    file('<stdin>',clsrel_OrderedGroup_Opordered__cancel__ab__semigroup__add_0) ).

fof(c_0_1047,axiom,
    ! [X54] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X54)
      | class_HOL_Oplus(X54) ),
    file('<stdin>',clsrel_OrderedGroup_Opordered__ab__semigroup__add__imp__le_8) ).

fof(c_0_1048,axiom,
    ! [X54] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X54)
      | class_OrderedGroup_Osemigroup__add(X54) ),
    file('<stdin>',clsrel_OrderedGroup_Opordered__ab__semigroup__add__imp__le_7) ).

fof(c_0_1049,axiom,
    ! [X54] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X54)
      | class_OrderedGroup_Ocancel__semigroup__add(X54) ),
    file('<stdin>',clsrel_OrderedGroup_Opordered__ab__semigroup__add__imp__le_6) ).

fof(c_0_1050,axiom,
    ! [X54] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X54)
      | class_OrderedGroup_Oab__semigroup__add(X54) ),
    file('<stdin>',clsrel_OrderedGroup_Opordered__ab__semigroup__add__imp__le_5) ).

fof(c_0_1051,axiom,
    ! [X54] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X54)
      | class_OrderedGroup_Ocancel__ab__semigroup__add(X54) ),
    file('<stdin>',clsrel_OrderedGroup_Opordered__ab__semigroup__add__imp__le_4) ).

fof(c_0_1052,axiom,
    ! [X54] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X54)
      | class_Orderings_Oord(X54) ),
    file('<stdin>',clsrel_OrderedGroup_Opordered__ab__semigroup__add__imp__le_3) ).

fof(c_0_1053,axiom,
    ! [X54] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X54)
      | class_Orderings_Oorder(X54) ),
    file('<stdin>',clsrel_OrderedGroup_Opordered__ab__semigroup__add__imp__le_2) ).

fof(c_0_1054,axiom,
    ! [X54] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X54)
      | class_OrderedGroup_Opordered__ab__semigroup__add(X54) ),
    file('<stdin>',clsrel_OrderedGroup_Opordered__ab__semigroup__add__imp__le_1) ).

fof(c_0_1055,axiom,
    ! [X54] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X54)
      | class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X54) ),
    file('<stdin>',clsrel_OrderedGroup_Opordered__ab__semigroup__add__imp__le_0) ).

fof(c_0_1056,axiom,
    ! [X54] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X54)
      | class_HOL_Oplus(X54) ),
    file('<stdin>',clsrel_OrderedGroup_Opordered__ab__semigroup__add_4) ).

fof(c_0_1057,axiom,
    ! [X54] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X54)
      | class_OrderedGroup_Osemigroup__add(X54) ),
    file('<stdin>',clsrel_OrderedGroup_Opordered__ab__semigroup__add_3) ).

fof(c_0_1058,axiom,
    ! [X54] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X54)
      | class_OrderedGroup_Oab__semigroup__add(X54) ),
    file('<stdin>',clsrel_OrderedGroup_Opordered__ab__semigroup__add_2) ).

fof(c_0_1059,axiom,
    ! [X54] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X54)
      | class_Orderings_Oord(X54) ),
    file('<stdin>',clsrel_OrderedGroup_Opordered__ab__semigroup__add_1) ).

fof(c_0_1060,axiom,
    ! [X54] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X54)
      | class_Orderings_Oorder(X54) ),
    file('<stdin>',clsrel_OrderedGroup_Opordered__ab__semigroup__add_0) ).

fof(c_0_1061,axiom,
    ! [X54] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add(X54)
      | class_OrderedGroup_Opordered__ab__semigroup__add(X54) ),
    file('<stdin>',clsrel_OrderedGroup_Opordered__ab__group__add_9) ).

fof(c_0_1062,axiom,
    ! [X54] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add(X54)
      | class_HOL_Oplus(X54) ),
    file('<stdin>',clsrel_OrderedGroup_Opordered__ab__group__add_8) ).

fof(c_0_1063,axiom,
    ! [X54] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add(X54)
      | class_OrderedGroup_Osemigroup__add(X54) ),
    file('<stdin>',clsrel_OrderedGroup_Opordered__ab__group__add_7) ).

fof(c_0_1064,axiom,
    ! [X54] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add(X54)
      | class_OrderedGroup_Ocancel__semigroup__add(X54) ),
    file('<stdin>',clsrel_OrderedGroup_Opordered__ab__group__add_6) ).

fof(c_0_1065,axiom,
    ! [X54] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add(X54)
      | class_OrderedGroup_Oab__semigroup__add(X54) ),
    file('<stdin>',clsrel_OrderedGroup_Opordered__ab__group__add_5) ).

fof(c_0_1066,axiom,
    ! [X54] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add(X54)
      | class_OrderedGroup_Ocancel__ab__semigroup__add(X54) ),
    file('<stdin>',clsrel_OrderedGroup_Opordered__ab__group__add_4) ).

fof(c_0_1067,axiom,
    ! [X54] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add(X54)
      | class_HOL_Ozero(X54) ),
    file('<stdin>',clsrel_OrderedGroup_Opordered__ab__group__add_3) ).

fof(c_0_1068,axiom,
    ! [X54] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add(X54)
      | class_OrderedGroup_Ocomm__monoid__add(X54) ),
    file('<stdin>',clsrel_OrderedGroup_Opordered__ab__group__add_2) ).

fof(c_0_1069,axiom,
    ! [X54] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add(X54)
      | class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X54) ),
    file('<stdin>',clsrel_OrderedGroup_Opordered__ab__group__add_13) ).

fof(c_0_1070,axiom,
    ! [X54] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add(X54)
      | class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X54) ),
    file('<stdin>',clsrel_OrderedGroup_Opordered__ab__group__add_12) ).

fof(c_0_1071,axiom,
    ! [X54] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add(X54)
      | class_Orderings_Oord(X54) ),
    file('<stdin>',clsrel_OrderedGroup_Opordered__ab__group__add_11) ).

fof(c_0_1072,axiom,
    ! [X54] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add(X54)
      | class_Orderings_Oorder(X54) ),
    file('<stdin>',clsrel_OrderedGroup_Opordered__ab__group__add_10) ).

fof(c_0_1073,axiom,
    ! [X54] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add(X54)
      | class_HOL_Ominus(X54) ),
    file('<stdin>',clsrel_OrderedGroup_Opordered__ab__group__add_1) ).

fof(c_0_1074,axiom,
    ! [X54] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add(X54)
      | class_OrderedGroup_Oab__group__add(X54) ),
    file('<stdin>',clsrel_OrderedGroup_Opordered__ab__group__add_0) ).

fof(c_0_1075,axiom,
    ! [X54] :
      ( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X54)
      | class_Orderings_Olinorder(X54) ),
    file('<stdin>',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_9) ).

fof(c_0_1076,axiom,
    ! [X54] :
      ( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X54)
      | class_HOL_Oplus(X54) ),
    file('<stdin>',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_8) ).

fof(c_0_1077,axiom,
    ! [X54] :
      ( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X54)
      | class_OrderedGroup_Osemigroup__add(X54) ),
    file('<stdin>',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_7) ).

fof(c_0_1078,axiom,
    ! [X54] :
      ( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X54)
      | class_OrderedGroup_Ocancel__semigroup__add(X54) ),
    file('<stdin>',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_6) ).

fof(c_0_1079,axiom,
    ! [X54] :
      ( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X54)
      | class_OrderedGroup_Oab__semigroup__add(X54) ),
    file('<stdin>',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_5) ).

fof(c_0_1080,axiom,
    ! [X54] :
      ( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X54)
      | class_OrderedGroup_Ocancel__ab__semigroup__add(X54) ),
    file('<stdin>',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_4) ).

fof(c_0_1081,axiom,
    ! [X54] :
      ( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X54)
      | class_Orderings_Oord(X54) ),
    file('<stdin>',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_3) ).

fof(c_0_1082,axiom,
    ! [X54] :
      ( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X54)
      | class_Orderings_Oorder(X54) ),
    file('<stdin>',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_2) ).

fof(c_0_1083,axiom,
    ! [X54] :
      ( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X54)
      | class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X54) ),
    file('<stdin>',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_13) ).

fof(c_0_1084,axiom,
    ! [X54] :
      ( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X54)
      | class_LOrder_Omeet__semilorder(X54) ),
    file('<stdin>',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_12) ).

fof(c_0_1085,axiom,
    ! [X54] :
      ( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X54)
      | class_LOrder_Ojoin__semilorder(X54) ),
    file('<stdin>',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_11) ).

fof(c_0_1086,axiom,
    ! [X54] :
      ( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X54)
      | class_LOrder_Olorder(X54) ),
    file('<stdin>',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_10) ).

fof(c_0_1087,axiom,
    ! [X54] :
      ( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X54)
      | class_OrderedGroup_Opordered__ab__semigroup__add(X54) ),
    file('<stdin>',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_1) ).

fof(c_0_1088,axiom,
    ! [X54] :
      ( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X54)
      | class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X54) ),
    file('<stdin>',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_0) ).

fof(c_0_1089,axiom,
    ! [X54] :
      ( ~ class_OrderedGroup_Omonoid__mult(X54)
      | class_HOL_Otimes(X54) ),
    file('<stdin>',clsrel_OrderedGroup_Omonoid__mult_2) ).

fof(c_0_1090,axiom,
    ! [X54] :
      ( ~ class_OrderedGroup_Omonoid__mult(X54)
      | class_OrderedGroup_Osemigroup__mult(X54) ),
    file('<stdin>',clsrel_OrderedGroup_Omonoid__mult_1) ).

fof(c_0_1091,axiom,
    ! [X54] :
      ( ~ class_OrderedGroup_Omonoid__mult(X54)
      | class_HOL_Oone(X54) ),
    file('<stdin>',clsrel_OrderedGroup_Omonoid__mult_0) ).

fof(c_0_1092,axiom,
    ! [X54] :
      ( ~ class_OrderedGroup_Olordered__ab__group__meet(X54)
      | class_Orderings_Oord(X54) ),
    file('<stdin>',clsrel_OrderedGroup_Olordered__ab__group__meet_9) ).

fof(c_0_1093,axiom,
    ! [X54] :
      ( ~ class_OrderedGroup_Olordered__ab__group__meet(X54)
      | class_Orderings_Oorder(X54) ),
    file('<stdin>',clsrel_OrderedGroup_Olordered__ab__group__meet_8) ).

fof(c_0_1094,axiom,
    ! [X54] :
      ( ~ class_OrderedGroup_Olordered__ab__group__meet(X54)
      | class_OrderedGroup_Opordered__ab__semigroup__add(X54) ),
    file('<stdin>',clsrel_OrderedGroup_Olordered__ab__group__meet_7) ).

fof(c_0_1095,axiom,
    ! [X54] :
      ( ~ class_OrderedGroup_Olordered__ab__group__meet(X54)
      | class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X54) ),
    file('<stdin>',clsrel_OrderedGroup_Olordered__ab__group__meet_6) ).

fof(c_0_1096,axiom,
    ! [X54] :
      ( ~ class_OrderedGroup_Olordered__ab__group__meet(X54)
      | class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X54) ),
    file('<stdin>',clsrel_OrderedGroup_Olordered__ab__group__meet_5) ).

fof(c_0_1097,axiom,
    ! [X54] :
      ( ~ class_OrderedGroup_Olordered__ab__group__meet(X54)
      | class_HOL_Ozero(X54) ),
    file('<stdin>',clsrel_OrderedGroup_Olordered__ab__group__meet_4) ).

fof(c_0_1098,axiom,
    ! [X54] :
      ( ~ class_OrderedGroup_Olordered__ab__group__meet(X54)
      | class_OrderedGroup_Ocomm__monoid__add(X54) ),
    file('<stdin>',clsrel_OrderedGroup_Olordered__ab__group__meet_3) ).

fof(c_0_1099,axiom,
    ! [X54] :
      ( ~ class_OrderedGroup_Olordered__ab__group__meet(X54)
      | class_HOL_Ominus(X54) ),
    file('<stdin>',clsrel_OrderedGroup_Olordered__ab__group__meet_2) ).

fof(c_0_1100,axiom,
    ! [X54] :
      ( ~ class_OrderedGroup_Olordered__ab__group__meet(X54)
      | class_LOrder_Ojoin__semilorder(X54) ),
    file('<stdin>',clsrel_OrderedGroup_Olordered__ab__group__meet_18) ).

fof(c_0_1101,axiom,
    ! [X54] :
      ( ~ class_OrderedGroup_Olordered__ab__group__meet(X54)
      | class_LOrder_Olorder(X54) ),
    file('<stdin>',clsrel_OrderedGroup_Olordered__ab__group__meet_17) ).

fof(c_0_1102,axiom,
    ! [X54] :
      ( ~ class_OrderedGroup_Olordered__ab__group__meet(X54)
      | class_OrderedGroup_Olordered__ab__group(X54) ),
    file('<stdin>',clsrel_OrderedGroup_Olordered__ab__group__meet_16) ).

fof(c_0_1103,axiom,
    ! [X54] :
      ( ~ class_OrderedGroup_Olordered__ab__group__meet(X54)
      | class_LOrder_Omeet__semilorder(X54) ),
    file('<stdin>',clsrel_OrderedGroup_Olordered__ab__group__meet_15) ).

fof(c_0_1104,axiom,
    ! [X54] :
      ( ~ class_OrderedGroup_Olordered__ab__group__meet(X54)
      | class_HOL_Oplus(X54) ),
    file('<stdin>',clsrel_OrderedGroup_Olordered__ab__group__meet_14) ).

fof(c_0_1105,axiom,
    ! [X54] :
      ( ~ class_OrderedGroup_Olordered__ab__group__meet(X54)
      | class_OrderedGroup_Osemigroup__add(X54) ),
    file('<stdin>',clsrel_OrderedGroup_Olordered__ab__group__meet_13) ).

fof(c_0_1106,axiom,
    ! [X54] :
      ( ~ class_OrderedGroup_Olordered__ab__group__meet(X54)
      | class_OrderedGroup_Ocancel__semigroup__add(X54) ),
    file('<stdin>',clsrel_OrderedGroup_Olordered__ab__group__meet_12) ).

fof(c_0_1107,axiom,
    ! [X54] :
      ( ~ class_OrderedGroup_Olordered__ab__group__meet(X54)
      | class_OrderedGroup_Oab__semigroup__add(X54) ),
    file('<stdin>',clsrel_OrderedGroup_Olordered__ab__group__meet_11) ).

fof(c_0_1108,axiom,
    ! [X54] :
      ( ~ class_OrderedGroup_Olordered__ab__group__meet(X54)
      | class_OrderedGroup_Ocancel__ab__semigroup__add(X54) ),
    file('<stdin>',clsrel_OrderedGroup_Olordered__ab__group__meet_10) ).

fof(c_0_1109,axiom,
    ! [X54] :
      ( ~ class_OrderedGroup_Olordered__ab__group__meet(X54)
      | class_OrderedGroup_Oab__group__add(X54) ),
    file('<stdin>',clsrel_OrderedGroup_Olordered__ab__group__meet_1) ).

fof(c_0_1110,axiom,
    ! [X54] :
      ( ~ class_OrderedGroup_Olordered__ab__group__meet(X54)
      | class_OrderedGroup_Opordered__ab__group__add(X54) ),
    file('<stdin>',clsrel_OrderedGroup_Olordered__ab__group__meet_0) ).

fof(c_0_1111,axiom,
    ! [X54] :
      ( ~ class_OrderedGroup_Olordered__ab__group__join(X54)
      | class_Orderings_Oord(X54) ),
    file('<stdin>',clsrel_OrderedGroup_Olordered__ab__group__join_9) ).

fof(c_0_1112,axiom,
    ! [X54] :
      ( ~ class_OrderedGroup_Olordered__ab__group__join(X54)
      | class_Orderings_Oorder(X54) ),
    file('<stdin>',clsrel_OrderedGroup_Olordered__ab__group__join_8) ).

fof(c_0_1113,axiom,
    ! [X54] :
      ( ~ class_OrderedGroup_Olordered__ab__group__join(X54)
      | class_OrderedGroup_Opordered__ab__semigroup__add(X54) ),
    file('<stdin>',clsrel_OrderedGroup_Olordered__ab__group__join_7) ).

fof(c_0_1114,axiom,
    ! [X54] :
      ( ~ class_OrderedGroup_Olordered__ab__group__join(X54)
      | class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X54) ),
    file('<stdin>',clsrel_OrderedGroup_Olordered__ab__group__join_6) ).

fof(c_0_1115,axiom,
    ! [X54] :
      ( ~ class_OrderedGroup_Olordered__ab__group__join(X54)
      | class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X54) ),
    file('<stdin>',clsrel_OrderedGroup_Olordered__ab__group__join_5) ).

fof(c_0_1116,axiom,
    ! [X54] :
      ( ~ class_OrderedGroup_Olordered__ab__group__join(X54)
      | class_HOL_Ozero(X54) ),
    file('<stdin>',clsrel_OrderedGroup_Olordered__ab__group__join_4) ).

fof(c_0_1117,axiom,
    ! [X54] :
      ( ~ class_OrderedGroup_Olordered__ab__group__join(X54)
      | class_OrderedGroup_Ocomm__monoid__add(X54) ),
    file('<stdin>',clsrel_OrderedGroup_Olordered__ab__group__join_3) ).

fof(c_0_1118,axiom,
    ! [X54] :
      ( ~ class_OrderedGroup_Olordered__ab__group__join(X54)
      | class_HOL_Ominus(X54) ),
    file('<stdin>',clsrel_OrderedGroup_Olordered__ab__group__join_2) ).

fof(c_0_1119,axiom,
    ! [X54] :
      ( ~ class_OrderedGroup_Olordered__ab__group__join(X54)
      | class_LOrder_Omeet__semilorder(X54) ),
    file('<stdin>',clsrel_OrderedGroup_Olordered__ab__group__join_18) ).

fof(c_0_1120,axiom,
    ! [X54] :
      ( ~ class_OrderedGroup_Olordered__ab__group__join(X54)
      | class_LOrder_Olorder(X54) ),
    file('<stdin>',clsrel_OrderedGroup_Olordered__ab__group__join_17) ).

fof(c_0_1121,axiom,
    ! [X54] :
      ( ~ class_OrderedGroup_Olordered__ab__group__join(X54)
      | class_OrderedGroup_Olordered__ab__group(X54) ),
    file('<stdin>',clsrel_OrderedGroup_Olordered__ab__group__join_16) ).

fof(c_0_1122,axiom,
    ! [X54] :
      ( ~ class_OrderedGroup_Olordered__ab__group__join(X54)
      | class_LOrder_Ojoin__semilorder(X54) ),
    file('<stdin>',clsrel_OrderedGroup_Olordered__ab__group__join_15) ).

fof(c_0_1123,axiom,
    ! [X54] :
      ( ~ class_OrderedGroup_Olordered__ab__group__join(X54)
      | class_HOL_Oplus(X54) ),
    file('<stdin>',clsrel_OrderedGroup_Olordered__ab__group__join_14) ).

fof(c_0_1124,axiom,
    ! [X54] :
      ( ~ class_OrderedGroup_Olordered__ab__group__join(X54)
      | class_OrderedGroup_Osemigroup__add(X54) ),
    file('<stdin>',clsrel_OrderedGroup_Olordered__ab__group__join_13) ).

fof(c_0_1125,axiom,
    ! [X54] :
      ( ~ class_OrderedGroup_Olordered__ab__group__join(X54)
      | class_OrderedGroup_Ocancel__semigroup__add(X54) ),
    file('<stdin>',clsrel_OrderedGroup_Olordered__ab__group__join_12) ).

fof(c_0_1126,axiom,
    ! [X54] :
      ( ~ class_OrderedGroup_Olordered__ab__group__join(X54)
      | class_OrderedGroup_Oab__semigroup__add(X54) ),
    file('<stdin>',clsrel_OrderedGroup_Olordered__ab__group__join_11) ).

fof(c_0_1127,axiom,
    ! [X54] :
      ( ~ class_OrderedGroup_Olordered__ab__group__join(X54)
      | class_OrderedGroup_Ocancel__ab__semigroup__add(X54) ),
    file('<stdin>',clsrel_OrderedGroup_Olordered__ab__group__join_10) ).

fof(c_0_1128,axiom,
    ! [X54] :
      ( ~ class_OrderedGroup_Olordered__ab__group__join(X54)
      | class_OrderedGroup_Oab__group__add(X54) ),
    file('<stdin>',clsrel_OrderedGroup_Olordered__ab__group__join_1) ).

fof(c_0_1129,axiom,
    ! [X54] :
      ( ~ class_OrderedGroup_Olordered__ab__group__join(X54)
      | class_OrderedGroup_Opordered__ab__group__add(X54) ),
    file('<stdin>',clsrel_OrderedGroup_Olordered__ab__group__join_0) ).

fof(c_0_1130,axiom,
    ! [X54] :
      ( ~ class_OrderedGroup_Olordered__ab__group__abs(X54)
      | class_OrderedGroup_Ocancel__ab__semigroup__add(X54) ),
    file('<stdin>',clsrel_OrderedGroup_Olordered__ab__group__abs_9) ).

fof(c_0_1131,axiom,
    ! [X54] :
      ( ~ class_OrderedGroup_Olordered__ab__group__abs(X54)
      | class_OrderedGroup_Opordered__ab__semigroup__add(X54) ),
    file('<stdin>',clsrel_OrderedGroup_Olordered__ab__group__abs_8) ).

fof(c_0_1132,axiom,
    ! [X54] :
      ( ~ class_OrderedGroup_Olordered__ab__group__abs(X54)
      | class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X54) ),
    file('<stdin>',clsrel_OrderedGroup_Olordered__ab__group__abs_7) ).

fof(c_0_1133,axiom,
    ! [X54] :
      ( ~ class_OrderedGroup_Olordered__ab__group__abs(X54)
      | class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X54) ),
    file('<stdin>',clsrel_OrderedGroup_Olordered__ab__group__abs_6) ).

fof(c_0_1134,axiom,
    ! [X54] :
      ( ~ class_OrderedGroup_Olordered__ab__group__abs(X54)
      | class_HOL_Ozero(X54) ),
    file('<stdin>',clsrel_OrderedGroup_Olordered__ab__group__abs_5) ).

fof(c_0_1135,axiom,
    ! [X54] :
      ( ~ class_OrderedGroup_Olordered__ab__group__abs(X54)
      | class_OrderedGroup_Ocomm__monoid__add(X54) ),
    file('<stdin>',clsrel_OrderedGroup_Olordered__ab__group__abs_4) ).

fof(c_0_1136,axiom,
    ! [X54] :
      ( ~ class_OrderedGroup_Olordered__ab__group__abs(X54)
      | class_HOL_Ominus(X54) ),
    file('<stdin>',clsrel_OrderedGroup_Olordered__ab__group__abs_3) ).

fof(c_0_1137,axiom,
    ! [X54] :
      ( ~ class_OrderedGroup_Olordered__ab__group__abs(X54)
      | class_OrderedGroup_Oab__group__add(X54) ),
    file('<stdin>',clsrel_OrderedGroup_Olordered__ab__group__abs_2) ).

fof(c_0_1138,axiom,
    ! [X54] :
      ( ~ class_OrderedGroup_Olordered__ab__group__abs(X54)
      | class_Orderings_Oord(X54) ),
    file('<stdin>',clsrel_OrderedGroup_Olordered__ab__group__abs_18) ).

fof(c_0_1139,axiom,
    ! [X54] :
      ( ~ class_OrderedGroup_Olordered__ab__group__abs(X54)
      | class_Orderings_Oorder(X54) ),
    file('<stdin>',clsrel_OrderedGroup_Olordered__ab__group__abs_17) ).

fof(c_0_1140,axiom,
    ! [X54] :
      ( ~ class_OrderedGroup_Olordered__ab__group__abs(X54)
      | class_LOrder_Omeet__semilorder(X54) ),
    file('<stdin>',clsrel_OrderedGroup_Olordered__ab__group__abs_16) ).

fof(c_0_1141,axiom,
    ! [X54] :
      ( ~ class_OrderedGroup_Olordered__ab__group__abs(X54)
      | class_LOrder_Ojoin__semilorder(X54) ),
    file('<stdin>',clsrel_OrderedGroup_Olordered__ab__group__abs_15) ).

fof(c_0_1142,axiom,
    ! [X54] :
      ( ~ class_OrderedGroup_Olordered__ab__group__abs(X54)
      | class_LOrder_Olorder(X54) ),
    file('<stdin>',clsrel_OrderedGroup_Olordered__ab__group__abs_14) ).

fof(c_0_1143,axiom,
    ! [X54] :
      ( ~ class_OrderedGroup_Olordered__ab__group__abs(X54)
      | class_HOL_Oplus(X54) ),
    file('<stdin>',clsrel_OrderedGroup_Olordered__ab__group__abs_13) ).

fof(c_0_1144,axiom,
    ! [X54] :
      ( ~ class_OrderedGroup_Olordered__ab__group__abs(X54)
      | class_OrderedGroup_Osemigroup__add(X54) ),
    file('<stdin>',clsrel_OrderedGroup_Olordered__ab__group__abs_12) ).

fof(c_0_1145,axiom,
    ! [X54] :
      ( ~ class_OrderedGroup_Olordered__ab__group__abs(X54)
      | class_OrderedGroup_Ocancel__semigroup__add(X54) ),
    file('<stdin>',clsrel_OrderedGroup_Olordered__ab__group__abs_11) ).

fof(c_0_1146,axiom,
    ! [X54] :
      ( ~ class_OrderedGroup_Olordered__ab__group__abs(X54)
      | class_OrderedGroup_Oab__semigroup__add(X54) ),
    file('<stdin>',clsrel_OrderedGroup_Olordered__ab__group__abs_10) ).

fof(c_0_1147,axiom,
    ! [X54] :
      ( ~ class_OrderedGroup_Olordered__ab__group__abs(X54)
      | class_OrderedGroup_Opordered__ab__group__add(X54) ),
    file('<stdin>',clsrel_OrderedGroup_Olordered__ab__group__abs_1) ).

fof(c_0_1148,axiom,
    ! [X54] :
      ( ~ class_OrderedGroup_Olordered__ab__group__abs(X54)
      | class_OrderedGroup_Olordered__ab__group(X54) ),
    file('<stdin>',clsrel_OrderedGroup_Olordered__ab__group__abs_0) ).

fof(c_0_1149,axiom,
    ! [X54] :
      ( ~ class_OrderedGroup_Olordered__ab__group(X54)
      | class_Orderings_Oord(X54) ),
    file('<stdin>',clsrel_OrderedGroup_Olordered__ab__group_9) ).

fof(c_0_1150,axiom,
    ! [X54] :
      ( ~ class_OrderedGroup_Olordered__ab__group(X54)
      | class_Orderings_Oorder(X54) ),
    file('<stdin>',clsrel_OrderedGroup_Olordered__ab__group_8) ).

fof(c_0_1151,axiom,
    ! [X54] :
      ( ~ class_OrderedGroup_Olordered__ab__group(X54)
      | class_OrderedGroup_Opordered__ab__semigroup__add(X54) ),
    file('<stdin>',clsrel_OrderedGroup_Olordered__ab__group_7) ).

fof(c_0_1152,axiom,
    ! [X54] :
      ( ~ class_OrderedGroup_Olordered__ab__group(X54)
      | class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X54) ),
    file('<stdin>',clsrel_OrderedGroup_Olordered__ab__group_6) ).

fof(c_0_1153,axiom,
    ! [X54] :
      ( ~ class_OrderedGroup_Olordered__ab__group(X54)
      | class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X54) ),
    file('<stdin>',clsrel_OrderedGroup_Olordered__ab__group_5) ).

fof(c_0_1154,axiom,
    ! [X54] :
      ( ~ class_OrderedGroup_Olordered__ab__group(X54)
      | class_HOL_Ozero(X54) ),
    file('<stdin>',clsrel_OrderedGroup_Olordered__ab__group_4) ).

fof(c_0_1155,axiom,
    ! [X54] :
      ( ~ class_OrderedGroup_Olordered__ab__group(X54)
      | class_OrderedGroup_Ocomm__monoid__add(X54) ),
    file('<stdin>',clsrel_OrderedGroup_Olordered__ab__group_3) ).

fof(c_0_1156,axiom,
    ! [X54] :
      ( ~ class_OrderedGroup_Olordered__ab__group(X54)
      | class_HOL_Ominus(X54) ),
    file('<stdin>',clsrel_OrderedGroup_Olordered__ab__group_2) ).

fof(c_0_1157,axiom,
    ! [X54] :
      ( ~ class_OrderedGroup_Olordered__ab__group(X54)
      | class_LOrder_Omeet__semilorder(X54) ),
    file('<stdin>',clsrel_OrderedGroup_Olordered__ab__group_17) ).

fof(c_0_1158,axiom,
    ! [X54] :
      ( ~ class_OrderedGroup_Olordered__ab__group(X54)
      | class_LOrder_Ojoin__semilorder(X54) ),
    file('<stdin>',clsrel_OrderedGroup_Olordered__ab__group_16) ).

fof(c_0_1159,axiom,
    ! [X54] :
      ( ~ class_OrderedGroup_Olordered__ab__group(X54)
      | class_LOrder_Olorder(X54) ),
    file('<stdin>',clsrel_OrderedGroup_Olordered__ab__group_15) ).

fof(c_0_1160,axiom,
    ! [X54] :
      ( ~ class_OrderedGroup_Olordered__ab__group(X54)
      | class_HOL_Oplus(X54) ),
    file('<stdin>',clsrel_OrderedGroup_Olordered__ab__group_14) ).

fof(c_0_1161,axiom,
    ! [X54] :
      ( ~ class_OrderedGroup_Olordered__ab__group(X54)
      | class_OrderedGroup_Osemigroup__add(X54) ),
    file('<stdin>',clsrel_OrderedGroup_Olordered__ab__group_13) ).

fof(c_0_1162,axiom,
    ! [X54] :
      ( ~ class_OrderedGroup_Olordered__ab__group(X54)
      | class_OrderedGroup_Ocancel__semigroup__add(X54) ),
    file('<stdin>',clsrel_OrderedGroup_Olordered__ab__group_12) ).

fof(c_0_1163,axiom,
    ! [X54] :
      ( ~ class_OrderedGroup_Olordered__ab__group(X54)
      | class_OrderedGroup_Oab__semigroup__add(X54) ),
    file('<stdin>',clsrel_OrderedGroup_Olordered__ab__group_11) ).

fof(c_0_1164,axiom,
    ! [X54] :
      ( ~ class_OrderedGroup_Olordered__ab__group(X54)
      | class_OrderedGroup_Ocancel__ab__semigroup__add(X54) ),
    file('<stdin>',clsrel_OrderedGroup_Olordered__ab__group_10) ).

fof(c_0_1165,axiom,
    ! [X54] :
      ( ~ class_OrderedGroup_Olordered__ab__group(X54)
      | class_OrderedGroup_Oab__group__add(X54) ),
    file('<stdin>',clsrel_OrderedGroup_Olordered__ab__group_1) ).

fof(c_0_1166,axiom,
    ! [X54] :
      ( ~ class_OrderedGroup_Olordered__ab__group(X54)
      | class_OrderedGroup_Opordered__ab__group__add(X54) ),
    file('<stdin>',clsrel_OrderedGroup_Olordered__ab__group_0) ).

fof(c_0_1167,axiom,
    ! [X54] :
      ( ~ class_OrderedGroup_Ocomm__monoid__mult(X54)
      | class_OrderedGroup_Omonoid__mult(X54) ),
    file('<stdin>',clsrel_OrderedGroup_Ocomm__monoid__mult_4) ).

fof(c_0_1168,axiom,
    ! [X54] :
      ( ~ class_OrderedGroup_Ocomm__monoid__mult(X54)
      | class_HOL_Otimes(X54) ),
    file('<stdin>',clsrel_OrderedGroup_Ocomm__monoid__mult_3) ).

fof(c_0_1169,axiom,
    ! [X54] :
      ( ~ class_OrderedGroup_Ocomm__monoid__mult(X54)
      | class_OrderedGroup_Osemigroup__mult(X54) ),
    file('<stdin>',clsrel_OrderedGroup_Ocomm__monoid__mult_2) ).

fof(c_0_1170,axiom,
    ! [X54] :
      ( ~ class_OrderedGroup_Ocomm__monoid__mult(X54)
      | class_OrderedGroup_Oab__semigroup__mult(X54) ),
    file('<stdin>',clsrel_OrderedGroup_Ocomm__monoid__mult_1) ).

fof(c_0_1171,axiom,
    ! [X54] :
      ( ~ class_OrderedGroup_Ocomm__monoid__mult(X54)
      | class_HOL_Oone(X54) ),
    file('<stdin>',clsrel_OrderedGroup_Ocomm__monoid__mult_0) ).

fof(c_0_1172,axiom,
    ! [X54] :
      ( ~ class_OrderedGroup_Ocomm__monoid__add(X54)
      | class_HOL_Oplus(X54) ),
    file('<stdin>',clsrel_OrderedGroup_Ocomm__monoid__add_3) ).

fof(c_0_1173,axiom,
    ! [X54] :
      ( ~ class_OrderedGroup_Ocomm__monoid__add(X54)
      | class_OrderedGroup_Osemigroup__add(X54) ),
    file('<stdin>',clsrel_OrderedGroup_Ocomm__monoid__add_2) ).

fof(c_0_1174,axiom,
    ! [X54] :
      ( ~ class_OrderedGroup_Ocomm__monoid__add(X54)
      | class_OrderedGroup_Oab__semigroup__add(X54) ),
    file('<stdin>',clsrel_OrderedGroup_Ocomm__monoid__add_1) ).

fof(c_0_1175,axiom,
    ! [X54] :
      ( ~ class_OrderedGroup_Ocomm__monoid__add(X54)
      | class_HOL_Ozero(X54) ),
    file('<stdin>',clsrel_OrderedGroup_Ocomm__monoid__add_0) ).

fof(c_0_1176,axiom,
    ! [X54] :
      ( ~ class_OrderedGroup_Ocancel__semigroup__add(X54)
      | class_HOL_Oplus(X54) ),
    file('<stdin>',clsrel_OrderedGroup_Ocancel__semigroup__add_1) ).

fof(c_0_1177,axiom,
    ! [X54] :
      ( ~ class_OrderedGroup_Ocancel__semigroup__add(X54)
      | class_OrderedGroup_Osemigroup__add(X54) ),
    file('<stdin>',clsrel_OrderedGroup_Ocancel__semigroup__add_0) ).

fof(c_0_1178,axiom,
    ! [X54] :
      ( ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X54)
      | class_OrderedGroup_Ocancel__semigroup__add(X54) ),
    file('<stdin>',clsrel_OrderedGroup_Ocancel__ab__semigroup__add_3) ).

fof(c_0_1179,axiom,
    ! [X54] :
      ( ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X54)
      | class_HOL_Oplus(X54) ),
    file('<stdin>',clsrel_OrderedGroup_Ocancel__ab__semigroup__add_2) ).

fof(c_0_1180,axiom,
    ! [X54] :
      ( ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X54)
      | class_OrderedGroup_Osemigroup__add(X54) ),
    file('<stdin>',clsrel_OrderedGroup_Ocancel__ab__semigroup__add_1) ).

fof(c_0_1181,axiom,
    ! [X54] :
      ( ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X54)
      | class_OrderedGroup_Oab__semigroup__add(X54) ),
    file('<stdin>',clsrel_OrderedGroup_Ocancel__ab__semigroup__add_0) ).

fof(c_0_1182,axiom,
    ! [X54] :
      ( ~ class_OrderedGroup_Oab__semigroup__mult(X54)
      | class_HOL_Otimes(X54) ),
    file('<stdin>',clsrel_OrderedGroup_Oab__semigroup__mult_1) ).

fof(c_0_1183,axiom,
    ! [X54] :
      ( ~ class_OrderedGroup_Oab__semigroup__mult(X54)
      | class_OrderedGroup_Osemigroup__mult(X54) ),
    file('<stdin>',clsrel_OrderedGroup_Oab__semigroup__mult_0) ).

fof(c_0_1184,axiom,
    ! [X54] :
      ( ~ class_OrderedGroup_Oab__semigroup__add(X54)
      | class_HOL_Oplus(X54) ),
    file('<stdin>',clsrel_OrderedGroup_Oab__semigroup__add_1) ).

fof(c_0_1185,axiom,
    ! [X54] :
      ( ~ class_OrderedGroup_Oab__semigroup__add(X54)
      | class_OrderedGroup_Osemigroup__add(X54) ),
    file('<stdin>',clsrel_OrderedGroup_Oab__semigroup__add_0) ).

fof(c_0_1186,axiom,
    ! [X54] :
      ( ~ class_OrderedGroup_Oab__group__add(X54)
      | class_OrderedGroup_Ocancel__semigroup__add(X54) ),
    file('<stdin>',clsrel_OrderedGroup_Oab__group__add_7) ).

fof(c_0_1187,axiom,
    ! [X54] :
      ( ~ class_OrderedGroup_Oab__group__add(X54)
      | class_OrderedGroup_Ocancel__ab__semigroup__add(X54) ),
    file('<stdin>',clsrel_OrderedGroup_Oab__group__add_6) ).

fof(c_0_1188,axiom,
    ! [X54] :
      ( ~ class_OrderedGroup_Oab__group__add(X54)
      | class_HOL_Oplus(X54) ),
    file('<stdin>',clsrel_OrderedGroup_Oab__group__add_5) ).

fof(c_0_1189,axiom,
    ! [X54] :
      ( ~ class_OrderedGroup_Oab__group__add(X54)
      | class_OrderedGroup_Osemigroup__add(X54) ),
    file('<stdin>',clsrel_OrderedGroup_Oab__group__add_4) ).

fof(c_0_1190,axiom,
    ! [X54] :
      ( ~ class_OrderedGroup_Oab__group__add(X54)
      | class_OrderedGroup_Oab__semigroup__add(X54) ),
    file('<stdin>',clsrel_OrderedGroup_Oab__group__add_3) ).

fof(c_0_1191,axiom,
    ! [X54] :
      ( ~ class_OrderedGroup_Oab__group__add(X54)
      | class_HOL_Ozero(X54) ),
    file('<stdin>',clsrel_OrderedGroup_Oab__group__add_2) ).

fof(c_0_1192,axiom,
    ! [X54] :
      ( ~ class_OrderedGroup_Oab__group__add(X54)
      | class_OrderedGroup_Ocomm__monoid__add(X54) ),
    file('<stdin>',clsrel_OrderedGroup_Oab__group__add_1) ).

fof(c_0_1193,axiom,
    ! [X54] :
      ( ~ class_OrderedGroup_Oab__group__add(X54)
      | class_HOL_Ominus(X54) ),
    file('<stdin>',clsrel_OrderedGroup_Oab__group__add_0) ).

fof(c_0_1194,axiom,
    ! [X54] :
      ( ~ class_Numeral_Onumber__ring(X54)
      | class_OrderedGroup_Ocomm__monoid__add(X54) ),
    file('<stdin>',clsrel_Numeral_Onumber__ring_9) ).

fof(c_0_1195,axiom,
    ! [X54] :
      ( ~ class_Numeral_Onumber__ring(X54)
      | class_HOL_Ozero(X54) ),
    file('<stdin>',clsrel_Numeral_Onumber__ring_8) ).

fof(c_0_1196,axiom,
    ! [X54] :
      ( ~ class_Numeral_Onumber__ring(X54)
      | class_Ring__and__Field_Ocomm__semiring(X54) ),
    file('<stdin>',clsrel_Numeral_Onumber__ring_7) ).

fof(c_0_1197,axiom,
    ! [X54] :
      ( ~ class_Numeral_Onumber__ring(X54)
      | class_Ring__and__Field_Osemiring(X54) ),
    file('<stdin>',clsrel_Numeral_Onumber__ring_6) ).

fof(c_0_1198,axiom,
    ! [X54] :
      ( ~ class_Numeral_Onumber__ring(X54)
      | class_OrderedGroup_Oab__semigroup__mult(X54) ),
    file('<stdin>',clsrel_Numeral_Onumber__ring_5) ).

fof(c_0_1199,axiom,
    ! [X54] :
      ( ~ class_Numeral_Onumber__ring(X54)
      | class_OrderedGroup_Osemigroup__mult(X54) ),
    file('<stdin>',clsrel_Numeral_Onumber__ring_4) ).

fof(c_0_1200,axiom,
    ! [X54] :
      ( ~ class_Numeral_Onumber__ring(X54)
      | class_Numeral_Onumber(X54) ),
    file('<stdin>',clsrel_Numeral_Onumber__ring_30) ).

fof(c_0_1201,axiom,
    ! [X54] :
      ( ~ class_Numeral_Onumber__ring(X54)
      | class_HOL_Otimes(X54) ),
    file('<stdin>',clsrel_Numeral_Onumber__ring_3) ).

fof(c_0_1202,axiom,
    ! [X54] :
      ( ~ class_Numeral_Onumber__ring(X54)
      | class_Ring__and__Field_Ocomm__ring__1(X54) ),
    file('<stdin>',clsrel_Numeral_Onumber__ring_29) ).

fof(c_0_1203,axiom,
    ! [X54] :
      ( ~ class_Numeral_Onumber__ring(X54)
      | class_Ring__and__Field_Ocomm__semiring__1__cancel(X54) ),
    file('<stdin>',clsrel_Numeral_Onumber__ring_28) ).

fof(c_0_1204,axiom,
    ! [X54] :
      ( ~ class_Numeral_Onumber__ring(X54)
      | class_Ring__and__Field_Oring__1(X54) ),
    file('<stdin>',clsrel_Numeral_Onumber__ring_27) ).

fof(c_0_1205,axiom,
    ! [X54] :
      ( ~ class_Numeral_Onumber__ring(X54)
      | class_Ring__and__Field_Osemiring__1__cancel(X54) ),
    file('<stdin>',clsrel_Numeral_Onumber__ring_26) ).

fof(c_0_1206,axiom,
    ! [X54] :
      ( ~ class_Numeral_Onumber__ring(X54)
      | class_Ring__and__Field_Ocomm__semiring__1(X54) ),
    file('<stdin>',clsrel_Numeral_Onumber__ring_25) ).

fof(c_0_1207,axiom,
    ! [X54] :
      ( ~ class_Numeral_Onumber__ring(X54)
      | class_Ring__and__Field_Osemiring__1(X54) ),
    file('<stdin>',clsrel_Numeral_Onumber__ring_24) ).

fof(c_0_1208,axiom,
    ! [X54] :
      ( ~ class_Numeral_Onumber__ring(X54)
      | class_OrderedGroup_Ocomm__monoid__mult(X54) ),
    file('<stdin>',clsrel_Numeral_Onumber__ring_23) ).

fof(c_0_1209,axiom,
    ! [X54] :
      ( ~ class_Numeral_Onumber__ring(X54)
      | class_OrderedGroup_Omonoid__mult(X54) ),
    file('<stdin>',clsrel_Numeral_Onumber__ring_22) ).

fof(c_0_1210,axiom,
    ! [X54] :
      ( ~ class_Numeral_Onumber__ring(X54)
      | class_Ring__and__Field_Oaxclass__0__neq__1(X54) ),
    file('<stdin>',clsrel_Numeral_Onumber__ring_21) ).

fof(c_0_1211,axiom,
    ! [X54] :
      ( ~ class_Numeral_Onumber__ring(X54)
      | class_HOL_Oone(X54) ),
    file('<stdin>',clsrel_Numeral_Onumber__ring_20) ).

fof(c_0_1212,axiom,
    ! [X54] :
      ( ~ class_Numeral_Onumber__ring(X54)
      | class_OrderedGroup_Oab__semigroup__add(X54) ),
    file('<stdin>',clsrel_Numeral_Onumber__ring_2) ).

fof(c_0_1213,axiom,
    ! [X54] :
      ( ~ class_Numeral_Onumber__ring(X54)
      | class_Ring__and__Field_Ocomm__ring(X54) ),
    file('<stdin>',clsrel_Numeral_Onumber__ring_19) ).

fof(c_0_1214,axiom,
    ! [X54] :
      ( ~ class_Numeral_Onumber__ring(X54)
      | class_Ring__and__Field_Ocomm__semiring__0__cancel(X54) ),
    file('<stdin>',clsrel_Numeral_Onumber__ring_18) ).

fof(c_0_1215,axiom,
    ! [X54] :
      ( ~ class_Numeral_Onumber__ring(X54)
      | class_Ring__and__Field_Oring(X54) ),
    file('<stdin>',clsrel_Numeral_Onumber__ring_17) ).

fof(c_0_1216,axiom,
    ! [X54] :
      ( ~ class_Numeral_Onumber__ring(X54)
      | class_Ring__and__Field_Osemiring__0__cancel(X54) ),
    file('<stdin>',clsrel_Numeral_Onumber__ring_16) ).

fof(c_0_1217,axiom,
    ! [X54] :
      ( ~ class_Numeral_Onumber__ring(X54)
      | class_OrderedGroup_Oab__group__add(X54) ),
    file('<stdin>',clsrel_Numeral_Onumber__ring_15) ).

fof(c_0_1218,axiom,
    ! [X54] :
      ( ~ class_Numeral_Onumber__ring(X54)
      | class_OrderedGroup_Ocancel__ab__semigroup__add(X54) ),
    file('<stdin>',clsrel_Numeral_Onumber__ring_14) ).

fof(c_0_1219,axiom,
    ! [X54] :
      ( ~ class_Numeral_Onumber__ring(X54)
      | class_OrderedGroup_Ocancel__semigroup__add(X54) ),
    file('<stdin>',clsrel_Numeral_Onumber__ring_13) ).

fof(c_0_1220,axiom,
    ! [X54] :
      ( ~ class_Numeral_Onumber__ring(X54)
      | class_HOL_Ominus(X54) ),
    file('<stdin>',clsrel_Numeral_Onumber__ring_12) ).

fof(c_0_1221,axiom,
    ! [X54] :
      ( ~ class_Numeral_Onumber__ring(X54)
      | class_Ring__and__Field_Ocomm__semiring__0(X54) ),
    file('<stdin>',clsrel_Numeral_Onumber__ring_11) ).

fof(c_0_1222,axiom,
    ! [X54] :
      ( ~ class_Numeral_Onumber__ring(X54)
      | class_Ring__and__Field_Osemiring__0(X54) ),
    file('<stdin>',clsrel_Numeral_Onumber__ring_10) ).

fof(c_0_1223,axiom,
    ! [X54] :
      ( ~ class_Numeral_Onumber__ring(X54)
      | class_OrderedGroup_Osemigroup__add(X54) ),
    file('<stdin>',clsrel_Numeral_Onumber__ring_1) ).

fof(c_0_1224,axiom,
    ! [X54] :
      ( ~ class_Numeral_Onumber__ring(X54)
      | class_HOL_Oplus(X54) ),
    file('<stdin>',clsrel_Numeral_Onumber__ring_0) ).

fof(c_0_1225,axiom,
    ! [X54] :
      ( ~ class_LOrder_Omeet__semilorder(X54)
      | class_Orderings_Oorder(X54) ),
    file('<stdin>',clsrel_LOrder_Omeet__semilorder_1) ).

fof(c_0_1226,axiom,
    ! [X54] :
      ( ~ class_LOrder_Omeet__semilorder(X54)
      | class_Orderings_Oord(X54) ),
    file('<stdin>',clsrel_LOrder_Omeet__semilorder_0) ).

fof(c_0_1227,axiom,
    ! [X54] :
      ( ~ class_LOrder_Olorder(X54)
      | class_LOrder_Ojoin__semilorder(X54) ),
    file('<stdin>',clsrel_LOrder_Olorder_3) ).

fof(c_0_1228,axiom,
    ! [X54] :
      ( ~ class_LOrder_Olorder(X54)
      | class_Orderings_Oorder(X54) ),
    file('<stdin>',clsrel_LOrder_Olorder_2) ).

fof(c_0_1229,axiom,
    ! [X54] :
      ( ~ class_LOrder_Olorder(X54)
      | class_Orderings_Oord(X54) ),
    file('<stdin>',clsrel_LOrder_Olorder_1) ).

fof(c_0_1230,axiom,
    ! [X54] :
      ( ~ class_LOrder_Olorder(X54)
      | class_LOrder_Omeet__semilorder(X54) ),
    file('<stdin>',clsrel_LOrder_Olorder_0) ).

fof(c_0_1231,axiom,
    ! [X54] :
      ( ~ class_LOrder_Ojoin__semilorder(X54)
      | class_Orderings_Oorder(X54) ),
    file('<stdin>',clsrel_LOrder_Ojoin__semilorder_1) ).

fof(c_0_1232,axiom,
    ! [X54] :
      ( ~ class_LOrder_Ojoin__semilorder(X54)
      | class_Orderings_Oord(X54) ),
    file('<stdin>',clsrel_LOrder_Ojoin__semilorder_0) ).

fof(c_0_1233,axiom,
    c_Wellfounded__Recursion_Owf(c_Wellfounded__Relations_Oless__than,tc_nat),
    file('<stdin>',cls_Wellfounded__Relations_Owf__less__than_0) ).

fof(c_0_1234,axiom,
    c_Relation_Otrans(c_Wellfounded__Relations_Oless__than,tc_nat),
    file('<stdin>',cls_Wellfounded__Relations_Otrans__less__than_0) ).

fof(c_0_1235,axiom,
    ! [X52] : class_Nat_Opower(tc_set(X52)),
    file('<stdin>',clsarity_set_4) ).

fof(c_0_1236,axiom,
    ! [X52] : class_Orderings_Oorder(tc_set(X52)),
    file('<stdin>',clsarity_set_2) ).

fof(c_0_1237,axiom,
    ! [X52] : class_Orderings_Oord(tc_set(X52)),
    file('<stdin>',clsarity_set_1) ).

fof(c_0_1238,axiom,
    ! [X52] : class_HOL_Ominus(tc_set(X52)),
    file('<stdin>',clsarity_set_0) ).

fof(c_0_1239,axiom,
    ! [X13] : c_0 != c_Suc(X13),
    file('<stdin>',cls_Nat_OZero__not__Suc__iff1_0) ).

fof(c_0_1240,axiom,
    ! [X13] : c_Suc(X13) != c_0,
    file('<stdin>',cls_Nat_OSuc__not__Zero__iff1_0) ).

fof(c_0_1241,axiom,
    class_HOL_Ominus(tc_nat),
    file('<stdin>',clsarity_nat_9) ).

fof(c_0_1242,axiom,
    class_Wellfounded__Recursion_Owellorder(tc_nat),
    file('<stdin>',clsarity_nat_8) ).

fof(c_0_1243,axiom,
    class_Orderings_Olinorder(tc_nat),
    file('<stdin>',clsarity_nat_7) ).

fof(c_0_1244,axiom,
    class_LOrder_Olorder(tc_nat),
    file('<stdin>',clsarity_nat_6) ).

fof(c_0_1245,axiom,
    class_LOrder_Ojoin__semilorder(tc_nat),
    file('<stdin>',clsarity_nat_5) ).

fof(c_0_1246,axiom,
    class_Parity_Oeven__odd(tc_nat),
    file('<stdin>',clsarity_nat_47) ).

fof(c_0_1247,axiom,
    class_Numeral_Onumber(tc_nat),
    file('<stdin>',clsarity_nat_46) ).

fof(c_0_1248,axiom,
    class_Power_Orecpower(tc_nat),
    file('<stdin>',clsarity_nat_45) ).

fof(c_0_1249,axiom,
    class_Divides_Odiv(tc_nat),
    file('<stdin>',clsarity_nat_44) ).

fof(c_0_1250,axiom,
    class_Ring__and__Field_Oordered__semidom(tc_nat),
    file('<stdin>',clsarity_nat_43) ).

fof(c_0_1251,axiom,
    class_Ring__and__Field_Oordered__comm__semiring__strict(tc_nat),
    file('<stdin>',clsarity_nat_42) ).

fof(c_0_1252,axiom,
    class_Ring__and__Field_Opordered__cancel__comm__semiring(tc_nat),
    file('<stdin>',clsarity_nat_41) ).

fof(c_0_1253,axiom,
    class_Ring__and__Field_Opordered__comm__semiring(tc_nat),
    file('<stdin>',clsarity_nat_40) ).

fof(c_0_1254,axiom,
    class_LOrder_Omeet__semilorder(tc_nat),
    file('<stdin>',clsarity_nat_4) ).

fof(c_0_1255,axiom,
    class_Ring__and__Field_Oordered__semiring__strict(tc_nat),
    file('<stdin>',clsarity_nat_39) ).

fof(c_0_1256,axiom,
    class_Ring__and__Field_Opordered__cancel__semiring(tc_nat),
    file('<stdin>',clsarity_nat_38) ).

fof(c_0_1257,axiom,
    class_Ring__and__Field_Opordered__semiring(tc_nat),
    file('<stdin>',clsarity_nat_37) ).

fof(c_0_1258,axiom,
    class_OrderedGroup_Oordered__cancel__ab__semigroup__add(tc_nat),
    file('<stdin>',clsarity_nat_36) ).

fof(c_0_1259,axiom,
    class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat),
    file('<stdin>',clsarity_nat_35) ).

fof(c_0_1260,axiom,
    class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat),
    file('<stdin>',clsarity_nat_34) ).

fof(c_0_1261,axiom,
    class_OrderedGroup_Opordered__ab__semigroup__add(tc_nat),
    file('<stdin>',clsarity_nat_33) ).

fof(c_0_1262,axiom,
    class_Ring__and__Field_Ocomm__semiring__1__cancel(tc_nat),
    file('<stdin>',clsarity_nat_32) ).

fof(c_0_1263,axiom,
    class_Ring__and__Field_Ocomm__semiring__0__cancel(tc_nat),
    file('<stdin>',clsarity_nat_31) ).

fof(c_0_1264,axiom,
    class_Ring__and__Field_Osemiring__1__cancel(tc_nat),
    file('<stdin>',clsarity_nat_30) ).

fof(c_0_1265,axiom,
    class_Orderings_Oorder(tc_nat),
    file('<stdin>',clsarity_nat_3) ).

fof(c_0_1266,axiom,
    class_Ring__and__Field_Osemiring__0__cancel(tc_nat),
    file('<stdin>',clsarity_nat_29) ).

fof(c_0_1267,axiom,
    class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat),
    file('<stdin>',clsarity_nat_28) ).

fof(c_0_1268,axiom,
    class_OrderedGroup_Ocancel__semigroup__add(tc_nat),
    file('<stdin>',clsarity_nat_27) ).

fof(c_0_1269,axiom,
    class_Ring__and__Field_Ocomm__semiring__1(tc_nat),
    file('<stdin>',clsarity_nat_26) ).

fof(c_0_1270,axiom,
    class_Ring__and__Field_Osemiring__1(tc_nat),
    file('<stdin>',clsarity_nat_25) ).

fof(c_0_1271,axiom,
    class_OrderedGroup_Ocomm__monoid__mult(tc_nat),
    file('<stdin>',clsarity_nat_24) ).

fof(c_0_1272,axiom,
    class_OrderedGroup_Omonoid__mult(tc_nat),
    file('<stdin>',clsarity_nat_23) ).

fof(c_0_1273,axiom,
    class_Ring__and__Field_Ocomm__semiring__0(tc_nat),
    file('<stdin>',clsarity_nat_22) ).

fof(c_0_1274,axiom,
    class_Ring__and__Field_Osemiring__0(tc_nat),
    file('<stdin>',clsarity_nat_21) ).

fof(c_0_1275,axiom,
    class_OrderedGroup_Ocomm__monoid__add(tc_nat),
    file('<stdin>',clsarity_nat_20) ).

fof(c_0_1276,axiom,
    class_Orderings_Oord(tc_nat),
    file('<stdin>',clsarity_nat_2) ).

fof(c_0_1277,axiom,
    class_Ring__and__Field_Ocomm__semiring(tc_nat),
    file('<stdin>',clsarity_nat_19) ).

fof(c_0_1278,axiom,
    class_Ring__and__Field_Osemiring(tc_nat),
    file('<stdin>',clsarity_nat_18) ).

fof(c_0_1279,axiom,
    class_OrderedGroup_Oab__semigroup__mult(tc_nat),
    file('<stdin>',clsarity_nat_17) ).

fof(c_0_1280,axiom,
    class_OrderedGroup_Osemigroup__mult(tc_nat),
    file('<stdin>',clsarity_nat_16) ).

fof(c_0_1281,axiom,
    class_OrderedGroup_Oab__semigroup__add(tc_nat),
    file('<stdin>',clsarity_nat_15) ).

fof(c_0_1282,axiom,
    class_OrderedGroup_Osemigroup__add(tc_nat),
    file('<stdin>',clsarity_nat_14) ).

fof(c_0_1283,axiom,
    class_Ring__and__Field_Oaxclass__0__neq__1(tc_nat),
    file('<stdin>',clsarity_nat_13) ).

fof(c_0_1284,axiom,
    class_Nat_Opower(tc_nat),
    file('<stdin>',clsarity_nat_12) ).

fof(c_0_1285,axiom,
    class_HOL_Otimes(tc_nat),
    file('<stdin>',clsarity_nat_11) ).

fof(c_0_1286,axiom,
    class_HOL_Oplus(tc_nat),
    file('<stdin>',clsarity_nat_10) ).

fof(c_0_1287,axiom,
    class_HOL_Ozero(tc_nat),
    file('<stdin>',clsarity_nat_1) ).

fof(c_0_1288,axiom,
    class_HOL_Oone(tc_nat),
    file('<stdin>',clsarity_nat_0) ).

fof(c_0_1289,axiom,
    class_Finite__Set_Ofinite(tc_bool),
    file('<stdin>',clsarity_bool_0) ).

fof(c_0_1290,axiom,
    class_Finite__Set_Ofinite(tc_Product__Type_Ounit),
    file('<stdin>',clsarity_Product____Type__Ounit_0) ).

fof(c_0_1291,axiom,
    class_OrderedGroup_Oab__semigroup__mult(tc_IntDef_Oint),
    file('<stdin>',clsarity_IntDef__Oint_9) ).

fof(c_0_1292,axiom,
    class_OrderedGroup_Osemigroup__mult(tc_IntDef_Oint),
    file('<stdin>',clsarity_IntDef__Oint_8) ).

fof(c_0_1293,axiom,
    class_OrderedGroup_Oab__semigroup__add(tc_IntDef_Oint),
    file('<stdin>',clsarity_IntDef__Oint_7) ).

fof(c_0_1294,axiom,
    class_Parity_Oeven__odd(tc_IntDef_Oint),
    file('<stdin>',clsarity_IntDef__Oint_64) ).

fof(c_0_1295,axiom,
    class_Power_Orecpower(tc_IntDef_Oint),
    file('<stdin>',clsarity_IntDef__Oint_63) ).

fof(c_0_1296,axiom,
    class_Nat_Opower(tc_IntDef_Oint),
    file('<stdin>',clsarity_IntDef__Oint_62) ).

fof(c_0_1297,axiom,
    class_Divides_Odiv(tc_IntDef_Oint),
    file('<stdin>',clsarity_IntDef__Oint_61) ).

fof(c_0_1298,axiom,
    class_Numeral_Onumber__ring(tc_IntDef_Oint),
    file('<stdin>',clsarity_IntDef__Oint_60) ).

fof(c_0_1299,axiom,
    class_OrderedGroup_Osemigroup__add(tc_IntDef_Oint),
    file('<stdin>',clsarity_IntDef__Oint_6) ).

fof(c_0_1300,axiom,
    class_Numeral_Onumber(tc_IntDef_Oint),
    file('<stdin>',clsarity_IntDef__Oint_59) ).

fof(c_0_1301,axiom,
    class_Ring__and__Field_Oordered__idom(tc_IntDef_Oint),
    file('<stdin>',clsarity_IntDef__Oint_58) ).

fof(c_0_1302,axiom,
    class_Ring__and__Field_Oidom(tc_IntDef_Oint),
    file('<stdin>',clsarity_IntDef__Oint_57) ).

fof(c_0_1303,axiom,
    class_Ring__and__Field_Oordered__semidom(tc_IntDef_Oint),
    file('<stdin>',clsarity_IntDef__Oint_56) ).

fof(c_0_1304,axiom,
    class_Ring__and__Field_Oordered__ring__strict(tc_IntDef_Oint),
    file('<stdin>',clsarity_IntDef__Oint_55) ).

fof(c_0_1305,axiom,
    class_Ring__and__Field_Oaxclass__no__zero__divisors(tc_IntDef_Oint),
    file('<stdin>',clsarity_IntDef__Oint_54) ).

fof(c_0_1306,axiom,
    class_Ring__and__Field_Olordered__ring(tc_IntDef_Oint),
    file('<stdin>',clsarity_IntDef__Oint_53) ).

fof(c_0_1307,axiom,
    class_OrderedGroup_Olordered__ab__group__join(tc_IntDef_Oint),
    file('<stdin>',clsarity_IntDef__Oint_52) ).

fof(c_0_1308,axiom,
    class_OrderedGroup_Olordered__ab__group__meet(tc_IntDef_Oint),
    file('<stdin>',clsarity_IntDef__Oint_51) ).

fof(c_0_1309,axiom,
    class_OrderedGroup_Olordered__ab__group__abs(tc_IntDef_Oint),
    file('<stdin>',clsarity_IntDef__Oint_50) ).

fof(c_0_1310,axiom,
    class_Orderings_Oord(tc_IntDef_Oint),
    file('<stdin>',clsarity_IntDef__Oint_5) ).

fof(c_0_1311,axiom,
    class_Ring__and__Field_Opordered__ring(tc_IntDef_Oint),
    file('<stdin>',clsarity_IntDef__Oint_49) ).

fof(c_0_1312,axiom,
    class_OrderedGroup_Olordered__ab__group(tc_IntDef_Oint),
    file('<stdin>',clsarity_IntDef__Oint_48) ).

fof(c_0_1313,axiom,
    class_OrderedGroup_Opordered__ab__group__add(tc_IntDef_Oint),
    file('<stdin>',clsarity_IntDef__Oint_47) ).

fof(c_0_1314,axiom,
    class_Ring__and__Field_Oaxclass__abs__if(tc_IntDef_Oint),
    file('<stdin>',clsarity_IntDef__Oint_46) ).

fof(c_0_1315,axiom,
    class_Ring__and__Field_Oordered__comm__semiring__strict(tc_IntDef_Oint),
    file('<stdin>',clsarity_IntDef__Oint_45) ).

fof(c_0_1316,axiom,
    class_Ring__and__Field_Opordered__cancel__comm__semiring(tc_IntDef_Oint),
    file('<stdin>',clsarity_IntDef__Oint_44) ).

fof(c_0_1317,axiom,
    class_Ring__and__Field_Opordered__comm__semiring(tc_IntDef_Oint),
    file('<stdin>',clsarity_IntDef__Oint_43) ).

fof(c_0_1318,axiom,
    class_Ring__and__Field_Oordered__semiring__strict(tc_IntDef_Oint),
    file('<stdin>',clsarity_IntDef__Oint_42) ).

fof(c_0_1319,axiom,
    class_Ring__and__Field_Opordered__cancel__semiring(tc_IntDef_Oint),
    file('<stdin>',clsarity_IntDef__Oint_41) ).

fof(c_0_1320,axiom,
    class_Ring__and__Field_Opordered__semiring(tc_IntDef_Oint),
    file('<stdin>',clsarity_IntDef__Oint_40) ).

fof(c_0_1321,axiom,
    class_HOL_Ozero(tc_IntDef_Oint),
    file('<stdin>',clsarity_IntDef__Oint_4) ).

fof(c_0_1322,axiom,
    class_OrderedGroup_Oordered__cancel__ab__semigroup__add(tc_IntDef_Oint),
    file('<stdin>',clsarity_IntDef__Oint_39) ).

fof(c_0_1323,axiom,
    class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_IntDef_Oint),
    file('<stdin>',clsarity_IntDef__Oint_38) ).

fof(c_0_1324,axiom,
    class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_IntDef_Oint),
    file('<stdin>',clsarity_IntDef__Oint_37) ).

fof(c_0_1325,axiom,
    class_OrderedGroup_Opordered__ab__semigroup__add(tc_IntDef_Oint),
    file('<stdin>',clsarity_IntDef__Oint_36) ).

fof(c_0_1326,axiom,
    class_Orderings_Olinorder(tc_IntDef_Oint),
    file('<stdin>',clsarity_IntDef__Oint_35) ).

fof(c_0_1327,axiom,
    class_LOrder_Olorder(tc_IntDef_Oint),
    file('<stdin>',clsarity_IntDef__Oint_34) ).

fof(c_0_1328,axiom,
    class_LOrder_Ojoin__semilorder(tc_IntDef_Oint),
    file('<stdin>',clsarity_IntDef__Oint_33) ).

fof(c_0_1329,axiom,
    class_LOrder_Omeet__semilorder(tc_IntDef_Oint),
    file('<stdin>',clsarity_IntDef__Oint_32) ).

fof(c_0_1330,axiom,
    class_Orderings_Oorder(tc_IntDef_Oint),
    file('<stdin>',clsarity_IntDef__Oint_31) ).

fof(c_0_1331,axiom,
    class_Ring__and__Field_Ocomm__ring__1(tc_IntDef_Oint),
    file('<stdin>',clsarity_IntDef__Oint_30) ).

fof(c_0_1332,axiom,
    class_HOL_Otimes(tc_IntDef_Oint),
    file('<stdin>',clsarity_IntDef__Oint_3) ).

fof(c_0_1333,axiom,
    class_Ring__and__Field_Ocomm__semiring__1__cancel(tc_IntDef_Oint),
    file('<stdin>',clsarity_IntDef__Oint_29) ).

fof(c_0_1334,axiom,
    class_Ring__and__Field_Oring__1(tc_IntDef_Oint),
    file('<stdin>',clsarity_IntDef__Oint_28) ).

fof(c_0_1335,axiom,
    class_Ring__and__Field_Osemiring__1__cancel(tc_IntDef_Oint),
    file('<stdin>',clsarity_IntDef__Oint_27) ).

fof(c_0_1336,axiom,
    class_Ring__and__Field_Ocomm__semiring__1(tc_IntDef_Oint),
    file('<stdin>',clsarity_IntDef__Oint_26) ).

fof(c_0_1337,axiom,
    class_Ring__and__Field_Osemiring__1(tc_IntDef_Oint),
    file('<stdin>',clsarity_IntDef__Oint_25) ).

fof(c_0_1338,axiom,
    class_OrderedGroup_Ocomm__monoid__mult(tc_IntDef_Oint),
    file('<stdin>',clsarity_IntDef__Oint_24) ).

fof(c_0_1339,axiom,
    class_OrderedGroup_Omonoid__mult(tc_IntDef_Oint),
    file('<stdin>',clsarity_IntDef__Oint_23) ).

fof(c_0_1340,axiom,
    class_Ring__and__Field_Oaxclass__0__neq__1(tc_IntDef_Oint),
    file('<stdin>',clsarity_IntDef__Oint_22) ).

fof(c_0_1341,axiom,
    class_Ring__and__Field_Ocomm__ring(tc_IntDef_Oint),
    file('<stdin>',clsarity_IntDef__Oint_21) ).

fof(c_0_1342,axiom,
    class_Ring__and__Field_Ocomm__semiring__0__cancel(tc_IntDef_Oint),
    file('<stdin>',clsarity_IntDef__Oint_20) ).

fof(c_0_1343,axiom,
    class_HOL_Oplus(tc_IntDef_Oint),
    file('<stdin>',clsarity_IntDef__Oint_2) ).

fof(c_0_1344,axiom,
    class_Ring__and__Field_Oring(tc_IntDef_Oint),
    file('<stdin>',clsarity_IntDef__Oint_19) ).

fof(c_0_1345,axiom,
    class_Ring__and__Field_Osemiring__0__cancel(tc_IntDef_Oint),
    file('<stdin>',clsarity_IntDef__Oint_18) ).

fof(c_0_1346,axiom,
    class_OrderedGroup_Oab__group__add(tc_IntDef_Oint),
    file('<stdin>',clsarity_IntDef__Oint_17) ).

fof(c_0_1347,axiom,
    class_OrderedGroup_Ocancel__ab__semigroup__add(tc_IntDef_Oint),
    file('<stdin>',clsarity_IntDef__Oint_16) ).

fof(c_0_1348,axiom,
    class_OrderedGroup_Ocancel__semigroup__add(tc_IntDef_Oint),
    file('<stdin>',clsarity_IntDef__Oint_15) ).

fof(c_0_1349,axiom,
    class_Ring__and__Field_Ocomm__semiring__0(tc_IntDef_Oint),
    file('<stdin>',clsarity_IntDef__Oint_14) ).

fof(c_0_1350,axiom,
    class_Ring__and__Field_Osemiring__0(tc_IntDef_Oint),
    file('<stdin>',clsarity_IntDef__Oint_13) ).

fof(c_0_1351,axiom,
    class_OrderedGroup_Ocomm__monoid__add(tc_IntDef_Oint),
    file('<stdin>',clsarity_IntDef__Oint_12) ).

fof(c_0_1352,axiom,
    class_Ring__and__Field_Ocomm__semiring(tc_IntDef_Oint),
    file('<stdin>',clsarity_IntDef__Oint_11) ).

fof(c_0_1353,axiom,
    class_Ring__and__Field_Osemiring(tc_IntDef_Oint),
    file('<stdin>',clsarity_IntDef__Oint_10) ).

fof(c_0_1354,axiom,
    class_HOL_Oone(tc_IntDef_Oint),
    file('<stdin>',clsarity_IntDef__Oint_1) ).

fof(c_0_1355,axiom,
    class_HOL_Ominus(tc_IntDef_Oint),
    file('<stdin>',clsarity_IntDef__Oint_0) ).

fof(c_0_1356,axiom,
    c_UNIV != c_emptyset,
    file('<stdin>',cls_Set_OUNIV__not__empty__iff1_0) ).

fof(c_0_1357,axiom,
    c_Numeral_Obit_OB1 != c_Numeral_Obit_OB0,
    file('<stdin>',cls_Numeral_Obit_Odistinct__2__iff1_0) ).

fof(c_0_1358,axiom,
    c_Numeral_Obit_OB0 != c_Numeral_Obit_OB1,
    file('<stdin>',cls_Numeral_Obit_Odistinct__1__iff1_0) ).

fof(c_0_1359,axiom,
    c_Extraction_Osumbool_ORight != c_Extraction_Osumbool_OLeft,
    file('<stdin>',cls_Extraction_Osumbool_Odistinct__2__iff1_0) ).

fof(c_0_1360,axiom,
    c_Extraction_Osumbool_OLeft != c_Extraction_Osumbool_ORight,
    file('<stdin>',cls_Extraction_Osumbool_Odistinct__1__iff1_0) ).

fof(c_0_1361,plain,
    ! [X46,X38,X14,X47,X7,X3] :
      ( ~ c_in(X46,c_Relation_Orel__comp(X14,X38,X47,X7,X3),tc_prod(X3,X7))
      | c_in(c_Pair(c_Main_Orel__compE__1(X14,X38,X46,X47,X7,X3),c_Main_Orel__compE__2(X14,X38,X46,X47,X7,X3),X3,X47),X38,tc_prod(X3,X47)) ),
    inference(fof_simplification,[status(thm)],[c_0_0]) ).

fof(c_0_1362,plain,
    ! [X46,X38,X14,X47,X7,X3] :
      ( ~ c_in(X46,c_Relation_Orel__comp(X14,X38,X47,X7,X3),tc_prod(X3,X7))
      | c_in(c_Pair(c_Main_Orel__compE__2(X14,X38,X46,X47,X7,X3),c_Main_Orel__compE__3(X14,X38,X46,X47,X7,X3),X47,X7),X14,tc_prod(X47,X7)) ),
    inference(fof_simplification,[status(thm)],[c_0_1]) ).

fof(c_0_1363,plain,
    ! [X46,X38,X14,X47,X7,X3] :
      ( ~ c_in(X46,c_Relation_Orel__comp(X14,X38,X47,X7,X3),tc_prod(X3,X7))
      | X46 = c_Pair(c_Main_Orel__compE__1(X14,X38,X46,X47,X7,X3),c_Main_Orel__compE__3(X14,X38,X46,X47,X7,X3),X3,X7) ),
    inference(fof_simplification,[status(thm)],[c_0_2]) ).

fof(c_0_1364,plain,
    ! [X38,X14,X35,X7,X3] :
      ( ~ c_in(X35,c_Datatype__Universe_Odprod(X14,X38,X3,X7),tc_prod(tc_set(tc_Datatype__Universe_Onode(X3,X7)),tc_set(tc_Datatype__Universe_Onode(X3,X7))))
      | X35 = c_Pair(c_Datatype__Universe_OScons(c_Main_OdprodE__1(X35,X14,X38,X3,X7),c_Main_OdprodE__2(X35,X14,X38,X3,X7),X3,X7),c_Datatype__Universe_OScons(c_Main_OdprodE__3(X35,X14,X38,X3,X7),c_Main_OdprodE__4(X35,X14,X38,X3,X7),X3,X7),tc_set(tc_Datatype__Universe_Onode(X3,X7)),tc_set(tc_Datatype__Universe_Onode(X3,X7))) ),
    inference(fof_simplification,[status(thm)],[c_0_3]) ).

fof(c_0_1365,plain,
    ! [X38,X14,X35,X7,X3] :
      ( ~ c_in(X35,c_Datatype__Universe_Odprod(X14,X38,X3,X7),tc_prod(tc_set(tc_Datatype__Universe_Onode(X3,X7)),tc_set(tc_Datatype__Universe_Onode(X3,X7))))
      | c_in(c_Pair(c_Main_OdprodE__1(X35,X14,X38,X3,X7),c_Main_OdprodE__3(X35,X14,X38,X3,X7),tc_set(tc_Datatype__Universe_Onode(X3,X7)),tc_set(tc_Datatype__Universe_Onode(X3,X7))),X14,tc_prod(tc_set(tc_Datatype__Universe_Onode(X3,X7)),tc_set(tc_Datatype__Universe_Onode(X3,X7)))) ),
    inference(fof_simplification,[status(thm)],[c_0_4]) ).

fof(c_0_1366,plain,
    ! [X38,X14,X35,X7,X3] :
      ( ~ c_in(X35,c_Datatype__Universe_Odprod(X14,X38,X3,X7),tc_prod(tc_set(tc_Datatype__Universe_Onode(X3,X7)),tc_set(tc_Datatype__Universe_Onode(X3,X7))))
      | c_in(c_Pair(c_Main_OdprodE__2(X35,X14,X38,X3,X7),c_Main_OdprodE__4(X35,X14,X38,X3,X7),tc_set(tc_Datatype__Universe_Onode(X3,X7)),tc_set(tc_Datatype__Universe_Onode(X3,X7))),X38,tc_prod(tc_set(tc_Datatype__Universe_Onode(X3,X7)),tc_set(tc_Datatype__Universe_Onode(X3,X7)))) ),
    inference(fof_simplification,[status(thm)],[c_0_5]) ).

fof(c_0_1367,plain,
    ! [X21,X38,X14,X7,X3] :
      ( ~ c_in(X21,c_Datatype__Universe_Odsum(X14,X38,X3,X7),tc_prod(tc_set(tc_Datatype__Universe_Onode(X3,X7)),tc_set(tc_Datatype__Universe_Onode(X3,X7))))
      | c_in(c_Pair(c_Main_OdsumE__1(X14,X21,X3,X7),c_Main_OdsumE__2(X14,X21,X3,X7),tc_set(tc_Datatype__Universe_Onode(X3,X7)),tc_set(tc_Datatype__Universe_Onode(X3,X7))),X14,tc_prod(tc_set(tc_Datatype__Universe_Onode(X3,X7)),tc_set(tc_Datatype__Universe_Onode(X3,X7))))
      | c_in(c_Pair(c_Main_OdsumE__3(X38,X21,X3,X7),c_Main_OdsumE__4(X38,X21,X3,X7),tc_set(tc_Datatype__Universe_Onode(X3,X7)),tc_set(tc_Datatype__Universe_Onode(X3,X7))),X38,tc_prod(tc_set(tc_Datatype__Universe_Onode(X3,X7)),tc_set(tc_Datatype__Universe_Onode(X3,X7)))) ),
    inference(fof_simplification,[status(thm)],[c_0_6]) ).

fof(c_0_1368,plain,
    ! [X21,X38,X14,X7,X3] :
      ( ~ c_in(X21,c_Datatype__Universe_Odsum(X14,X38,X3,X7),tc_prod(tc_set(tc_Datatype__Universe_Onode(X3,X7)),tc_set(tc_Datatype__Universe_Onode(X3,X7))))
      | c_in(c_Pair(c_Main_OdsumE__1(X14,X21,X3,X7),c_Main_OdsumE__2(X14,X21,X3,X7),tc_set(tc_Datatype__Universe_Onode(X3,X7)),tc_set(tc_Datatype__Universe_Onode(X3,X7))),X14,tc_prod(tc_set(tc_Datatype__Universe_Onode(X3,X7)),tc_set(tc_Datatype__Universe_Onode(X3,X7))))
      | X21 = c_Pair(c_Datatype__Universe_OIn1(c_Main_OdsumE__3(X38,X21,X3,X7),X3,X7),c_Datatype__Universe_OIn1(c_Main_OdsumE__4(X38,X21,X3,X7),X3,X7),tc_set(tc_Datatype__Universe_Onode(X3,X7)),tc_set(tc_Datatype__Universe_Onode(X3,X7))) ),
    inference(fof_simplification,[status(thm)],[c_0_7]) ).

fof(c_0_1369,plain,
    ! [X21,X38,X14,X7,X3] :
      ( ~ c_in(X21,c_Datatype__Universe_Odsum(X14,X38,X3,X7),tc_prod(tc_set(tc_Datatype__Universe_Onode(X3,X7)),tc_set(tc_Datatype__Universe_Onode(X3,X7))))
      | c_in(c_Pair(c_Main_OdsumE__3(X38,X21,X3,X7),c_Main_OdsumE__4(X38,X21,X3,X7),tc_set(tc_Datatype__Universe_Onode(X3,X7)),tc_set(tc_Datatype__Universe_Onode(X3,X7))),X38,tc_prod(tc_set(tc_Datatype__Universe_Onode(X3,X7)),tc_set(tc_Datatype__Universe_Onode(X3,X7))))
      | X21 = c_Pair(c_Datatype__Universe_OIn0(c_Main_OdsumE__1(X14,X21,X3,X7),X3,X7),c_Datatype__Universe_OIn0(c_Main_OdsumE__2(X14,X21,X3,X7),X3,X7),tc_set(tc_Datatype__Universe_Onode(X3,X7)),tc_set(tc_Datatype__Universe_Onode(X3,X7))) ),
    inference(fof_simplification,[status(thm)],[c_0_8]) ).

fof(c_0_1370,plain,
    ! [X23,X24,X22,X14,X3] :
      ( ~ c_in(c_Pair(X22,c_List_Olist_OCons(X24,X23,X3),tc_List_Olist(X3),tc_List_Olist(X3)),c_List_Olistrel(X14,X3),tc_prod(tc_List_Olist(X3),tc_List_Olist(X3)))
      | c_in(c_Pair(c_Main_Olistrel__Cons2__2(X14,X22,X24,X23,X3),X23,tc_List_Olist(X3),tc_List_Olist(X3)),c_List_Olistrel(X14,X3),tc_prod(tc_List_Olist(X3),tc_List_Olist(X3))) ),
    inference(fof_simplification,[status(thm)],[c_0_9]) ).

fof(c_0_1371,plain,
    ! [X23,X24,X22,X14,X3] :
      ( ~ c_in(c_Pair(c_List_Olist_OCons(X24,X23,X3),X22,tc_List_Olist(X3),tc_List_Olist(X3)),c_List_Olistrel(X14,X3),tc_prod(tc_List_Olist(X3),tc_List_Olist(X3)))
      | c_in(c_Pair(X23,c_Main_Olistrel__Cons1__2(X14,X22,X24,X23,X3),tc_List_Olist(X3),tc_List_Olist(X3)),c_List_Olistrel(X14,X3),tc_prod(tc_List_Olist(X3),tc_List_Olist(X3))) ),
    inference(fof_simplification,[status(thm)],[c_0_10]) ).

fof(c_0_1372,plain,
    ! [X38,X14,X11,X8,X12,X9,X7,X3] :
      ( ~ c_in(c_Pair(X8,X11,tc_set(tc_Datatype__Universe_Onode(X3,X7)),tc_set(tc_Datatype__Universe_Onode(X3,X7))),X38,tc_prod(tc_set(tc_Datatype__Universe_Onode(X3,X7)),tc_set(tc_Datatype__Universe_Onode(X3,X7))))
      | ~ c_in(c_Pair(X9,X12,tc_set(tc_Datatype__Universe_Onode(X3,X7)),tc_set(tc_Datatype__Universe_Onode(X3,X7))),X14,tc_prod(tc_set(tc_Datatype__Universe_Onode(X3,X7)),tc_set(tc_Datatype__Universe_Onode(X3,X7))))
      | c_in(c_Pair(c_Datatype__Universe_OScons(X9,X8,X3,X7),c_Datatype__Universe_OScons(X12,X11,X3,X7),tc_set(tc_Datatype__Universe_Onode(X3,X7)),tc_set(tc_Datatype__Universe_Onode(X3,X7))),c_Datatype__Universe_Odprod(X14,X38,X3,X7),tc_prod(tc_set(tc_Datatype__Universe_Onode(X3,X7)),tc_set(tc_Datatype__Universe_Onode(X3,X7)))) ),
    inference(fof_simplification,[status(thm)],[c_0_11]) ).

fof(c_0_1373,plain,
    ! [X23,X24,X22,X14,X3] :
      ( ~ c_in(c_Pair(X22,c_List_Olist_OCons(X24,X23,X3),tc_List_Olist(X3),tc_List_Olist(X3)),c_List_Olistrel(X14,X3),tc_prod(tc_List_Olist(X3),tc_List_Olist(X3)))
      | c_in(c_Pair(c_Main_Olistrel__Cons2__1(X14,X22,X24,X23,X3),X24,X3,X3),X14,tc_prod(X3,X3)) ),
    inference(fof_simplification,[status(thm)],[c_0_12]) ).

fof(c_0_1374,plain,
    ! [X23,X24,X22,X14,X3] :
      ( ~ c_in(c_Pair(c_List_Olist_OCons(X24,X23,X3),X22,tc_List_Olist(X3),tc_List_Olist(X3)),c_List_Olistrel(X14,X3),tc_prod(tc_List_Olist(X3),tc_List_Olist(X3)))
      | c_in(c_Pair(X24,c_Main_Olistrel__Cons1__1(X14,X22,X24,X23,X3),X3,X3),X14,tc_prod(X3,X3)) ),
    inference(fof_simplification,[status(thm)],[c_0_13]) ).

fof(c_0_1375,plain,
    ! [X21,X38,X14,X7,X3] :
      ( ~ c_in(X21,c_Datatype__Universe_Odsum(X14,X38,X3,X7),tc_prod(tc_set(tc_Datatype__Universe_Onode(X3,X7)),tc_set(tc_Datatype__Universe_Onode(X3,X7))))
      | X21 = c_Pair(c_Datatype__Universe_OIn0(c_Main_OdsumE__1(X14,X21,X3,X7),X3,X7),c_Datatype__Universe_OIn0(c_Main_OdsumE__2(X14,X21,X3,X7),X3,X7),tc_set(tc_Datatype__Universe_Onode(X3,X7)),tc_set(tc_Datatype__Universe_Onode(X3,X7)))
      | X21 = c_Pair(c_Datatype__Universe_OIn1(c_Main_OdsumE__3(X38,X21,X3,X7),X3,X7),c_Datatype__Universe_OIn1(c_Main_OdsumE__4(X38,X21,X3,X7),X3,X7),tc_set(tc_Datatype__Universe_Onode(X3,X7)),tc_set(tc_Datatype__Universe_Onode(X3,X7))) ),
    inference(fof_simplification,[status(thm)],[c_0_14]) ).

fof(c_0_1376,plain,
    ! [X14,X6,X15,X7,X3] :
      ( ~ c_in(X6,c_Relation_OImage(X14,X15,X7,X3),X3)
      | c_in(c_Pair(c_Main_OImageE__1(X15,X6,X14,X7,X3),X6,X7,X3),X14,tc_prod(X7,X3)) ),
    inference(fof_simplification,[status(thm)],[c_0_15]) ).

fof(c_0_1377,plain,
    ! [X23,X24,X22,X14,X3] :
      ( ~ c_in(c_Pair(X22,c_List_Olist_OCons(X24,X23,X3),tc_List_Olist(X3),tc_List_Olist(X3)),c_List_Olistrel(X14,X3),tc_prod(tc_List_Olist(X3),tc_List_Olist(X3)))
      | X22 = c_List_Olist_OCons(c_Main_Olistrel__Cons2__1(X14,X22,X24,X23,X3),c_Main_Olistrel__Cons2__2(X14,X22,X24,X23,X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_16]) ).

fof(c_0_1378,plain,
    ! [X23,X24,X22,X14,X3] :
      ( ~ c_in(c_Pair(c_List_Olist_OCons(X24,X23,X3),X22,tc_List_Olist(X3),tc_List_Olist(X3)),c_List_Olistrel(X14,X3),tc_prod(tc_List_Olist(X3),tc_List_Olist(X3)))
      | X22 = c_List_Olist_OCons(c_Main_Olistrel__Cons1__1(X14,X22,X24,X23,X3),c_Main_Olistrel__Cons1__2(X14,X22,X24,X23,X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_17]) ).

fof(c_0_1379,plain,
    ! [X35,X16,X15,X7,X3] :
      ( ~ c_in(X35,c_Datatype__Universe_Ouprod(X15,X16,X3,X7),tc_set(tc_Datatype__Universe_Onode(X3,X7)))
      | X35 = c_Datatype__Universe_OScons(c_Main_OuprodE__1(X15,X16,X35,X3,X7),c_Main_OuprodE__2(X15,X16,X35,X3,X7),X3,X7) ),
    inference(fof_simplification,[status(thm)],[c_0_18]) ).

fof(c_0_1380,plain,
    ! [X38,X14,X35,X6,X5,X47,X7,X3] :
      ( ~ c_in(c_Pair(X6,X35,X7,X47),X14,tc_prod(X7,X47))
      | ~ c_in(c_Pair(X5,X6,X3,X7),X38,tc_prod(X3,X7))
      | c_in(c_Pair(X5,X35,X3,X47),c_Relation_Orel__comp(X14,X38,X7,X47,X3),tc_prod(X3,X47)) ),
    inference(fof_simplification,[status(thm)],[c_0_19]) ).

fof(c_0_1381,plain,
    ! [X38,X14,X11,X8,X7,X3] :
      ( ~ c_in(c_Pair(X8,X11,tc_set(tc_Datatype__Universe_Onode(X3,X7)),tc_set(tc_Datatype__Universe_Onode(X3,X7))),X38,tc_prod(tc_set(tc_Datatype__Universe_Onode(X3,X7)),tc_set(tc_Datatype__Universe_Onode(X3,X7))))
      | c_in(c_Pair(c_Datatype__Universe_OIn1(X8,X3,X7),c_Datatype__Universe_OIn1(X11,X3,X7),tc_set(tc_Datatype__Universe_Onode(X3,X7)),tc_set(tc_Datatype__Universe_Onode(X3,X7))),c_Datatype__Universe_Odsum(X14,X38,X3,X7),tc_prod(tc_set(tc_Datatype__Universe_Onode(X3,X7)),tc_set(tc_Datatype__Universe_Onode(X3,X7)))) ),
    inference(fof_simplification,[status(thm)],[c_0_20]) ).

fof(c_0_1382,plain,
    ! [X38,X14,X12,X9,X7,X3] :
      ( ~ c_in(c_Pair(X9,X12,tc_set(tc_Datatype__Universe_Onode(X3,X7)),tc_set(tc_Datatype__Universe_Onode(X3,X7))),X14,tc_prod(tc_set(tc_Datatype__Universe_Onode(X3,X7)),tc_set(tc_Datatype__Universe_Onode(X3,X7))))
      | c_in(c_Pair(c_Datatype__Universe_OIn0(X9,X3,X7),c_Datatype__Universe_OIn0(X12,X3,X7),tc_set(tc_Datatype__Universe_Onode(X3,X7)),tc_set(tc_Datatype__Universe_Onode(X3,X7))),c_Datatype__Universe_Odsum(X14,X38,X3,X7),tc_prod(tc_set(tc_Datatype__Universe_Onode(X3,X7)),tc_set(tc_Datatype__Universe_Onode(X3,X7)))) ),
    inference(fof_simplification,[status(thm)],[c_0_21]) ).

fof(c_0_1383,plain,
    ! [X35,X16,X15,X7,X3] :
      ( ~ c_in(X35,c_Datatype__Universe_Ouprod(X15,X16,X3,X7),tc_set(tc_Datatype__Universe_Onode(X3,X7)))
      | c_in(c_Main_OuprodE__1(X15,X16,X35,X3,X7),X15,tc_set(tc_Datatype__Universe_Onode(X3,X7))) ),
    inference(fof_simplification,[status(thm)],[c_0_22]) ).

fof(c_0_1384,plain,
    ! [X35,X16,X15,X7,X3] :
      ( ~ c_in(X35,c_Datatype__Universe_Ouprod(X15,X16,X3,X7),tc_set(tc_Datatype__Universe_Onode(X3,X7)))
      | c_in(c_Main_OuprodE__2(X15,X16,X35,X3,X7),X16,tc_set(tc_Datatype__Universe_Onode(X3,X7))) ),
    inference(fof_simplification,[status(thm)],[c_0_23]) ).

fof(c_0_1385,plain,
    ! [X14,X6,X15,X7,X3] :
      ( ~ c_in(X6,c_Relation_OImage(X14,X15,X7,X3),X3)
      | c_in(c_Main_OImageE__1(X15,X6,X14,X7,X3),X15,X7) ),
    inference(fof_simplification,[status(thm)],[c_0_24]) ).

fof(c_0_1386,plain,
    ! [X45,X14,X7,X3] :
      ( ~ c_in(X45,c_Relation_Oconverse(X14,X7,X3),tc_prod(X3,X7))
      | c_in(c_Pair(c_Main_OconverseE__1(X14,X45,X7,X3),c_Main_OconverseE__2(X14,X45,X7,X3),X7,X3),X14,tc_prod(X7,X3)) ),
    inference(fof_simplification,[status(thm)],[c_0_25]) ).

fof(c_0_1387,plain,
    ! [X24,X2,X14,X3] :
      ( ~ c_Wellfounded__Recursion_Owf(c_insert(c_Pair(X24,X2,X3,X3),X14,tc_prod(X3,X3)),X3)
      | ~ c_in(c_Pair(X2,X24,X3,X3),c_Transitive__Closure_Ortrancl(X14,X3),tc_prod(X3,X3)) ),
    inference(fof_simplification,[status(thm)],[c_0_26]) ).

fof(c_0_1388,plain,
    ! [X24,X2,X14,X3] :
      ( ~ c_Wellfounded__Recursion_Oacyclic(c_insert(c_Pair(X24,X2,X3,X3),X14,tc_prod(X3,X3)),X3)
      | ~ c_in(c_Pair(X2,X24,X3,X3),c_Transitive__Closure_Ortrancl(X14,X3),tc_prod(X3,X3)) ),
    inference(fof_simplification,[status(thm)],[c_0_27]) ).

fof(c_0_1389,plain,
    ! [X39,X16,X15,X7,X3] :
      ( ~ c_in(X39,c_Datatype__Universe_Ousum(X15,X16,X3,X7),tc_set(tc_Datatype__Universe_Onode(X3,X7)))
      | c_in(c_Main_OusumE__1(X15,X39,X3,X7),X15,tc_set(tc_Datatype__Universe_Onode(X3,X7)))
      | c_in(c_Main_OusumE__2(X16,X39,X3,X7),X16,tc_set(tc_Datatype__Universe_Onode(X3,X7))) ),
    inference(fof_simplification,[status(thm)],[c_0_28]) ).

fof(c_0_1390,plain,
    ! [X39,X16,X15,X7,X3] :
      ( ~ c_in(X39,c_Datatype__Universe_Ousum(X15,X16,X3,X7),tc_set(tc_Datatype__Universe_Onode(X3,X7)))
      | c_in(c_Main_OusumE__1(X15,X39,X3,X7),X15,tc_set(tc_Datatype__Universe_Onode(X3,X7)))
      | X39 = c_Datatype__Universe_OIn1(c_Main_OusumE__2(X16,X39,X3,X7),X3,X7) ),
    inference(fof_simplification,[status(thm)],[c_0_29]) ).

fof(c_0_1391,plain,
    ! [X39,X16,X15,X7,X3] :
      ( ~ c_in(X39,c_Datatype__Universe_Ousum(X15,X16,X3,X7),tc_set(tc_Datatype__Universe_Onode(X3,X7)))
      | c_in(c_Main_OusumE__2(X16,X39,X3,X7),X16,tc_set(tc_Datatype__Universe_Onode(X3,X7)))
      | X39 = c_Datatype__Universe_OIn0(c_Main_OusumE__1(X15,X39,X3,X7),X3,X7) ),
    inference(fof_simplification,[status(thm)],[c_0_30]) ).

fof(c_0_1392,plain,
    ! [X39,X16,X15,X7,X3] :
      ( ~ c_in(X39,c_Datatype__Universe_Ousum(X15,X16,X3,X7),tc_set(tc_Datatype__Universe_Onode(X3,X7)))
      | X39 = c_Datatype__Universe_OIn0(c_Main_OusumE__1(X15,X39,X3,X7),X3,X7)
      | X39 = c_Datatype__Universe_OIn1(c_Main_OusumE__2(X16,X39,X3,X7),X3,X7) ),
    inference(fof_simplification,[status(thm)],[c_0_31]) ).

fof(c_0_1393,plain,
    ! [X39,X16,X15,X7,X3] :
      ( ~ c_in(X39,c_Sum__Type_OPlus(X15,X16,X3,X7),tc_sum(X3,X7))
      | X39 = c_Sum__Type_OInl(c_Main_OPlusE__1(X15,X39,X3,X7),X3,X7)
      | X39 = c_Sum__Type_OInr(c_Main_OPlusE__2(X16,X39,X7,X3),X7,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_32]) ).

fof(c_0_1394,plain,
    ! [X39,X16,X15,X7,X3] :
      ( ~ c_in(X39,c_Sum__Type_OPlus(X15,X16,X3,X7),tc_sum(X3,X7))
      | c_in(c_Main_OPlusE__1(X15,X39,X3,X7),X15,X3)
      | X39 = c_Sum__Type_OInr(c_Main_OPlusE__2(X16,X39,X7,X3),X7,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_33]) ).

fof(c_0_1395,plain,
    ! [X39,X16,X15,X7,X3] :
      ( ~ c_in(X39,c_Sum__Type_OPlus(X15,X16,X3,X7),tc_sum(X3,X7))
      | c_in(c_Main_OPlusE__2(X16,X39,X7,X3),X16,X7)
      | X39 = c_Sum__Type_OInl(c_Main_OPlusE__1(X15,X39,X3,X7),X3,X7) ),
    inference(fof_simplification,[status(thm)],[c_0_34]) ).

fof(c_0_1396,plain,
    ! [X39,X16,X15,X7,X3] :
      ( ~ c_in(X39,c_Sum__Type_OPlus(X15,X16,X3,X7),tc_sum(X3,X7))
      | c_in(c_Main_OPlusE__1(X15,X39,X3,X7),X15,X3)
      | c_in(c_Main_OPlusE__2(X16,X39,X7,X3),X16,X7) ),
    inference(fof_simplification,[status(thm)],[c_0_35]) ).

fof(c_0_1397,plain,
    ! [X24,X2,X14,X3] :
      ( ~ c_Wellfounded__Recursion_Owf(c_insert(c_Pair(X24,X2,X3,X3),X14,tc_prod(X3,X3)),X3)
      | c_Wellfounded__Recursion_Owf(X14,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_36]) ).

fof(c_0_1398,plain,
    ! [X24,X2,X14,X3] :
      ( ~ c_Wellfounded__Recursion_Oacyclic(c_insert(c_Pair(X24,X2,X3,X3),X14,tc_prod(X3,X3)),X3)
      | c_Wellfounded__Recursion_Oacyclic(X14,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_37]) ).

fof(c_0_1399,plain,
    ! [X14,X6,X7,X3] :
      ( ~ c_in(X6,c_Relation_ORange(X14,X7,X3),X3)
      | c_in(c_Pair(c_Main_ORangeE__1(X6,X14,X3,X7),X6,X7,X3),X14,tc_prod(X7,X3)) ),
    inference(fof_simplification,[status(thm)],[c_0_38]) ).

fof(c_0_1400,plain,
    ! [X14,X5,X7,X3] :
      ( ~ c_in(X5,c_Relation_ODomain(X14,X3,X7),X3)
      | c_in(c_Pair(X5,c_Main_ODomainE__1(X5,X14,X3,X7),X3,X7),X14,tc_prod(X3,X7)) ),
    inference(fof_simplification,[status(thm)],[c_0_39]) ).

fof(c_0_1401,plain,
    ! [X24,X2,X14,X3] :
      ( ~ c_Wellfounded__Recursion_Owf(X14,X3)
      | c_Wellfounded__Recursion_Owf(c_insert(c_Pair(X24,X2,X3,X3),X14,tc_prod(X3,X3)),X3)
      | c_in(c_Pair(X2,X24,X3,X3),c_Transitive__Closure_Ortrancl(X14,X3),tc_prod(X3,X3)) ),
    inference(fof_simplification,[status(thm)],[c_0_40]) ).

fof(c_0_1402,plain,
    ! [X24,X2,X14,X3] :
      ( ~ c_Wellfounded__Recursion_Oacyclic(X14,X3)
      | c_Wellfounded__Recursion_Oacyclic(c_insert(c_Pair(X24,X2,X3,X3),X14,tc_prod(X3,X3)),X3)
      | c_in(c_Pair(X2,X24,X3,X3),c_Transitive__Closure_Ortrancl(X14,X3),tc_prod(X3,X3)) ),
    inference(fof_simplification,[status(thm)],[c_0_41]) ).

fof(c_0_1403,plain,
    ! [X14,X6,X5,X7,X3] :
      ( ~ c_in(X6,c_Relation_OImage(X14,c_insert(X5,c_emptyset,X7),X7,X3),X3)
      | c_in(c_Pair(X5,X6,X7,X3),X14,tc_prod(X7,X3)) ),
    inference(fof_simplification,[status(thm)],[c_0_42]) ).

fof(c_0_1404,plain,
    ! [X19,X13,X10] :
      ( ~ c_Divides_Oop_Advd(X10,c_GCD_Ogcd(c_Pair(X13,X19,tc_nat,tc_nat)),tc_nat)
      | c_Divides_Oop_Advd(X10,X19,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_43]) ).

fof(c_0_1405,plain,
    ! [X19,X13,X10] :
      ( ~ c_Divides_Oop_Advd(X10,c_GCD_Ogcd(c_Pair(X13,X19,tc_nat,tc_nat)),tc_nat)
      | c_Divides_Oop_Advd(X10,X13,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_44]) ).

fof(c_0_1406,plain,
    ! [X14,X6,X5,X7,X3] :
      ( ~ c_in(c_Pair(X5,X6,X7,X3),X14,tc_prod(X7,X3))
      | c_in(X6,c_Relation_OImage(X14,c_insert(X5,c_emptyset,X7),X7,X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_45]) ).

fof(c_0_1407,plain,
    ! [X14,X6,X5,X7,X3] :
      ( ~ c_in(c_Pair(X5,X6,X3,X7),c_Relation_Oconverse(X14,X7,X3),tc_prod(X3,X7))
      | c_in(c_Pair(X6,X5,X7,X3),X14,tc_prod(X7,X3)) ),
    inference(fof_simplification,[status(thm)],[c_0_46]) ).

fof(c_0_1408,plain,
    ! [X14,X6,X5,X7,X3] :
      ( ~ c_in(c_Pair(X6,X5,X7,X3),X14,tc_prod(X7,X3))
      | c_in(c_Pair(X5,X6,X3,X7),c_Relation_Oconverse(X14,X7,X3),tc_prod(X3,X7)) ),
    inference(fof_simplification,[status(thm)],[c_0_47]) ).

fof(c_0_1409,plain,
    ! [X14,X6,X5,X3] :
      ( ~ c_in(c_Pair(X5,X6,X3,X3),c_Transitive__Closure_Otrancl(X14,X3),tc_prod(X3,X3))
      | c_in(c_Pair(X5,X6,X3,X3),c_Transitive__Closure_Ortrancl(X14,X3),tc_prod(X3,X3)) ),
    inference(fof_simplification,[status(thm)],[c_0_48]) ).

fof(c_0_1410,plain,
    ! [X14,X6,X5,X15,X7,X3] :
      ( ~ c_in(X5,X15,X3)
      | ~ c_in(c_Pair(X5,X6,X3,X7),X14,tc_prod(X3,X7))
      | c_in(X6,c_Relation_OImage(X14,X15,X3,X7),X7) ),
    inference(fof_simplification,[status(thm)],[c_0_49]) ).

fof(c_0_1411,plain,
    ! [X45,X14,X7,X3] :
      ( ~ c_in(X45,c_Relation_Oconverse(X14,X7,X3),tc_prod(X3,X7))
      | X45 = c_Pair(c_Main_OconverseE__2(X14,X45,X7,X3),c_Main_OconverseE__1(X14,X45,X7,X3),X3,X7) ),
    inference(fof_simplification,[status(thm)],[c_0_50]) ).

fof(c_0_1412,plain,
    ! [X14,X6,X5,X3] :
      ( ~ c_in(c_Pair(X5,X6,X3,X3),X14,tc_prod(X3,X3))
      | c_in(c_Pair(X5,X6,X3,X3),c_Transitive__Closure_Otrancl(X14,X3),tc_prod(X3,X3)) ),
    inference(fof_simplification,[status(thm)],[c_0_51]) ).

fof(c_0_1413,plain,
    ! [X8,X9,X16,X15,X7,X3] :
      ( ~ c_in(X8,X16,tc_set(tc_Datatype__Universe_Onode(X3,X7)))
      | ~ c_in(X9,X15,tc_set(tc_Datatype__Universe_Onode(X3,X7)))
      | c_in(c_Datatype__Universe_OScons(X9,X8,X3,X7),c_Datatype__Universe_Ouprod(X15,X16,X3,X7),tc_set(tc_Datatype__Universe_Onode(X3,X7))) ),
    inference(fof_simplification,[status(thm)],[c_0_52]) ).

fof(c_0_1414,plain,
    ! [X19,X13,X10] :
      ( ~ c_Divides_Oop_Advd(X10,X19,tc_nat)
      | ~ c_Divides_Oop_Advd(X10,X13,tc_nat)
      | c_Divides_Oop_Advd(X10,c_GCD_Ogcd(c_Pair(X13,X19,tc_nat,tc_nat)),tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_53]) ).

fof(c_0_1415,plain,
    ! [X14,X6,X5,X7,X3] :
      ( ~ c_in(c_Pair(X5,X6,X3,X7),X14,tc_prod(X3,X7))
      | c_in(X6,c_Relation_ORange(X14,X3,X7),X7) ),
    inference(fof_simplification,[status(thm)],[c_0_54]) ).

fof(c_0_1416,plain,
    ! [X14,X6,X5,X7,X3] :
      ( ~ c_in(c_Pair(X5,X6,X3,X7),X14,tc_prod(X3,X7))
      | c_in(X5,c_Relation_ODomain(X14,X3,X7),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_55]) ).

fof(c_0_1417,plain,
    ! [X37,X16,X15,X3] :
      ( ~ c_lessequals(X16,c_Zorn_OUnion__lemma0__1(X15,X16,X37,X3),tc_set(X3))
      | c_lessequals(X16,c_Union(X37,X3),tc_set(X3))
      | c_lessequals(c_Union(X37,X3),X15,tc_set(X3)) ),
    inference(fof_simplification,[status(thm)],[c_0_56]) ).

fof(c_0_1418,plain,
    ! [X37,X16,X15,X3] :
      ( ~ c_lessequals(c_Zorn_OUnion__lemma0__1(X15,X16,X37,X3),X15,tc_set(X3))
      | c_lessequals(X16,c_Union(X37,X3),tc_set(X3))
      | c_lessequals(c_Union(X37,X3),X15,tc_set(X3)) ),
    inference(fof_simplification,[status(thm)],[c_0_57]) ).

fof(c_0_1419,axiom,
    ! [X19,X13] : c_Divides_Oop_Advd(c_GCD_Ogcd(c_Pair(X13,X19,tc_nat,tc_nat)),X19,tc_nat),
    c_0_58 ).

fof(c_0_1420,axiom,
    ! [X19,X13] : c_Divides_Oop_Advd(c_GCD_Ogcd(c_Pair(X13,X19,tc_nat,tc_nat)),X13,tc_nat),
    c_0_59 ).

fof(c_0_1421,plain,
    ! [X22,X14,X3] :
      ( ~ c_in(c_Pair(X22,c_List_Olist_ONil,tc_List_Olist(X3),tc_List_Olist(X3)),c_List_Olistrel(X14,X3),tc_prod(tc_List_Olist(X3),tc_List_Olist(X3)))
      | X22 = c_List_Olist_ONil ),
    inference(fof_simplification,[status(thm)],[c_0_60]) ).

fof(c_0_1422,plain,
    ! [X22,X14,X3] :
      ( ~ c_in(c_Pair(c_List_Olist_ONil,X22,tc_List_Olist(X3),tc_List_Olist(X3)),c_List_Olistrel(X14,X3),tc_prod(tc_List_Olist(X3),tc_List_Olist(X3)))
      | X22 = c_List_Olist_ONil ),
    inference(fof_simplification,[status(thm)],[c_0_61]) ).

fof(c_0_1423,plain,
    ! [X23,X14,X3] : ~ c_in(c_Pair(c_List_Olist_ONil,X23,tc_List_Olist(X3),tc_List_Olist(X3)),c_List_Olex(X14,X3),tc_prod(tc_List_Olist(X3),tc_List_Olist(X3))),
    inference(fof_simplification,[status(thm)],[c_0_62]) ).

fof(c_0_1424,plain,
    ! [X22,X14,X3] : ~ c_in(c_Pair(X22,c_List_Olist_ONil,tc_List_Olist(X3),tc_List_Olist(X3)),c_List_Olex(X14,X3),tc_prod(tc_List_Olist(X3),tc_List_Olist(X3))),
    inference(fof_simplification,[status(thm)],[c_0_63]) ).

fof(c_0_1425,plain,
    ! [X24,X2] :
      ( ~ c_in(c_Pair(X2,X24,tc_nat,tc_nat),c_Wellfounded__Relations_Oless__than,tc_prod(tc_nat,tc_nat))
      | c_less(X2,X24,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_64]) ).

fof(c_0_1426,plain,
    ! [X6,X5,X3] :
      ( ~ c_in(c_Pair(X5,X6,X3,X3),c_Relation_OId,tc_prod(X3,X3))
      | X5 = X6 ),
    inference(fof_simplification,[status(thm)],[c_0_65]) ).

fof(c_0_1427,plain,
    ! [X8,X16,X15,X7,X3] :
      ( ~ c_in(X8,X16,tc_set(tc_Datatype__Universe_Onode(X3,X7)))
      | c_in(c_Datatype__Universe_OIn1(X8,X3,X7),c_Datatype__Universe_Ousum(X15,X16,X3,X7),tc_set(tc_Datatype__Universe_Onode(X3,X7))) ),
    inference(fof_simplification,[status(thm)],[c_0_66]) ).

fof(c_0_1428,plain,
    ! [X9,X16,X15,X7,X3] :
      ( ~ c_in(X9,X15,tc_set(tc_Datatype__Universe_Onode(X3,X7)))
      | c_in(c_Datatype__Universe_OIn0(X9,X3,X7),c_Datatype__Universe_Ousum(X15,X16,X3,X7),tc_set(tc_Datatype__Universe_Onode(X3,X7))) ),
    inference(fof_simplification,[status(thm)],[c_0_67]) ).

fof(c_0_1429,plain,
    ! [X5,X16,X15,X3] :
      ( ~ c_in(c_minus(X15,c_insert(X5,X16,X3),tc_set(X3)),c_Finite__Set_OFinites,tc_set(X3))
      | c_in(c_minus(X15,X16,tc_set(X3)),c_Finite__Set_OFinites,tc_set(X3)) ),
    inference(fof_simplification,[status(thm)],[c_0_68]) ).

fof(c_0_1430,axiom,
    ! [X34,X6,X4,X5,X7,X3] :
      ( c_Pair(X5,X6,X3,X7) != c_Pair(X4,X34,X3,X7)
      | X6 = X34 ),
    c_0_69 ).

fof(c_0_1431,axiom,
    ! [X34,X6,X4,X5,X7,X3] :
      ( c_Pair(X5,X6,X3,X7) != c_Pair(X4,X34,X3,X7)
      | X5 = X4 ),
    c_0_70 ).

fof(c_0_1432,axiom,
    ! [X11,X8,X12,X9,X7,X3] :
      ( c_Datatype__Universe_OScons(X9,X8,X3,X7) != c_Datatype__Universe_OScons(X12,X11,X3,X7)
      | X8 = X11 ),
    c_0_71 ).

fof(c_0_1433,axiom,
    ! [X11,X8,X12,X9,X7,X3] :
      ( c_Datatype__Universe_OScons(X9,X8,X3,X7) != c_Datatype__Universe_OScons(X12,X11,X3,X7)
      | X9 = X12 ),
    c_0_72 ).

fof(c_0_1434,plain,
    ! [X6,X16,X15,X7,X3] :
      ( ~ c_in(X6,X16,X3)
      | c_in(c_Sum__Type_OInr(X6,X3,X7),c_Sum__Type_OPlus(X15,X16,X7,X3),tc_sum(X7,X3)) ),
    inference(fof_simplification,[status(thm)],[c_0_73]) ).

fof(c_0_1435,plain,
    ! [X5,X16,X15,X7,X3] :
      ( ~ c_in(X5,X15,X3)
      | c_in(c_Sum__Type_OInl(X5,X3,X7),c_Sum__Type_OPlus(X15,X16,X3,X7),tc_sum(X3,X7)) ),
    inference(fof_simplification,[status(thm)],[c_0_74]) ).

fof(c_0_1436,axiom,
    ! [X37,X16,X15,X3] :
      ( c_in(c_Zorn_OUnion__lemma0__1(X15,X16,X37,X3),X37,tc_set(X3))
      | c_lessequals(X16,c_Union(X37,X3),tc_set(X3))
      | c_lessequals(c_Union(X37,X3),X15,tc_set(X3)) ),
    c_0_75 ).

fof(c_0_1437,plain,
    ! [X5,X15,X3] :
      ( ~ c_in(X5,X15,X3)
      | c_in(c_Pair(X5,X5,X3,X3),c_Relation_Odiag(X15,X3),tc_prod(X3,X3)) ),
    inference(fof_simplification,[status(thm)],[c_0_76]) ).

fof(c_0_1438,plain,
    ! [X5,X16,X15,X3] :
      ( ~ c_in(c_minus(X15,X16,tc_set(X3)),c_Finite__Set_OFinites,tc_set(X3))
      | c_in(c_minus(X15,c_insert(X5,X16,X3),tc_set(X3)),c_Finite__Set_OFinites,tc_set(X3)) ),
    inference(fof_simplification,[status(thm)],[c_0_77]) ).

fof(c_0_1439,plain,
    ! [X24,X2] :
      ( ~ c_less(X2,X24,tc_nat)
      | c_in(c_Pair(X2,X24,tc_nat,tc_nat),c_Wellfounded__Relations_Oless__than,tc_prod(tc_nat,tc_nat)) ),
    inference(fof_simplification,[status(thm)],[c_0_78]) ).

fof(c_0_1440,plain,
    ! [X35,X15,X3] :
      ( ~ c_in(X35,c_Relation_Odiag(X15,X3),tc_prod(X3,X3))
      | X35 = c_Pair(c_Main_OdiagE__1(X15,X35,X3),c_Main_OdiagE__1(X15,X35,X3),X3,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_79]) ).

fof(c_0_1441,axiom,
    ! [X14,X5,X3] : c_in(c_Pair(X5,X5,X3,X3),c_Transitive__Closure_Ortrancl(X14,X3),tc_prod(X3,X3)),
    c_0_80 ).

fof(c_0_1442,plain,
    ! [X50,X51,X7,X3] :
      ( ~ c_Wellfounded__Recursion_Owf(X50,X7)
      | ~ c_Wellfounded__Recursion_Owf(X51,X3)
      | c_Wellfounded__Recursion_Owf(c_Wellfounded__Relations_Olex__prod(X51,X50,X3,X7),tc_prod(X3,X7)) ),
    inference(fof_simplification,[status(thm)],[c_0_81]) ).

fof(c_0_1443,plain,
    ! [X48,X49,X7,X3] :
      ( ~ c_Relation_Otrans(X48,X7)
      | ~ c_Relation_Otrans(X49,X3)
      | c_Relation_Otrans(c_Wellfounded__Relations_Olex__prod(X49,X48,X3,X7),tc_prod(X3,X7)) ),
    inference(fof_simplification,[status(thm)],[c_0_82]) ).

fof(c_0_1444,axiom,
    ! [X5,X3] : c_in(c_Pair(X5,X5,X3,X3),c_Relation_OId,tc_prod(X3,X3)),
    c_0_83 ).

fof(c_0_1445,axiom,
    ! [X23,X24,X22,X2,X3] :
      ( c_append(X22,c_List_Olist_OCons(X2,c_List_Olist_ONil,X3),X3) != c_append(X23,c_List_Olist_OCons(X24,c_List_Olist_ONil,X3),X3)
      | X2 = X24 ),
    c_0_84 ).

fof(c_0_1446,axiom,
    ! [X23,X24,X22,X2,X3] :
      ( c_append(X22,c_List_Olist_OCons(X2,c_List_Olist_ONil,X3),X3) != c_append(X23,c_List_Olist_OCons(X24,c_List_Olist_ONil,X3),X3)
      | X22 = X23 ),
    c_0_85 ).

fof(c_0_1447,axiom,
    ! [X10,X8,X9,X7,X3] : c_Datatype__Universe_OScons(X9,X8,X3,X7) != c_Datatype__Universe_ONumb(X10,X3,X7),
    c_0_86 ).

fof(c_0_1448,axiom,
    ! [X5,X8,X9,X7,X3] : c_Datatype__Universe_OScons(X9,X8,X3,X7) != c_Datatype__Universe_OLeaf(X5,X3,X7),
    c_0_87 ).

fof(c_0_1449,axiom,
    ! [X5,X8,X9,X7,X3] : c_Datatype__Universe_OScons(X9,X8,X3,X7) != c_Datatype__Universe_OAtom(X5,X3,X7),
    c_0_88 ).

fof(c_0_1450,axiom,
    ! [X10,X8,X9,X7,X3] : c_Datatype__Universe_ONumb(X10,X3,X7) != c_Datatype__Universe_OScons(X9,X8,X3,X7),
    c_0_89 ).

fof(c_0_1451,axiom,
    ! [X5,X8,X9,X7,X3] : c_Datatype__Universe_OLeaf(X5,X3,X7) != c_Datatype__Universe_OScons(X9,X8,X3,X7),
    c_0_90 ).

fof(c_0_1452,axiom,
    ! [X5,X8,X9,X7,X3] : c_Datatype__Universe_OAtom(X5,X3,X7) != c_Datatype__Universe_OScons(X9,X8,X3,X7),
    c_0_91 ).

fof(c_0_1453,plain,
    ! [X23,X22,X15,X3] :
      ( ~ c_in(X23,c_List_Olists(X15,X3),tc_List_Olist(X3))
      | ~ c_in(X22,c_List_Olists(X15,X3),tc_List_Olist(X3))
      | c_in(c_append(X22,X23,X3),c_List_Olists(X15,X3),tc_List_Olist(X3)) ),
    inference(fof_simplification,[status(thm)],[c_0_92]) ).

fof(c_0_1454,plain,
    ! [X14,X7,X3] :
      ( ~ c_in(c_Relation_Oconverse(X14,X7,X3),c_Finite__Set_OFinites,tc_set(tc_prod(X3,X7)))
      | c_in(X14,c_Finite__Set_OFinites,tc_set(tc_prod(X7,X3))) ),
    inference(fof_simplification,[status(thm)],[c_0_93]) ).

fof(c_0_1455,axiom,
    ! [X23,X24,X3] : c_List_Orev(c_append(c_List_Orev(X23,X3),c_List_Olist_OCons(X24,c_List_Olist_ONil,X3),X3),X3) = c_List_Olist_OCons(X24,X23,X3),
    c_0_94 ).

fof(c_0_1456,plain,
    ! [X44,X3] :
      ( ~ c_in(X44,c_Relation_OId,tc_prod(X3,X3))
      | X44 = c_Pair(c_Main_OIdE__1(X44,X3),c_Main_OIdE__1(X44,X3),X3,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_95]) ).

fof(c_0_1457,plain,
    ! [X43,X5,X15,X3] :
      ( ~ c_in(X5,X15,X3)
      | ~ c_in(X43,c_List_Olists(X15,X3),tc_List_Olist(X3))
      | c_in(c_List_Olist_OCons(X5,X43,X3),c_List_Olists(X15,X3),tc_List_Olist(X3)) ),
    inference(fof_simplification,[status(thm)],[c_0_96]) ).

fof(c_0_1458,plain,
    ! [X14,X7,X3] :
      ( ~ c_in(X14,c_Finite__Set_OFinites,tc_set(tc_prod(X7,X3)))
      | c_in(c_Relation_Oconverse(X14,X7,X3),c_Finite__Set_OFinites,tc_set(tc_prod(X3,X7))) ),
    inference(fof_simplification,[status(thm)],[c_0_97]) ).

fof(c_0_1459,plain,
    ! [X2,X43,X15,X3] :
      ( ~ c_in(c_List_Olist_OCons(X2,X43,X3),c_List_Olists(X15,X3),tc_List_Olist(X3))
      | c_in(X43,c_List_Olists(X15,X3),tc_List_Olist(X3)) ),
    inference(fof_simplification,[status(thm)],[c_0_98]) ).

fof(c_0_1460,plain,
    ! [X23,X22,X15,X3] :
      ( ~ c_in(c_append(X22,X23,X3),c_List_Olists(X15,X3),tc_List_Olist(X3))
      | c_in(X23,c_List_Olists(X15,X3),tc_List_Olist(X3)) ),
    inference(fof_simplification,[status(thm)],[c_0_99]) ).

fof(c_0_1461,plain,
    ! [X23,X22,X15,X3] :
      ( ~ c_in(c_append(X22,X23,X3),c_List_Olists(X15,X3),tc_List_Olist(X3))
      | c_in(X22,c_List_Olists(X15,X3),tc_List_Olist(X3)) ),
    inference(fof_simplification,[status(thm)],[c_0_100]) ).

fof(c_0_1462,plain,
    ! [X2,X15,X3] :
      ( ~ c_lessequals(X15,c_insert(X2,c_emptyset,X3),tc_set(X3))
      | c_insert(X2,c_emptyset,X3) = c_insert(X2,X15,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_101]) ).

fof(c_0_1463,plain,
    ! [X2,X15,X3] :
      ( ~ c_lessequals(X15,c_insert(X2,c_emptyset,X3),tc_set(X3))
      | c_insert(X2,X15,X3) = c_insert(X2,c_emptyset,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_102]) ).

fof(c_0_1464,plain,
    ! [X35,X16,X15,X3] :
      ( ~ c_in(X35,c_union(X15,X16,X3),X3)
      | c_in(X35,X16,X3)
      | c_in(X35,X15,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_103]) ).

fof(c_0_1465,plain,
    ! [X35,X16,X15,X3] :
      ( ~ c_in(X35,X16,X3)
      | ~ c_in(X35,c_minus(X15,X16,tc_set(X3)),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_104]) ).

fof(c_0_1466,plain,
    ! [X2,X43,X15,X3] :
      ( ~ c_in(c_List_Olist_OCons(X2,X43,X3),c_List_Olists(X15,X3),tc_List_Olist(X3))
      | c_in(X2,X15,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_105]) ).

fof(c_0_1467,plain,
    ! [X17,X18,X3] :
      ( ~ c_in(X17,c_Finite__Set_OFinites,tc_set(X3))
      | ~ c_in(X18,c_Finite__Set_OFinites,tc_set(X3))
      | c_in(c_union(X18,X17,X3),c_Finite__Set_OFinites,tc_set(X3)) ),
    inference(fof_simplification,[status(thm)],[c_0_106]) ).

fof(c_0_1468,plain,
    ! [X19,X13] :
      ( ~ c_less(c_0,c_plus(X13,X19,tc_nat),tc_nat)
      | c_less(c_0,X19,tc_nat)
      | c_less(c_0,X13,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_107]) ).

fof(c_0_1469,plain,
    ! [X22,X15,X3] :
      ( ~ c_in(c_Main_Oin__listsI__1(X15,X22,X3),X15,X3)
      | c_in(X22,c_List_Olists(X15,X3),tc_List_Olist(X3)) ),
    inference(fof_simplification,[status(thm)],[c_0_108]) ).

fof(c_0_1470,plain,
    ! [X37,X15,X3] :
      ( ~ c_in(X15,c_Main_OInterI__1(X15,X37,X3),X3)
      | c_in(X15,c_Inter(X37,X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_109]) ).

fof(c_0_1471,plain,
    ! [X35,X16,X15,X3] :
      ( ~ c_in(X35,X16,X3)
      | ~ c_in(X35,X15,X3)
      | c_in(X35,c_inter(X15,X16,X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_110]) ).

fof(c_0_1472,axiom,
    ! [X6,X5,X15,X3] :
      ( c_insert(X6,c_emptyset,X3) != c_insert(X5,X15,X3)
      | c_lessequals(X15,c_insert(X6,c_emptyset,X3),tc_set(X3)) ),
    c_0_111 ).

fof(c_0_1473,axiom,
    ! [X6,X5,X15,X3] :
      ( c_insert(X5,X15,X3) != c_insert(X6,c_emptyset,X3)
      | c_lessequals(X15,c_insert(X6,c_emptyset,X3),tc_set(X3)) ),
    c_0_112 ).

fof(c_0_1474,plain,
    ! [X15,X3] :
      ( ~ c_in(X15,c_Finite__Set_OFinites,tc_set(tc_set(X3)))
      | ~ c_in(c_Main_Ofinite__Union__1(X15,X3),c_Finite__Set_OFinites,tc_set(X3))
      | c_in(c_Union(X15,X3),c_Finite__Set_OFinites,tc_set(X3)) ),
    inference(fof_simplification,[status(thm)],[c_0_113]) ).

fof(c_0_1475,plain,
    ! [X35,X15,X3] :
      ( ~ c_in(X35,c_Relation_Odiag(X15,X3),tc_prod(X3,X3))
      | c_in(c_Main_OdiagE__1(X15,X35,X3),X15,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_114]) ).

fof(c_0_1476,plain,
    ! [X35,X16,X15,X3] :
      ( ~ c_in(X35,c_minus(X15,X16,tc_set(X3)),X3)
      | c_in(X35,X15,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_115]) ).

fof(c_0_1477,plain,
    ! [X17,X18,X3] :
      ( ~ c_in(c_union(X18,X17,X3),c_Finite__Set_OFinites,tc_set(X3))
      | c_in(X17,c_Finite__Set_OFinites,tc_set(X3)) ),
    inference(fof_simplification,[status(thm)],[c_0_116]) ).

fof(c_0_1478,plain,
    ! [X17,X18,X3] :
      ( ~ c_in(c_union(X18,X17,X3),c_Finite__Set_OFinites,tc_set(X3))
      | c_in(X18,c_Finite__Set_OFinites,tc_set(X3)) ),
    inference(fof_simplification,[status(thm)],[c_0_117]) ).

fof(c_0_1479,plain,
    ! [X22,X42,X15,X3] :
      ( ~ c_in(X22,c_List_Olists(X15,X3),tc_List_Olist(X3))
      | ~ c_in(X42,c_List_Oset(X22,X3),X3)
      | c_in(X42,X15,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_118]) ).

fof(c_0_1480,plain,
    ! [X16,X15,X3] :
      ( ~ c_in(c_Main_OsubsetI__1(X15,X16,X3),X16,X3)
      | c_lessequals(X15,X16,tc_set(X3)) ),
    inference(fof_simplification,[status(thm)],[c_0_119]) ).

fof(c_0_1481,plain,
    ! [X35,X16,X15,X3] :
      ( ~ c_in(X35,X15,X3)
      | c_in(X35,X16,X3)
      | c_in(X35,c_minus(X15,X16,tc_set(X3)),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_120]) ).

fof(c_0_1482,plain,
    ! [X6,X5,X15,X3] :
      ( ~ c_in(X5,c_insert(X6,X15,X3),X3)
      | c_in(X5,X15,X3)
      | X5 = X6 ),
    inference(fof_simplification,[status(thm)],[c_0_121]) ).

fof(c_0_1483,plain,
    ! [X35,X16,X15,X3] :
      ( ~ c_in(X35,c_inter(X15,X16,X3),X3)
      | c_in(X35,X15,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_122]) ).

fof(c_0_1484,plain,
    ! [X35,X16,X15,X3] :
      ( ~ c_in(X35,c_inter(X15,X16,X3),X3)
      | c_in(X35,X16,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_123]) ).

fof(c_0_1485,plain,
    ! [X24,X2,X41,X3] :
      ( ~ c_lessequals(X2,X24,tc_set(tc_set(X3)))
      | c_lessequals(X2,c_Zorn_Osucc(X41,X24,X3),tc_set(tc_set(X3))) ),
    inference(fof_simplification,[status(thm)],[c_0_124]) ).

fof(c_0_1486,plain,
    ! [X37,X15,X3] :
      ( ~ c_in(X15,c_Union(X37,X3),X3)
      | c_in(c_Main_OUnionE__1(X15,X37,X3),X37,tc_set(X3)) ),
    inference(fof_simplification,[status(thm)],[c_0_125]) ).

fof(c_0_1487,axiom,
    ! [X23,X24,X22,X3] :
      ( c_List_Orev(X22,X3) != c_List_Olist_OCons(X24,X23,X3)
      | X22 = c_append(c_List_Orev(X23,X3),c_List_Olist_OCons(X24,c_List_Olist_ONil,X3),X3) ),
    c_0_126 ).

fof(c_0_1488,plain,
    ! [X37,X15,X3] :
      ( ~ c_in(X15,c_Union(X37,X3),X3)
      | c_in(X15,c_Main_OUnionE__1(X15,X37,X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_127]) ).

fof(c_0_1489,plain,
    ! [X15,X3] :
      ( ~ c_in(X15,c_Finite__Set_OFinites,tc_set(tc_set(X3)))
      | c_in(c_Main_Ofinite__Union__1(X15,X3),X15,tc_set(X3))
      | c_in(c_Union(X15,X3),c_Finite__Set_OFinites,tc_set(X3)) ),
    inference(fof_simplification,[status(thm)],[c_0_128]) ).

fof(c_0_1490,plain,
    ! [X36,X37,X15,X3] :
      ( ~ c_in(X36,X37,tc_set(X3))
      | ~ c_in(X15,c_Inter(X37,X3),X3)
      | c_in(X15,X36,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_129]) ).

fof(c_0_1491,plain,
    ! [X16,X15,X3] :
      ( ~ c_lessequals(c_uminus(X15,tc_set(X3)),c_uminus(X16,tc_set(X3)),tc_set(X3))
      | c_lessequals(X16,X15,tc_set(X3)) ),
    inference(fof_simplification,[status(thm)],[c_0_130]) ).

fof(c_0_1492,axiom,
    ! [X22,X15,X3] :
      ( c_in(X22,c_List_Olists(X15,X3),tc_List_Olist(X3))
      | c_in(c_Main_Oin__listsI__1(X15,X22,X3),c_List_Oset(X22,X3),X3) ),
    c_0_131 ).

fof(c_0_1493,plain,
    ! [X36,X37,X15,X3] :
      ( ~ c_in(X15,X36,X3)
      | ~ c_in(X36,X37,tc_set(X3))
      | c_in(X15,c_Union(X37,X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_132]) ).

fof(c_0_1494,plain,
    ! [X17,X18,X3] :
      ( ~ c_in(X17,c_Finite__Set_OFinites,tc_set(X3))
      | c_in(c_inter(X18,X17,X3),c_Finite__Set_OFinites,tc_set(X3)) ),
    inference(fof_simplification,[status(thm)],[c_0_133]) ).

fof(c_0_1495,plain,
    ! [X17,X18,X3] :
      ( ~ c_in(X18,c_Finite__Set_OFinites,tc_set(X3))
      | c_in(c_inter(X18,X17,X3),c_Finite__Set_OFinites,tc_set(X3)) ),
    inference(fof_simplification,[status(thm)],[c_0_134]) ).

fof(c_0_1496,plain,
    ! [X5,X15,X3] :
      ( ~ c_in(X15,c_Finite__Set_OFinites,tc_set(X3))
      | c_in(c_insert(X5,X15,X3),c_Finite__Set_OFinites,tc_set(X3)) ),
    inference(fof_simplification,[status(thm)],[c_0_135]) ).

fof(c_0_1497,plain,
    ! [X6,X5,X3] :
      ( ~ c_in(X6,c_insert(X5,c_emptyset,X3),X3)
      | X6 = X5 ),
    inference(fof_simplification,[status(thm)],[c_0_136]) ).

fof(c_0_1498,axiom,
    ! [X37,X15,X3] :
      ( c_in(X15,c_Inter(X37,X3),X3)
      | c_in(c_Main_OInterI__1(X15,X37,X3),X37,tc_set(X3)) ),
    c_0_137 ).

fof(c_0_1499,plain,
    ! [X6,X5,X16,X3] :
      ( ~ c_in(X5,X16,X3)
      | c_in(X5,c_insert(X6,X16,X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_138]) ).

fof(c_0_1500,plain,
    ! [X35,X16,X15,X3] :
      ( ~ c_in(X35,X15,X3)
      | c_in(X35,c_union(X15,X16,X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_139]) ).

fof(c_0_1501,plain,
    ! [X35,X16,X15,X3] :
      ( ~ c_in(X35,X16,X3)
      | c_in(X35,c_union(X15,X16,X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_140]) ).

fof(c_0_1502,plain,
    ! [X33,X32] : ~ c_less(c_plus(X33,X32,tc_nat),X32,tc_nat),
    inference(fof_simplification,[status(thm)],[c_0_141]) ).

fof(c_0_1503,plain,
    ! [X33,X32] : ~ c_less(c_plus(X32,X33,tc_nat),X32,tc_nat),
    inference(fof_simplification,[status(thm)],[c_0_142]) ).

fof(c_0_1504,plain,
    ! [X24,X2,X3] :
      ( ~ class_Orderings_Olinorder(X3)
      | ~ c_lessequals(c_SetInterval_OlessThan(X2,X3),c_SetInterval_OlessThan(X24,X3),tc_set(X3))
      | c_lessequals(X2,X24,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_143]) ).

fof(c_0_1505,plain,
    ! [X24,X2,X3] :
      ( ~ class_Orderings_Olinorder(X3)
      | ~ c_lessequals(c_SetInterval_OgreaterThan(X2,X3),c_SetInterval_OgreaterThan(X24,X3),tc_set(X3))
      | c_lessequals(X24,X2,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_144]) ).

fof(c_0_1506,plain,
    ! [X24,X2,X3] :
      ( ~ class_Orderings_Oorder(X3)
      | ~ c_lessequals(c_SetInterval_OatMost(X2,X3),c_SetInterval_OatMost(X24,X3),tc_set(X3))
      | c_lessequals(X2,X24,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_145]) ).

fof(c_0_1507,plain,
    ! [X24,X2,X3] :
      ( ~ class_Orderings_Oorder(X3)
      | ~ c_lessequals(c_SetInterval_OatLeast(X2,X3),c_SetInterval_OatLeast(X24,X3),tc_set(X3))
      | c_lessequals(X24,X2,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_146]) ).

fof(c_0_1508,plain,
    ! [X35,X16,X15,X3] :
      ( ~ c_in(X35,X15,X3)
      | ~ c_lessequals(X15,X16,tc_set(X3))
      | c_in(X35,X16,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_147]) ).

fof(c_0_1509,plain,
    ! [X19,X13] :
      ( ~ c_less(c_0,X19,tc_nat)
      | c_less(c_0,c_plus(X13,X19,tc_nat),tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_148]) ).

fof(c_0_1510,plain,
    ! [X19,X13] :
      ( ~ c_less(c_0,X13,tc_nat)
      | c_less(c_0,c_plus(X13,X19,tc_nat),tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_149]) ).

fof(c_0_1511,plain,
    ! [X14,X44,X3] :
      ( ~ c_in(X44,X14,tc_prod(X3,X3))
      | c_in(X44,c_Transitive__Closure_Ortrancl(X14,X3),tc_prod(X3,X3)) ),
    inference(fof_simplification,[status(thm)],[c_0_150]) ).

fof(c_0_1512,plain,
    ! [X16,X15,X3] :
      ( ~ c_lessequals(X16,X15,tc_set(X3))
      | c_lessequals(c_uminus(X15,tc_set(X3)),c_uminus(X16,tc_set(X3)),tc_set(X3)) ),
    inference(fof_simplification,[status(thm)],[c_0_151]) ).

fof(c_0_1513,plain,
    ! [X35,X15,X3] :
      ( ~ c_in(X35,X15,X3)
      | ~ c_in(X35,c_uminus(X15,tc_set(X3)),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_152]) ).

fof(c_0_1514,axiom,
    ! [X16,X15,X3] :
      ( c_in(c_Main_OsubsetI__1(X15,X16,X3),X15,X3)
      | c_lessequals(X15,X16,tc_set(X3)) ),
    c_0_153 ).

fof(c_0_1515,plain,
    ! [X15,X3] :
      ( ~ c_in(c_Pow(X15,X3),c_Finite__Set_OFinites,tc_set(tc_set(X3)))
      | c_in(X15,c_Finite__Set_OFinites,tc_set(X3)) ),
    inference(fof_simplification,[status(thm)],[c_0_154]) ).

fof(c_0_1516,plain,
    ! [X24,X2,X3] :
      ( ~ class_Orderings_Olinorder(X3)
      | ~ c_lessequals(X2,X24,X3)
      | c_lessequals(c_SetInterval_OlessThan(X2,X3),c_SetInterval_OlessThan(X24,X3),tc_set(X3)) ),
    inference(fof_simplification,[status(thm)],[c_0_155]) ).

fof(c_0_1517,plain,
    ! [X24,X2,X3] :
      ( ~ class_Orderings_Olinorder(X3)
      | ~ c_lessequals(X24,X2,X3)
      | c_lessequals(c_SetInterval_OgreaterThan(X2,X3),c_SetInterval_OgreaterThan(X24,X3),tc_set(X3)) ),
    inference(fof_simplification,[status(thm)],[c_0_156]) ).

fof(c_0_1518,plain,
    ! [X24,X2,X3] :
      ( ~ class_Orderings_Oorder(X3)
      | ~ c_lessequals(X2,X24,X3)
      | c_lessequals(c_SetInterval_OatMost(X2,X3),c_SetInterval_OatMost(X24,X3),tc_set(X3)) ),
    inference(fof_simplification,[status(thm)],[c_0_157]) ).

fof(c_0_1519,plain,
    ! [X24,X2,X3] :
      ( ~ class_Orderings_Oorder(X3)
      | ~ c_lessequals(X24,X2,X3)
      | c_lessequals(c_SetInterval_OatLeast(X2,X3),c_SetInterval_OatLeast(X24,X3),tc_set(X3)) ),
    inference(fof_simplification,[status(thm)],[c_0_158]) ).

fof(c_0_1520,plain,
    ! [X14,X3] :
      ( ~ c_Wellfounded__Recursion_Oacyclic(c_Relation_Oconverse(X14,X3,X3),X3)
      | c_Wellfounded__Recursion_Oacyclic(X14,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_159]) ).

fof(c_0_1521,plain,
    ! [X24,X2,X41,X3] :
      ( ~ c_Infinite__Set_Oatmost__one(X41,X3)
      | ~ c_in(X24,X41,X3)
      | ~ c_in(X2,X41,X3)
      | X24 = X2 ),
    inference(fof_simplification,[status(thm)],[c_0_160]) ).

fof(c_0_1522,plain,
    ! [X16,X15,X3] :
      ( ~ c_in(X15,c_Pow(X16,X3),tc_set(X3))
      | c_lessequals(X15,X16,tc_set(X3)) ),
    inference(fof_simplification,[status(thm)],[c_0_161]) ).

fof(c_0_1523,plain,
    ! [X16,X15,X3] :
      ( ~ c_lessequals(X16,X15,tc_set(X3))
      | ~ c_lessequals(X15,X16,tc_set(X3))
      | X15 = X16 ),
    inference(fof_simplification,[status(thm)],[c_0_162]) ).

fof(c_0_1524,plain,
    ! [X16,X15,X3] :
      ( ~ c_less(X15,X16,tc_set(X3))
      | ~ c_lessequals(X16,X15,tc_set(X3)) ),
    inference(fof_simplification,[status(thm)],[c_0_163]) ).

fof(c_0_1525,plain,
    ! [X15,X3] :
      ( ~ c_in(X15,c_Finite__Set_OFinites,tc_set(X3))
      | c_in(c_Pow(X15,X3),c_Finite__Set_OFinites,tc_set(tc_set(X3))) ),
    inference(fof_simplification,[status(thm)],[c_0_164]) ).

fof(c_0_1526,plain,
    ! [X10,X32,X3] :
      ( ~ class_Orderings_Oord(X3)
      | ~ c_in(X32,c_SetInterval_OlessThan(X10,X3),X3)
      | c_less(X32,X10,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_165]) ).

fof(c_0_1527,plain,
    ! [X10,X32,X3] :
      ( ~ class_Orderings_Oord(X3)
      | ~ c_in(X32,c_SetInterval_OgreaterThan(X10,X3),X3)
      | c_less(X10,X32,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_166]) ).

fof(c_0_1528,plain,
    ! [X10,X32,X3] :
      ( ~ class_Orderings_Oord(X3)
      | ~ c_in(X32,c_SetInterval_OatMost(X10,X3),X3)
      | c_lessequals(X32,X10,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_167]) ).

fof(c_0_1529,plain,
    ! [X10,X32,X3] :
      ( ~ class_Orderings_Oord(X3)
      | ~ c_in(X32,c_SetInterval_OatLeast(X10,X3),X3)
      | c_lessequals(X10,X32,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_168]) ).

fof(c_0_1530,plain,
    ! [X16,X15,X3] :
      ( ~ c_lessequals(X15,X16,tc_set(X3))
      | c_in(X15,c_Pow(X16,X3),tc_set(X3)) ),
    inference(fof_simplification,[status(thm)],[c_0_169]) ).

fof(c_0_1531,axiom,
    ! [X22,X3] : c_lessequals(c_Nat_Osize(c_List_Oremdups(X22,X3),tc_List_Olist(X3)),c_Nat_Osize(X22,tc_List_Olist(X3)),tc_nat),
    c_0_170 ).

fof(c_0_1532,plain,
    ! [X10,X32,X3] :
      ( ~ class_Orderings_Oord(X3)
      | ~ c_less(X32,X10,X3)
      | c_in(X32,c_SetInterval_OlessThan(X10,X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_171]) ).

fof(c_0_1533,plain,
    ! [X10,X32,X3] :
      ( ~ class_Orderings_Oord(X3)
      | ~ c_less(X10,X32,X3)
      | c_in(X32,c_SetInterval_OgreaterThan(X10,X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_172]) ).

fof(c_0_1534,plain,
    ! [X10,X32,X3] :
      ( ~ class_Orderings_Oord(X3)
      | ~ c_lessequals(X32,X10,X3)
      | c_in(X32,c_SetInterval_OatMost(X10,X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_173]) ).

fof(c_0_1535,plain,
    ! [X10,X32,X3] :
      ( ~ class_Orderings_Oord(X3)
      | ~ c_lessequals(X10,X32,X3)
      | c_in(X32,c_SetInterval_OatLeast(X10,X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_174]) ).

fof(c_0_1536,axiom,
    ! [X24,X2,X7,X3] :
      ( c_Datatype__Universe_ONumb(X2,X3,X7) != c_Datatype__Universe_ONumb(X24,X3,X7)
      | X2 = X24 ),
    c_0_175 ).

fof(c_0_1537,axiom,
    ! [X24,X2,X7,X3] :
      ( c_Datatype__Universe_OLeaf(X2,X3,X7) != c_Datatype__Universe_OLeaf(X24,X3,X7)
      | X2 = X24 ),
    c_0_176 ).

fof(c_0_1538,axiom,
    ! [X24,X2,X7,X3] :
      ( c_Sum__Type_OInr(X2,X7,X3) != c_Sum__Type_OInr(X24,X7,X3)
      | X2 = X24 ),
    c_0_177 ).

fof(c_0_1539,axiom,
    ! [X24,X2,X7,X3] :
      ( c_Sum__Type_OInl(X2,X3,X7) != c_Sum__Type_OInl(X24,X3,X7)
      | X2 = X24 ),
    c_0_178 ).

fof(c_0_1540,axiom,
    ! [X25,X23,X22,X3] :
      ( c_append(X22,X23,X3) != c_append(X22,X25,X3)
      | X23 = X25 ),
    c_0_179 ).

fof(c_0_1541,axiom,
    ! [X30,X31,X4,X5,X3] :
      ( c_List_Olist_OCons(X5,X31,X3) != c_List_Olist_OCons(X4,X30,X3)
      | X31 = X30 ),
    c_0_180 ).

fof(c_0_1542,axiom,
    ! [X30,X31,X4,X5,X3] :
      ( c_List_Olist_OCons(X5,X31,X3) != c_List_Olist_OCons(X4,X30,X3)
      | X5 = X4 ),
    c_0_181 ).

fof(c_0_1543,axiom,
    ! [X25,X23,X22,X3] :
      ( c_append(X23,X22,X3) != c_append(X25,X22,X3)
      | X23 = X25 ),
    c_0_182 ).

fof(c_0_1544,axiom,
    ! [X8,X9,X7,X3] :
      ( c_Datatype__Universe_OIn1(X9,X3,X7) != c_Datatype__Universe_OIn1(X8,X3,X7)
      | X9 = X8 ),
    c_0_183 ).

fof(c_0_1545,axiom,
    ! [X8,X9,X7,X3] :
      ( c_Datatype__Universe_OIn0(X9,X3,X7) != c_Datatype__Universe_OIn0(X8,X3,X7)
      | X9 = X8 ),
    c_0_184 ).

fof(c_0_1546,axiom,
    ! [X6,X5,X7,X3] :
      ( c_Datatype__Universe_OAtom(X5,X3,X7) != c_Datatype__Universe_OAtom(X6,X3,X7)
      | X5 = X6 ),
    c_0_185 ).

fof(c_0_1547,plain,
    ! [X20,X21] :
      ( ~ c_Divides_Oop_Advd(c_uminus(X20,tc_IntDef_Oint),X21,tc_IntDef_Oint)
      | c_Divides_Oop_Advd(X20,X21,tc_IntDef_Oint) ),
    inference(fof_simplification,[status(thm)],[c_0_186]) ).

fof(c_0_1548,plain,
    ! [X20,X21] :
      ( ~ c_Divides_Oop_Advd(X20,c_uminus(X21,tc_IntDef_Oint),tc_IntDef_Oint)
      | c_Divides_Oop_Advd(X20,X21,tc_IntDef_Oint) ),
    inference(fof_simplification,[status(thm)],[c_0_187]) ).

fof(c_0_1549,axiom,
    ! [X6,X5,X7,X3] : c_Sum__Type_OInr(X6,X7,X3) != c_Sum__Type_OInl(X5,X3,X7),
    c_0_188 ).

fof(c_0_1550,axiom,
    ! [X6,X5,X7,X3] : c_Sum__Type_OInl(X5,X3,X7) != c_Sum__Type_OInr(X6,X7,X3),
    c_0_189 ).

fof(c_0_1551,axiom,
    ! [X10,X5,X7,X3] : c_Datatype__Universe_ONumb(X10,X3,X7) != c_Datatype__Universe_OLeaf(X5,X3,X7),
    c_0_190 ).

fof(c_0_1552,axiom,
    ! [X10,X5,X7,X3] : c_Datatype__Universe_OLeaf(X5,X3,X7) != c_Datatype__Universe_ONumb(X10,X3,X7),
    c_0_191 ).

fof(c_0_1553,axiom,
    ! [X8,X9,X7,X3] : c_Datatype__Universe_OIn1(X8,X3,X7) != c_Datatype__Universe_OIn0(X9,X3,X7),
    c_0_192 ).

fof(c_0_1554,axiom,
    ! [X8,X9,X7,X3] : c_Datatype__Universe_OIn0(X9,X3,X7) != c_Datatype__Universe_OIn1(X8,X3,X7),
    c_0_193 ).

fof(c_0_1555,axiom,
    ! [X6,X5,X15,X3] :
      ( c_insert(X6,c_emptyset,X3) != c_insert(X5,X15,X3)
      | X5 = X6 ),
    c_0_194 ).

fof(c_0_1556,axiom,
    ! [X6,X5,X15,X3] :
      ( c_insert(X5,X15,X3) != c_insert(X6,c_emptyset,X3)
      | X5 = X6 ),
    c_0_195 ).

fof(c_0_1557,axiom,
    ! [X6,X5,X3] :
      ( c_insert(X5,c_emptyset,X3) != c_insert(X6,c_emptyset,X3)
      | X5 = X6 ),
    c_0_196 ).

fof(c_0_1558,axiom,
    ! [X13,X40] :
      ( c_Divides_Oop_Amod(X13,X40,tc_IntDef_Oint) != c_0
      | X13 = c_times(X40,c_Main_Ozmod__eq__0D__dest__1(X40,X13),tc_IntDef_Oint) ),
    c_0_197 ).

fof(c_0_1559,axiom,
    ! [X13,X40] :
      ( c_Divides_Oop_Amod(X13,X40,tc_nat) != c_0
      | X13 = c_times(X40,c_Main_Omod__eq__0D__dest__1(X40,X13),tc_nat) ),
    c_0_198 ).

fof(c_0_1560,axiom,
    ! [X2,X16,X3] : c_in(X2,c_insert(X2,X16,X3),X3),
    c_0_199 ).

fof(c_0_1561,axiom,
    ! [X39,X43] : c_in(c_SetInterval_OgreaterThanLessThan(X43,X39,tc_IntDef_Oint),c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)),
    c_0_200 ).

fof(c_0_1562,axiom,
    ! [X39,X43] : c_in(c_SetInterval_OgreaterThanLessThan(X43,X39,tc_nat),c_Finite__Set_OFinites,tc_set(tc_nat)),
    c_0_201 ).

fof(c_0_1563,axiom,
    ! [X39,X43] : c_in(c_SetInterval_OgreaterThanAtMost(X43,X39,tc_IntDef_Oint),c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)),
    c_0_202 ).

fof(c_0_1564,axiom,
    ! [X39,X43] : c_in(c_SetInterval_OgreaterThanAtMost(X43,X39,tc_nat),c_Finite__Set_OFinites,tc_set(tc_nat)),
    c_0_203 ).

fof(c_0_1565,axiom,
    ! [X39,X43] : c_in(c_SetInterval_OatLeastLessThan(X43,X39,tc_IntDef_Oint),c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)),
    c_0_204 ).

fof(c_0_1566,axiom,
    ! [X39,X43] : c_in(c_SetInterval_OatLeastLessThan(X43,X39,tc_nat),c_Finite__Set_OFinites,tc_set(tc_nat)),
    c_0_205 ).

fof(c_0_1567,axiom,
    ! [X39,X43] : c_in(c_SetInterval_OatLeastAtMost(X43,X39,tc_IntDef_Oint),c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)),
    c_0_206 ).

fof(c_0_1568,axiom,
    ! [X39,X43] : c_in(c_SetInterval_OatLeastAtMost(X43,X39,tc_nat),c_Finite__Set_OFinites,tc_set(tc_nat)),
    c_0_207 ).

fof(c_0_1569,plain,
    ! [X20,X21] :
      ( ~ c_Divides_Oop_Advd(X20,X21,tc_IntDef_Oint)
      | c_Divides_Oop_Advd(c_uminus(X20,tc_IntDef_Oint),X21,tc_IntDef_Oint) ),
    inference(fof_simplification,[status(thm)],[c_0_208]) ).

fof(c_0_1570,plain,
    ! [X20,X21] :
      ( ~ c_Divides_Oop_Advd(X20,X21,tc_IntDef_Oint)
      | c_Divides_Oop_Advd(X20,c_uminus(X21,tc_IntDef_Oint),tc_IntDef_Oint) ),
    inference(fof_simplification,[status(thm)],[c_0_209]) ).

fof(c_0_1571,plain,
    ! [X16,X15,X3] :
      ( ~ c_lessequals(X15,X16,tc_set(X3))
      | c_less(X15,X16,tc_set(X3))
      | X15 = X16 ),
    inference(fof_simplification,[status(thm)],[c_0_210]) ).

fof(c_0_1572,axiom,
    ! [X5,X3] : c_in(X5,c_insert(X5,c_emptyset,X3),X3),
    c_0_211 ).

fof(c_0_1573,axiom,
    ! [X13,X10] : c_Divides_Oop_Advd(X10,c_times(X13,X10,tc_IntDef_Oint),tc_IntDef_Oint),
    c_0_212 ).

fof(c_0_1574,axiom,
    ! [X13,X10] : c_Divides_Oop_Advd(X10,c_times(X10,X13,tc_IntDef_Oint),tc_IntDef_Oint),
    c_0_213 ).

fof(c_0_1575,axiom,
    ! [X13,X10] : c_Divides_Oop_Advd(X10,c_times(X13,X10,tc_nat),tc_nat),
    c_0_214 ).

fof(c_0_1576,axiom,
    ! [X13,X10] : c_Divides_Oop_Advd(X10,c_times(X10,X13,tc_nat),tc_nat),
    c_0_215 ).

fof(c_0_1577,plain,
    ! [X16,X15,X3] :
      ( ~ c_less(X15,X16,tc_set(X3))
      | c_lessequals(X15,X16,tc_set(X3)) ),
    inference(fof_simplification,[status(thm)],[c_0_216]) ).

fof(c_0_1578,plain,
    ! [X19,X13] :
      ( ~ c_less(c_Suc(X13),c_Suc(X19),tc_nat)
      | c_less(X13,X19,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_217]) ).

fof(c_0_1579,plain,
    ! [X19,X13] :
      ( ~ c_lessequals(c_Suc(X19),c_Suc(X13),tc_nat)
      | c_lessequals(X19,X13,tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_218]) ).

fof(c_0_1580,plain,
    ! [X19,X13] :
      ( ~ c_less(X13,X19,tc_nat)
      | c_less(c_Suc(X13),c_Suc(X19),tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_219]) ).

fof(c_0_1581,plain,
    ! [X19,X13] :
      ( ~ c_lessequals(X19,X13,tc_nat)
      | c_lessequals(c_Suc(X19),c_Suc(X13),tc_nat) ),
    inference(fof_simplification,[status(thm)],[c_0_220]) ).

fof(c_0_1582,axiom,
    ! [X35,X15,X3] :
      ( c_in(X35,X15,X3)
      | c_in(X35,c_uminus(X15,tc_set(X3)),X3) ),
    c_0_221 ).

fof(c_0_1583,plain,
    ! [X14,X3] :
      ( ~ c_Wellfounded__Recursion_Oacyclic(X14,X3)
      | c_Wellfounded__Recursion_Oacyclic(c_Relation_Oconverse(X14,X3,X3),X3) ),
    inference(fof_simplification,[status(thm)],[c_0_222]) ).

fof(c_0_1584,plain,
    ! [X1,X2,X3] :
      ( ~ c_in(X2,c_Datatype_Oo2s(X1,X3),X3)
      | X1 = c_Datatype_Ooption_OSome(X2,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_223]) ).

fof(c_0_1585,plain,
    ! [X3] : ~ c_less(c_0,c_Nat_Osize(c_List_Olist_ONil,tc_List_Olist(X3)),tc_nat),
    inference(fof_simplification,[status(thm)],[c_0_224]) ).

fof(c_0_1586,axiom,
    ! [X2,X3] : c_in(X2,c_Datatype_Oo2s(c_Datatype_Ooption_OSome(X2,X3),X3),X3),
    c_0_225 ).

fof(c_0_1587,axiom,
    ! [X22,X3] :
      ( c_Nat_Osize(c_List_Oremdups(X22,X3),tc_List_Olist(X3)) != c_Nat_Osize(X22,tc_List_Olist(X3))
      | c_List_Oremdups(X22,X3) = X22 ),
    c_0_226 ).

fof(c_0_1588,axiom,
    ! [X19,X13] : c_less(c_uminus(c_IntDef_Oint(c_Suc(X19)),tc_IntDef_Oint),c_IntDef_Oint(X13),tc_IntDef_Oint),
    c_0_227 ).

fof(c_0_1589,axiom,
    ! [X19,X13] : c_lessequals(c_uminus(c_IntDef_Oint(X19),tc_IntDef_Oint),c_IntDef_Oint(X13),tc_IntDef_Oint),
    c_0_228 ).

fof(c_0_1590,plain,
    ! [X15,X3] : ~ c_less(X15,c_emptyset,tc_set(X3)),
    inference(fof_simplification,[status(thm)],[c_0_229]) ).

fof(c_0_1591,plain,
    ! [X2,X3] :
      ( ~ class_Orderings_Oorder(X3)
      | ~ c_less(X2,X2,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_230]) ).

fof(c_0_1592,axiom,
    ! [X22,X3] :
      ( c_less(c_0,c_Nat_Osize(X22,tc_List_Olist(X3)),tc_nat)
      | X22 = c_List_Olist_ONil ),
    c_0_231 ).

fof(c_0_1593,axiom,
    ! [X22,X3] :
      ( c_List_Oremdups(X22,X3) != X22
      | c_Nat_Osize(c_List_Oremdups(X22,X3),tc_List_Olist(X3)) = c_Nat_Osize(X22,tc_List_Olist(X3)) ),
    c_0_232 ).

fof(c_0_1594,plain,
    ! [X19] :
      ( ~ c_less(X19,c_Suc(c_0),tc_nat)
      | X19 = c_0 ),
    inference(fof_simplification,[status(thm)],[c_0_233]) ).

fof(c_0_1595,axiom,
    ! [X23,X22,X3] :
      ( X22 != c_append(X22,X23,X3)
      | X23 = c_List_Olist_ONil ),
    c_0_234 ).

fof(c_0_1596,axiom,
    ! [X23,X22,X3] :
      ( X23 != c_append(X22,X23,X3)
      | X22 = c_List_Olist_ONil ),
    c_0_235 ).

fof(c_0_1597,axiom,
    ! [X23,X22,X3] :
      ( c_append(X22,X23,X3) != X22
      | X23 = c_List_Olist_ONil ),
    c_0_236 ).

fof(c_0_1598,axiom,
    ! [X23,X22,X3] :
      ( c_append(X22,X23,X3) != X23
      | X22 = c_List_Olist_ONil ),
    c_0_237 ).

fof(c_0_1599,axiom,
    ! [X16,X15,X3] :
      ( c_union(X15,X16,X3) != c_emptyset
      | X16 = c_emptyset ),
    c_0_238 ).

fof(c_0_1600,axiom,
    ! [X16,X15,X3] :
      ( c_union(X15,X16,X3) != c_emptyset
      | X15 = c_emptyset ),
    c_0_239 ).

fof(c_0_1601,axiom,
    ! [X23,X22,X3] :
      ( c_append(X22,X23,X3) != c_List_Olist_ONil
      | X23 = c_List_Olist_ONil ),
    c_0_240 ).

fof(c_0_1602,axiom,
    ! [X23,X22,X3] :
      ( c_append(X22,X23,X3) != c_List_Olist_ONil
      | X22 = c_List_Olist_ONil ),
    c_0_241 ).

fof(c_0_1603,axiom,
    ! [X23,X22,X3] :
      ( c_List_Olist_ONil != c_append(X22,X23,X3)
      | X23 = c_List_Olist_ONil ),
    c_0_242 ).

fof(c_0_1604,axiom,
    ! [X23,X22,X3] :
      ( c_List_Olist_ONil != c_append(X22,X23,X3)
      | X22 = c_List_Olist_ONil ),
    c_0_243 ).

fof(c_0_1605,axiom,
    ! [X14,X15,X3] :
      ( c_Equiv__Relations_Oquotient(X15,X14,X3) != c_emptyset
      | X15 = c_emptyset ),
    c_0_244 ).

fof(c_0_1606,axiom,
    ! [X14,X15,X3] :
      ( c_emptyset != c_Equiv__Relations_Oquotient(X15,X14,X3)
      | X15 = c_emptyset ),
    c_0_245 ).

fof(c_0_1607,axiom,
    ! [X30,X4,X3] : c_List_Olist_OCons(X4,X30,X3) != c_List_Olist_ONil,
    c_0_246 ).

fof(c_0_1608,axiom,
    ! [X30,X4,X3] : c_List_Olist_ONil != c_List_Olist_OCons(X4,X30,X3),
    c_0_247 ).

fof(c_0_1609,plain,
    ~ c_in(c_UNIV,c_Finite__Set_OFinites,tc_set(tc_nat)),
    inference(fof_simplification,[status(thm)],[c_0_248]) ).

fof(c_0_1610,axiom,
    ! [X15,X3] : c_in(c_List_Olist_ONil,c_List_Olists(X15,X3),tc_List_Olist(X3)),
    c_0_249 ).

fof(c_0_1611,axiom,
    ! [X22,X3] : c_in(c_List_Oset(X22,X3),c_Finite__Set_OFinites,tc_set(X3)),
    c_0_250 ).

fof(c_0_1612,axiom,
    ! [X19,X13] :
      ( c_plus(X13,X19,tc_nat) != c_0
      | X19 = c_0 ),
    c_0_251 ).

fof(c_0_1613,axiom,
    ! [X19,X13] :
      ( c_plus(X13,X19,tc_nat) != c_0
      | X13 = c_0 ),
    c_0_252 ).

fof(c_0_1614,plain,
    ! [X19] : ~ c_less(X19,X19,tc_nat),
    inference(fof_simplification,[status(thm)],[c_0_253]) ).

fof(c_0_1615,plain,
    ! [X5,X3] : ~ c_in(X5,c_emptyset,X3),
    inference(fof_simplification,[status(thm)],[c_0_254]) ).

fof(c_0_1616,plain,
    ! [X19] :
      ( ~ c_less(X19,c_1,tc_nat)
      | X19 = c_0 ),
    inference(fof_simplification,[status(thm)],[c_0_255]) ).

fof(c_0_1617,plain,
    ! [X32] :
      ( ~ c_lessequals(X32,c_0,tc_nat)
      | X32 = c_0 ),
    inference(fof_simplification,[status(thm)],[c_0_256]) ).

fof(c_0_1618,plain,
    ! [X13] :
      ( ~ c_Divides_Oop_Advd(c_0,X13,tc_IntDef_Oint)
      | X13 = c_0 ),
    inference(fof_simplification,[status(thm)],[c_0_257]) ).

fof(c_0_1619,plain,
    ! [X13] :
      ( ~ c_Divides_Oop_Advd(c_0,X13,tc_nat)
      | X13 = c_0 ),
    inference(fof_simplification,[status(thm)],[c_0_258]) ).

fof(c_0_1620,plain,
    ! [X19] : ~ c_less(X19,c_0,tc_nat),
    inference(fof_simplification,[status(thm)],[c_0_259]) ).

fof(c_0_1621,axiom,
    ! [X10] : c_in(c_SetInterval_OlessThan(X10,tc_nat),c_Finite__Set_OFinites,tc_set(tc_nat)),
    c_0_260 ).

fof(c_0_1622,axiom,
    ! [X10] : c_in(c_SetInterval_OatMost(X10,tc_nat),c_Finite__Set_OFinites,tc_set(tc_nat)),
    c_0_261 ).

fof(c_0_1623,plain,
    ~ c_less(c_0,c_0,tc_nat),
    inference(fof_simplification,[status(thm)],[c_0_262]) ).

fof(c_0_1624,plain,
    ! [X14,X3] :
      ( ~ c_Wellfounded__Recursion_Owf(X14,X3)
      | c_Wellfounded__Recursion_Owf(c_List_Olex(X14,X3),tc_List_Olist(X3)) ),
    inference(fof_simplification,[status(thm)],[c_0_263]) ).

fof(c_0_1625,plain,
    ! [X14,X3] :
      ( ~ c_Wellfounded__Recursion_Owf(X14,X3)
      | c_Wellfounded__Recursion_Owf(c_List_Olenlex(X14,X3),tc_List_Olist(X3)) ),
    inference(fof_simplification,[status(thm)],[c_0_264]) ).

fof(c_0_1626,axiom,
    ! [X16,X15,X3] :
      ( c_uminus(X15,tc_set(X3)) != c_uminus(X16,tc_set(X3))
      | X15 = X16 ),
    c_0_265 ).

fof(c_0_1627,plain,
    ! [X2,X3] :
      ( ~ class_Orderings_Oorder(X3)
      | c_lessequals(X2,X2,X3) ),
    inference(fof_simplification,[status(thm)],[c_0_266]) ).

fof(c_0_1628,axiom,
    ! [X15,X3] : c_lessequals(X15,X15,tc_set(X3)),
    c_0_267 ).

fof(c_0_1629,axiom,
    ! [X15,X3] : c_lessequals(c_emptyset,X15,tc_set(X3)),
    c_0_268 ).

fof(c_0_1630,axiom,
    ! [X19] : c_less(X19,c_Suc(X19),tc_nat),
    c_0_269 ).

fof(c_0_1631,axiom,
    ! [X19] : c_less(c_0,c_Suc(X19),tc_nat),
    c_0_270 ).

fof(c_0_1632,axiom,
    ! [X3] : c_in(c_emptyset,c_Finite__Set_OFinites,tc_set(X3)),
    c_0_271 ).

fof(c_0_1633,axiom,
    ! [X10] : c_Divides_Oop_Advd(c_Suc(c_0),X10,tc_nat),
    c_0_272 ).

fof(c_0_1634,axiom,
    c_less(c_0,c_Suc(c_0),tc_nat),
    c_0_273 ).

fof(c_0_1635,axiom,
    ! [X22,X3] : X22 = c_append(X22,c_List_Olist_ONil,X3),
    c_0_274 ).

fof(c_0_1636,axiom,
    ! [X23,X3] : X23 = c_append(c_List_Olist_ONil,X23,X3),
    c_0_275 ).

fof(c_0_1637,axiom,
    ! [X22,X3] : c_append(X22,c_List_Olist_ONil,X3) = X22,
    c_0_276 ).

fof(c_0_1638,axiom,
    ! [X23,X3] : c_append(c_List_Olist_ONil,X23,X3) = X23,
    c_0_277 ).

fof(c_0_1639,plain,
    ! [X24,X2,X3] :
      ( ~ class_Orderings_Olinorder(X3)
      | c_SetInterval_OlessThan(X2,X3) != c_SetInterval_OlessThan(X24,X3)
      | X2 = X24 ),
    inference(fof_simplification,[status(thm)],[c_0_278]) ).

fof(c_0_1640,plain,
    ! [X24,X2,X3] :
      ( ~ class_Orderings_Olinorder(X3)
      | c_SetInterval_OgreaterThan(X2,X3) != c_SetInterval_OgreaterThan(X24,X3)
      | X2 = X24 ),
    inference(fof_simplification,[status(thm)],[c_0_279]) ).

fof(c_0_1641,plain,
    ! [X24,X2,X3] :
      ( ~ class_Orderings_Olinorder(X3)
      | c_SetInterval_OatMost(X2,X3) != c_SetInterval_OatMost(X24,X3)
      | X2 = X24 ),
    inference(fof_simplification,[status(thm)],[c_0_280]) ).

fof(c_0_1642,plain,
    ! [X24,X2,X3] :
      ( ~ class_Orderings_Olinorder(X3)
      | c_SetInterval_OatLeast(X2,X3) != c_SetInterval_OatLeast(X24,X3)
      | X2 = X24 ),
    inference(fof_simplification,[status(thm)],[c_0_281]) ).

fof(c_0_1643,axiom,
    ! [X2,X3] : c_in(X2,c_UNIV,X3),
    c_0_282 ).

fof(c_0_1644,axiom,
    ! [X19] :
      ( c_less(c_0,X19,tc_nat)
      | X19 = c_0 ),
    c_0_283 ).

fof(c_0_1645,axiom,
    ! [X14,X3] : c_Equiv__Relations_Oquotient(c_emptyset,X14,X3) = c_emptyset,
    c_0_284 ).

fof(c_0_1646,axiom,
    ! [X14,X3] : c_emptyset = c_Equiv__Relations_Oquotient(c_emptyset,X14,X3),
    c_0_285 ).

fof(c_0_1647,axiom,
    ! [X19] : c_lessequals(c_0,X19,tc_nat),
    c_0_286 ).

fof(c_0_1648,axiom,
    ! [X13] : c_Divides_Oop_Advd(c_1,X13,tc_IntDef_Oint),
    c_0_287 ).

fof(c_0_1649,axiom,
    ! [X13] : c_Divides_Oop_Advd(X13,c_0,tc_IntDef_Oint),
    c_0_288 ).

fof(c_0_1650,axiom,
    ! [X13] : c_Divides_Oop_Advd(X13,c_0,tc_nat),
    c_0_289 ).

fof(c_0_1651,axiom,
    ! [X3] : c_union(c_emptyset,c_emptyset,X3) = c_emptyset,
    c_0_290 ).

fof(c_0_1652,axiom,
    ! [X3] : c_append(c_List_Olist_ONil,c_List_Olist_ONil,X3) = c_List_Olist_ONil,
    c_0_291 ).

fof(c_0_1653,axiom,
    ! [X3] : c_List_Olist_ONil = c_append(c_List_Olist_ONil,c_List_Olist_ONil,X3),
    c_0_292 ).

fof(c_0_1654,axiom,
    c_less(c_0,c_1,tc_nat),
    c_0_293 ).

fof(c_0_1655,axiom,
    c_lessequals(c_0,c_0,tc_nat),
    c_0_294 ).

fof(c_0_1656,axiom,
    c_plus(c_0,c_0,tc_nat) = c_0,
    c_0_295 ).

fof(c_0_1657,axiom,
    c_Divides_Oop_Advd(c_0,c_0,tc_IntDef_Oint),
    c_0_296 ).

fof(c_0_1658,axiom,
    c_Divides_Oop_Advd(c_0,c_0,tc_nat),
    c_0_297 ).

fof(c_0_1659,axiom,
    ! [X23,X22,X3] :
      ( c_List_Orev(X22,X3) != c_List_Orev(X23,X3)
      | X22 = X23 ),
    c_0_298 ).

fof(c_0_1660,axiom,
    ! [X26,X27,X28,X29] :
      ( c_List_Ochar_OChar(X29,X27) != c_List_Ochar_OChar(X28,X26)
      | X27 = X26 ),
    c_0_299 ).

fof(c_0_1661,axiom,
    ! [X26,X27,X28,X29] :
      ( c_List_Ochar_OChar(X29,X27) != c_List_Ochar_OChar(X28,X26)
      | X29 = X28 ),
    c_0_300 ).

fof(c_0_1662,axiom,
    ! [X4,X5,X3] :
      ( c_Datatype_Ooption_OSome(X5,X3) != c_Datatype_Ooption_OSome(X4,X3)
      | X5 = X4 ),
    c_0_301 ).

fof(c_0_1663,plain,
    ! [X53,X52] :
      ( class_Finite__Set_Ofinite(tc_sum(X53,X52))
      | ~ class_Finite__Set_Ofinite(X52)
      | ~ class_Finite__Set_Ofinite(X53) ),
    inference(fof_simplification,[status(thm)],[c_0_302]) ).

fof(c_0_1664,plain,
    ! [X53,X52] :
      ( class_Finite__Set_Ofinite(tc_prod(X53,X52))
      | ~ class_Finite__Set_Ofinite(X52)
      | ~ class_Finite__Set_Ofinite(X53) ),
    inference(fof_simplification,[status(thm)],[c_0_303]) ).

fof(c_0_1665,plain,
    ! [X53,X52] :
      ( class_Finite__Set_Ofinite(tc_fun(X53,X52))
      | ~ class_Finite__Set_Ofinite(X52)
      | ~ class_Finite__Set_Ofinite(X53) ),
    inference(fof_simplification,[status(thm)],[c_0_304]) ).

fof(c_0_1666,axiom,
    ! [X2,X3] :
      ( X2 = c_Datatype_Ooption_ONone
      | X2 = c_Datatype_Ooption_OSome(c_Main_Onot__Some__eq__iff1__1(X2,X3),X3) ),
    c_0_305 ).

fof(c_0_1667,axiom,
    ! [X2,X3] :
      ( X2 = c_Datatype_Ooption_ONone
      | X2 = c_Datatype_Ooption_OSome(c_Main_Onot__None__eq__iff1__1(X2,X3),X3) ),
    c_0_306 ).

fof(c_0_1668,axiom,
    ! [X22,X3] : c_List_Odistinct(c_List_Oremdups(X22,X3),X3),
    c_0_307 ).

fof(c_0_1669,axiom,
    ! [X22,X3] :
      ( c_Nat_Osize(X22,tc_List_Olist(X3)) != c_0
      | X22 = c_List_Olist_ONil ),
    c_0_308 ).

fof(c_0_1670,axiom,
    ! [X53,X52] : class_Nat_Opower(tc_fun(X53,X52)),
    c_0_309 ).

fof(c_0_1671,axiom,
    ! [X22,X3] :
      ( c_List_Oset(X22,X3) != c_emptyset
      | X22 = c_List_Olist_ONil ),
    c_0_310 ).

fof(c_0_1672,axiom,
    ! [X22,X3] :
      ( c_emptyset != c_List_Oset(X22,X3)
      | X22 = c_List_Olist_ONil ),
    c_0_311 ).

fof(c_0_1673,axiom,
    ! [X22,X3] :
      ( c_List_Orev(X22,X3) != c_List_Olist_ONil
      | X22 = c_List_Olist_ONil ),
    c_0_312 ).

fof(c_0_1674,axiom,
    ! [X22,X3] :
      ( c_List_Olist_ONil != c_List_Orev(X22,X3)
      | X22 = c_List_Olist_ONil ),
    c_0_313 ).

fof(c_0_1675,axiom,
    ! [X4,X3] : c_Datatype_Ooption_OSome(X4,X3) != c_Datatype_Ooption_ONone,
    c_0_314 ).

fof(c_0_1676,axiom,
    ! [X4,X3] : c_Datatype_Ooption_ONone != c_Datatype_Ooption_OSome(X4,X3),
    c_0_315 ).

fof(c_0_1677,axiom,
    ! [X3] : c_Nat_Osize(c_List_Olist_ONil,tc_List_Olist(X3)) = c_0,
    c_0_316 ).

fof(c_0_1678,plain,
    ! [X52] :
      ( class_Finite__Set_Ofinite(tc_set(X52))
      | ~ class_Finite__Set_Ofinite(X52) ),
    inference(fof_simplification,[status(thm)],[c_0_317]) ).

fof(c_0_1679,plain,
    ! [X52] :
      ( class_Finite__Set_Ofinite(tc_Datatype_Ooption(X52))
      | ~ class_Finite__Set_Ofinite(X52) ),
    inference(fof_simplification,[status(thm)],[c_0_318]) ).

fof(c_0_1680,axiom,
    ! [X19,X13] :
      ( c_Suc(X13) != c_Suc(X19)
      | X13 = X19 ),
    c_0_319 ).

fof(c_0_1681,axiom,
    ! [X19,X13] :
      ( c_IntDef_Oint(X13) != c_IntDef_Oint(X19)
      | X13 = X19 ),
    c_0_320 ).

fof(c_0_1682,axiom,
    ! [X3] : c_Wellfounded__Recursion_Owf(c_emptyset,X3),
    c_0_321 ).

fof(c_0_1683,axiom,
    ! [X3] : c_List_Oset(c_List_Olist_ONil,X3) = c_emptyset,
    c_0_322 ).

fof(c_0_1684,axiom,
    ! [X3] : c_emptyset = c_List_Oset(c_List_Olist_ONil,X3),
    c_0_323 ).

fof(c_0_1685,axiom,
    ! [X3] : c_List_Orev(c_List_Olist_ONil,X3) = c_List_Olist_ONil,
    c_0_324 ).

fof(c_0_1686,axiom,
    ! [X3] : c_List_Olist_ONil = c_List_Orev(c_List_Olist_ONil,X3),
    c_0_325 ).

fof(c_0_1687,plain,
    ! [X54] :
      ( ~ class_Wellfounded__Recursion_Owellorder(X54)
      | class_Orderings_Olinorder(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_326]) ).

fof(c_0_1688,plain,
    ! [X54] :
      ( ~ class_Wellfounded__Recursion_Owellorder(X54)
      | class_LOrder_Olorder(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_327]) ).

fof(c_0_1689,plain,
    ! [X54] :
      ( ~ class_Wellfounded__Recursion_Owellorder(X54)
      | class_LOrder_Ojoin__semilorder(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_328]) ).

fof(c_0_1690,plain,
    ! [X54] :
      ( ~ class_Wellfounded__Recursion_Owellorder(X54)
      | class_LOrder_Omeet__semilorder(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_329]) ).

fof(c_0_1691,plain,
    ! [X54] :
      ( ~ class_Wellfounded__Recursion_Owellorder(X54)
      | class_Orderings_Oorder(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_330]) ).

fof(c_0_1692,plain,
    ! [X54] :
      ( ~ class_Wellfounded__Recursion_Owellorder(X54)
      | class_Orderings_Oord(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_331]) ).

fof(c_0_1693,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Osemiring__1__cancel(X54)
      | class_OrderedGroup_Omonoid__mult(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_332]) ).

fof(c_0_1694,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Osemiring__1__cancel(X54)
      | class_HOL_Oplus(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_333]) ).

fof(c_0_1695,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Osemiring__1__cancel(X54)
      | class_OrderedGroup_Osemigroup__add(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_334]) ).

fof(c_0_1696,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Osemiring__1__cancel(X54)
      | class_OrderedGroup_Oab__semigroup__add(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_335]) ).

fof(c_0_1697,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Osemiring__1__cancel(X54)
      | class_HOL_Ozero(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_336]) ).

fof(c_0_1698,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Osemiring__1__cancel(X54)
      | class_OrderedGroup_Ocomm__monoid__add(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_337]) ).

fof(c_0_1699,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Osemiring__1__cancel(X54)
      | class_Ring__and__Field_Osemiring(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_338]) ).

fof(c_0_1700,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Osemiring__1__cancel(X54)
      | class_Ring__and__Field_Osemiring__0(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_339]) ).

fof(c_0_1701,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Osemiring__1__cancel(X54)
      | class_Ring__and__Field_Osemiring__0__cancel(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_340]) ).

fof(c_0_1702,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Osemiring__1__cancel(X54)
      | class_OrderedGroup_Ocancel__semigroup__add(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_341]) ).

fof(c_0_1703,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Osemiring__1__cancel(X54)
      | class_OrderedGroup_Ocancel__ab__semigroup__add(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_342]) ).

fof(c_0_1704,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Osemiring__1__cancel(X54)
      | class_HOL_Otimes(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_343]) ).

fof(c_0_1705,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Osemiring__1__cancel(X54)
      | class_OrderedGroup_Osemigroup__mult(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_344]) ).

fof(c_0_1706,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Osemiring__1__cancel(X54)
      | class_HOL_Oone(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_345]) ).

fof(c_0_1707,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Osemiring__1__cancel(X54)
      | class_Ring__and__Field_Oaxclass__0__neq__1(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_346]) ).

fof(c_0_1708,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Osemiring__1__cancel(X54)
      | class_Ring__and__Field_Osemiring__1(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_347]) ).

fof(c_0_1709,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Osemiring__1(X54)
      | class_OrderedGroup_Osemigroup__add(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_348]) ).

fof(c_0_1710,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Osemiring__1(X54)
      | class_OrderedGroup_Oab__semigroup__add(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_349]) ).

fof(c_0_1711,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Osemiring__1(X54)
      | class_OrderedGroup_Ocomm__monoid__add(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_350]) ).

fof(c_0_1712,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Osemiring__1(X54)
      | class_HOL_Otimes(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_351]) ).

fof(c_0_1713,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Osemiring__1(X54)
      | class_OrderedGroup_Osemigroup__mult(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_352]) ).

fof(c_0_1714,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Osemiring__1(X54)
      | class_Ring__and__Field_Osemiring(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_353]) ).

fof(c_0_1715,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Osemiring__1(X54)
      | class_Ring__and__Field_Osemiring__0(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_354]) ).

fof(c_0_1716,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Osemiring__1(X54)
      | class_HOL_Oone(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_355]) ).

fof(c_0_1717,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Osemiring__1(X54)
      | class_OrderedGroup_Omonoid__mult(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_356]) ).

fof(c_0_1718,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Osemiring__1(X54)
      | class_HOL_Oplus(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_357]) ).

fof(c_0_1719,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Osemiring__1(X54)
      | class_HOL_Ozero(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_358]) ).

fof(c_0_1720,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Osemiring__1(X54)
      | class_Ring__and__Field_Oaxclass__0__neq__1(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_359]) ).

fof(c_0_1721,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Osemiring__0__cancel(X54)
      | class_OrderedGroup_Ocancel__ab__semigroup__add(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_360]) ).

fof(c_0_1722,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Osemiring__0__cancel(X54)
      | class_HOL_Ozero(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_361]) ).

fof(c_0_1723,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Osemiring__0__cancel(X54)
      | class_HOL_Oplus(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_362]) ).

fof(c_0_1724,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Osemiring__0__cancel(X54)
      | class_OrderedGroup_Osemigroup__add(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_363]) ).

fof(c_0_1725,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Osemiring__0__cancel(X54)
      | class_OrderedGroup_Oab__semigroup__add(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_364]) ).

fof(c_0_1726,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Osemiring__0__cancel(X54)
      | class_OrderedGroup_Ocomm__monoid__add(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_365]) ).

fof(c_0_1727,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Osemiring__0__cancel(X54)
      | class_HOL_Otimes(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_366]) ).

fof(c_0_1728,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Osemiring__0__cancel(X54)
      | class_OrderedGroup_Osemigroup__mult(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_367]) ).

fof(c_0_1729,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Osemiring__0__cancel(X54)
      | class_OrderedGroup_Ocancel__semigroup__add(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_368]) ).

fof(c_0_1730,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Osemiring__0__cancel(X54)
      | class_Ring__and__Field_Osemiring(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_369]) ).

fof(c_0_1731,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Osemiring__0__cancel(X54)
      | class_Ring__and__Field_Osemiring__0(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_370]) ).

fof(c_0_1732,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Osemiring__0(X54)
      | class_HOL_Ozero(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_371]) ).

fof(c_0_1733,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Osemiring__0(X54)
      | class_OrderedGroup_Ocomm__monoid__add(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_372]) ).

fof(c_0_1734,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Osemiring__0(X54)
      | class_HOL_Otimes(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_373]) ).

fof(c_0_1735,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Osemiring__0(X54)
      | class_OrderedGroup_Osemigroup__mult(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_374]) ).

fof(c_0_1736,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Osemiring__0(X54)
      | class_HOL_Oplus(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_375]) ).

fof(c_0_1737,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Osemiring__0(X54)
      | class_OrderedGroup_Osemigroup__add(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_376]) ).

fof(c_0_1738,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Osemiring__0(X54)
      | class_OrderedGroup_Oab__semigroup__add(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_377]) ).

fof(c_0_1739,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Osemiring__0(X54)
      | class_Ring__and__Field_Osemiring(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_378]) ).

fof(c_0_1740,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Osemiring(X54)
      | class_HOL_Otimes(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_379]) ).

fof(c_0_1741,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Osemiring(X54)
      | class_OrderedGroup_Osemigroup__mult(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_380]) ).

fof(c_0_1742,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Osemiring(X54)
      | class_HOL_Oplus(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_381]) ).

fof(c_0_1743,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Osemiring(X54)
      | class_OrderedGroup_Osemigroup__add(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_382]) ).

fof(c_0_1744,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Osemiring(X54)
      | class_OrderedGroup_Oab__semigroup__add(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_383]) ).

fof(c_0_1745,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oring__1(X54)
      | class_HOL_Otimes(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_384]) ).

fof(c_0_1746,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oring__1(X54)
      | class_OrderedGroup_Osemigroup__mult(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_385]) ).

fof(c_0_1747,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oring__1(X54)
      | class_Ring__and__Field_Osemiring(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_386]) ).

fof(c_0_1748,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oring__1(X54)
      | class_Ring__and__Field_Osemiring__0(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_387]) ).

fof(c_0_1749,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oring__1(X54)
      | class_OrderedGroup_Ocancel__semigroup__add(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_388]) ).

fof(c_0_1750,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oring__1(X54)
      | class_OrderedGroup_Ocancel__ab__semigroup__add(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_389]) ).

fof(c_0_1751,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oring__1(X54)
      | class_Ring__and__Field_Osemiring__0__cancel(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_390]) ).

fof(c_0_1752,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oring__1(X54)
      | class_HOL_Ominus(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_391]) ).

fof(c_0_1753,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oring__1(X54)
      | class_Ring__and__Field_Osemiring__1__cancel(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_392]) ).

fof(c_0_1754,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oring__1(X54)
      | class_HOL_Oone(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_393]) ).

fof(c_0_1755,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oring__1(X54)
      | class_OrderedGroup_Omonoid__mult(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_394]) ).

fof(c_0_1756,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oring__1(X54)
      | class_Ring__and__Field_Oaxclass__0__neq__1(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_395]) ).

fof(c_0_1757,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oring__1(X54)
      | class_Ring__and__Field_Osemiring__1(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_396]) ).

fof(c_0_1758,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oring__1(X54)
      | class_HOL_Ozero(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_397]) ).

fof(c_0_1759,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oring__1(X54)
      | class_HOL_Oplus(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_398]) ).

fof(c_0_1760,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oring__1(X54)
      | class_OrderedGroup_Osemigroup__add(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_399]) ).

fof(c_0_1761,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oring__1(X54)
      | class_OrderedGroup_Oab__semigroup__add(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_400]) ).

fof(c_0_1762,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oring__1(X54)
      | class_OrderedGroup_Ocomm__monoid__add(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_401]) ).

fof(c_0_1763,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oring__1(X54)
      | class_OrderedGroup_Oab__group__add(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_402]) ).

fof(c_0_1764,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oring__1(X54)
      | class_Ring__and__Field_Oring(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_403]) ).

fof(c_0_1765,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oring(X54)
      | class_HOL_Ozero(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_404]) ).

fof(c_0_1766,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oring(X54)
      | class_OrderedGroup_Ocomm__monoid__add(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_405]) ).

fof(c_0_1767,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oring(X54)
      | class_HOL_Ominus(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_406]) ).

fof(c_0_1768,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oring(X54)
      | class_OrderedGroup_Oab__group__add(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_407]) ).

fof(c_0_1769,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oring(X54)
      | class_HOL_Otimes(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_408]) ).

fof(c_0_1770,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oring(X54)
      | class_OrderedGroup_Osemigroup__mult(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_409]) ).

fof(c_0_1771,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oring(X54)
      | class_HOL_Oplus(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_410]) ).

fof(c_0_1772,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oring(X54)
      | class_OrderedGroup_Osemigroup__add(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_411]) ).

fof(c_0_1773,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oring(X54)
      | class_Ring__and__Field_Osemiring__0(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_412]) ).

fof(c_0_1774,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oring(X54)
      | class_Ring__and__Field_Osemiring__0__cancel(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_413]) ).

fof(c_0_1775,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oring(X54)
      | class_OrderedGroup_Ocancel__semigroup__add(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_414]) ).

fof(c_0_1776,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oring(X54)
      | class_OrderedGroup_Ocancel__ab__semigroup__add(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_415]) ).

fof(c_0_1777,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oring(X54)
      | class_OrderedGroup_Oab__semigroup__add(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_416]) ).

fof(c_0_1778,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oring(X54)
      | class_Ring__and__Field_Osemiring(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_417]) ).

fof(c_0_1779,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Opordered__semiring(X54)
      | class_OrderedGroup_Opordered__ab__semigroup__add(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_418]) ).

fof(c_0_1780,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Opordered__semiring(X54)
      | class_HOL_Ozero(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_419]) ).

fof(c_0_1781,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Opordered__semiring(X54)
      | class_HOL_Oplus(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_420]) ).

fof(c_0_1782,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Opordered__semiring(X54)
      | class_OrderedGroup_Osemigroup__add(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_421]) ).

fof(c_0_1783,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Opordered__semiring(X54)
      | class_OrderedGroup_Oab__semigroup__add(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_422]) ).

fof(c_0_1784,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Opordered__semiring(X54)
      | class_OrderedGroup_Ocomm__monoid__add(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_423]) ).

fof(c_0_1785,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Opordered__semiring(X54)
      | class_HOL_Otimes(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_424]) ).

fof(c_0_1786,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Opordered__semiring(X54)
      | class_OrderedGroup_Osemigroup__mult(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_425]) ).

fof(c_0_1787,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Opordered__semiring(X54)
      | class_Orderings_Oord(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_426]) ).

fof(c_0_1788,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Opordered__semiring(X54)
      | class_Orderings_Oorder(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_427]) ).

fof(c_0_1789,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Opordered__semiring(X54)
      | class_Ring__and__Field_Osemiring(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_428]) ).

fof(c_0_1790,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Opordered__semiring(X54)
      | class_Ring__and__Field_Osemiring__0(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_429]) ).

fof(c_0_1791,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Opordered__ring(X54)
      | class_HOL_Otimes(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_430]) ).

fof(c_0_1792,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Opordered__ring(X54)
      | class_OrderedGroup_Osemigroup__mult(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_431]) ).

fof(c_0_1793,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Opordered__ring(X54)
      | class_Ring__and__Field_Osemiring(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_432]) ).

fof(c_0_1794,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Opordered__ring(X54)
      | class_Ring__and__Field_Osemiring__0(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_433]) ).

fof(c_0_1795,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Opordered__ring(X54)
      | class_OrderedGroup_Ocancel__semigroup__add(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_434]) ).

fof(c_0_1796,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Opordered__ring(X54)
      | class_OrderedGroup_Ocancel__ab__semigroup__add(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_435]) ).

fof(c_0_1797,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Opordered__ring(X54)
      | class_Ring__and__Field_Osemiring__0__cancel(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_436]) ).

fof(c_0_1798,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Opordered__ring(X54)
      | class_Ring__and__Field_Opordered__cancel__semiring(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_437]) ).

fof(c_0_1799,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Opordered__ring(X54)
      | class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_438]) ).

fof(c_0_1800,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Opordered__ring(X54)
      | class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_439]) ).

fof(c_0_1801,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Opordered__ring(X54)
      | class_HOL_Ominus(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_440]) ).

fof(c_0_1802,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Opordered__ring(X54)
      | class_OrderedGroup_Opordered__ab__group__add(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_441]) ).

fof(c_0_1803,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Opordered__ring(X54)
      | class_Orderings_Oord(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_442]) ).

fof(c_0_1804,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Opordered__ring(X54)
      | class_Orderings_Oorder(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_443]) ).

fof(c_0_1805,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Opordered__ring(X54)
      | class_OrderedGroup_Opordered__ab__semigroup__add(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_444]) ).

fof(c_0_1806,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Opordered__ring(X54)
      | class_Ring__and__Field_Opordered__semiring(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_445]) ).

fof(c_0_1807,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Opordered__ring(X54)
      | class_HOL_Ozero(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_446]) ).

fof(c_0_1808,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Opordered__ring(X54)
      | class_HOL_Oplus(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_447]) ).

fof(c_0_1809,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Opordered__ring(X54)
      | class_OrderedGroup_Osemigroup__add(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_448]) ).

fof(c_0_1810,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Opordered__ring(X54)
      | class_OrderedGroup_Oab__semigroup__add(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_449]) ).

fof(c_0_1811,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Opordered__ring(X54)
      | class_OrderedGroup_Ocomm__monoid__add(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_450]) ).

fof(c_0_1812,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Opordered__ring(X54)
      | class_OrderedGroup_Oab__group__add(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_451]) ).

fof(c_0_1813,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Opordered__ring(X54)
      | class_Ring__and__Field_Oring(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_452]) ).

fof(c_0_1814,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Opordered__comm__semiring(X54)
      | class_OrderedGroup_Osemigroup__add(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_453]) ).

fof(c_0_1815,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Opordered__comm__semiring(X54)
      | class_OrderedGroup_Oab__semigroup__add(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_454]) ).

fof(c_0_1816,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Opordered__comm__semiring(X54)
      | class_OrderedGroup_Ocomm__monoid__add(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_455]) ).

fof(c_0_1817,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Opordered__comm__semiring(X54)
      | class_HOL_Otimes(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_456]) ).

fof(c_0_1818,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Opordered__comm__semiring(X54)
      | class_OrderedGroup_Osemigroup__mult(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_457]) ).

fof(c_0_1819,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Opordered__comm__semiring(X54)
      | class_Ring__and__Field_Osemiring(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_458]) ).

fof(c_0_1820,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Opordered__comm__semiring(X54)
      | class_Ring__and__Field_Osemiring__0(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_459]) ).

fof(c_0_1821,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Opordered__comm__semiring(X54)
      | class_OrderedGroup_Oab__semigroup__mult(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_460]) ).

fof(c_0_1822,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Opordered__comm__semiring(X54)
      | class_Ring__and__Field_Opordered__semiring(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_461]) ).

fof(c_0_1823,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Opordered__comm__semiring(X54)
      | class_Orderings_Oord(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_462]) ).

fof(c_0_1824,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Opordered__comm__semiring(X54)
      | class_Orderings_Oorder(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_463]) ).

fof(c_0_1825,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Opordered__comm__semiring(X54)
      | class_OrderedGroup_Opordered__ab__semigroup__add(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_464]) ).

fof(c_0_1826,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Opordered__comm__semiring(X54)
      | class_HOL_Ozero(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_465]) ).

fof(c_0_1827,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Opordered__comm__semiring(X54)
      | class_HOL_Oplus(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_466]) ).

fof(c_0_1828,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Opordered__comm__semiring(X54)
      | class_Ring__and__Field_Ocomm__semiring(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_467]) ).

fof(c_0_1829,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Opordered__comm__semiring(X54)
      | class_Ring__and__Field_Ocomm__semiring__0(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_468]) ).

fof(c_0_1830,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Opordered__comm__ring(X54)
      | class_Ring__and__Field_Osemiring__0(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_469]) ).

fof(c_0_1831,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Opordered__comm__ring(X54)
      | class_Ring__and__Field_Osemiring__0__cancel(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_470]) ).

fof(c_0_1832,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Opordered__comm__ring(X54)
      | class_OrderedGroup_Oab__semigroup__mult(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_471]) ).

fof(c_0_1833,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Opordered__comm__ring(X54)
      | class_Ring__and__Field_Ocomm__semiring(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_472]) ).

fof(c_0_1834,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Opordered__comm__ring(X54)
      | class_Ring__and__Field_Ocomm__semiring__0(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_473]) ).

fof(c_0_1835,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Opordered__comm__ring(X54)
      | class_Ring__and__Field_Ocomm__semiring__0__cancel(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_474]) ).

fof(c_0_1836,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Opordered__comm__ring(X54)
      | class_HOL_Ominus(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_475]) ).

fof(c_0_1837,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Opordered__comm__ring(X54)
      | class_Orderings_Oord(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_476]) ).

fof(c_0_1838,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Opordered__comm__ring(X54)
      | class_Orderings_Oorder(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_477]) ).

fof(c_0_1839,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Opordered__comm__ring(X54)
      | class_OrderedGroup_Opordered__ab__semigroup__add(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_478]) ).

fof(c_0_1840,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Opordered__comm__ring(X54)
      | class_Ring__and__Field_Opordered__semiring(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_479]) ).

fof(c_0_1841,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Opordered__comm__ring(X54)
      | class_Ring__and__Field_Opordered__comm__semiring(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_480]) ).

fof(c_0_1842,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Opordered__comm__ring(X54)
      | class_OrderedGroup_Oab__group__add(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_481]) ).

fof(c_0_1843,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Opordered__comm__ring(X54)
      | class_HOL_Oplus(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_482]) ).

fof(c_0_1844,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Opordered__comm__ring(X54)
      | class_OrderedGroup_Osemigroup__add(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_483]) ).

fof(c_0_1845,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Opordered__comm__ring(X54)
      | class_OrderedGroup_Ocancel__semigroup__add(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_484]) ).

fof(c_0_1846,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Opordered__comm__ring(X54)
      | class_OrderedGroup_Oab__semigroup__add(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_485]) ).

fof(c_0_1847,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Opordered__comm__ring(X54)
      | class_OrderedGroup_Ocancel__ab__semigroup__add(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_486]) ).

fof(c_0_1848,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Opordered__comm__ring(X54)
      | class_HOL_Ozero(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_487]) ).

fof(c_0_1849,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Opordered__comm__ring(X54)
      | class_OrderedGroup_Ocomm__monoid__add(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_488]) ).

fof(c_0_1850,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Opordered__comm__ring(X54)
      | class_HOL_Otimes(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_489]) ).

fof(c_0_1851,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Opordered__comm__ring(X54)
      | class_OrderedGroup_Osemigroup__mult(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_490]) ).

fof(c_0_1852,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Opordered__comm__ring(X54)
      | class_Ring__and__Field_Osemiring(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_491]) ).

fof(c_0_1853,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Opordered__comm__ring(X54)
      | class_Ring__and__Field_Oring(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_492]) ).

fof(c_0_1854,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Opordered__comm__ring(X54)
      | class_Ring__and__Field_Ocomm__ring(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_493]) ).

fof(c_0_1855,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Opordered__cancel__semiring(X54)
      | class_OrderedGroup_Osemigroup__add(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_494]) ).

fof(c_0_1856,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Opordered__cancel__semiring(X54)
      | class_OrderedGroup_Oab__semigroup__add(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_495]) ).

fof(c_0_1857,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Opordered__cancel__semiring(X54)
      | class_OrderedGroup_Opordered__ab__semigroup__add(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_496]) ).

fof(c_0_1858,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Opordered__cancel__semiring(X54)
      | class_HOL_Ozero(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_497]) ).

fof(c_0_1859,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Opordered__cancel__semiring(X54)
      | class_OrderedGroup_Ocomm__monoid__add(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_498]) ).

fof(c_0_1860,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Opordered__cancel__semiring(X54)
      | class_HOL_Otimes(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_499]) ).

fof(c_0_1861,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Opordered__cancel__semiring(X54)
      | class_OrderedGroup_Osemigroup__mult(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_500]) ).

fof(c_0_1862,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Opordered__cancel__semiring(X54)
      | class_Ring__and__Field_Osemiring(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_501]) ).

fof(c_0_1863,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Opordered__cancel__semiring(X54)
      | class_Ring__and__Field_Osemiring__0__cancel(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_502]) ).

fof(c_0_1864,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Opordered__cancel__semiring(X54)
      | class_OrderedGroup_Ocancel__semigroup__add(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_503]) ).

fof(c_0_1865,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Opordered__cancel__semiring(X54)
      | class_OrderedGroup_Ocancel__ab__semigroup__add(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_504]) ).

fof(c_0_1866,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Opordered__cancel__semiring(X54)
      | class_Orderings_Oord(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_505]) ).

fof(c_0_1867,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Opordered__cancel__semiring(X54)
      | class_Orderings_Oorder(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_506]) ).

fof(c_0_1868,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Opordered__cancel__semiring(X54)
      | class_HOL_Oplus(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_507]) ).

fof(c_0_1869,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Opordered__cancel__semiring(X54)
      | class_Ring__and__Field_Osemiring__0(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_508]) ).

fof(c_0_1870,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Opordered__cancel__semiring(X54)
      | class_Ring__and__Field_Opordered__semiring(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_509]) ).

fof(c_0_1871,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X54)
      | class_HOL_Ozero(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_510]) ).

fof(c_0_1872,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X54)
      | class_OrderedGroup_Ocomm__monoid__add(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_511]) ).

fof(c_0_1873,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X54)
      | class_HOL_Otimes(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_512]) ).

fof(c_0_1874,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X54)
      | class_OrderedGroup_Osemigroup__mult(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_513]) ).

fof(c_0_1875,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X54)
      | class_Ring__and__Field_Osemiring(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_514]) ).

fof(c_0_1876,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X54)
      | class_Ring__and__Field_Osemiring__0(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_515]) ).

fof(c_0_1877,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X54)
      | class_OrderedGroup_Oab__semigroup__mult(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_516]) ).

fof(c_0_1878,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X54)
      | class_Ring__and__Field_Osemiring__0__cancel(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_517]) ).

fof(c_0_1879,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X54)
      | class_Ring__and__Field_Ocomm__semiring(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_518]) ).

fof(c_0_1880,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X54)
      | class_Ring__and__Field_Opordered__cancel__semiring(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_519]) ).

fof(c_0_1881,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X54)
      | class_Ring__and__Field_Opordered__semiring(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_520]) ).

fof(c_0_1882,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X54)
      | class_OrderedGroup_Ocancel__semigroup__add(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_521]) ).

fof(c_0_1883,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X54)
      | class_OrderedGroup_Ocancel__ab__semigroup__add(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_522]) ).

fof(c_0_1884,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X54)
      | class_Orderings_Oord(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_523]) ).

fof(c_0_1885,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X54)
      | class_Orderings_Oorder(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_524]) ).

fof(c_0_1886,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X54)
      | class_HOL_Oplus(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_525]) ).

fof(c_0_1887,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X54)
      | class_OrderedGroup_Osemigroup__add(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_526]) ).

fof(c_0_1888,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X54)
      | class_OrderedGroup_Oab__semigroup__add(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_527]) ).

fof(c_0_1889,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X54)
      | class_OrderedGroup_Opordered__ab__semigroup__add(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_528]) ).

fof(c_0_1890,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X54)
      | class_Ring__and__Field_Ocomm__semiring__0(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_529]) ).

fof(c_0_1891,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X54)
      | class_Ring__and__Field_Opordered__comm__semiring(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_530]) ).

fof(c_0_1892,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X54)
      | class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_531]) ).

fof(c_0_1893,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X54)
      | class_HOL_Ozero(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_532]) ).

fof(c_0_1894,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X54)
      | class_HOL_Oplus(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_533]) ).

fof(c_0_1895,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X54)
      | class_OrderedGroup_Osemigroup__add(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_534]) ).

fof(c_0_1896,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X54)
      | class_OrderedGroup_Oab__semigroup__add(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_535]) ).

fof(c_0_1897,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X54)
      | class_OrderedGroup_Ocomm__monoid__add(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_536]) ).

fof(c_0_1898,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X54)
      | class_HOL_Otimes(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_537]) ).

fof(c_0_1899,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X54)
      | class_Ring__and__Field_Opordered__semiring(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_538]) ).

fof(c_0_1900,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X54)
      | class_Ring__and__Field_Opordered__cancel__semiring(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_539]) ).

fof(c_0_1901,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X54)
      | class_Ring__and__Field_Osemiring__0__cancel(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_540]) ).

fof(c_0_1902,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X54)
      | class_OrderedGroup_Ocancel__semigroup__add(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_541]) ).

fof(c_0_1903,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X54)
      | class_OrderedGroup_Osemigroup__mult(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_542]) ).

fof(c_0_1904,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X54)
      | class_OrderedGroup_Ocancel__ab__semigroup__add(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_543]) ).

fof(c_0_1905,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X54)
      | class_Orderings_Oord(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_544]) ).

fof(c_0_1906,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X54)
      | class_Orderings_Oorder(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_545]) ).

fof(c_0_1907,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X54)
      | class_OrderedGroup_Opordered__ab__semigroup__add(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_546]) ).

fof(c_0_1908,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X54)
      | class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_547]) ).

fof(c_0_1909,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X54)
      | class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_548]) ).

fof(c_0_1910,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X54)
      | class_LOrder_Omeet__semilorder(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_549]) ).

fof(c_0_1911,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X54)
      | class_LOrder_Ojoin__semilorder(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_550]) ).

fof(c_0_1912,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X54)
      | class_LOrder_Olorder(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_551]) ).

fof(c_0_1913,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X54)
      | class_Orderings_Olinorder(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_552]) ).

fof(c_0_1914,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X54)
      | class_Ring__and__Field_Osemiring(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_553]) ).

fof(c_0_1915,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X54)
      | class_Ring__and__Field_Osemiring__0(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_554]) ).

fof(c_0_1916,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X54)
      | class_Ring__and__Field_Ocomm__semiring__0(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_555]) ).

fof(c_0_1917,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X54)
      | class_Ring__and__Field_Ocomm__semiring__0__cancel(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_556]) ).

fof(c_0_1918,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X54)
      | class_HOL_Oone(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_557]) ).

fof(c_0_1919,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X54)
      | class_OrderedGroup_Omonoid__mult(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_558]) ).

fof(c_0_1920,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X54)
      | class_Ring__and__Field_Oaxclass__0__neq__1(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_559]) ).

fof(c_0_1921,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X54)
      | class_Ring__and__Field_Osemiring__1(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_560]) ).

fof(c_0_1922,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X54)
      | class_Orderings_Oord(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_561]) ).

fof(c_0_1923,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X54)
      | class_Orderings_Oorder(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_562]) ).

fof(c_0_1924,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X54)
      | class_OrderedGroup_Opordered__ab__semigroup__add(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_563]) ).

fof(c_0_1925,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X54)
      | class_Ring__and__Field_Opordered__semiring(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_564]) ).

fof(c_0_1926,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X54)
      | class_Ring__and__Field_Opordered__comm__semiring(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_565]) ).

fof(c_0_1927,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X54)
      | class_Ring__and__Field_Opordered__cancel__semiring(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_566]) ).

fof(c_0_1928,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X54)
      | class_Ring__and__Field_Opordered__cancel__comm__semiring(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_567]) ).

fof(c_0_1929,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X54)
      | class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_568]) ).

fof(c_0_1930,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X54)
      | class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_569]) ).

fof(c_0_1931,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X54)
      | class_LOrder_Omeet__semilorder(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_570]) ).

fof(c_0_1932,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X54)
      | class_Ring__and__Field_Osemiring__1__cancel(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_571]) ).

fof(c_0_1933,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X54)
      | class_LOrder_Ojoin__semilorder(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_572]) ).

fof(c_0_1934,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X54)
      | class_LOrder_Olorder(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_573]) ).

fof(c_0_1935,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X54)
      | class_Orderings_Olinorder(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_574]) ).

fof(c_0_1936,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X54)
      | class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_575]) ).

fof(c_0_1937,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X54)
      | class_Ring__and__Field_Oordered__semiring__strict(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_576]) ).

fof(c_0_1938,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X54)
      | class_Ring__and__Field_Oordered__comm__semiring__strict(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_577]) ).

fof(c_0_1939,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X54)
      | class_HOL_Oplus(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_578]) ).

fof(c_0_1940,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X54)
      | class_OrderedGroup_Osemigroup__add(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_579]) ).

fof(c_0_1941,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X54)
      | class_OrderedGroup_Ocancel__semigroup__add(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_580]) ).

fof(c_0_1942,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X54)
      | class_OrderedGroup_Oab__semigroup__add(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_581]) ).

fof(c_0_1943,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X54)
      | class_OrderedGroup_Ocomm__monoid__mult(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_582]) ).

fof(c_0_1944,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X54)
      | class_OrderedGroup_Ocancel__ab__semigroup__add(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_583]) ).

fof(c_0_1945,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X54)
      | class_HOL_Ozero(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_584]) ).

fof(c_0_1946,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X54)
      | class_OrderedGroup_Ocomm__monoid__add(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_585]) ).

fof(c_0_1947,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X54)
      | class_HOL_Otimes(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_586]) ).

fof(c_0_1948,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X54)
      | class_OrderedGroup_Osemigroup__mult(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_587]) ).

fof(c_0_1949,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X54)
      | class_Ring__and__Field_Osemiring(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_588]) ).

fof(c_0_1950,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X54)
      | class_Ring__and__Field_Osemiring__0(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_589]) ).

fof(c_0_1951,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X54)
      | class_Ring__and__Field_Osemiring__0__cancel(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_590]) ).

fof(c_0_1952,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X54)
      | class_OrderedGroup_Oab__semigroup__mult(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_591]) ).

fof(c_0_1953,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X54)
      | class_Ring__and__Field_Ocomm__semiring(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_592]) ).

fof(c_0_1954,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X54)
      | class_Ring__and__Field_Ocomm__semiring__1(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_593]) ).

fof(c_0_1955,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X54)
      | class_Ring__and__Field_Ocomm__semiring__1__cancel(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_594]) ).

fof(c_0_1956,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X54)
      | class_HOL_Otimes(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_595]) ).

fof(c_0_1957,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X54)
      | class_OrderedGroup_Osemigroup__mult(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_596]) ).

fof(c_0_1958,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X54)
      | class_Ring__and__Field_Osemiring(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_597]) ).

fof(c_0_1959,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X54)
      | class_Ring__and__Field_Osemiring__0(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_598]) ).

fof(c_0_1960,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X54)
      | class_OrderedGroup_Ocancel__semigroup__add(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_599]) ).

fof(c_0_1961,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X54)
      | class_OrderedGroup_Ocancel__ab__semigroup__add(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_600]) ).

fof(c_0_1962,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X54)
      | class_Ring__and__Field_Oaxclass__no__zero__divisors(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_601]) ).

fof(c_0_1963,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X54)
      | class_OrderedGroup_Olordered__ab__group__join(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_602]) ).

fof(c_0_1964,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X54)
      | class_OrderedGroup_Olordered__ab__group__meet(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_603]) ).

fof(c_0_1965,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X54)
      | class_OrderedGroup_Olordered__ab__group__abs(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_604]) ).

fof(c_0_1966,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X54)
      | class_Ring__and__Field_Opordered__ring(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_605]) ).

fof(c_0_1967,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X54)
      | class_Ring__and__Field_Olordered__ring(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_606]) ).

fof(c_0_1968,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X54)
      | class_OrderedGroup_Opordered__ab__group__add(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_607]) ).

fof(c_0_1969,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X54)
      | class_Ring__and__Field_Osemiring__0__cancel(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_608]) ).

fof(c_0_1970,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X54)
      | class_OrderedGroup_Olordered__ab__group(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_609]) ).

fof(c_0_1971,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X54)
      | class_Ring__and__Field_Oaxclass__abs__if(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_610]) ).

fof(c_0_1972,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X54)
      | class_Orderings_Oord(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_611]) ).

fof(c_0_1973,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X54)
      | class_Orderings_Oorder(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_612]) ).

fof(c_0_1974,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X54)
      | class_OrderedGroup_Opordered__ab__semigroup__add(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_613]) ).

fof(c_0_1975,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X54)
      | class_Ring__and__Field_Opordered__semiring(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_614]) ).

fof(c_0_1976,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X54)
      | class_Ring__and__Field_Opordered__cancel__semiring(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_615]) ).

fof(c_0_1977,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X54)
      | class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_616]) ).

fof(c_0_1978,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X54)
      | class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_617]) ).

fof(c_0_1979,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X54)
      | class_LOrder_Omeet__semilorder(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_618]) ).

fof(c_0_1980,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X54)
      | class_HOL_Ominus(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_619]) ).

fof(c_0_1981,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X54)
      | class_LOrder_Ojoin__semilorder(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_620]) ).

fof(c_0_1982,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X54)
      | class_LOrder_Olorder(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_621]) ).

fof(c_0_1983,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X54)
      | class_Orderings_Olinorder(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_622]) ).

fof(c_0_1984,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X54)
      | class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_623]) ).

fof(c_0_1985,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X54)
      | class_Ring__and__Field_Oordered__semiring__strict(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_624]) ).

fof(c_0_1986,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X54)
      | class_HOL_Ozero(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_625]) ).

fof(c_0_1987,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X54)
      | class_HOL_Oplus(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_626]) ).

fof(c_0_1988,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X54)
      | class_OrderedGroup_Osemigroup__add(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_627]) ).

fof(c_0_1989,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X54)
      | class_OrderedGroup_Oab__semigroup__add(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_628]) ).

fof(c_0_1990,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X54)
      | class_OrderedGroup_Ocomm__monoid__add(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_629]) ).

fof(c_0_1991,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X54)
      | class_OrderedGroup_Oab__group__add(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_630]) ).

fof(c_0_1992,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X54)
      | class_Ring__and__Field_Oring(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_631]) ).

fof(c_0_1993,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__idom(X54)
      | class_Ring__and__Field_Osemiring__1__cancel(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_632]) ).

fof(c_0_1994,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__idom(X54)
      | class_OrderedGroup_Ocomm__monoid__mult(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_633]) ).

fof(c_0_1995,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__idom(X54)
      | class_Ring__and__Field_Ocomm__semiring__1(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_634]) ).

fof(c_0_1996,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__idom(X54)
      | class_Ring__and__Field_Ocomm__semiring__1__cancel(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_635]) ).

fof(c_0_1997,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__idom(X54)
      | class_Ring__and__Field_Oidom(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_636]) ).

fof(c_0_1998,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__idom(X54)
      | class_Ring__and__Field_Oaxclass__no__zero__divisors(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_637]) ).

fof(c_0_1999,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__idom(X54)
      | class_Ring__and__Field_Oordered__semidom(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_638]) ).

fof(c_0_2000,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__idom(X54)
      | class_OrderedGroup_Opordered__ab__group__add(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_639]) ).

fof(c_0_2001,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__idom(X54)
      | class_OrderedGroup_Olordered__ab__group(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_640]) ).

fof(c_0_2002,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__idom(X54)
      | class_OrderedGroup_Olordered__ab__group__join(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_641]) ).

fof(c_0_2003,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__idom(X54)
      | class_OrderedGroup_Olordered__ab__group__meet(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_642]) ).

fof(c_0_2004,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__idom(X54)
      | class_OrderedGroup_Olordered__ab__group__abs(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_643]) ).

fof(c_0_2005,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__idom(X54)
      | class_HOL_Ominus(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_644]) ).

fof(c_0_2006,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__idom(X54)
      | class_Ring__and__Field_Opordered__ring(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_645]) ).

fof(c_0_2007,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__idom(X54)
      | class_Ring__and__Field_Olordered__ring(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_646]) ).

fof(c_0_2008,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__idom(X54)
      | class_Ring__and__Field_Oordered__ring__strict(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_647]) ).

fof(c_0_2009,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__idom(X54)
      | class_Ring__and__Field_Oaxclass__abs__if(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_648]) ).

fof(c_0_2010,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__idom(X54)
      | class_Orderings_Oord(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_649]) ).

fof(c_0_2011,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__idom(X54)
      | class_Orderings_Oorder(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_650]) ).

fof(c_0_2012,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__idom(X54)
      | class_OrderedGroup_Opordered__ab__semigroup__add(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_651]) ).

fof(c_0_2013,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__idom(X54)
      | class_Ring__and__Field_Opordered__semiring(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_652]) ).

fof(c_0_2014,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__idom(X54)
      | class_Ring__and__Field_Opordered__comm__semiring(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_653]) ).

fof(c_0_2015,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__idom(X54)
      | class_Ring__and__Field_Opordered__cancel__semiring(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_654]) ).

fof(c_0_2016,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__idom(X54)
      | class_OrderedGroup_Oab__group__add(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_655]) ).

fof(c_0_2017,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__idom(X54)
      | class_Ring__and__Field_Opordered__cancel__comm__semiring(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_656]) ).

fof(c_0_2018,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__idom(X54)
      | class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_657]) ).

fof(c_0_2019,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__idom(X54)
      | class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_658]) ).

fof(c_0_2020,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__idom(X54)
      | class_LOrder_Omeet__semilorder(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_659]) ).

fof(c_0_2021,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__idom(X54)
      | class_LOrder_Ojoin__semilorder(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_660]) ).

fof(c_0_2022,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__idom(X54)
      | class_LOrder_Olorder(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_661]) ).

fof(c_0_2023,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__idom(X54)
      | class_Orderings_Olinorder(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_662]) ).

fof(c_0_2024,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__idom(X54)
      | class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_663]) ).

fof(c_0_2025,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__idom(X54)
      | class_Ring__and__Field_Oordered__semiring__strict(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_664]) ).

fof(c_0_2026,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__idom(X54)
      | class_Ring__and__Field_Oordered__comm__semiring__strict(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_665]) ).

fof(c_0_2027,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__idom(X54)
      | class_Ring__and__Field_Oring(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_666]) ).

fof(c_0_2028,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__idom(X54)
      | class_HOL_Oplus(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_667]) ).

fof(c_0_2029,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__idom(X54)
      | class_OrderedGroup_Osemigroup__add(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_668]) ).

fof(c_0_2030,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__idom(X54)
      | class_OrderedGroup_Ocancel__semigroup__add(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_669]) ).

fof(c_0_2031,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__idom(X54)
      | class_OrderedGroup_Oab__semigroup__add(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_670]) ).

fof(c_0_2032,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__idom(X54)
      | class_OrderedGroup_Ocancel__ab__semigroup__add(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_671]) ).

fof(c_0_2033,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__idom(X54)
      | class_HOL_Ozero(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_672]) ).

fof(c_0_2034,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__idom(X54)
      | class_OrderedGroup_Ocomm__monoid__add(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_673]) ).

fof(c_0_2035,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__idom(X54)
      | class_HOL_Otimes(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_674]) ).

fof(c_0_2036,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__idom(X54)
      | class_OrderedGroup_Osemigroup__mult(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_675]) ).

fof(c_0_2037,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__idom(X54)
      | class_Ring__and__Field_Osemiring(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_676]) ).

fof(c_0_2038,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__idom(X54)
      | class_Ring__and__Field_Oring__1(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_677]) ).

fof(c_0_2039,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__idom(X54)
      | class_Ring__and__Field_Osemiring__0(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_678]) ).

fof(c_0_2040,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__idom(X54)
      | class_Ring__and__Field_Osemiring__0__cancel(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_679]) ).

fof(c_0_2041,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__idom(X54)
      | class_OrderedGroup_Oab__semigroup__mult(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_680]) ).

fof(c_0_2042,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__idom(X54)
      | class_Ring__and__Field_Ocomm__semiring(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_681]) ).

fof(c_0_2043,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__idom(X54)
      | class_Ring__and__Field_Ocomm__semiring__0(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_682]) ).

fof(c_0_2044,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__idom(X54)
      | class_Ring__and__Field_Ocomm__semiring__0__cancel(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_683]) ).

fof(c_0_2045,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__idom(X54)
      | class_HOL_Oone(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_684]) ).

fof(c_0_2046,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__idom(X54)
      | class_OrderedGroup_Omonoid__mult(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_685]) ).

fof(c_0_2047,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__idom(X54)
      | class_Ring__and__Field_Oaxclass__0__neq__1(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_686]) ).

fof(c_0_2048,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__idom(X54)
      | class_Ring__and__Field_Osemiring__1(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_687]) ).

fof(c_0_2049,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__idom(X54)
      | class_Ring__and__Field_Ocomm__ring(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_688]) ).

fof(c_0_2050,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__idom(X54)
      | class_Ring__and__Field_Ocomm__ring__1(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_689]) ).

fof(c_0_2051,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__field(X54)
      | class_Ring__and__Field_Ocomm__semiring__1__cancel(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_690]) ).

fof(c_0_2052,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__field(X54)
      | class_HOL_Ominus(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_691]) ).

fof(c_0_2053,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__field(X54)
      | class_OrderedGroup_Oab__group__add(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_692]) ).

fof(c_0_2054,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__field(X54)
      | class_Ring__and__Field_Oordered__semidom(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_693]) ).

fof(c_0_2055,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__field(X54)
      | class_Ring__and__Field_Oring(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_694]) ).

fof(c_0_2056,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__field(X54)
      | class_Orderings_Oord(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_695]) ).

fof(c_0_2057,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__field(X54)
      | class_Orderings_Oorder(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_696]) ).

fof(c_0_2058,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__field(X54)
      | class_OrderedGroup_Opordered__ab__semigroup__add(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_697]) ).

fof(c_0_2059,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__field(X54)
      | class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_698]) ).

fof(c_0_2060,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__field(X54)
      | class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_699]) ).

fof(c_0_2061,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__field(X54)
      | class_OrderedGroup_Opordered__ab__group__add(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_700]) ).

fof(c_0_2062,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__field(X54)
      | class_LOrder_Omeet__semilorder(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_701]) ).

fof(c_0_2063,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__field(X54)
      | class_LOrder_Ojoin__semilorder(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_702]) ).

fof(c_0_2064,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__field(X54)
      | class_LOrder_Olorder(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_703]) ).

fof(c_0_2065,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__field(X54)
      | class_OrderedGroup_Olordered__ab__group(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_704]) ).

fof(c_0_2066,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__field(X54)
      | class_Ring__and__Field_Oring__1(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_705]) ).

fof(c_0_2067,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__field(X54)
      | class_OrderedGroup_Olordered__ab__group__join(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_706]) ).

fof(c_0_2068,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__field(X54)
      | class_OrderedGroup_Olordered__ab__group__meet(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_707]) ).

fof(c_0_2069,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__field(X54)
      | class_OrderedGroup_Olordered__ab__group__abs(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_708]) ).

fof(c_0_2070,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__field(X54)
      | class_Ring__and__Field_Opordered__semiring(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_709]) ).

fof(c_0_2071,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__field(X54)
      | class_Ring__and__Field_Opordered__cancel__semiring(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_710]) ).

fof(c_0_2072,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__field(X54)
      | class_Ring__and__Field_Opordered__ring(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_711]) ).

fof(c_0_2073,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__field(X54)
      | class_Ring__and__Field_Olordered__ring(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_712]) ).

fof(c_0_2074,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__field(X54)
      | class_Ring__and__Field_Oaxclass__abs__if(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_713]) ).

fof(c_0_2075,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__field(X54)
      | class_Orderings_Olinorder(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_714]) ).

fof(c_0_2076,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__field(X54)
      | class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_715]) ).

fof(c_0_2077,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__field(X54)
      | class_Ring__and__Field_Ocomm__ring(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_716]) ).

fof(c_0_2078,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__field(X54)
      | class_Ring__and__Field_Oordered__semiring__strict(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_717]) ).

fof(c_0_2079,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__field(X54)
      | class_Ring__and__Field_Oordered__ring__strict(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_718]) ).

fof(c_0_2080,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__field(X54)
      | class_Ring__and__Field_Opordered__comm__semiring(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_719]) ).

fof(c_0_2081,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__field(X54)
      | class_Ring__and__Field_Opordered__cancel__comm__semiring(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_720]) ).

fof(c_0_2082,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__field(X54)
      | class_Ring__and__Field_Oordered__comm__semiring__strict(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_721]) ).

fof(c_0_2083,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__field(X54)
      | class_Ring__and__Field_Oordered__idom(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_722]) ).

fof(c_0_2084,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__field(X54)
      | class_HOL_Otimes(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_723]) ).

fof(c_0_2085,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__field(X54)
      | class_HOL_Ozero(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_724]) ).

fof(c_0_2086,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__field(X54)
      | class_Ring__and__Field_Oaxclass__no__zero__divisors(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_725]) ).

fof(c_0_2087,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__field(X54)
      | class_HOL_Oplus(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_726]) ).

fof(c_0_2088,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__field(X54)
      | class_Ring__and__Field_Ocomm__ring__1(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_727]) ).

fof(c_0_2089,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__field(X54)
      | class_OrderedGroup_Osemigroup__add(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_728]) ).

fof(c_0_2090,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__field(X54)
      | class_OrderedGroup_Ocancel__semigroup__add(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_729]) ).

fof(c_0_2091,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__field(X54)
      | class_OrderedGroup_Oab__semigroup__add(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_730]) ).

fof(c_0_2092,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__field(X54)
      | class_OrderedGroup_Ocancel__ab__semigroup__add(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_731]) ).

fof(c_0_2093,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__field(X54)
      | class_OrderedGroup_Ocomm__monoid__add(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_732]) ).

fof(c_0_2094,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__field(X54)
      | class_OrderedGroup_Osemigroup__mult(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_733]) ).

fof(c_0_2095,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__field(X54)
      | class_Ring__and__Field_Osemiring(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_734]) ).

fof(c_0_2096,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__field(X54)
      | class_Ring__and__Field_Osemiring__0(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_735]) ).

fof(c_0_2097,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__field(X54)
      | class_Ring__and__Field_Osemiring__0__cancel(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_736]) ).

fof(c_0_2098,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__field(X54)
      | class_OrderedGroup_Oab__semigroup__mult(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_737]) ).

fof(c_0_2099,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__field(X54)
      | class_Ring__and__Field_Oidom(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_738]) ).

fof(c_0_2100,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__field(X54)
      | class_Ring__and__Field_Ocomm__semiring(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_739]) ).

fof(c_0_2101,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__field(X54)
      | class_Ring__and__Field_Ocomm__semiring__0(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_740]) ).

fof(c_0_2102,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__field(X54)
      | class_Ring__and__Field_Ocomm__semiring__0__cancel(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_741]) ).

fof(c_0_2103,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__field(X54)
      | class_HOL_Oone(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_742]) ).

fof(c_0_2104,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__field(X54)
      | class_OrderedGroup_Omonoid__mult(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_743]) ).

fof(c_0_2105,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__field(X54)
      | class_Ring__and__Field_Oaxclass__0__neq__1(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_744]) ).

fof(c_0_2106,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__field(X54)
      | class_Ring__and__Field_Osemiring__1(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_745]) ).

fof(c_0_2107,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__field(X54)
      | class_Ring__and__Field_Osemiring__1__cancel(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_746]) ).

fof(c_0_2108,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__field(X54)
      | class_OrderedGroup_Ocomm__monoid__mult(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_747]) ).

fof(c_0_2109,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__field(X54)
      | class_Ring__and__Field_Ocomm__semiring__1(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_748]) ).

fof(c_0_2110,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__field(X54)
      | class_HOL_Oinverse(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_749]) ).

fof(c_0_2111,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__field(X54)
      | class_Ring__and__Field_Ofield(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_750]) ).

fof(c_0_2112,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X54)
      | class_OrderedGroup_Osemigroup__add(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_751]) ).

fof(c_0_2113,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X54)
      | class_OrderedGroup_Oab__semigroup__add(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_752]) ).

fof(c_0_2114,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X54)
      | class_OrderedGroup_Ocomm__monoid__add(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_753]) ).

fof(c_0_2115,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X54)
      | class_HOL_Otimes(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_754]) ).

fof(c_0_2116,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X54)
      | class_OrderedGroup_Osemigroup__mult(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_755]) ).

fof(c_0_2117,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X54)
      | class_Ring__and__Field_Osemiring(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_756]) ).

fof(c_0_2118,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X54)
      | class_Ring__and__Field_Osemiring__0(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_757]) ).

fof(c_0_2119,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X54)
      | class_Ring__and__Field_Opordered__comm__semiring(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_758]) ).

fof(c_0_2120,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X54)
      | class_Ring__and__Field_Opordered__cancel__comm__semiring(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_759]) ).

fof(c_0_2121,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X54)
      | class_Ring__and__Field_Opordered__semiring(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_760]) ).

fof(c_0_2122,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X54)
      | class_Ring__and__Field_Osemiring__0__cancel(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_761]) ).

fof(c_0_2123,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X54)
      | class_Ring__and__Field_Opordered__cancel__semiring(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_762]) ).

fof(c_0_2124,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X54)
      | class_Ring__and__Field_Oordered__semiring__strict(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_763]) ).

fof(c_0_2125,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X54)
      | class_OrderedGroup_Ocancel__semigroup__add(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_764]) ).

fof(c_0_2126,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X54)
      | class_OrderedGroup_Ocancel__ab__semigroup__add(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_765]) ).

fof(c_0_2127,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X54)
      | class_Orderings_Oord(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_766]) ).

fof(c_0_2128,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X54)
      | class_Orderings_Oorder(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_767]) ).

fof(c_0_2129,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X54)
      | class_OrderedGroup_Oab__semigroup__mult(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_768]) ).

fof(c_0_2130,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X54)
      | class_OrderedGroup_Opordered__ab__semigroup__add(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_769]) ).

fof(c_0_2131,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X54)
      | class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_770]) ).

fof(c_0_2132,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X54)
      | class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_771]) ).

fof(c_0_2133,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X54)
      | class_LOrder_Omeet__semilorder(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_772]) ).

fof(c_0_2134,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X54)
      | class_LOrder_Ojoin__semilorder(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_773]) ).

fof(c_0_2135,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X54)
      | class_LOrder_Olorder(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_774]) ).

fof(c_0_2136,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X54)
      | class_Orderings_Olinorder(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_775]) ).

fof(c_0_2137,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X54)
      | class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_776]) ).

fof(c_0_2138,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X54)
      | class_HOL_Ozero(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_777]) ).

fof(c_0_2139,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X54)
      | class_HOL_Oplus(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_778]) ).

fof(c_0_2140,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X54)
      | class_Ring__and__Field_Ocomm__semiring(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_779]) ).

fof(c_0_2141,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X54)
      | class_Ring__and__Field_Ocomm__semiring__0(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_780]) ).

fof(c_0_2142,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Olordered__ring(X54)
      | class_OrderedGroup_Opordered__ab__semigroup__add(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_781]) ).

fof(c_0_2143,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Olordered__ring(X54)
      | class_Ring__and__Field_Opordered__semiring(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_782]) ).

fof(c_0_2144,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Olordered__ring(X54)
      | class_Ring__and__Field_Opordered__cancel__semiring(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_783]) ).

fof(c_0_2145,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Olordered__ring(X54)
      | class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_784]) ).

fof(c_0_2146,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Olordered__ring(X54)
      | class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_785]) ).

fof(c_0_2147,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Olordered__ring(X54)
      | class_HOL_Ominus(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_786]) ).

fof(c_0_2148,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Olordered__ring(X54)
      | class_OrderedGroup_Olordered__ab__group__join(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_787]) ).

fof(c_0_2149,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Olordered__ring(X54)
      | class_OrderedGroup_Oab__group__add(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_788]) ).

fof(c_0_2150,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Olordered__ring(X54)
      | class_OrderedGroup_Olordered__ab__group__meet(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_789]) ).

fof(c_0_2151,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Olordered__ring(X54)
      | class_LOrder_Omeet__semilorder(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_790]) ).

fof(c_0_2152,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Olordered__ring(X54)
      | class_LOrder_Ojoin__semilorder(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_791]) ).

fof(c_0_2153,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Olordered__ring(X54)
      | class_LOrder_Olorder(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_792]) ).

fof(c_0_2154,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Olordered__ring(X54)
      | class_OrderedGroup_Olordered__ab__group(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_793]) ).

fof(c_0_2155,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Olordered__ring(X54)
      | class_OrderedGroup_Olordered__ab__group__abs(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_794]) ).

fof(c_0_2156,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Olordered__ring(X54)
      | class_HOL_Oplus(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_795]) ).

fof(c_0_2157,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Olordered__ring(X54)
      | class_OrderedGroup_Osemigroup__add(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_796]) ).

fof(c_0_2158,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Olordered__ring(X54)
      | class_OrderedGroup_Ocancel__semigroup__add(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_797]) ).

fof(c_0_2159,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Olordered__ring(X54)
      | class_OrderedGroup_Oab__semigroup__add(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_798]) ).

fof(c_0_2160,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Olordered__ring(X54)
      | class_OrderedGroup_Opordered__ab__group__add(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_799]) ).

fof(c_0_2161,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Olordered__ring(X54)
      | class_OrderedGroup_Ocancel__ab__semigroup__add(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_800]) ).

fof(c_0_2162,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Olordered__ring(X54)
      | class_HOL_Ozero(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_801]) ).

fof(c_0_2163,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Olordered__ring(X54)
      | class_OrderedGroup_Ocomm__monoid__add(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_802]) ).

fof(c_0_2164,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Olordered__ring(X54)
      | class_HOL_Otimes(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_803]) ).

fof(c_0_2165,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Olordered__ring(X54)
      | class_OrderedGroup_Osemigroup__mult(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_804]) ).

fof(c_0_2166,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Olordered__ring(X54)
      | class_Ring__and__Field_Osemiring(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_805]) ).

fof(c_0_2167,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Olordered__ring(X54)
      | class_Ring__and__Field_Osemiring__0(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_806]) ).

fof(c_0_2168,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Olordered__ring(X54)
      | class_Ring__and__Field_Osemiring__0__cancel(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_807]) ).

fof(c_0_2169,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Olordered__ring(X54)
      | class_Orderings_Oord(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_808]) ).

fof(c_0_2170,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Olordered__ring(X54)
      | class_Orderings_Oorder(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_809]) ).

fof(c_0_2171,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Olordered__ring(X54)
      | class_Ring__and__Field_Oring(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_810]) ).

fof(c_0_2172,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Olordered__ring(X54)
      | class_Ring__and__Field_Opordered__ring(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_811]) ).

fof(c_0_2173,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oidom(X54)
      | class_Ring__and__Field_Osemiring__1__cancel(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_812]) ).

fof(c_0_2174,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oidom(X54)
      | class_OrderedGroup_Ocomm__monoid__mult(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_813]) ).

fof(c_0_2175,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oidom(X54)
      | class_Ring__and__Field_Ocomm__semiring__1(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_814]) ).

fof(c_0_2176,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oidom(X54)
      | class_Ring__and__Field_Ocomm__semiring__1__cancel(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_815]) ).

fof(c_0_2177,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oidom(X54)
      | class_HOL_Ominus(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_816]) ).

fof(c_0_2178,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oidom(X54)
      | class_OrderedGroup_Oab__group__add(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_817]) ).

fof(c_0_2179,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oidom(X54)
      | class_Ring__and__Field_Oaxclass__no__zero__divisors(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_818]) ).

fof(c_0_2180,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oidom(X54)
      | class_Ring__and__Field_Oring(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_819]) ).

fof(c_0_2181,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oidom(X54)
      | class_HOL_Oplus(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_820]) ).

fof(c_0_2182,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oidom(X54)
      | class_OrderedGroup_Osemigroup__add(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_821]) ).

fof(c_0_2183,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oidom(X54)
      | class_OrderedGroup_Ocancel__semigroup__add(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_822]) ).

fof(c_0_2184,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oidom(X54)
      | class_OrderedGroup_Oab__semigroup__add(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_823]) ).

fof(c_0_2185,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oidom(X54)
      | class_OrderedGroup_Ocancel__ab__semigroup__add(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_824]) ).

fof(c_0_2186,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oidom(X54)
      | class_HOL_Ozero(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_825]) ).

fof(c_0_2187,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oidom(X54)
      | class_OrderedGroup_Ocomm__monoid__add(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_826]) ).

fof(c_0_2188,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oidom(X54)
      | class_HOL_Otimes(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_827]) ).

fof(c_0_2189,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oidom(X54)
      | class_OrderedGroup_Osemigroup__mult(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_828]) ).

fof(c_0_2190,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oidom(X54)
      | class_Ring__and__Field_Osemiring(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_829]) ).

fof(c_0_2191,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oidom(X54)
      | class_Ring__and__Field_Oring__1(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_830]) ).

fof(c_0_2192,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oidom(X54)
      | class_Ring__and__Field_Osemiring__0(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_831]) ).

fof(c_0_2193,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oidom(X54)
      | class_Ring__and__Field_Osemiring__0__cancel(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_832]) ).

fof(c_0_2194,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oidom(X54)
      | class_OrderedGroup_Oab__semigroup__mult(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_833]) ).

fof(c_0_2195,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oidom(X54)
      | class_Ring__and__Field_Ocomm__semiring(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_834]) ).

fof(c_0_2196,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oidom(X54)
      | class_Ring__and__Field_Ocomm__semiring__0(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_835]) ).

fof(c_0_2197,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oidom(X54)
      | class_Ring__and__Field_Ocomm__semiring__0__cancel(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_836]) ).

fof(c_0_2198,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oidom(X54)
      | class_HOL_Oone(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_837]) ).

fof(c_0_2199,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oidom(X54)
      | class_OrderedGroup_Omonoid__mult(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_838]) ).

fof(c_0_2200,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oidom(X54)
      | class_Ring__and__Field_Oaxclass__0__neq__1(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_839]) ).

fof(c_0_2201,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oidom(X54)
      | class_Ring__and__Field_Osemiring__1(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_840]) ).

fof(c_0_2202,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oidom(X54)
      | class_Ring__and__Field_Ocomm__ring(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_841]) ).

fof(c_0_2203,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oidom(X54)
      | class_Ring__and__Field_Ocomm__ring__1(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_842]) ).

fof(c_0_2204,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Ofield(X54)
      | class_Ring__and__Field_Osemiring__1__cancel(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_843]) ).

fof(c_0_2205,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Ofield(X54)
      | class_OrderedGroup_Ocomm__monoid__mult(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_844]) ).

fof(c_0_2206,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Ofield(X54)
      | class_Ring__and__Field_Ocomm__semiring__1(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_845]) ).

fof(c_0_2207,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Ofield(X54)
      | class_Ring__and__Field_Ocomm__semiring__1__cancel(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_846]) ).

fof(c_0_2208,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Ofield(X54)
      | class_HOL_Ominus(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_847]) ).

fof(c_0_2209,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Ofield(X54)
      | class_OrderedGroup_Oab__group__add(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_848]) ).

fof(c_0_2210,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Ofield(X54)
      | class_Ring__and__Field_Oaxclass__no__zero__divisors(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_849]) ).

fof(c_0_2211,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Ofield(X54)
      | class_Ring__and__Field_Oidom(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_850]) ).

fof(c_0_2212,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Ofield(X54)
      | class_HOL_Oinverse(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_851]) ).

fof(c_0_2213,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Ofield(X54)
      | class_Ring__and__Field_Oring(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_852]) ).

fof(c_0_2214,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Ofield(X54)
      | class_HOL_Oplus(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_853]) ).

fof(c_0_2215,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Ofield(X54)
      | class_OrderedGroup_Osemigroup__add(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_854]) ).

fof(c_0_2216,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Ofield(X54)
      | class_OrderedGroup_Ocancel__semigroup__add(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_855]) ).

fof(c_0_2217,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Ofield(X54)
      | class_OrderedGroup_Oab__semigroup__add(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_856]) ).

fof(c_0_2218,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Ofield(X54)
      | class_OrderedGroup_Ocancel__ab__semigroup__add(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_857]) ).

fof(c_0_2219,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Ofield(X54)
      | class_HOL_Ozero(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_858]) ).

fof(c_0_2220,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Ofield(X54)
      | class_OrderedGroup_Ocomm__monoid__add(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_859]) ).

fof(c_0_2221,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Ofield(X54)
      | class_HOL_Otimes(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_860]) ).

fof(c_0_2222,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Ofield(X54)
      | class_OrderedGroup_Osemigroup__mult(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_861]) ).

fof(c_0_2223,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Ofield(X54)
      | class_Ring__and__Field_Osemiring(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_862]) ).

fof(c_0_2224,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Ofield(X54)
      | class_Ring__and__Field_Oring__1(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_863]) ).

fof(c_0_2225,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Ofield(X54)
      | class_Ring__and__Field_Osemiring__0(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_864]) ).

fof(c_0_2226,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Ofield(X54)
      | class_Ring__and__Field_Osemiring__0__cancel(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_865]) ).

fof(c_0_2227,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Ofield(X54)
      | class_OrderedGroup_Oab__semigroup__mult(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_866]) ).

fof(c_0_2228,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Ofield(X54)
      | class_Ring__and__Field_Ocomm__semiring(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_867]) ).

fof(c_0_2229,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Ofield(X54)
      | class_Ring__and__Field_Ocomm__semiring__0(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_868]) ).

fof(c_0_2230,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Ofield(X54)
      | class_Ring__and__Field_Ocomm__semiring__0__cancel(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_869]) ).

fof(c_0_2231,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Ofield(X54)
      | class_HOL_Oone(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_870]) ).

fof(c_0_2232,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Ofield(X54)
      | class_OrderedGroup_Omonoid__mult(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_871]) ).

fof(c_0_2233,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Ofield(X54)
      | class_Ring__and__Field_Oaxclass__0__neq__1(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_872]) ).

fof(c_0_2234,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Ofield(X54)
      | class_Ring__and__Field_Osemiring__1(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_873]) ).

fof(c_0_2235,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Ofield(X54)
      | class_Ring__and__Field_Ocomm__ring(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_874]) ).

fof(c_0_2236,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Ofield(X54)
      | class_Ring__and__Field_Ocomm__ring__1(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_875]) ).

fof(c_0_2237,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Odivision__by__zero(X54)
      | class_HOL_Oinverse(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_876]) ).

fof(c_0_2238,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Odivision__by__zero(X54)
      | class_HOL_Ozero(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_877]) ).

fof(c_0_2239,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X54)
      | class_OrderedGroup_Ocomm__monoid__add(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_878]) ).

fof(c_0_2240,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X54)
      | class_Ring__and__Field_Osemiring(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_879]) ).

fof(c_0_2241,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X54)
      | class_Ring__and__Field_Osemiring__0(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_880]) ).

fof(c_0_2242,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X54)
      | class_Ring__and__Field_Oaxclass__0__neq__1(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_881]) ).

fof(c_0_2243,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X54)
      | class_Ring__and__Field_Osemiring__1(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_882]) ).

fof(c_0_2244,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X54)
      | class_OrderedGroup_Oab__semigroup__mult(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_883]) ).

fof(c_0_2245,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X54)
      | class_OrderedGroup_Ocomm__monoid__mult(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_884]) ).

fof(c_0_2246,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X54)
      | class_Ring__and__Field_Ocomm__semiring__0__cancel(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_885]) ).

fof(c_0_2247,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X54)
      | class_Ring__and__Field_Osemiring__0__cancel(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_886]) ).

fof(c_0_2248,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X54)
      | class_Ring__and__Field_Osemiring__1__cancel(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_887]) ).

fof(c_0_2249,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X54)
      | class_Ring__and__Field_Ocomm__semiring(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_888]) ).

fof(c_0_2250,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X54)
      | class_OrderedGroup_Ocancel__semigroup__add(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_889]) ).

fof(c_0_2251,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X54)
      | class_OrderedGroup_Ocancel__ab__semigroup__add(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_890]) ).

fof(c_0_2252,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X54)
      | class_HOL_Otimes(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_891]) ).

fof(c_0_2253,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X54)
      | class_OrderedGroup_Osemigroup__mult(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_892]) ).

fof(c_0_2254,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X54)
      | class_HOL_Oone(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_893]) ).

fof(c_0_2255,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X54)
      | class_OrderedGroup_Omonoid__mult(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_894]) ).

fof(c_0_2256,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X54)
      | class_HOL_Oplus(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_895]) ).

fof(c_0_2257,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X54)
      | class_OrderedGroup_Osemigroup__add(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_896]) ).

fof(c_0_2258,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X54)
      | class_OrderedGroup_Oab__semigroup__add(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_897]) ).

fof(c_0_2259,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X54)
      | class_HOL_Ozero(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_898]) ).

fof(c_0_2260,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X54)
      | class_Ring__and__Field_Ocomm__semiring__0(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_899]) ).

fof(c_0_2261,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X54)
      | class_Ring__and__Field_Ocomm__semiring__1(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_900]) ).

fof(c_0_2262,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X54)
      | class_HOL_Otimes(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_901]) ).

fof(c_0_2263,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X54)
      | class_OrderedGroup_Osemigroup__mult(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_902]) ).

fof(c_0_2264,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X54)
      | class_Ring__and__Field_Osemiring(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_903]) ).

fof(c_0_2265,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X54)
      | class_Ring__and__Field_Osemiring__0(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_904]) ).

fof(c_0_2266,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X54)
      | class_OrderedGroup_Oab__semigroup__mult(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_905]) ).

fof(c_0_2267,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X54)
      | class_Ring__and__Field_Ocomm__semiring(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_906]) ).

fof(c_0_2268,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X54)
      | class_Ring__and__Field_Ocomm__semiring__0(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_907]) ).

fof(c_0_2269,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X54)
      | class_HOL_Oone(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_908]) ).

fof(c_0_2270,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X54)
      | class_Ring__and__Field_Osemiring__1(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_909]) ).

fof(c_0_2271,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X54)
      | class_OrderedGroup_Omonoid__mult(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_910]) ).

fof(c_0_2272,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X54)
      | class_OrderedGroup_Ocomm__monoid__mult(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_911]) ).

fof(c_0_2273,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X54)
      | class_HOL_Oplus(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_912]) ).

fof(c_0_2274,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X54)
      | class_OrderedGroup_Osemigroup__add(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_913]) ).

fof(c_0_2275,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X54)
      | class_OrderedGroup_Oab__semigroup__add(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_914]) ).

fof(c_0_2276,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X54)
      | class_OrderedGroup_Ocomm__monoid__add(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_915]) ).

fof(c_0_2277,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X54)
      | class_HOL_Ozero(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_916]) ).

fof(c_0_2278,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X54)
      | class_Ring__and__Field_Oaxclass__0__neq__1(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_917]) ).

fof(c_0_2279,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X54)
      | class_OrderedGroup_Osemigroup__add(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_918]) ).

fof(c_0_2280,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X54)
      | class_OrderedGroup_Oab__semigroup__add(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_919]) ).

fof(c_0_2281,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X54)
      | class_OrderedGroup_Ocomm__monoid__add(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_920]) ).

fof(c_0_2282,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X54)
      | class_HOL_Otimes(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_921]) ).

fof(c_0_2283,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X54)
      | class_OrderedGroup_Osemigroup__mult(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_922]) ).

fof(c_0_2284,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X54)
      | class_Ring__and__Field_Osemiring(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_923]) ).

fof(c_0_2285,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X54)
      | class_Ring__and__Field_Osemiring__0(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_924]) ).

fof(c_0_2286,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X54)
      | class_OrderedGroup_Oab__semigroup__mult(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_925]) ).

fof(c_0_2287,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X54)
      | class_Ring__and__Field_Osemiring__0__cancel(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_926]) ).

fof(c_0_2288,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X54)
      | class_OrderedGroup_Ocancel__semigroup__add(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_927]) ).

fof(c_0_2289,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X54)
      | class_OrderedGroup_Ocancel__ab__semigroup__add(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_928]) ).

fof(c_0_2290,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X54)
      | class_HOL_Ozero(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_929]) ).

fof(c_0_2291,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X54)
      | class_HOL_Oplus(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_930]) ).

fof(c_0_2292,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X54)
      | class_Ring__and__Field_Ocomm__semiring(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_931]) ).

fof(c_0_2293,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X54)
      | class_Ring__and__Field_Ocomm__semiring__0(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_932]) ).

fof(c_0_2294,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__0(X54)
      | class_HOL_Ozero(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_933]) ).

fof(c_0_2295,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__0(X54)
      | class_OrderedGroup_Ocomm__monoid__add(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_934]) ).

fof(c_0_2296,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__0(X54)
      | class_HOL_Otimes(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_935]) ).

fof(c_0_2297,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__0(X54)
      | class_OrderedGroup_Osemigroup__mult(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_936]) ).

fof(c_0_2298,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__0(X54)
      | class_HOL_Oplus(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_937]) ).

fof(c_0_2299,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__0(X54)
      | class_OrderedGroup_Osemigroup__add(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_938]) ).

fof(c_0_2300,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__0(X54)
      | class_OrderedGroup_Oab__semigroup__add(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_939]) ).

fof(c_0_2301,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__0(X54)
      | class_Ring__and__Field_Osemiring(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_940]) ).

fof(c_0_2302,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__0(X54)
      | class_Ring__and__Field_Osemiring__0(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_941]) ).

fof(c_0_2303,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__0(X54)
      | class_OrderedGroup_Oab__semigroup__mult(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_942]) ).

fof(c_0_2304,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__0(X54)
      | class_Ring__and__Field_Ocomm__semiring(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_943]) ).

fof(c_0_2305,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Ocomm__semiring(X54)
      | class_Ring__and__Field_Osemiring(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_944]) ).

fof(c_0_2306,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Ocomm__semiring(X54)
      | class_HOL_Otimes(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_945]) ).

fof(c_0_2307,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Ocomm__semiring(X54)
      | class_OrderedGroup_Osemigroup__mult(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_946]) ).

fof(c_0_2308,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Ocomm__semiring(X54)
      | class_OrderedGroup_Oab__semigroup__mult(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_947]) ).

fof(c_0_2309,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Ocomm__semiring(X54)
      | class_HOL_Oplus(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_948]) ).

fof(c_0_2310,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Ocomm__semiring(X54)
      | class_OrderedGroup_Osemigroup__add(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_949]) ).

fof(c_0_2311,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Ocomm__semiring(X54)
      | class_OrderedGroup_Oab__semigroup__add(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_950]) ).

fof(c_0_2312,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Ocomm__ring__1(X54)
      | class_Ring__and__Field_Osemiring__0(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_951]) ).

fof(c_0_2313,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Ocomm__ring__1(X54)
      | class_Ring__and__Field_Osemiring__0__cancel(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_952]) ).

fof(c_0_2314,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Ocomm__ring__1(X54)
      | class_OrderedGroup_Oab__semigroup__mult(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_953]) ).

fof(c_0_2315,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Ocomm__ring__1(X54)
      | class_Ring__and__Field_Ocomm__semiring(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_954]) ).

fof(c_0_2316,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Ocomm__ring__1(X54)
      | class_Ring__and__Field_Ocomm__semiring__0(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_955]) ).

fof(c_0_2317,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Ocomm__ring__1(X54)
      | class_Ring__and__Field_Ocomm__semiring__0__cancel(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_956]) ).

fof(c_0_2318,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Ocomm__ring__1(X54)
      | class_HOL_Ominus(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_957]) ).

fof(c_0_2319,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Ocomm__ring__1(X54)
      | class_Ring__and__Field_Ocomm__semiring__1__cancel(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_958]) ).

fof(c_0_2320,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Ocomm__ring__1(X54)
      | class_Ring__and__Field_Osemiring__1__cancel(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_959]) ).

fof(c_0_2321,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Ocomm__ring__1(X54)
      | class_Ring__and__Field_Oring__1(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_960]) ).

fof(c_0_2322,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Ocomm__ring__1(X54)
      | class_HOL_Oone(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_961]) ).

fof(c_0_2323,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Ocomm__ring__1(X54)
      | class_OrderedGroup_Omonoid__mult(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_962]) ).

fof(c_0_2324,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Ocomm__ring__1(X54)
      | class_Ring__and__Field_Oaxclass__0__neq__1(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_963]) ).

fof(c_0_2325,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Ocomm__ring__1(X54)
      | class_Ring__and__Field_Osemiring__1(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_964]) ).

fof(c_0_2326,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Ocomm__ring__1(X54)
      | class_OrderedGroup_Ocomm__monoid__mult(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_965]) ).

fof(c_0_2327,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Ocomm__ring__1(X54)
      | class_Ring__and__Field_Ocomm__semiring__1(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_966]) ).

fof(c_0_2328,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Ocomm__ring__1(X54)
      | class_OrderedGroup_Oab__group__add(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_967]) ).

fof(c_0_2329,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Ocomm__ring__1(X54)
      | class_HOL_Oplus(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_968]) ).

fof(c_0_2330,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Ocomm__ring__1(X54)
      | class_OrderedGroup_Osemigroup__add(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_969]) ).

fof(c_0_2331,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Ocomm__ring__1(X54)
      | class_OrderedGroup_Ocancel__semigroup__add(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_970]) ).

fof(c_0_2332,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Ocomm__ring__1(X54)
      | class_OrderedGroup_Oab__semigroup__add(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_971]) ).

fof(c_0_2333,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Ocomm__ring__1(X54)
      | class_OrderedGroup_Ocancel__ab__semigroup__add(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_972]) ).

fof(c_0_2334,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Ocomm__ring__1(X54)
      | class_HOL_Ozero(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_973]) ).

fof(c_0_2335,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Ocomm__ring__1(X54)
      | class_OrderedGroup_Ocomm__monoid__add(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_974]) ).

fof(c_0_2336,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Ocomm__ring__1(X54)
      | class_HOL_Otimes(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_975]) ).

fof(c_0_2337,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Ocomm__ring__1(X54)
      | class_OrderedGroup_Osemigroup__mult(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_976]) ).

fof(c_0_2338,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Ocomm__ring__1(X54)
      | class_Ring__and__Field_Osemiring(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_977]) ).

fof(c_0_2339,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Ocomm__ring__1(X54)
      | class_Ring__and__Field_Oring(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_978]) ).

fof(c_0_2340,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Ocomm__ring__1(X54)
      | class_Ring__and__Field_Ocomm__ring(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_979]) ).

fof(c_0_2341,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Ocomm__ring(X54)
      | class_OrderedGroup_Osemigroup__add(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_980]) ).

fof(c_0_2342,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Ocomm__ring(X54)
      | class_OrderedGroup_Oab__semigroup__add(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_981]) ).

fof(c_0_2343,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Ocomm__ring(X54)
      | class_OrderedGroup_Ocomm__monoid__add(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_982]) ).

fof(c_0_2344,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Ocomm__ring(X54)
      | class_HOL_Otimes(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_983]) ).

fof(c_0_2345,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Ocomm__ring(X54)
      | class_OrderedGroup_Osemigroup__mult(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_984]) ).

fof(c_0_2346,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Ocomm__ring(X54)
      | class_Ring__and__Field_Osemiring(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_985]) ).

fof(c_0_2347,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Ocomm__ring(X54)
      | class_Ring__and__Field_Osemiring__0(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_986]) ).

fof(c_0_2348,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Ocomm__ring(X54)
      | class_OrderedGroup_Oab__semigroup__mult(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_987]) ).

fof(c_0_2349,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Ocomm__ring(X54)
      | class_Ring__and__Field_Ocomm__semiring__0__cancel(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_988]) ).

fof(c_0_2350,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Ocomm__ring(X54)
      | class_Ring__and__Field_Osemiring__0__cancel(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_989]) ).

fof(c_0_2351,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Ocomm__ring(X54)
      | class_Ring__and__Field_Oring(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_990]) ).

fof(c_0_2352,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Ocomm__ring(X54)
      | class_OrderedGroup_Ocancel__semigroup__add(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_991]) ).

fof(c_0_2353,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Ocomm__ring(X54)
      | class_OrderedGroup_Ocancel__ab__semigroup__add(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_992]) ).

fof(c_0_2354,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Ocomm__ring(X54)
      | class_HOL_Ominus(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_993]) ).

fof(c_0_2355,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Ocomm__ring(X54)
      | class_OrderedGroup_Oab__group__add(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_994]) ).

fof(c_0_2356,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Ocomm__ring(X54)
      | class_HOL_Ozero(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_995]) ).

fof(c_0_2357,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Ocomm__ring(X54)
      | class_HOL_Oplus(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_996]) ).

fof(c_0_2358,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Ocomm__ring(X54)
      | class_Ring__and__Field_Ocomm__semiring(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_997]) ).

fof(c_0_2359,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Ocomm__ring(X54)
      | class_Ring__and__Field_Ocomm__semiring__0(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_998]) ).

fof(c_0_2360,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oaxclass__no__zero__divisors(X54)
      | class_HOL_Otimes(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_999]) ).

fof(c_0_2361,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oaxclass__no__zero__divisors(X54)
      | class_HOL_Ozero(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_1000]) ).

fof(c_0_2362,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oaxclass__abs__if(X54)
      | class_HOL_Ozero(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_1001]) ).

fof(c_0_2363,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oaxclass__abs__if(X54)
      | class_Orderings_Oord(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_1002]) ).

fof(c_0_2364,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oaxclass__abs__if(X54)
      | class_HOL_Ominus(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_1003]) ).

fof(c_0_2365,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oaxclass__0__neq__1(X54)
      | class_HOL_Oone(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_1004]) ).

fof(c_0_2366,plain,
    ! [X54] :
      ( ~ class_Ring__and__Field_Oaxclass__0__neq__1(X54)
      | class_HOL_Ozero(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_1005]) ).

fof(c_0_2367,plain,
    ! [X54] :
      ( ~ class_Power_Orecpower(X54)
      | class_OrderedGroup_Oab__semigroup__mult(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_1006]) ).

fof(c_0_2368,plain,
    ! [X54] :
      ( ~ class_Power_Orecpower(X54)
      | class_OrderedGroup_Osemigroup__mult(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_1007]) ).

fof(c_0_2369,plain,
    ! [X54] :
      ( ~ class_Power_Orecpower(X54)
      | class_HOL_Otimes(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_1008]) ).

fof(c_0_2370,plain,
    ! [X54] :
      ( ~ class_Power_Orecpower(X54)
      | class_OrderedGroup_Oab__semigroup__add(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_1009]) ).

fof(c_0_2371,plain,
    ! [X54] :
      ( ~ class_Power_Orecpower(X54)
      | class_OrderedGroup_Osemigroup__add(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_1010]) ).

fof(c_0_2372,plain,
    ! [X54] :
      ( ~ class_Power_Orecpower(X54)
      | class_HOL_Oplus(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_1011]) ).

fof(c_0_2373,plain,
    ! [X54] :
      ( ~ class_Power_Orecpower(X54)
      | class_Ring__and__Field_Oaxclass__0__neq__1(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_1012]) ).

fof(c_0_2374,plain,
    ! [X54] :
      ( ~ class_Power_Orecpower(X54)
      | class_Ring__and__Field_Ocomm__semiring__1__cancel(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_1013]) ).

fof(c_0_2375,plain,
    ! [X54] :
      ( ~ class_Power_Orecpower(X54)
      | class_Ring__and__Field_Ocomm__semiring__0__cancel(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_1014]) ).

fof(c_0_2376,plain,
    ! [X54] :
      ( ~ class_Power_Orecpower(X54)
      | class_Ring__and__Field_Osemiring__1__cancel(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_1015]) ).

fof(c_0_2377,plain,
    ! [X54] :
      ( ~ class_Power_Orecpower(X54)
      | class_Ring__and__Field_Osemiring__0__cancel(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_1016]) ).

fof(c_0_2378,plain,
    ! [X54] :
      ( ~ class_Power_Orecpower(X54)
      | class_OrderedGroup_Ocancel__ab__semigroup__add(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_1017]) ).

fof(c_0_2379,plain,
    ! [X54] :
      ( ~ class_Power_Orecpower(X54)
      | class_HOL_Oone(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_1018]) ).

fof(c_0_2380,plain,
    ! [X54] :
      ( ~ class_Power_Orecpower(X54)
      | class_OrderedGroup_Ocancel__semigroup__add(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_1019]) ).

fof(c_0_2381,plain,
    ! [X54] :
      ( ~ class_Power_Orecpower(X54)
      | class_Ring__and__Field_Ocomm__semiring__1(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_1020]) ).

fof(c_0_2382,plain,
    ! [X54] :
      ( ~ class_Power_Orecpower(X54)
      | class_Ring__and__Field_Osemiring__1(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_1021]) ).

fof(c_0_2383,plain,
    ! [X54] :
      ( ~ class_Power_Orecpower(X54)
      | class_OrderedGroup_Ocomm__monoid__mult(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_1022]) ).

fof(c_0_2384,plain,
    ! [X54] :
      ( ~ class_Power_Orecpower(X54)
      | class_OrderedGroup_Omonoid__mult(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_1023]) ).

fof(c_0_2385,plain,
    ! [X54] :
      ( ~ class_Power_Orecpower(X54)
      | class_Ring__and__Field_Ocomm__semiring__0(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_1024]) ).

fof(c_0_2386,plain,
    ! [X54] :
      ( ~ class_Power_Orecpower(X54)
      | class_Ring__and__Field_Osemiring__0(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_1025]) ).

fof(c_0_2387,plain,
    ! [X54] :
      ( ~ class_Power_Orecpower(X54)
      | class_OrderedGroup_Ocomm__monoid__add(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_1026]) ).

fof(c_0_2388,plain,
    ! [X54] :
      ( ~ class_Power_Orecpower(X54)
      | class_Ring__and__Field_Ocomm__semiring(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_1027]) ).

fof(c_0_2389,plain,
    ! [X54] :
      ( ~ class_Power_Orecpower(X54)
      | class_Ring__and__Field_Osemiring(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_1028]) ).

fof(c_0_2390,plain,
    ! [X54] :
      ( ~ class_Power_Orecpower(X54)
      | class_HOL_Ozero(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_1029]) ).

fof(c_0_2391,plain,
    ! [X54] :
      ( ~ class_Power_Orecpower(X54)
      | class_Nat_Opower(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_1030]) ).

fof(c_0_2392,plain,
    ! [X54] :
      ( ~ class_Orderings_Oorder(X54)
      | class_Orderings_Oord(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_1031]) ).

fof(c_0_2393,plain,
    ! [X54] :
      ( ~ class_Orderings_Olinorder(X54)
      | class_Orderings_Oorder(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_1032]) ).

fof(c_0_2394,plain,
    ! [X54] :
      ( ~ class_Orderings_Olinorder(X54)
      | class_Orderings_Oord(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_1033]) ).

fof(c_0_2395,plain,
    ! [X54] :
      ( ~ class_Orderings_Olinorder(X54)
      | class_LOrder_Omeet__semilorder(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_1034]) ).

fof(c_0_2396,plain,
    ! [X54] :
      ( ~ class_Orderings_Olinorder(X54)
      | class_LOrder_Ojoin__semilorder(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_1035]) ).

fof(c_0_2397,plain,
    ! [X54] :
      ( ~ class_Orderings_Olinorder(X54)
      | class_LOrder_Olorder(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_1036]) ).

fof(c_0_2398,plain,
    ! [X54] :
      ( ~ class_OrderedGroup_Osemigroup__mult(X54)
      | class_HOL_Otimes(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_1037]) ).

fof(c_0_2399,plain,
    ! [X54] :
      ( ~ class_OrderedGroup_Osemigroup__add(X54)
      | class_HOL_Oplus(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_1038]) ).

fof(c_0_2400,plain,
    ! [X54] :
      ( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X54)
      | class_OrderedGroup_Ocancel__semigroup__add(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_1039]) ).

fof(c_0_2401,plain,
    ! [X54] :
      ( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X54)
      | class_OrderedGroup_Ocancel__ab__semigroup__add(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_1040]) ).

fof(c_0_2402,plain,
    ! [X54] :
      ( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X54)
      | class_HOL_Oplus(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_1041]) ).

fof(c_0_2403,plain,
    ! [X54] :
      ( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X54)
      | class_OrderedGroup_Osemigroup__add(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_1042]) ).

fof(c_0_2404,plain,
    ! [X54] :
      ( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X54)
      | class_OrderedGroup_Oab__semigroup__add(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_1043]) ).

fof(c_0_2405,plain,
    ! [X54] :
      ( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X54)
      | class_Orderings_Oord(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_1044]) ).

fof(c_0_2406,plain,
    ! [X54] :
      ( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X54)
      | class_Orderings_Oorder(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_1045]) ).

fof(c_0_2407,plain,
    ! [X54] :
      ( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X54)
      | class_OrderedGroup_Opordered__ab__semigroup__add(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_1046]) ).

fof(c_0_2408,plain,
    ! [X54] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X54)
      | class_HOL_Oplus(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_1047]) ).

fof(c_0_2409,plain,
    ! [X54] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X54)
      | class_OrderedGroup_Osemigroup__add(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_1048]) ).

fof(c_0_2410,plain,
    ! [X54] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X54)
      | class_OrderedGroup_Ocancel__semigroup__add(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_1049]) ).

fof(c_0_2411,plain,
    ! [X54] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X54)
      | class_OrderedGroup_Oab__semigroup__add(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_1050]) ).

fof(c_0_2412,plain,
    ! [X54] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X54)
      | class_OrderedGroup_Ocancel__ab__semigroup__add(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_1051]) ).

fof(c_0_2413,plain,
    ! [X54] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X54)
      | class_Orderings_Oord(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_1052]) ).

fof(c_0_2414,plain,
    ! [X54] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X54)
      | class_Orderings_Oorder(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_1053]) ).

fof(c_0_2415,plain,
    ! [X54] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X54)
      | class_OrderedGroup_Opordered__ab__semigroup__add(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_1054]) ).

fof(c_0_2416,plain,
    ! [X54] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X54)
      | class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_1055]) ).

fof(c_0_2417,plain,
    ! [X54] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X54)
      | class_HOL_Oplus(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_1056]) ).

fof(c_0_2418,plain,
    ! [X54] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X54)
      | class_OrderedGroup_Osemigroup__add(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_1057]) ).

fof(c_0_2419,plain,
    ! [X54] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X54)
      | class_OrderedGroup_Oab__semigroup__add(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_1058]) ).

fof(c_0_2420,plain,
    ! [X54] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X54)
      | class_Orderings_Oord(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_1059]) ).

fof(c_0_2421,plain,
    ! [X54] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X54)
      | class_Orderings_Oorder(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_1060]) ).

fof(c_0_2422,plain,
    ! [X54] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add(X54)
      | class_OrderedGroup_Opordered__ab__semigroup__add(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_1061]) ).

fof(c_0_2423,plain,
    ! [X54] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add(X54)
      | class_HOL_Oplus(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_1062]) ).

fof(c_0_2424,plain,
    ! [X54] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add(X54)
      | class_OrderedGroup_Osemigroup__add(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_1063]) ).

fof(c_0_2425,plain,
    ! [X54] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add(X54)
      | class_OrderedGroup_Ocancel__semigroup__add(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_1064]) ).

fof(c_0_2426,plain,
    ! [X54] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add(X54)
      | class_OrderedGroup_Oab__semigroup__add(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_1065]) ).

fof(c_0_2427,plain,
    ! [X54] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add(X54)
      | class_OrderedGroup_Ocancel__ab__semigroup__add(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_1066]) ).

fof(c_0_2428,plain,
    ! [X54] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add(X54)
      | class_HOL_Ozero(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_1067]) ).

fof(c_0_2429,plain,
    ! [X54] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add(X54)
      | class_OrderedGroup_Ocomm__monoid__add(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_1068]) ).

fof(c_0_2430,plain,
    ! [X54] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add(X54)
      | class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_1069]) ).

fof(c_0_2431,plain,
    ! [X54] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add(X54)
      | class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_1070]) ).

fof(c_0_2432,plain,
    ! [X54] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add(X54)
      | class_Orderings_Oord(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_1071]) ).

fof(c_0_2433,plain,
    ! [X54] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add(X54)
      | class_Orderings_Oorder(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_1072]) ).

fof(c_0_2434,plain,
    ! [X54] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add(X54)
      | class_HOL_Ominus(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_1073]) ).

fof(c_0_2435,plain,
    ! [X54] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add(X54)
      | class_OrderedGroup_Oab__group__add(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_1074]) ).

fof(c_0_2436,plain,
    ! [X54] :
      ( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X54)
      | class_Orderings_Olinorder(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_1075]) ).

fof(c_0_2437,plain,
    ! [X54] :
      ( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X54)
      | class_HOL_Oplus(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_1076]) ).

fof(c_0_2438,plain,
    ! [X54] :
      ( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X54)
      | class_OrderedGroup_Osemigroup__add(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_1077]) ).

fof(c_0_2439,plain,
    ! [X54] :
      ( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X54)
      | class_OrderedGroup_Ocancel__semigroup__add(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_1078]) ).

fof(c_0_2440,plain,
    ! [X54] :
      ( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X54)
      | class_OrderedGroup_Oab__semigroup__add(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_1079]) ).

fof(c_0_2441,plain,
    ! [X54] :
      ( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X54)
      | class_OrderedGroup_Ocancel__ab__semigroup__add(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_1080]) ).

fof(c_0_2442,plain,
    ! [X54] :
      ( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X54)
      | class_Orderings_Oord(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_1081]) ).

fof(c_0_2443,plain,
    ! [X54] :
      ( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X54)
      | class_Orderings_Oorder(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_1082]) ).

fof(c_0_2444,plain,
    ! [X54] :
      ( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X54)
      | class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_1083]) ).

fof(c_0_2445,plain,
    ! [X54] :
      ( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X54)
      | class_LOrder_Omeet__semilorder(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_1084]) ).

fof(c_0_2446,plain,
    ! [X54] :
      ( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X54)
      | class_LOrder_Ojoin__semilorder(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_1085]) ).

fof(c_0_2447,plain,
    ! [X54] :
      ( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X54)
      | class_LOrder_Olorder(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_1086]) ).

fof(c_0_2448,plain,
    ! [X54] :
      ( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X54)
      | class_OrderedGroup_Opordered__ab__semigroup__add(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_1087]) ).

fof(c_0_2449,plain,
    ! [X54] :
      ( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X54)
      | class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_1088]) ).

fof(c_0_2450,plain,
    ! [X54] :
      ( ~ class_OrderedGroup_Omonoid__mult(X54)
      | class_HOL_Otimes(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_1089]) ).

fof(c_0_2451,plain,
    ! [X54] :
      ( ~ class_OrderedGroup_Omonoid__mult(X54)
      | class_OrderedGroup_Osemigroup__mult(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_1090]) ).

fof(c_0_2452,plain,
    ! [X54] :
      ( ~ class_OrderedGroup_Omonoid__mult(X54)
      | class_HOL_Oone(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_1091]) ).

fof(c_0_2453,plain,
    ! [X54] :
      ( ~ class_OrderedGroup_Olordered__ab__group__meet(X54)
      | class_Orderings_Oord(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_1092]) ).

fof(c_0_2454,plain,
    ! [X54] :
      ( ~ class_OrderedGroup_Olordered__ab__group__meet(X54)
      | class_Orderings_Oorder(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_1093]) ).

fof(c_0_2455,plain,
    ! [X54] :
      ( ~ class_OrderedGroup_Olordered__ab__group__meet(X54)
      | class_OrderedGroup_Opordered__ab__semigroup__add(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_1094]) ).

fof(c_0_2456,plain,
    ! [X54] :
      ( ~ class_OrderedGroup_Olordered__ab__group__meet(X54)
      | class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_1095]) ).

fof(c_0_2457,plain,
    ! [X54] :
      ( ~ class_OrderedGroup_Olordered__ab__group__meet(X54)
      | class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_1096]) ).

fof(c_0_2458,plain,
    ! [X54] :
      ( ~ class_OrderedGroup_Olordered__ab__group__meet(X54)
      | class_HOL_Ozero(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_1097]) ).

fof(c_0_2459,plain,
    ! [X54] :
      ( ~ class_OrderedGroup_Olordered__ab__group__meet(X54)
      | class_OrderedGroup_Ocomm__monoid__add(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_1098]) ).

fof(c_0_2460,plain,
    ! [X54] :
      ( ~ class_OrderedGroup_Olordered__ab__group__meet(X54)
      | class_HOL_Ominus(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_1099]) ).

fof(c_0_2461,plain,
    ! [X54] :
      ( ~ class_OrderedGroup_Olordered__ab__group__meet(X54)
      | class_LOrder_Ojoin__semilorder(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_1100]) ).

fof(c_0_2462,plain,
    ! [X54] :
      ( ~ class_OrderedGroup_Olordered__ab__group__meet(X54)
      | class_LOrder_Olorder(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_1101]) ).

fof(c_0_2463,plain,
    ! [X54] :
      ( ~ class_OrderedGroup_Olordered__ab__group__meet(X54)
      | class_OrderedGroup_Olordered__ab__group(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_1102]) ).

fof(c_0_2464,plain,
    ! [X54] :
      ( ~ class_OrderedGroup_Olordered__ab__group__meet(X54)
      | class_LOrder_Omeet__semilorder(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_1103]) ).

fof(c_0_2465,plain,
    ! [X54] :
      ( ~ class_OrderedGroup_Olordered__ab__group__meet(X54)
      | class_HOL_Oplus(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_1104]) ).

fof(c_0_2466,plain,
    ! [X54] :
      ( ~ class_OrderedGroup_Olordered__ab__group__meet(X54)
      | class_OrderedGroup_Osemigroup__add(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_1105]) ).

fof(c_0_2467,plain,
    ! [X54] :
      ( ~ class_OrderedGroup_Olordered__ab__group__meet(X54)
      | class_OrderedGroup_Ocancel__semigroup__add(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_1106]) ).

fof(c_0_2468,plain,
    ! [X54] :
      ( ~ class_OrderedGroup_Olordered__ab__group__meet(X54)
      | class_OrderedGroup_Oab__semigroup__add(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_1107]) ).

fof(c_0_2469,plain,
    ! [X54] :
      ( ~ class_OrderedGroup_Olordered__ab__group__meet(X54)
      | class_OrderedGroup_Ocancel__ab__semigroup__add(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_1108]) ).

fof(c_0_2470,plain,
    ! [X54] :
      ( ~ class_OrderedGroup_Olordered__ab__group__meet(X54)
      | class_OrderedGroup_Oab__group__add(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_1109]) ).

fof(c_0_2471,plain,
    ! [X54] :
      ( ~ class_OrderedGroup_Olordered__ab__group__meet(X54)
      | class_OrderedGroup_Opordered__ab__group__add(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_1110]) ).

fof(c_0_2472,plain,
    ! [X54] :
      ( ~ class_OrderedGroup_Olordered__ab__group__join(X54)
      | class_Orderings_Oord(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_1111]) ).

fof(c_0_2473,plain,
    ! [X54] :
      ( ~ class_OrderedGroup_Olordered__ab__group__join(X54)
      | class_Orderings_Oorder(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_1112]) ).

fof(c_0_2474,plain,
    ! [X54] :
      ( ~ class_OrderedGroup_Olordered__ab__group__join(X54)
      | class_OrderedGroup_Opordered__ab__semigroup__add(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_1113]) ).

fof(c_0_2475,plain,
    ! [X54] :
      ( ~ class_OrderedGroup_Olordered__ab__group__join(X54)
      | class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_1114]) ).

fof(c_0_2476,plain,
    ! [X54] :
      ( ~ class_OrderedGroup_Olordered__ab__group__join(X54)
      | class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_1115]) ).

fof(c_0_2477,plain,
    ! [X54] :
      ( ~ class_OrderedGroup_Olordered__ab__group__join(X54)
      | class_HOL_Ozero(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_1116]) ).

fof(c_0_2478,plain,
    ! [X54] :
      ( ~ class_OrderedGroup_Olordered__ab__group__join(X54)
      | class_OrderedGroup_Ocomm__monoid__add(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_1117]) ).

fof(c_0_2479,plain,
    ! [X54] :
      ( ~ class_OrderedGroup_Olordered__ab__group__join(X54)
      | class_HOL_Ominus(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_1118]) ).

fof(c_0_2480,plain,
    ! [X54] :
      ( ~ class_OrderedGroup_Olordered__ab__group__join(X54)
      | class_LOrder_Omeet__semilorder(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_1119]) ).

fof(c_0_2481,plain,
    ! [X54] :
      ( ~ class_OrderedGroup_Olordered__ab__group__join(X54)
      | class_LOrder_Olorder(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_1120]) ).

fof(c_0_2482,plain,
    ! [X54] :
      ( ~ class_OrderedGroup_Olordered__ab__group__join(X54)
      | class_OrderedGroup_Olordered__ab__group(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_1121]) ).

fof(c_0_2483,plain,
    ! [X54] :
      ( ~ class_OrderedGroup_Olordered__ab__group__join(X54)
      | class_LOrder_Ojoin__semilorder(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_1122]) ).

fof(c_0_2484,plain,
    ! [X54] :
      ( ~ class_OrderedGroup_Olordered__ab__group__join(X54)
      | class_HOL_Oplus(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_1123]) ).

fof(c_0_2485,plain,
    ! [X54] :
      ( ~ class_OrderedGroup_Olordered__ab__group__join(X54)
      | class_OrderedGroup_Osemigroup__add(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_1124]) ).

fof(c_0_2486,plain,
    ! [X54] :
      ( ~ class_OrderedGroup_Olordered__ab__group__join(X54)
      | class_OrderedGroup_Ocancel__semigroup__add(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_1125]) ).

fof(c_0_2487,plain,
    ! [X54] :
      ( ~ class_OrderedGroup_Olordered__ab__group__join(X54)
      | class_OrderedGroup_Oab__semigroup__add(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_1126]) ).

fof(c_0_2488,plain,
    ! [X54] :
      ( ~ class_OrderedGroup_Olordered__ab__group__join(X54)
      | class_OrderedGroup_Ocancel__ab__semigroup__add(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_1127]) ).

fof(c_0_2489,plain,
    ! [X54] :
      ( ~ class_OrderedGroup_Olordered__ab__group__join(X54)
      | class_OrderedGroup_Oab__group__add(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_1128]) ).

fof(c_0_2490,plain,
    ! [X54] :
      ( ~ class_OrderedGroup_Olordered__ab__group__join(X54)
      | class_OrderedGroup_Opordered__ab__group__add(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_1129]) ).

fof(c_0_2491,plain,
    ! [X54] :
      ( ~ class_OrderedGroup_Olordered__ab__group__abs(X54)
      | class_OrderedGroup_Ocancel__ab__semigroup__add(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_1130]) ).

fof(c_0_2492,plain,
    ! [X54] :
      ( ~ class_OrderedGroup_Olordered__ab__group__abs(X54)
      | class_OrderedGroup_Opordered__ab__semigroup__add(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_1131]) ).

fof(c_0_2493,plain,
    ! [X54] :
      ( ~ class_OrderedGroup_Olordered__ab__group__abs(X54)
      | class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_1132]) ).

fof(c_0_2494,plain,
    ! [X54] :
      ( ~ class_OrderedGroup_Olordered__ab__group__abs(X54)
      | class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_1133]) ).

fof(c_0_2495,plain,
    ! [X54] :
      ( ~ class_OrderedGroup_Olordered__ab__group__abs(X54)
      | class_HOL_Ozero(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_1134]) ).

fof(c_0_2496,plain,
    ! [X54] :
      ( ~ class_OrderedGroup_Olordered__ab__group__abs(X54)
      | class_OrderedGroup_Ocomm__monoid__add(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_1135]) ).

fof(c_0_2497,plain,
    ! [X54] :
      ( ~ class_OrderedGroup_Olordered__ab__group__abs(X54)
      | class_HOL_Ominus(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_1136]) ).

fof(c_0_2498,plain,
    ! [X54] :
      ( ~ class_OrderedGroup_Olordered__ab__group__abs(X54)
      | class_OrderedGroup_Oab__group__add(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_1137]) ).

fof(c_0_2499,plain,
    ! [X54] :
      ( ~ class_OrderedGroup_Olordered__ab__group__abs(X54)
      | class_Orderings_Oord(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_1138]) ).

fof(c_0_2500,plain,
    ! [X54] :
      ( ~ class_OrderedGroup_Olordered__ab__group__abs(X54)
      | class_Orderings_Oorder(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_1139]) ).

fof(c_0_2501,plain,
    ! [X54] :
      ( ~ class_OrderedGroup_Olordered__ab__group__abs(X54)
      | class_LOrder_Omeet__semilorder(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_1140]) ).

fof(c_0_2502,plain,
    ! [X54] :
      ( ~ class_OrderedGroup_Olordered__ab__group__abs(X54)
      | class_LOrder_Ojoin__semilorder(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_1141]) ).

fof(c_0_2503,plain,
    ! [X54] :
      ( ~ class_OrderedGroup_Olordered__ab__group__abs(X54)
      | class_LOrder_Olorder(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_1142]) ).

fof(c_0_2504,plain,
    ! [X54] :
      ( ~ class_OrderedGroup_Olordered__ab__group__abs(X54)
      | class_HOL_Oplus(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_1143]) ).

fof(c_0_2505,plain,
    ! [X54] :
      ( ~ class_OrderedGroup_Olordered__ab__group__abs(X54)
      | class_OrderedGroup_Osemigroup__add(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_1144]) ).

fof(c_0_2506,plain,
    ! [X54] :
      ( ~ class_OrderedGroup_Olordered__ab__group__abs(X54)
      | class_OrderedGroup_Ocancel__semigroup__add(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_1145]) ).

fof(c_0_2507,plain,
    ! [X54] :
      ( ~ class_OrderedGroup_Olordered__ab__group__abs(X54)
      | class_OrderedGroup_Oab__semigroup__add(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_1146]) ).

fof(c_0_2508,plain,
    ! [X54] :
      ( ~ class_OrderedGroup_Olordered__ab__group__abs(X54)
      | class_OrderedGroup_Opordered__ab__group__add(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_1147]) ).

fof(c_0_2509,plain,
    ! [X54] :
      ( ~ class_OrderedGroup_Olordered__ab__group__abs(X54)
      | class_OrderedGroup_Olordered__ab__group(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_1148]) ).

fof(c_0_2510,plain,
    ! [X54] :
      ( ~ class_OrderedGroup_Olordered__ab__group(X54)
      | class_Orderings_Oord(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_1149]) ).

fof(c_0_2511,plain,
    ! [X54] :
      ( ~ class_OrderedGroup_Olordered__ab__group(X54)
      | class_Orderings_Oorder(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_1150]) ).

fof(c_0_2512,plain,
    ! [X54] :
      ( ~ class_OrderedGroup_Olordered__ab__group(X54)
      | class_OrderedGroup_Opordered__ab__semigroup__add(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_1151]) ).

fof(c_0_2513,plain,
    ! [X54] :
      ( ~ class_OrderedGroup_Olordered__ab__group(X54)
      | class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_1152]) ).

fof(c_0_2514,plain,
    ! [X54] :
      ( ~ class_OrderedGroup_Olordered__ab__group(X54)
      | class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_1153]) ).

fof(c_0_2515,plain,
    ! [X54] :
      ( ~ class_OrderedGroup_Olordered__ab__group(X54)
      | class_HOL_Ozero(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_1154]) ).

fof(c_0_2516,plain,
    ! [X54] :
      ( ~ class_OrderedGroup_Olordered__ab__group(X54)
      | class_OrderedGroup_Ocomm__monoid__add(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_1155]) ).

fof(c_0_2517,plain,
    ! [X54] :
      ( ~ class_OrderedGroup_Olordered__ab__group(X54)
      | class_HOL_Ominus(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_1156]) ).

fof(c_0_2518,plain,
    ! [X54] :
      ( ~ class_OrderedGroup_Olordered__ab__group(X54)
      | class_LOrder_Omeet__semilorder(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_1157]) ).

fof(c_0_2519,plain,
    ! [X54] :
      ( ~ class_OrderedGroup_Olordered__ab__group(X54)
      | class_LOrder_Ojoin__semilorder(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_1158]) ).

fof(c_0_2520,plain,
    ! [X54] :
      ( ~ class_OrderedGroup_Olordered__ab__group(X54)
      | class_LOrder_Olorder(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_1159]) ).

fof(c_0_2521,plain,
    ! [X54] :
      ( ~ class_OrderedGroup_Olordered__ab__group(X54)
      | class_HOL_Oplus(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_1160]) ).

fof(c_0_2522,plain,
    ! [X54] :
      ( ~ class_OrderedGroup_Olordered__ab__group(X54)
      | class_OrderedGroup_Osemigroup__add(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_1161]) ).

fof(c_0_2523,plain,
    ! [X54] :
      ( ~ class_OrderedGroup_Olordered__ab__group(X54)
      | class_OrderedGroup_Ocancel__semigroup__add(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_1162]) ).

fof(c_0_2524,plain,
    ! [X54] :
      ( ~ class_OrderedGroup_Olordered__ab__group(X54)
      | class_OrderedGroup_Oab__semigroup__add(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_1163]) ).

fof(c_0_2525,plain,
    ! [X54] :
      ( ~ class_OrderedGroup_Olordered__ab__group(X54)
      | class_OrderedGroup_Ocancel__ab__semigroup__add(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_1164]) ).

fof(c_0_2526,plain,
    ! [X54] :
      ( ~ class_OrderedGroup_Olordered__ab__group(X54)
      | class_OrderedGroup_Oab__group__add(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_1165]) ).

fof(c_0_2527,plain,
    ! [X54] :
      ( ~ class_OrderedGroup_Olordered__ab__group(X54)
      | class_OrderedGroup_Opordered__ab__group__add(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_1166]) ).

fof(c_0_2528,plain,
    ! [X54] :
      ( ~ class_OrderedGroup_Ocomm__monoid__mult(X54)
      | class_OrderedGroup_Omonoid__mult(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_1167]) ).

fof(c_0_2529,plain,
    ! [X54] :
      ( ~ class_OrderedGroup_Ocomm__monoid__mult(X54)
      | class_HOL_Otimes(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_1168]) ).

fof(c_0_2530,plain,
    ! [X54] :
      ( ~ class_OrderedGroup_Ocomm__monoid__mult(X54)
      | class_OrderedGroup_Osemigroup__mult(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_1169]) ).

fof(c_0_2531,plain,
    ! [X54] :
      ( ~ class_OrderedGroup_Ocomm__monoid__mult(X54)
      | class_OrderedGroup_Oab__semigroup__mult(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_1170]) ).

fof(c_0_2532,plain,
    ! [X54] :
      ( ~ class_OrderedGroup_Ocomm__monoid__mult(X54)
      | class_HOL_Oone(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_1171]) ).

fof(c_0_2533,plain,
    ! [X54] :
      ( ~ class_OrderedGroup_Ocomm__monoid__add(X54)
      | class_HOL_Oplus(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_1172]) ).

fof(c_0_2534,plain,
    ! [X54] :
      ( ~ class_OrderedGroup_Ocomm__monoid__add(X54)
      | class_OrderedGroup_Osemigroup__add(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_1173]) ).

fof(c_0_2535,plain,
    ! [X54] :
      ( ~ class_OrderedGroup_Ocomm__monoid__add(X54)
      | class_OrderedGroup_Oab__semigroup__add(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_1174]) ).

fof(c_0_2536,plain,
    ! [X54] :
      ( ~ class_OrderedGroup_Ocomm__monoid__add(X54)
      | class_HOL_Ozero(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_1175]) ).

fof(c_0_2537,plain,
    ! [X54] :
      ( ~ class_OrderedGroup_Ocancel__semigroup__add(X54)
      | class_HOL_Oplus(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_1176]) ).

fof(c_0_2538,plain,
    ! [X54] :
      ( ~ class_OrderedGroup_Ocancel__semigroup__add(X54)
      | class_OrderedGroup_Osemigroup__add(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_1177]) ).

fof(c_0_2539,plain,
    ! [X54] :
      ( ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X54)
      | class_OrderedGroup_Ocancel__semigroup__add(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_1178]) ).

fof(c_0_2540,plain,
    ! [X54] :
      ( ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X54)
      | class_HOL_Oplus(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_1179]) ).

fof(c_0_2541,plain,
    ! [X54] :
      ( ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X54)
      | class_OrderedGroup_Osemigroup__add(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_1180]) ).

fof(c_0_2542,plain,
    ! [X54] :
      ( ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X54)
      | class_OrderedGroup_Oab__semigroup__add(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_1181]) ).

fof(c_0_2543,plain,
    ! [X54] :
      ( ~ class_OrderedGroup_Oab__semigroup__mult(X54)
      | class_HOL_Otimes(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_1182]) ).

fof(c_0_2544,plain,
    ! [X54] :
      ( ~ class_OrderedGroup_Oab__semigroup__mult(X54)
      | class_OrderedGroup_Osemigroup__mult(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_1183]) ).

fof(c_0_2545,plain,
    ! [X54] :
      ( ~ class_OrderedGroup_Oab__semigroup__add(X54)
      | class_HOL_Oplus(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_1184]) ).

fof(c_0_2546,plain,
    ! [X54] :
      ( ~ class_OrderedGroup_Oab__semigroup__add(X54)
      | class_OrderedGroup_Osemigroup__add(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_1185]) ).

fof(c_0_2547,plain,
    ! [X54] :
      ( ~ class_OrderedGroup_Oab__group__add(X54)
      | class_OrderedGroup_Ocancel__semigroup__add(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_1186]) ).

fof(c_0_2548,plain,
    ! [X54] :
      ( ~ class_OrderedGroup_Oab__group__add(X54)
      | class_OrderedGroup_Ocancel__ab__semigroup__add(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_1187]) ).

fof(c_0_2549,plain,
    ! [X54] :
      ( ~ class_OrderedGroup_Oab__group__add(X54)
      | class_HOL_Oplus(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_1188]) ).

fof(c_0_2550,plain,
    ! [X54] :
      ( ~ class_OrderedGroup_Oab__group__add(X54)
      | class_OrderedGroup_Osemigroup__add(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_1189]) ).

fof(c_0_2551,plain,
    ! [X54] :
      ( ~ class_OrderedGroup_Oab__group__add(X54)
      | class_OrderedGroup_Oab__semigroup__add(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_1190]) ).

fof(c_0_2552,plain,
    ! [X54] :
      ( ~ class_OrderedGroup_Oab__group__add(X54)
      | class_HOL_Ozero(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_1191]) ).

fof(c_0_2553,plain,
    ! [X54] :
      ( ~ class_OrderedGroup_Oab__group__add(X54)
      | class_OrderedGroup_Ocomm__monoid__add(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_1192]) ).

fof(c_0_2554,plain,
    ! [X54] :
      ( ~ class_OrderedGroup_Oab__group__add(X54)
      | class_HOL_Ominus(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_1193]) ).

fof(c_0_2555,plain,
    ! [X54] :
      ( ~ class_Numeral_Onumber__ring(X54)
      | class_OrderedGroup_Ocomm__monoid__add(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_1194]) ).

fof(c_0_2556,plain,
    ! [X54] :
      ( ~ class_Numeral_Onumber__ring(X54)
      | class_HOL_Ozero(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_1195]) ).

fof(c_0_2557,plain,
    ! [X54] :
      ( ~ class_Numeral_Onumber__ring(X54)
      | class_Ring__and__Field_Ocomm__semiring(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_1196]) ).

fof(c_0_2558,plain,
    ! [X54] :
      ( ~ class_Numeral_Onumber__ring(X54)
      | class_Ring__and__Field_Osemiring(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_1197]) ).

fof(c_0_2559,plain,
    ! [X54] :
      ( ~ class_Numeral_Onumber__ring(X54)
      | class_OrderedGroup_Oab__semigroup__mult(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_1198]) ).

fof(c_0_2560,plain,
    ! [X54] :
      ( ~ class_Numeral_Onumber__ring(X54)
      | class_OrderedGroup_Osemigroup__mult(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_1199]) ).

fof(c_0_2561,plain,
    ! [X54] :
      ( ~ class_Numeral_Onumber__ring(X54)
      | class_Numeral_Onumber(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_1200]) ).

fof(c_0_2562,plain,
    ! [X54] :
      ( ~ class_Numeral_Onumber__ring(X54)
      | class_HOL_Otimes(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_1201]) ).

fof(c_0_2563,plain,
    ! [X54] :
      ( ~ class_Numeral_Onumber__ring(X54)
      | class_Ring__and__Field_Ocomm__ring__1(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_1202]) ).

fof(c_0_2564,plain,
    ! [X54] :
      ( ~ class_Numeral_Onumber__ring(X54)
      | class_Ring__and__Field_Ocomm__semiring__1__cancel(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_1203]) ).

fof(c_0_2565,plain,
    ! [X54] :
      ( ~ class_Numeral_Onumber__ring(X54)
      | class_Ring__and__Field_Oring__1(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_1204]) ).

fof(c_0_2566,plain,
    ! [X54] :
      ( ~ class_Numeral_Onumber__ring(X54)
      | class_Ring__and__Field_Osemiring__1__cancel(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_1205]) ).

fof(c_0_2567,plain,
    ! [X54] :
      ( ~ class_Numeral_Onumber__ring(X54)
      | class_Ring__and__Field_Ocomm__semiring__1(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_1206]) ).

fof(c_0_2568,plain,
    ! [X54] :
      ( ~ class_Numeral_Onumber__ring(X54)
      | class_Ring__and__Field_Osemiring__1(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_1207]) ).

fof(c_0_2569,plain,
    ! [X54] :
      ( ~ class_Numeral_Onumber__ring(X54)
      | class_OrderedGroup_Ocomm__monoid__mult(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_1208]) ).

fof(c_0_2570,plain,
    ! [X54] :
      ( ~ class_Numeral_Onumber__ring(X54)
      | class_OrderedGroup_Omonoid__mult(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_1209]) ).

fof(c_0_2571,plain,
    ! [X54] :
      ( ~ class_Numeral_Onumber__ring(X54)
      | class_Ring__and__Field_Oaxclass__0__neq__1(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_1210]) ).

fof(c_0_2572,plain,
    ! [X54] :
      ( ~ class_Numeral_Onumber__ring(X54)
      | class_HOL_Oone(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_1211]) ).

fof(c_0_2573,plain,
    ! [X54] :
      ( ~ class_Numeral_Onumber__ring(X54)
      | class_OrderedGroup_Oab__semigroup__add(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_1212]) ).

fof(c_0_2574,plain,
    ! [X54] :
      ( ~ class_Numeral_Onumber__ring(X54)
      | class_Ring__and__Field_Ocomm__ring(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_1213]) ).

fof(c_0_2575,plain,
    ! [X54] :
      ( ~ class_Numeral_Onumber__ring(X54)
      | class_Ring__and__Field_Ocomm__semiring__0__cancel(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_1214]) ).

fof(c_0_2576,plain,
    ! [X54] :
      ( ~ class_Numeral_Onumber__ring(X54)
      | class_Ring__and__Field_Oring(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_1215]) ).

fof(c_0_2577,plain,
    ! [X54] :
      ( ~ class_Numeral_Onumber__ring(X54)
      | class_Ring__and__Field_Osemiring__0__cancel(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_1216]) ).

fof(c_0_2578,plain,
    ! [X54] :
      ( ~ class_Numeral_Onumber__ring(X54)
      | class_OrderedGroup_Oab__group__add(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_1217]) ).

fof(c_0_2579,plain,
    ! [X54] :
      ( ~ class_Numeral_Onumber__ring(X54)
      | class_OrderedGroup_Ocancel__ab__semigroup__add(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_1218]) ).

fof(c_0_2580,plain,
    ! [X54] :
      ( ~ class_Numeral_Onumber__ring(X54)
      | class_OrderedGroup_Ocancel__semigroup__add(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_1219]) ).

fof(c_0_2581,plain,
    ! [X54] :
      ( ~ class_Numeral_Onumber__ring(X54)
      | class_HOL_Ominus(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_1220]) ).

fof(c_0_2582,plain,
    ! [X54] :
      ( ~ class_Numeral_Onumber__ring(X54)
      | class_Ring__and__Field_Ocomm__semiring__0(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_1221]) ).

fof(c_0_2583,plain,
    ! [X54] :
      ( ~ class_Numeral_Onumber__ring(X54)
      | class_Ring__and__Field_Osemiring__0(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_1222]) ).

fof(c_0_2584,plain,
    ! [X54] :
      ( ~ class_Numeral_Onumber__ring(X54)
      | class_OrderedGroup_Osemigroup__add(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_1223]) ).

fof(c_0_2585,plain,
    ! [X54] :
      ( ~ class_Numeral_Onumber__ring(X54)
      | class_HOL_Oplus(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_1224]) ).

fof(c_0_2586,plain,
    ! [X54] :
      ( ~ class_LOrder_Omeet__semilorder(X54)
      | class_Orderings_Oorder(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_1225]) ).

fof(c_0_2587,plain,
    ! [X54] :
      ( ~ class_LOrder_Omeet__semilorder(X54)
      | class_Orderings_Oord(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_1226]) ).

fof(c_0_2588,plain,
    ! [X54] :
      ( ~ class_LOrder_Olorder(X54)
      | class_LOrder_Ojoin__semilorder(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_1227]) ).

fof(c_0_2589,plain,
    ! [X54] :
      ( ~ class_LOrder_Olorder(X54)
      | class_Orderings_Oorder(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_1228]) ).

fof(c_0_2590,plain,
    ! [X54] :
      ( ~ class_LOrder_Olorder(X54)
      | class_Orderings_Oord(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_1229]) ).

fof(c_0_2591,plain,
    ! [X54] :
      ( ~ class_LOrder_Olorder(X54)
      | class_LOrder_Omeet__semilorder(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_1230]) ).

fof(c_0_2592,plain,
    ! [X54] :
      ( ~ class_LOrder_Ojoin__semilorder(X54)
      | class_Orderings_Oorder(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_1231]) ).

fof(c_0_2593,plain,
    ! [X54] :
      ( ~ class_LOrder_Ojoin__semilorder(X54)
      | class_Orderings_Oord(X54) ),
    inference(fof_simplification,[status(thm)],[c_0_1232]) ).

fof(c_0_2594,axiom,
    c_Wellfounded__Recursion_Owf(c_Wellfounded__Relations_Oless__than,tc_nat),
    c_0_1233 ).

fof(c_0_2595,axiom,
    c_Relation_Otrans(c_Wellfounded__Relations_Oless__than,tc_nat),
    c_0_1234 ).

fof(c_0_2596,axiom,
    ! [X52] : class_Nat_Opower(tc_set(X52)),
    c_0_1235 ).

fof(c_0_2597,axiom,
    ! [X52] : class_Orderings_Oorder(tc_set(X52)),
    c_0_1236 ).

fof(c_0_2598,axiom,
    ! [X52] : class_Orderings_Oord(tc_set(X52)),
    c_0_1237 ).

fof(c_0_2599,axiom,
    ! [X52] : class_HOL_Ominus(tc_set(X52)),
    c_0_1238 ).

fof(c_0_2600,axiom,
    ! [X13] : c_0 != c_Suc(X13),
    c_0_1239 ).

fof(c_0_2601,axiom,
    ! [X13] : c_Suc(X13) != c_0,
    c_0_1240 ).

fof(c_0_2602,axiom,
    class_HOL_Ominus(tc_nat),
    c_0_1241 ).

fof(c_0_2603,axiom,
    class_Wellfounded__Recursion_Owellorder(tc_nat),
    c_0_1242 ).

fof(c_0_2604,axiom,
    class_Orderings_Olinorder(tc_nat),
    c_0_1243 ).

fof(c_0_2605,axiom,
    class_LOrder_Olorder(tc_nat),
    c_0_1244 ).

fof(c_0_2606,axiom,
    class_LOrder_Ojoin__semilorder(tc_nat),
    c_0_1245 ).

fof(c_0_2607,axiom,
    class_Parity_Oeven__odd(tc_nat),
    c_0_1246 ).

fof(c_0_2608,axiom,
    class_Numeral_Onumber(tc_nat),
    c_0_1247 ).

fof(c_0_2609,axiom,
    class_Power_Orecpower(tc_nat),
    c_0_1248 ).

fof(c_0_2610,axiom,
    class_Divides_Odiv(tc_nat),
    c_0_1249 ).

fof(c_0_2611,axiom,
    class_Ring__and__Field_Oordered__semidom(tc_nat),
    c_0_1250 ).

fof(c_0_2612,axiom,
    class_Ring__and__Field_Oordered__comm__semiring__strict(tc_nat),
    c_0_1251 ).

fof(c_0_2613,axiom,
    class_Ring__and__Field_Opordered__cancel__comm__semiring(tc_nat),
    c_0_1252 ).

fof(c_0_2614,axiom,
    class_Ring__and__Field_Opordered__comm__semiring(tc_nat),
    c_0_1253 ).

fof(c_0_2615,axiom,
    class_LOrder_Omeet__semilorder(tc_nat),
    c_0_1254 ).

fof(c_0_2616,axiom,
    class_Ring__and__Field_Oordered__semiring__strict(tc_nat),
    c_0_1255 ).

fof(c_0_2617,axiom,
    class_Ring__and__Field_Opordered__cancel__semiring(tc_nat),
    c_0_1256 ).

fof(c_0_2618,axiom,
    class_Ring__and__Field_Opordered__semiring(tc_nat),
    c_0_1257 ).

fof(c_0_2619,axiom,
    class_OrderedGroup_Oordered__cancel__ab__semigroup__add(tc_nat),
    c_0_1258 ).

fof(c_0_2620,axiom,
    class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat),
    c_0_1259 ).

fof(c_0_2621,axiom,
    class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat),
    c_0_1260 ).

fof(c_0_2622,axiom,
    class_OrderedGroup_Opordered__ab__semigroup__add(tc_nat),
    c_0_1261 ).

fof(c_0_2623,axiom,
    class_Ring__and__Field_Ocomm__semiring__1__cancel(tc_nat),
    c_0_1262 ).

fof(c_0_2624,axiom,
    class_Ring__and__Field_Ocomm__semiring__0__cancel(tc_nat),
    c_0_1263 ).

fof(c_0_2625,axiom,
    class_Ring__and__Field_Osemiring__1__cancel(tc_nat),
    c_0_1264 ).

fof(c_0_2626,axiom,
    class_Orderings_Oorder(tc_nat),
    c_0_1265 ).

fof(c_0_2627,axiom,
    class_Ring__and__Field_Osemiring__0__cancel(tc_nat),
    c_0_1266 ).

fof(c_0_2628,axiom,
    class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat),
    c_0_1267 ).

fof(c_0_2629,axiom,
    class_OrderedGroup_Ocancel__semigroup__add(tc_nat),
    c_0_1268 ).

fof(c_0_2630,axiom,
    class_Ring__and__Field_Ocomm__semiring__1(tc_nat),
    c_0_1269 ).

fof(c_0_2631,axiom,
    class_Ring__and__Field_Osemiring__1(tc_nat),
    c_0_1270 ).

fof(c_0_2632,axiom,
    class_OrderedGroup_Ocomm__monoid__mult(tc_nat),
    c_0_1271 ).

fof(c_0_2633,axiom,
    class_OrderedGroup_Omonoid__mult(tc_nat),
    c_0_1272 ).

fof(c_0_2634,axiom,
    class_Ring__and__Field_Ocomm__semiring__0(tc_nat),
    c_0_1273 ).

fof(c_0_2635,axiom,
    class_Ring__and__Field_Osemiring__0(tc_nat),
    c_0_1274 ).

fof(c_0_2636,axiom,
    class_OrderedGroup_Ocomm__monoid__add(tc_nat),
    c_0_1275 ).

fof(c_0_2637,axiom,
    class_Orderings_Oord(tc_nat),
    c_0_1276 ).

fof(c_0_2638,axiom,
    class_Ring__and__Field_Ocomm__semiring(tc_nat),
    c_0_1277 ).

fof(c_0_2639,axiom,
    class_Ring__and__Field_Osemiring(tc_nat),
    c_0_1278 ).

fof(c_0_2640,axiom,
    class_OrderedGroup_Oab__semigroup__mult(tc_nat),
    c_0_1279 ).

fof(c_0_2641,axiom,
    class_OrderedGroup_Osemigroup__mult(tc_nat),
    c_0_1280 ).

fof(c_0_2642,axiom,
    class_OrderedGroup_Oab__semigroup__add(tc_nat),
    c_0_1281 ).

fof(c_0_2643,axiom,
    class_OrderedGroup_Osemigroup__add(tc_nat),
    c_0_1282 ).

fof(c_0_2644,axiom,
    class_Ring__and__Field_Oaxclass__0__neq__1(tc_nat),
    c_0_1283 ).

fof(c_0_2645,axiom,
    class_Nat_Opower(tc_nat),
    c_0_1284 ).

fof(c_0_2646,axiom,
    class_HOL_Otimes(tc_nat),
    c_0_1285 ).

fof(c_0_2647,axiom,
    class_HOL_Oplus(tc_nat),
    c_0_1286 ).

fof(c_0_2648,axiom,
    class_HOL_Ozero(tc_nat),
    c_0_1287 ).

fof(c_0_2649,axiom,
    class_HOL_Oone(tc_nat),
    c_0_1288 ).

fof(c_0_2650,axiom,
    class_Finite__Set_Ofinite(tc_bool),
    c_0_1289 ).

fof(c_0_2651,axiom,
    class_Finite__Set_Ofinite(tc_Product__Type_Ounit),
    c_0_1290 ).

fof(c_0_2652,axiom,
    class_OrderedGroup_Oab__semigroup__mult(tc_IntDef_Oint),
    c_0_1291 ).

fof(c_0_2653,axiom,
    class_OrderedGroup_Osemigroup__mult(tc_IntDef_Oint),
    c_0_1292 ).

fof(c_0_2654,axiom,
    class_OrderedGroup_Oab__semigroup__add(tc_IntDef_Oint),
    c_0_1293 ).

fof(c_0_2655,axiom,
    class_Parity_Oeven__odd(tc_IntDef_Oint),
    c_0_1294 ).

fof(c_0_2656,axiom,
    class_Power_Orecpower(tc_IntDef_Oint),
    c_0_1295 ).

fof(c_0_2657,axiom,
    class_Nat_Opower(tc_IntDef_Oint),
    c_0_1296 ).

fof(c_0_2658,axiom,
    class_Divides_Odiv(tc_IntDef_Oint),
    c_0_1297 ).

fof(c_0_2659,axiom,
    class_Numeral_Onumber__ring(tc_IntDef_Oint),
    c_0_1298 ).

fof(c_0_2660,axiom,
    class_OrderedGroup_Osemigroup__add(tc_IntDef_Oint),
    c_0_1299 ).

fof(c_0_2661,axiom,
    class_Numeral_Onumber(tc_IntDef_Oint),
    c_0_1300 ).

fof(c_0_2662,axiom,
    class_Ring__and__Field_Oordered__idom(tc_IntDef_Oint),
    c_0_1301 ).

fof(c_0_2663,axiom,
    class_Ring__and__Field_Oidom(tc_IntDef_Oint),
    c_0_1302 ).

fof(c_0_2664,axiom,
    class_Ring__and__Field_Oordered__semidom(tc_IntDef_Oint),
    c_0_1303 ).

fof(c_0_2665,axiom,
    class_Ring__and__Field_Oordered__ring__strict(tc_IntDef_Oint),
    c_0_1304 ).

fof(c_0_2666,axiom,
    class_Ring__and__Field_Oaxclass__no__zero__divisors(tc_IntDef_Oint),
    c_0_1305 ).

fof(c_0_2667,axiom,
    class_Ring__and__Field_Olordered__ring(tc_IntDef_Oint),
    c_0_1306 ).

fof(c_0_2668,axiom,
    class_OrderedGroup_Olordered__ab__group__join(tc_IntDef_Oint),
    c_0_1307 ).

fof(c_0_2669,axiom,
    class_OrderedGroup_Olordered__ab__group__meet(tc_IntDef_Oint),
    c_0_1308 ).

fof(c_0_2670,axiom,
    class_OrderedGroup_Olordered__ab__group__abs(tc_IntDef_Oint),
    c_0_1309 ).

fof(c_0_2671,axiom,
    class_Orderings_Oord(tc_IntDef_Oint),
    c_0_1310 ).

fof(c_0_2672,axiom,
    class_Ring__and__Field_Opordered__ring(tc_IntDef_Oint),
    c_0_1311 ).

fof(c_0_2673,axiom,
    class_OrderedGroup_Olordered__ab__group(tc_IntDef_Oint),
    c_0_1312 ).

fof(c_0_2674,axiom,
    class_OrderedGroup_Opordered__ab__group__add(tc_IntDef_Oint),
    c_0_1313 ).

fof(c_0_2675,axiom,
    class_Ring__and__Field_Oaxclass__abs__if(tc_IntDef_Oint),
    c_0_1314 ).

fof(c_0_2676,axiom,
    class_Ring__and__Field_Oordered__comm__semiring__strict(tc_IntDef_Oint),
    c_0_1315 ).

fof(c_0_2677,axiom,
    class_Ring__and__Field_Opordered__cancel__comm__semiring(tc_IntDef_Oint),
    c_0_1316 ).

fof(c_0_2678,axiom,
    class_Ring__and__Field_Opordered__comm__semiring(tc_IntDef_Oint),
    c_0_1317 ).

fof(c_0_2679,axiom,
    class_Ring__and__Field_Oordered__semiring__strict(tc_IntDef_Oint),
    c_0_1318 ).

fof(c_0_2680,axiom,
    class_Ring__and__Field_Opordered__cancel__semiring(tc_IntDef_Oint),
    c_0_1319 ).

fof(c_0_2681,axiom,
    class_Ring__and__Field_Opordered__semiring(tc_IntDef_Oint),
    c_0_1320 ).

fof(c_0_2682,axiom,
    class_HOL_Ozero(tc_IntDef_Oint),
    c_0_1321 ).

fof(c_0_2683,axiom,
    class_OrderedGroup_Oordered__cancel__ab__semigroup__add(tc_IntDef_Oint),
    c_0_1322 ).

fof(c_0_2684,axiom,
    class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_IntDef_Oint),
    c_0_1323 ).

fof(c_0_2685,axiom,
    class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_IntDef_Oint),
    c_0_1324 ).

fof(c_0_2686,axiom,
    class_OrderedGroup_Opordered__ab__semigroup__add(tc_IntDef_Oint),
    c_0_1325 ).

fof(c_0_2687,axiom,
    class_Orderings_Olinorder(tc_IntDef_Oint),
    c_0_1326 ).

fof(c_0_2688,axiom,
    class_LOrder_Olorder(tc_IntDef_Oint),
    c_0_1327 ).

fof(c_0_2689,axiom,
    class_LOrder_Ojoin__semilorder(tc_IntDef_Oint),
    c_0_1328 ).

fof(c_0_2690,axiom,
    class_LOrder_Omeet__semilorder(tc_IntDef_Oint),
    c_0_1329 ).

fof(c_0_2691,axiom,
    class_Orderings_Oorder(tc_IntDef_Oint),
    c_0_1330 ).

fof(c_0_2692,axiom,
    class_Ring__and__Field_Ocomm__ring__1(tc_IntDef_Oint),
    c_0_1331 ).

fof(c_0_2693,axiom,
    class_HOL_Otimes(tc_IntDef_Oint),
    c_0_1332 ).

fof(c_0_2694,axiom,
    class_Ring__and__Field_Ocomm__semiring__1__cancel(tc_IntDef_Oint),
    c_0_1333 ).

fof(c_0_2695,axiom,
    class_Ring__and__Field_Oring__1(tc_IntDef_Oint),
    c_0_1334 ).

fof(c_0_2696,axiom,
    class_Ring__and__Field_Osemiring__1__cancel(tc_IntDef_Oint),
    c_0_1335 ).

fof(c_0_2697,axiom,
    class_Ring__and__Field_Ocomm__semiring__1(tc_IntDef_Oint),
    c_0_1336 ).

fof(c_0_2698,axiom,
    class_Ring__and__Field_Osemiring__1(tc_IntDef_Oint),
    c_0_1337 ).

fof(c_0_2699,axiom,
    class_OrderedGroup_Ocomm__monoid__mult(tc_IntDef_Oint),
    c_0_1338 ).

fof(c_0_2700,axiom,
    class_OrderedGroup_Omonoid__mult(tc_IntDef_Oint),
    c_0_1339 ).

fof(c_0_2701,axiom,
    class_Ring__and__Field_Oaxclass__0__neq__1(tc_IntDef_Oint),
    c_0_1340 ).

fof(c_0_2702,axiom,
    class_Ring__and__Field_Ocomm__ring(tc_IntDef_Oint),
    c_0_1341 ).

fof(c_0_2703,axiom,
    class_Ring__and__Field_Ocomm__semiring__0__cancel(tc_IntDef_Oint),
    c_0_1342 ).

fof(c_0_2704,axiom,
    class_HOL_Oplus(tc_IntDef_Oint),
    c_0_1343 ).

fof(c_0_2705,axiom,
    class_Ring__and__Field_Oring(tc_IntDef_Oint),
    c_0_1344 ).

fof(c_0_2706,axiom,
    class_Ring__and__Field_Osemiring__0__cancel(tc_IntDef_Oint),
    c_0_1345 ).

fof(c_0_2707,axiom,
    class_OrderedGroup_Oab__group__add(tc_IntDef_Oint),
    c_0_1346 ).

fof(c_0_2708,axiom,
    class_OrderedGroup_Ocancel__ab__semigroup__add(tc_IntDef_Oint),
    c_0_1347 ).

fof(c_0_2709,axiom,
    class_OrderedGroup_Ocancel__semigroup__add(tc_IntDef_Oint),
    c_0_1348 ).

fof(c_0_2710,axiom,
    class_Ring__and__Field_Ocomm__semiring__0(tc_IntDef_Oint),
    c_0_1349 ).

fof(c_0_2711,axiom,
    class_Ring__and__Field_Osemiring__0(tc_IntDef_Oint),
    c_0_1350 ).

fof(c_0_2712,axiom,
    class_OrderedGroup_Ocomm__monoid__add(tc_IntDef_Oint),
    c_0_1351 ).

fof(c_0_2713,axiom,
    class_Ring__and__Field_Ocomm__semiring(tc_IntDef_Oint),
    c_0_1352 ).

fof(c_0_2714,axiom,
    class_Ring__and__Field_Osemiring(tc_IntDef_Oint),
    c_0_1353 ).

fof(c_0_2715,axiom,
    class_HOL_Oone(tc_IntDef_Oint),
    c_0_1354 ).

fof(c_0_2716,axiom,
    class_HOL_Ominus(tc_IntDef_Oint),
    c_0_1355 ).

fof(c_0_2717,axiom,
    c_UNIV != c_emptyset,
    c_0_1356 ).

fof(c_0_2718,axiom,
    c_Numeral_Obit_OB1 != c_Numeral_Obit_OB0,
    c_0_1357 ).

fof(c_0_2719,axiom,
    c_Numeral_Obit_OB0 != c_Numeral_Obit_OB1,
    c_0_1358 ).

fof(c_0_2720,axiom,
    c_Extraction_Osumbool_ORight != c_Extraction_Osumbool_OLeft,
    c_0_1359 ).

fof(c_0_2721,axiom,
    c_Extraction_Osumbool_OLeft != c_Extraction_Osumbool_ORight,
    c_0_1360 ).

fof(c_0_2722,plain,
    ! [X48,X49,X50,X51,X52,X53] :
      ( ~ c_in(X48,c_Relation_Orel__comp(X50,X49,X51,X52,X53),tc_prod(X53,X52))
      | c_in(c_Pair(c_Main_Orel__compE__1(X50,X49,X48,X51,X52,X53),c_Main_Orel__compE__2(X50,X49,X48,X51,X52,X53),X53,X51),X49,tc_prod(X53,X51)) ),
    inference(variable_rename,[status(thm)],[c_0_1361]) ).

fof(c_0_2723,plain,
    ! [X48,X49,X50,X51,X52,X53] :
      ( ~ c_in(X48,c_Relation_Orel__comp(X50,X49,X51,X52,X53),tc_prod(X53,X52))
      | c_in(c_Pair(c_Main_Orel__compE__2(X50,X49,X48,X51,X52,X53),c_Main_Orel__compE__3(X50,X49,X48,X51,X52,X53),X51,X52),X50,tc_prod(X51,X52)) ),
    inference(variable_rename,[status(thm)],[c_0_1362]) ).

fof(c_0_2724,plain,
    ! [X48,X49,X50,X51,X52,X53] :
      ( ~ c_in(X48,c_Relation_Orel__comp(X50,X49,X51,X52,X53),tc_prod(X53,X52))
      | X48 = c_Pair(c_Main_Orel__compE__1(X50,X49,X48,X51,X52,X53),c_Main_Orel__compE__3(X50,X49,X48,X51,X52,X53),X53,X52) ),
    inference(variable_rename,[status(thm)],[c_0_1363]) ).

fof(c_0_2725,plain,
    ! [X39,X40,X41,X42,X43] :
      ( ~ c_in(X41,c_Datatype__Universe_Odprod(X40,X39,X43,X42),tc_prod(tc_set(tc_Datatype__Universe_Onode(X43,X42)),tc_set(tc_Datatype__Universe_Onode(X43,X42))))
      | X41 = c_Pair(c_Datatype__Universe_OScons(c_Main_OdprodE__1(X41,X40,X39,X43,X42),c_Main_OdprodE__2(X41,X40,X39,X43,X42),X43,X42),c_Datatype__Universe_OScons(c_Main_OdprodE__3(X41,X40,X39,X43,X42),c_Main_OdprodE__4(X41,X40,X39,X43,X42),X43,X42),tc_set(tc_Datatype__Universe_Onode(X43,X42)),tc_set(tc_Datatype__Universe_Onode(X43,X42))) ),
    inference(variable_rename,[status(thm)],[c_0_1364]) ).

fof(c_0_2726,plain,
    ! [X39,X40,X41,X42,X43] :
      ( ~ c_in(X41,c_Datatype__Universe_Odprod(X40,X39,X43,X42),tc_prod(tc_set(tc_Datatype__Universe_Onode(X43,X42)),tc_set(tc_Datatype__Universe_Onode(X43,X42))))
      | c_in(c_Pair(c_Main_OdprodE__1(X41,X40,X39,X43,X42),c_Main_OdprodE__3(X41,X40,X39,X43,X42),tc_set(tc_Datatype__Universe_Onode(X43,X42)),tc_set(tc_Datatype__Universe_Onode(X43,X42))),X40,tc_prod(tc_set(tc_Datatype__Universe_Onode(X43,X42)),tc_set(tc_Datatype__Universe_Onode(X43,X42)))) ),
    inference(variable_rename,[status(thm)],[c_0_1365]) ).

fof(c_0_2727,plain,
    ! [X39,X40,X41,X42,X43] :
      ( ~ c_in(X41,c_Datatype__Universe_Odprod(X40,X39,X43,X42),tc_prod(tc_set(tc_Datatype__Universe_Onode(X43,X42)),tc_set(tc_Datatype__Universe_Onode(X43,X42))))
      | c_in(c_Pair(c_Main_OdprodE__2(X41,X40,X39,X43,X42),c_Main_OdprodE__4(X41,X40,X39,X43,X42),tc_set(tc_Datatype__Universe_Onode(X43,X42)),tc_set(tc_Datatype__Universe_Onode(X43,X42))),X39,tc_prod(tc_set(tc_Datatype__Universe_Onode(X43,X42)),tc_set(tc_Datatype__Universe_Onode(X43,X42)))) ),
    inference(variable_rename,[status(thm)],[c_0_1366]) ).

fof(c_0_2728,plain,
    ! [X39,X40,X41,X42,X43] :
      ( ~ c_in(X39,c_Datatype__Universe_Odsum(X41,X40,X43,X42),tc_prod(tc_set(tc_Datatype__Universe_Onode(X43,X42)),tc_set(tc_Datatype__Universe_Onode(X43,X42))))
      | c_in(c_Pair(c_Main_OdsumE__1(X41,X39,X43,X42),c_Main_OdsumE__2(X41,X39,X43,X42),tc_set(tc_Datatype__Universe_Onode(X43,X42)),tc_set(tc_Datatype__Universe_Onode(X43,X42))),X41,tc_prod(tc_set(tc_Datatype__Universe_Onode(X43,X42)),tc_set(tc_Datatype__Universe_Onode(X43,X42))))
      | c_in(c_Pair(c_Main_OdsumE__3(X40,X39,X43,X42),c_Main_OdsumE__4(X40,X39,X43,X42),tc_set(tc_Datatype__Universe_Onode(X43,X42)),tc_set(tc_Datatype__Universe_Onode(X43,X42))),X40,tc_prod(tc_set(tc_Datatype__Universe_Onode(X43,X42)),tc_set(tc_Datatype__Universe_Onode(X43,X42)))) ),
    inference(variable_rename,[status(thm)],[c_0_1367]) ).

fof(c_0_2729,plain,
    ! [X39,X40,X41,X42,X43] :
      ( ~ c_in(X39,c_Datatype__Universe_Odsum(X41,X40,X43,X42),tc_prod(tc_set(tc_Datatype__Universe_Onode(X43,X42)),tc_set(tc_Datatype__Universe_Onode(X43,X42))))
      | c_in(c_Pair(c_Main_OdsumE__1(X41,X39,X43,X42),c_Main_OdsumE__2(X41,X39,X43,X42),tc_set(tc_Datatype__Universe_Onode(X43,X42)),tc_set(tc_Datatype__Universe_Onode(X43,X42))),X41,tc_prod(tc_set(tc_Datatype__Universe_Onode(X43,X42)),tc_set(tc_Datatype__Universe_Onode(X43,X42))))
      | X39 = c_Pair(c_Datatype__Universe_OIn1(c_Main_OdsumE__3(X40,X39,X43,X42),X43,X42),c_Datatype__Universe_OIn1(c_Main_OdsumE__4(X40,X39,X43,X42),X43,X42),tc_set(tc_Datatype__Universe_Onode(X43,X42)),tc_set(tc_Datatype__Universe_Onode(X43,X42))) ),
    inference(variable_rename,[status(thm)],[c_0_1368]) ).

fof(c_0_2730,plain,
    ! [X39,X40,X41,X42,X43] :
      ( ~ c_in(X39,c_Datatype__Universe_Odsum(X41,X40,X43,X42),tc_prod(tc_set(tc_Datatype__Universe_Onode(X43,X42)),tc_set(tc_Datatype__Universe_Onode(X43,X42))))
      | c_in(c_Pair(c_Main_OdsumE__3(X40,X39,X43,X42),c_Main_OdsumE__4(X40,X39,X43,X42),tc_set(tc_Datatype__Universe_Onode(X43,X42)),tc_set(tc_Datatype__Universe_Onode(X43,X42))),X40,tc_prod(tc_set(tc_Datatype__Universe_Onode(X43,X42)),tc_set(tc_Datatype__Universe_Onode(X43,X42))))
      | X39 = c_Pair(c_Datatype__Universe_OIn0(c_Main_OdsumE__1(X41,X39,X43,X42),X43,X42),c_Datatype__Universe_OIn0(c_Main_OdsumE__2(X41,X39,X43,X42),X43,X42),tc_set(tc_Datatype__Universe_Onode(X43,X42)),tc_set(tc_Datatype__Universe_Onode(X43,X42))) ),
    inference(variable_rename,[status(thm)],[c_0_1369]) ).

fof(c_0_2731,plain,
    ! [X25,X26,X27,X28,X29] :
      ( ~ c_in(c_Pair(X27,c_List_Olist_OCons(X26,X25,X29),tc_List_Olist(X29),tc_List_Olist(X29)),c_List_Olistrel(X28,X29),tc_prod(tc_List_Olist(X29),tc_List_Olist(X29)))
      | c_in(c_Pair(c_Main_Olistrel__Cons2__2(X28,X27,X26,X25,X29),X25,tc_List_Olist(X29),tc_List_Olist(X29)),c_List_Olistrel(X28,X29),tc_prod(tc_List_Olist(X29),tc_List_Olist(X29))) ),
    inference(variable_rename,[status(thm)],[c_0_1370]) ).

fof(c_0_2732,plain,
    ! [X25,X26,X27,X28,X29] :
      ( ~ c_in(c_Pair(c_List_Olist_OCons(X26,X25,X29),X27,tc_List_Olist(X29),tc_List_Olist(X29)),c_List_Olistrel(X28,X29),tc_prod(tc_List_Olist(X29),tc_List_Olist(X29)))
      | c_in(c_Pair(X25,c_Main_Olistrel__Cons1__2(X28,X27,X26,X25,X29),tc_List_Olist(X29),tc_List_Olist(X29)),c_List_Olistrel(X28,X29),tc_prod(tc_List_Olist(X29),tc_List_Olist(X29))) ),
    inference(variable_rename,[status(thm)],[c_0_1371]) ).

fof(c_0_2733,plain,
    ! [X39,X40,X41,X42,X43,X44,X45,X46] :
      ( ~ c_in(c_Pair(X42,X41,tc_set(tc_Datatype__Universe_Onode(X46,X45)),tc_set(tc_Datatype__Universe_Onode(X46,X45))),X39,tc_prod(tc_set(tc_Datatype__Universe_Onode(X46,X45)),tc_set(tc_Datatype__Universe_Onode(X46,X45))))
      | ~ c_in(c_Pair(X44,X43,tc_set(tc_Datatype__Universe_Onode(X46,X45)),tc_set(tc_Datatype__Universe_Onode(X46,X45))),X40,tc_prod(tc_set(tc_Datatype__Universe_Onode(X46,X45)),tc_set(tc_Datatype__Universe_Onode(X46,X45))))
      | c_in(c_Pair(c_Datatype__Universe_OScons(X44,X42,X46,X45),c_Datatype__Universe_OScons(X43,X41,X46,X45),tc_set(tc_Datatype__Universe_Onode(X46,X45)),tc_set(tc_Datatype__Universe_Onode(X46,X45))),c_Datatype__Universe_Odprod(X40,X39,X46,X45),tc_prod(tc_set(tc_Datatype__Universe_Onode(X46,X45)),tc_set(tc_Datatype__Universe_Onode(X46,X45)))) ),
    inference(variable_rename,[status(thm)],[c_0_1372]) ).

fof(c_0_2734,plain,
    ! [X25,X26,X27,X28,X29] :
      ( ~ c_in(c_Pair(X27,c_List_Olist_OCons(X26,X25,X29),tc_List_Olist(X29),tc_List_Olist(X29)),c_List_Olistrel(X28,X29),tc_prod(tc_List_Olist(X29),tc_List_Olist(X29)))
      | c_in(c_Pair(c_Main_Olistrel__Cons2__1(X28,X27,X26,X25,X29),X26,X29,X29),X28,tc_prod(X29,X29)) ),
    inference(variable_rename,[status(thm)],[c_0_1373]) ).

fof(c_0_2735,plain,
    ! [X25,X26,X27,X28,X29] :
      ( ~ c_in(c_Pair(c_List_Olist_OCons(X26,X25,X29),X27,tc_List_Olist(X29),tc_List_Olist(X29)),c_List_Olistrel(X28,X29),tc_prod(tc_List_Olist(X29),tc_List_Olist(X29)))
      | c_in(c_Pair(X26,c_Main_Olistrel__Cons1__1(X28,X27,X26,X25,X29),X29,X29),X28,tc_prod(X29,X29)) ),
    inference(variable_rename,[status(thm)],[c_0_1374]) ).

fof(c_0_2736,plain,
    ! [X39,X40,X41,X42,X43] :
      ( ~ c_in(X39,c_Datatype__Universe_Odsum(X41,X40,X43,X42),tc_prod(tc_set(tc_Datatype__Universe_Onode(X43,X42)),tc_set(tc_Datatype__Universe_Onode(X43,X42))))
      | X39 = c_Pair(c_Datatype__Universe_OIn0(c_Main_OdsumE__1(X41,X39,X43,X42),X43,X42),c_Datatype__Universe_OIn0(c_Main_OdsumE__2(X41,X39,X43,X42),X43,X42),tc_set(tc_Datatype__Universe_Onode(X43,X42)),tc_set(tc_Datatype__Universe_Onode(X43,X42)))
      | X39 = c_Pair(c_Datatype__Universe_OIn1(c_Main_OdsumE__3(X40,X39,X43,X42),X43,X42),c_Datatype__Universe_OIn1(c_Main_OdsumE__4(X40,X39,X43,X42),X43,X42),tc_set(tc_Datatype__Universe_Onode(X43,X42)),tc_set(tc_Datatype__Universe_Onode(X43,X42))) ),
    inference(variable_rename,[status(thm)],[c_0_1375]) ).

fof(c_0_2737,plain,
    ! [X16,X17,X18,X19,X20] :
      ( ~ c_in(X17,c_Relation_OImage(X16,X18,X19,X20),X20)
      | c_in(c_Pair(c_Main_OImageE__1(X18,X17,X16,X19,X20),X17,X19,X20),X16,tc_prod(X19,X20)) ),
    inference(variable_rename,[status(thm)],[c_0_1376]) ).

fof(c_0_2738,plain,
    ! [X25,X26,X27,X28,X29] :
      ( ~ c_in(c_Pair(X27,c_List_Olist_OCons(X26,X25,X29),tc_List_Olist(X29),tc_List_Olist(X29)),c_List_Olistrel(X28,X29),tc_prod(tc_List_Olist(X29),tc_List_Olist(X29)))
      | X27 = c_List_Olist_OCons(c_Main_Olistrel__Cons2__1(X28,X27,X26,X25,X29),c_Main_Olistrel__Cons2__2(X28,X27,X26,X25,X29),X29) ),
    inference(variable_rename,[status(thm)],[c_0_1377]) ).

fof(c_0_2739,plain,
    ! [X25,X26,X27,X28,X29] :
      ( ~ c_in(c_Pair(c_List_Olist_OCons(X26,X25,X29),X27,tc_List_Olist(X29),tc_List_Olist(X29)),c_List_Olistrel(X28,X29),tc_prod(tc_List_Olist(X29),tc_List_Olist(X29)))
      | X27 = c_List_Olist_OCons(c_Main_Olistrel__Cons1__1(X28,X27,X26,X25,X29),c_Main_Olistrel__Cons1__2(X28,X27,X26,X25,X29),X29) ),
    inference(variable_rename,[status(thm)],[c_0_1378]) ).

fof(c_0_2740,plain,
    ! [X36,X37,X38,X39,X40] :
      ( ~ c_in(X36,c_Datatype__Universe_Ouprod(X38,X37,X40,X39),tc_set(tc_Datatype__Universe_Onode(X40,X39)))
      | X36 = c_Datatype__Universe_OScons(c_Main_OuprodE__1(X38,X37,X36,X40,X39),c_Main_OuprodE__2(X38,X37,X36,X40,X39),X40,X39) ),
    inference(variable_rename,[status(thm)],[c_0_1379]) ).

fof(c_0_2741,plain,
    ! [X48,X49,X50,X51,X52,X53,X54,X55] :
      ( ~ c_in(c_Pair(X51,X50,X54,X53),X49,tc_prod(X54,X53))
      | ~ c_in(c_Pair(X52,X51,X55,X54),X48,tc_prod(X55,X54))
      | c_in(c_Pair(X52,X50,X55,X53),c_Relation_Orel__comp(X49,X48,X54,X53,X55),tc_prod(X55,X53)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1380])])]) ).

fof(c_0_2742,plain,
    ! [X39,X40,X41,X42,X43,X44] :
      ( ~ c_in(c_Pair(X42,X41,tc_set(tc_Datatype__Universe_Onode(X44,X43)),tc_set(tc_Datatype__Universe_Onode(X44,X43))),X39,tc_prod(tc_set(tc_Datatype__Universe_Onode(X44,X43)),tc_set(tc_Datatype__Universe_Onode(X44,X43))))
      | c_in(c_Pair(c_Datatype__Universe_OIn1(X42,X44,X43),c_Datatype__Universe_OIn1(X41,X44,X43),tc_set(tc_Datatype__Universe_Onode(X44,X43)),tc_set(tc_Datatype__Universe_Onode(X44,X43))),c_Datatype__Universe_Odsum(X40,X39,X44,X43),tc_prod(tc_set(tc_Datatype__Universe_Onode(X44,X43)),tc_set(tc_Datatype__Universe_Onode(X44,X43)))) ),
    inference(variable_rename,[status(thm)],[c_0_1381]) ).

fof(c_0_2743,plain,
    ! [X39,X40,X41,X42,X43,X44] :
      ( ~ c_in(c_Pair(X42,X41,tc_set(tc_Datatype__Universe_Onode(X44,X43)),tc_set(tc_Datatype__Universe_Onode(X44,X43))),X40,tc_prod(tc_set(tc_Datatype__Universe_Onode(X44,X43)),tc_set(tc_Datatype__Universe_Onode(X44,X43))))
      | c_in(c_Pair(c_Datatype__Universe_OIn0(X42,X44,X43),c_Datatype__Universe_OIn0(X41,X44,X43),tc_set(tc_Datatype__Universe_Onode(X44,X43)),tc_set(tc_Datatype__Universe_Onode(X44,X43))),c_Datatype__Universe_Odsum(X40,X39,X44,X43),tc_prod(tc_set(tc_Datatype__Universe_Onode(X44,X43)),tc_set(tc_Datatype__Universe_Onode(X44,X43)))) ),
    inference(variable_rename,[status(thm)],[c_0_1382]) ).

fof(c_0_2744,plain,
    ! [X36,X37,X38,X39,X40] :
      ( ~ c_in(X36,c_Datatype__Universe_Ouprod(X38,X37,X40,X39),tc_set(tc_Datatype__Universe_Onode(X40,X39)))
      | c_in(c_Main_OuprodE__1(X38,X37,X36,X40,X39),X38,tc_set(tc_Datatype__Universe_Onode(X40,X39))) ),
    inference(variable_rename,[status(thm)],[c_0_1383]) ).

fof(c_0_2745,plain,
    ! [X36,X37,X38,X39,X40] :
      ( ~ c_in(X36,c_Datatype__Universe_Ouprod(X38,X37,X40,X39),tc_set(tc_Datatype__Universe_Onode(X40,X39)))
      | c_in(c_Main_OuprodE__2(X38,X37,X36,X40,X39),X37,tc_set(tc_Datatype__Universe_Onode(X40,X39))) ),
    inference(variable_rename,[status(thm)],[c_0_1384]) ).

fof(c_0_2746,plain,
    ! [X16,X17,X18,X19,X20] :
      ( ~ c_in(X17,c_Relation_OImage(X16,X18,X19,X20),X20)
      | c_in(c_Main_OImageE__1(X18,X17,X16,X19,X20),X18,X19) ),
    inference(variable_rename,[status(thm)],[c_0_1385]) ).

fof(c_0_2747,plain,
    ! [X46,X47,X48,X49] :
      ( ~ c_in(X46,c_Relation_Oconverse(X47,X48,X49),tc_prod(X49,X48))
      | c_in(c_Pair(c_Main_OconverseE__1(X47,X46,X48,X49),c_Main_OconverseE__2(X47,X46,X48,X49),X48,X49),X47,tc_prod(X48,X49)) ),
    inference(variable_rename,[status(thm)],[c_0_1386]) ).

fof(c_0_2748,plain,
    ! [X25,X26,X27,X28] :
      ( ~ c_Wellfounded__Recursion_Owf(c_insert(c_Pair(X25,X26,X28,X28),X27,tc_prod(X28,X28)),X28)
      | ~ c_in(c_Pair(X26,X25,X28,X28),c_Transitive__Closure_Ortrancl(X27,X28),tc_prod(X28,X28)) ),
    inference(variable_rename,[status(thm)],[c_0_1387]) ).

fof(c_0_2749,plain,
    ! [X25,X26,X27,X28] :
      ( ~ c_Wellfounded__Recursion_Oacyclic(c_insert(c_Pair(X25,X26,X28,X28),X27,tc_prod(X28,X28)),X28)
      | ~ c_in(c_Pair(X26,X25,X28,X28),c_Transitive__Closure_Ortrancl(X27,X28),tc_prod(X28,X28)) ),
    inference(variable_rename,[status(thm)],[c_0_1388]) ).

fof(c_0_2750,plain,
    ! [X40,X41,X42,X43,X44] :
      ( ~ c_in(X40,c_Datatype__Universe_Ousum(X42,X41,X44,X43),tc_set(tc_Datatype__Universe_Onode(X44,X43)))
      | c_in(c_Main_OusumE__1(X42,X40,X44,X43),X42,tc_set(tc_Datatype__Universe_Onode(X44,X43)))
      | c_in(c_Main_OusumE__2(X41,X40,X44,X43),X41,tc_set(tc_Datatype__Universe_Onode(X44,X43))) ),
    inference(variable_rename,[status(thm)],[c_0_1389]) ).

fof(c_0_2751,plain,
    ! [X40,X41,X42,X43,X44] :
      ( ~ c_in(X40,c_Datatype__Universe_Ousum(X42,X41,X44,X43),tc_set(tc_Datatype__Universe_Onode(X44,X43)))
      | c_in(c_Main_OusumE__1(X42,X40,X44,X43),X42,tc_set(tc_Datatype__Universe_Onode(X44,X43)))
      | X40 = c_Datatype__Universe_OIn1(c_Main_OusumE__2(X41,X40,X44,X43),X44,X43) ),
    inference(variable_rename,[status(thm)],[c_0_1390]) ).

fof(c_0_2752,plain,
    ! [X40,X41,X42,X43,X44] :
      ( ~ c_in(X40,c_Datatype__Universe_Ousum(X42,X41,X44,X43),tc_set(tc_Datatype__Universe_Onode(X44,X43)))
      | c_in(c_Main_OusumE__2(X41,X40,X44,X43),X41,tc_set(tc_Datatype__Universe_Onode(X44,X43)))
      | X40 = c_Datatype__Universe_OIn0(c_Main_OusumE__1(X42,X40,X44,X43),X44,X43) ),
    inference(variable_rename,[status(thm)],[c_0_1391]) ).

fof(c_0_2753,plain,
    ! [X40,X41,X42,X43,X44] :
      ( ~ c_in(X40,c_Datatype__Universe_Ousum(X42,X41,X44,X43),tc_set(tc_Datatype__Universe_Onode(X44,X43)))
      | X40 = c_Datatype__Universe_OIn0(c_Main_OusumE__1(X42,X40,X44,X43),X44,X43)
      | X40 = c_Datatype__Universe_OIn1(c_Main_OusumE__2(X41,X40,X44,X43),X44,X43) ),
    inference(variable_rename,[status(thm)],[c_0_1392]) ).

fof(c_0_2754,plain,
    ! [X40,X41,X42,X43,X44] :
      ( ~ c_in(X40,c_Sum__Type_OPlus(X42,X41,X44,X43),tc_sum(X44,X43))
      | X40 = c_Sum__Type_OInl(c_Main_OPlusE__1(X42,X40,X44,X43),X44,X43)
      | X40 = c_Sum__Type_OInr(c_Main_OPlusE__2(X41,X40,X43,X44),X43,X44) ),
    inference(variable_rename,[status(thm)],[c_0_1393]) ).

fof(c_0_2755,plain,
    ! [X40,X41,X42,X43,X44] :
      ( ~ c_in(X40,c_Sum__Type_OPlus(X42,X41,X44,X43),tc_sum(X44,X43))
      | c_in(c_Main_OPlusE__1(X42,X40,X44,X43),X42,X44)
      | X40 = c_Sum__Type_OInr(c_Main_OPlusE__2(X41,X40,X43,X44),X43,X44) ),
    inference(variable_rename,[status(thm)],[c_0_1394]) ).

fof(c_0_2756,plain,
    ! [X40,X41,X42,X43,X44] :
      ( ~ c_in(X40,c_Sum__Type_OPlus(X42,X41,X44,X43),tc_sum(X44,X43))
      | c_in(c_Main_OPlusE__2(X41,X40,X43,X44),X41,X43)
      | X40 = c_Sum__Type_OInl(c_Main_OPlusE__1(X42,X40,X44,X43),X44,X43) ),
    inference(variable_rename,[status(thm)],[c_0_1395]) ).

fof(c_0_2757,plain,
    ! [X40,X41,X42,X43,X44] :
      ( ~ c_in(X40,c_Sum__Type_OPlus(X42,X41,X44,X43),tc_sum(X44,X43))
      | c_in(c_Main_OPlusE__1(X42,X40,X44,X43),X42,X44)
      | c_in(c_Main_OPlusE__2(X41,X40,X43,X44),X41,X43) ),
    inference(variable_rename,[status(thm)],[c_0_1396]) ).

fof(c_0_2758,plain,
    ! [X25,X26,X27,X28] :
      ( ~ c_Wellfounded__Recursion_Owf(c_insert(c_Pair(X25,X26,X28,X28),X27,tc_prod(X28,X28)),X28)
      | c_Wellfounded__Recursion_Owf(X27,X28) ),
    inference(variable_rename,[status(thm)],[c_0_1397]) ).

fof(c_0_2759,plain,
    ! [X25,X26,X27,X28] :
      ( ~ c_Wellfounded__Recursion_Oacyclic(c_insert(c_Pair(X25,X26,X28,X28),X27,tc_prod(X28,X28)),X28)
      | c_Wellfounded__Recursion_Oacyclic(X27,X28) ),
    inference(variable_rename,[status(thm)],[c_0_1398]) ).

fof(c_0_2760,plain,
    ! [X15,X16,X17,X18] :
      ( ~ c_in(X16,c_Relation_ORange(X15,X17,X18),X18)
      | c_in(c_Pair(c_Main_ORangeE__1(X16,X15,X18,X17),X16,X17,X18),X15,tc_prod(X17,X18)) ),
    inference(variable_rename,[status(thm)],[c_0_1399]) ).

fof(c_0_2761,plain,
    ! [X15,X16,X17,X18] :
      ( ~ c_in(X16,c_Relation_ODomain(X15,X18,X17),X18)
      | c_in(c_Pair(X16,c_Main_ODomainE__1(X16,X15,X18,X17),X18,X17),X15,tc_prod(X18,X17)) ),
    inference(variable_rename,[status(thm)],[c_0_1400]) ).

fof(c_0_2762,plain,
    ! [X25,X26,X27,X28] :
      ( ~ c_Wellfounded__Recursion_Owf(X27,X28)
      | c_Wellfounded__Recursion_Owf(c_insert(c_Pair(X25,X26,X28,X28),X27,tc_prod(X28,X28)),X28)
      | c_in(c_Pair(X26,X25,X28,X28),c_Transitive__Closure_Ortrancl(X27,X28),tc_prod(X28,X28)) ),
    inference(variable_rename,[status(thm)],[c_0_1401]) ).

fof(c_0_2763,plain,
    ! [X25,X26,X27,X28] :
      ( ~ c_Wellfounded__Recursion_Oacyclic(X27,X28)
      | c_Wellfounded__Recursion_Oacyclic(c_insert(c_Pair(X25,X26,X28,X28),X27,tc_prod(X28,X28)),X28)
      | c_in(c_Pair(X26,X25,X28,X28),c_Transitive__Closure_Ortrancl(X27,X28),tc_prod(X28,X28)) ),
    inference(variable_rename,[status(thm)],[c_0_1402]) ).

fof(c_0_2764,plain,
    ! [X15,X16,X17,X18,X19] :
      ( ~ c_in(X16,c_Relation_OImage(X15,c_insert(X17,c_emptyset,X18),X18,X19),X19)
      | c_in(c_Pair(X17,X16,X18,X19),X15,tc_prod(X18,X19)) ),
    inference(variable_rename,[status(thm)],[c_0_1403]) ).

fof(c_0_2765,plain,
    ! [X20,X21,X22] :
      ( ~ c_Divides_Oop_Advd(X22,c_GCD_Ogcd(c_Pair(X21,X20,tc_nat,tc_nat)),tc_nat)
      | c_Divides_Oop_Advd(X22,X20,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_1404]) ).

fof(c_0_2766,plain,
    ! [X20,X21,X22] :
      ( ~ c_Divides_Oop_Advd(X22,c_GCD_Ogcd(c_Pair(X21,X20,tc_nat,tc_nat)),tc_nat)
      | c_Divides_Oop_Advd(X22,X21,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_1405]) ).

fof(c_0_2767,plain,
    ! [X15,X16,X17,X18,X19] :
      ( ~ c_in(c_Pair(X17,X16,X18,X19),X15,tc_prod(X18,X19))
      | c_in(X16,c_Relation_OImage(X15,c_insert(X17,c_emptyset,X18),X18,X19),X19) ),
    inference(variable_rename,[status(thm)],[c_0_1406]) ).

fof(c_0_2768,plain,
    ! [X15,X16,X17,X18,X19] :
      ( ~ c_in(c_Pair(X17,X16,X19,X18),c_Relation_Oconverse(X15,X18,X19),tc_prod(X19,X18))
      | c_in(c_Pair(X16,X17,X18,X19),X15,tc_prod(X18,X19)) ),
    inference(variable_rename,[status(thm)],[c_0_1407]) ).

fof(c_0_2769,plain,
    ! [X15,X16,X17,X18,X19] :
      ( ~ c_in(c_Pair(X16,X17,X18,X19),X15,tc_prod(X18,X19))
      | c_in(c_Pair(X17,X16,X19,X18),c_Relation_Oconverse(X15,X18,X19),tc_prod(X19,X18)) ),
    inference(variable_rename,[status(thm)],[c_0_1408]) ).

fof(c_0_2770,plain,
    ! [X15,X16,X17,X18] :
      ( ~ c_in(c_Pair(X17,X16,X18,X18),c_Transitive__Closure_Otrancl(X15,X18),tc_prod(X18,X18))
      | c_in(c_Pair(X17,X16,X18,X18),c_Transitive__Closure_Ortrancl(X15,X18),tc_prod(X18,X18)) ),
    inference(variable_rename,[status(thm)],[c_0_1409]) ).

fof(c_0_2771,plain,
    ! [X16,X17,X18,X19,X20,X21] :
      ( ~ c_in(X18,X19,X21)
      | ~ c_in(c_Pair(X18,X17,X21,X20),X16,tc_prod(X21,X20))
      | c_in(X17,c_Relation_OImage(X16,X19,X21,X20),X20) ),
    inference(variable_rename,[status(thm)],[c_0_1410]) ).

fof(c_0_2772,plain,
    ! [X46,X47,X48,X49] :
      ( ~ c_in(X46,c_Relation_Oconverse(X47,X48,X49),tc_prod(X49,X48))
      | X46 = c_Pair(c_Main_OconverseE__2(X47,X46,X48,X49),c_Main_OconverseE__1(X47,X46,X48,X49),X49,X48) ),
    inference(variable_rename,[status(thm)],[c_0_1411]) ).

fof(c_0_2773,plain,
    ! [X15,X16,X17,X18] :
      ( ~ c_in(c_Pair(X17,X16,X18,X18),X15,tc_prod(X18,X18))
      | c_in(c_Pair(X17,X16,X18,X18),c_Transitive__Closure_Otrancl(X15,X18),tc_prod(X18,X18)) ),
    inference(variable_rename,[status(thm)],[c_0_1412]) ).

fof(c_0_2774,plain,
    ! [X17,X18,X19,X20,X21,X22] :
      ( ~ c_in(X17,X19,tc_set(tc_Datatype__Universe_Onode(X22,X21)))
      | ~ c_in(X18,X20,tc_set(tc_Datatype__Universe_Onode(X22,X21)))
      | c_in(c_Datatype__Universe_OScons(X18,X17,X22,X21),c_Datatype__Universe_Ouprod(X20,X19,X22,X21),tc_set(tc_Datatype__Universe_Onode(X22,X21))) ),
    inference(variable_rename,[status(thm)],[c_0_1413]) ).

fof(c_0_2775,plain,
    ! [X20,X21,X22] :
      ( ~ c_Divides_Oop_Advd(X22,X20,tc_nat)
      | ~ c_Divides_Oop_Advd(X22,X21,tc_nat)
      | c_Divides_Oop_Advd(X22,c_GCD_Ogcd(c_Pair(X21,X20,tc_nat,tc_nat)),tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_1414]) ).

fof(c_0_2776,plain,
    ! [X15,X16,X17,X18,X19] :
      ( ~ c_in(c_Pair(X17,X16,X19,X18),X15,tc_prod(X19,X18))
      | c_in(X16,c_Relation_ORange(X15,X19,X18),X18) ),
    inference(variable_rename,[status(thm)],[c_0_1415]) ).

fof(c_0_2777,plain,
    ! [X15,X16,X17,X18,X19] :
      ( ~ c_in(c_Pair(X17,X16,X19,X18),X15,tc_prod(X19,X18))
      | c_in(X17,c_Relation_ODomain(X15,X19,X18),X19) ),
    inference(variable_rename,[status(thm)],[c_0_1416]) ).

fof(c_0_2778,plain,
    ! [X38,X39,X40,X41] :
      ( ~ c_lessequals(X39,c_Zorn_OUnion__lemma0__1(X40,X39,X38,X41),tc_set(X41))
      | c_lessequals(X39,c_Union(X38,X41),tc_set(X41))
      | c_lessequals(c_Union(X38,X41),X40,tc_set(X41)) ),
    inference(variable_rename,[status(thm)],[c_0_1417]) ).

fof(c_0_2779,plain,
    ! [X38,X39,X40,X41] :
      ( ~ c_lessequals(c_Zorn_OUnion__lemma0__1(X40,X39,X38,X41),X40,tc_set(X41))
      | c_lessequals(X39,c_Union(X38,X41),tc_set(X41))
      | c_lessequals(c_Union(X38,X41),X40,tc_set(X41)) ),
    inference(variable_rename,[status(thm)],[c_0_1418]) ).

fof(c_0_2780,plain,
    ! [X20,X21] : c_Divides_Oop_Advd(c_GCD_Ogcd(c_Pair(X21,X20,tc_nat,tc_nat)),X20,tc_nat),
    inference(variable_rename,[status(thm)],[c_0_1419]) ).

fof(c_0_2781,plain,
    ! [X20,X21] : c_Divides_Oop_Advd(c_GCD_Ogcd(c_Pair(X21,X20,tc_nat,tc_nat)),X21,tc_nat),
    inference(variable_rename,[status(thm)],[c_0_1420]) ).

fof(c_0_2782,plain,
    ! [X23,X24,X25] :
      ( ~ c_in(c_Pair(X23,c_List_Olist_ONil,tc_List_Olist(X25),tc_List_Olist(X25)),c_List_Olistrel(X24,X25),tc_prod(tc_List_Olist(X25),tc_List_Olist(X25)))
      | X23 = c_List_Olist_ONil ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1421])])]) ).

fof(c_0_2783,plain,
    ! [X23,X24,X25] :
      ( ~ c_in(c_Pair(c_List_Olist_ONil,X23,tc_List_Olist(X25),tc_List_Olist(X25)),c_List_Olistrel(X24,X25),tc_prod(tc_List_Olist(X25),tc_List_Olist(X25)))
      | X23 = c_List_Olist_ONil ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1422])])]) ).

fof(c_0_2784,plain,
    ! [X24,X25,X26] : ~ c_in(c_Pair(c_List_Olist_ONil,X24,tc_List_Olist(X26),tc_List_Olist(X26)),c_List_Olex(X25,X26),tc_prod(tc_List_Olist(X26),tc_List_Olist(X26))),
    inference(variable_rename,[status(thm)],[c_0_1423]) ).

fof(c_0_2785,plain,
    ! [X23,X24,X25] : ~ c_in(c_Pair(X23,c_List_Olist_ONil,tc_List_Olist(X25),tc_List_Olist(X25)),c_List_Olex(X24,X25),tc_prod(tc_List_Olist(X25),tc_List_Olist(X25))),
    inference(variable_rename,[status(thm)],[c_0_1424]) ).

fof(c_0_2786,plain,
    ! [X25,X26] :
      ( ~ c_in(c_Pair(X26,X25,tc_nat,tc_nat),c_Wellfounded__Relations_Oless__than,tc_prod(tc_nat,tc_nat))
      | c_less(X26,X25,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_1425]) ).

fof(c_0_2787,plain,
    ! [X7,X8,X9] :
      ( ~ c_in(c_Pair(X8,X7,X9,X9),c_Relation_OId,tc_prod(X9,X9))
      | X8 = X7 ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1426])])]) ).

fof(c_0_2788,plain,
    ! [X17,X18,X19,X20,X21] :
      ( ~ c_in(X17,X18,tc_set(tc_Datatype__Universe_Onode(X21,X20)))
      | c_in(c_Datatype__Universe_OIn1(X17,X21,X20),c_Datatype__Universe_Ousum(X19,X18,X21,X20),tc_set(tc_Datatype__Universe_Onode(X21,X20))) ),
    inference(variable_rename,[status(thm)],[c_0_1427]) ).

fof(c_0_2789,plain,
    ! [X17,X18,X19,X20,X21] :
      ( ~ c_in(X17,X19,tc_set(tc_Datatype__Universe_Onode(X21,X20)))
      | c_in(c_Datatype__Universe_OIn0(X17,X21,X20),c_Datatype__Universe_Ousum(X19,X18,X21,X20),tc_set(tc_Datatype__Universe_Onode(X21,X20))) ),
    inference(variable_rename,[status(thm)],[c_0_1428]) ).

fof(c_0_2790,plain,
    ! [X17,X18,X19,X20] :
      ( ~ c_in(c_minus(X19,c_insert(X17,X18,X20),tc_set(X20)),c_Finite__Set_OFinites,tc_set(X20))
      | c_in(c_minus(X19,X18,tc_set(X20)),c_Finite__Set_OFinites,tc_set(X20)) ),
    inference(variable_rename,[status(thm)],[c_0_1429]) ).

fof(c_0_2791,plain,
    ! [X35,X36,X37,X38,X39,X40] :
      ( c_Pair(X38,X36,X40,X39) != c_Pair(X37,X35,X40,X39)
      | X36 = X35 ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1430])])]) ).

fof(c_0_2792,plain,
    ! [X35,X36,X37,X38,X39,X40] :
      ( c_Pair(X38,X36,X40,X39) != c_Pair(X37,X35,X40,X39)
      | X38 = X37 ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1431])])]) ).

fof(c_0_2793,plain,
    ! [X13,X14,X15,X16,X17,X18] :
      ( c_Datatype__Universe_OScons(X16,X14,X18,X17) != c_Datatype__Universe_OScons(X15,X13,X18,X17)
      | X14 = X13 ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1432])])]) ).

fof(c_0_2794,plain,
    ! [X13,X14,X15,X16,X17,X18] :
      ( c_Datatype__Universe_OScons(X16,X14,X18,X17) != c_Datatype__Universe_OScons(X15,X13,X18,X17)
      | X16 = X15 ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1433])])]) ).

fof(c_0_2795,plain,
    ! [X17,X18,X19,X20,X21] :
      ( ~ c_in(X17,X18,X21)
      | c_in(c_Sum__Type_OInr(X17,X21,X20),c_Sum__Type_OPlus(X19,X18,X20,X21),tc_sum(X20,X21)) ),
    inference(variable_rename,[status(thm)],[c_0_1434]) ).

fof(c_0_2796,plain,
    ! [X17,X18,X19,X20,X21] :
      ( ~ c_in(X17,X19,X21)
      | c_in(c_Sum__Type_OInl(X17,X21,X20),c_Sum__Type_OPlus(X19,X18,X21,X20),tc_sum(X21,X20)) ),
    inference(variable_rename,[status(thm)],[c_0_1435]) ).

fof(c_0_2797,plain,
    ! [X38,X39,X40,X41] :
      ( c_in(c_Zorn_OUnion__lemma0__1(X40,X39,X38,X41),X38,tc_set(X41))
      | c_lessequals(X39,c_Union(X38,X41),tc_set(X41))
      | c_lessequals(c_Union(X38,X41),X40,tc_set(X41)) ),
    inference(variable_rename,[status(thm)],[c_0_1436]) ).

fof(c_0_2798,plain,
    ! [X16,X17,X18] :
      ( ~ c_in(X16,X17,X18)
      | c_in(c_Pair(X16,X16,X18,X18),c_Relation_Odiag(X17,X18),tc_prod(X18,X18)) ),
    inference(variable_rename,[status(thm)],[c_0_1437]) ).

fof(c_0_2799,plain,
    ! [X17,X18,X19,X20] :
      ( ~ c_in(c_minus(X19,X18,tc_set(X20)),c_Finite__Set_OFinites,tc_set(X20))
      | c_in(c_minus(X19,c_insert(X17,X18,X20),tc_set(X20)),c_Finite__Set_OFinites,tc_set(X20)) ),
    inference(variable_rename,[status(thm)],[c_0_1438]) ).

fof(c_0_2800,plain,
    ! [X25,X26] :
      ( ~ c_less(X26,X25,tc_nat)
      | c_in(c_Pair(X26,X25,tc_nat,tc_nat),c_Wellfounded__Relations_Oless__than,tc_prod(tc_nat,tc_nat)) ),
    inference(variable_rename,[status(thm)],[c_0_1439]) ).

fof(c_0_2801,plain,
    ! [X36,X37,X38] :
      ( ~ c_in(X36,c_Relation_Odiag(X37,X38),tc_prod(X38,X38))
      | X36 = c_Pair(c_Main_OdiagE__1(X37,X36,X38),c_Main_OdiagE__1(X37,X36,X38),X38,X38) ),
    inference(variable_rename,[status(thm)],[c_0_1440]) ).

fof(c_0_2802,plain,
    ! [X15,X16,X17] : c_in(c_Pair(X16,X16,X17,X17),c_Transitive__Closure_Ortrancl(X15,X17),tc_prod(X17,X17)),
    inference(variable_rename,[status(thm)],[c_0_1441]) ).

fof(c_0_2803,plain,
    ! [X52,X53,X54,X55] :
      ( ~ c_Wellfounded__Recursion_Owf(X52,X54)
      | ~ c_Wellfounded__Recursion_Owf(X53,X55)
      | c_Wellfounded__Recursion_Owf(c_Wellfounded__Relations_Olex__prod(X53,X52,X55,X54),tc_prod(X55,X54)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1442])])]) ).

fof(c_0_2804,plain,
    ! [X50,X51,X52,X53] :
      ( ~ c_Relation_Otrans(X50,X52)
      | ~ c_Relation_Otrans(X51,X53)
      | c_Relation_Otrans(c_Wellfounded__Relations_Olex__prod(X51,X50,X53,X52),tc_prod(X53,X52)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1443])])]) ).

fof(c_0_2805,plain,
    ! [X6,X7] : c_in(c_Pair(X6,X6,X7,X7),c_Relation_OId,tc_prod(X7,X7)),
    inference(variable_rename,[status(thm)],[c_0_1444]) ).

fof(c_0_2806,plain,
    ! [X25,X26,X27,X28,X29] :
      ( c_append(X27,c_List_Olist_OCons(X28,c_List_Olist_ONil,X29),X29) != c_append(X25,c_List_Olist_OCons(X26,c_List_Olist_ONil,X29),X29)
      | X28 = X26 ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1445])])]) ).

fof(c_0_2807,plain,
    ! [X25,X26,X27,X28,X29] :
      ( c_append(X27,c_List_Olist_OCons(X28,c_List_Olist_ONil,X29),X29) != c_append(X25,c_List_Olist_OCons(X26,c_List_Olist_ONil,X29),X29)
      | X27 = X25 ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1446])])]) ).

fof(c_0_2808,plain,
    ! [X11,X12,X13,X14,X15] : c_Datatype__Universe_OScons(X13,X12,X15,X14) != c_Datatype__Universe_ONumb(X11,X15,X14),
    inference(variable_rename,[status(thm)],[c_0_1447]) ).

fof(c_0_2809,plain,
    ! [X10,X11,X12,X13,X14] : c_Datatype__Universe_OScons(X12,X11,X14,X13) != c_Datatype__Universe_OLeaf(X10,X14,X13),
    inference(variable_rename,[status(thm)],[c_0_1448]) ).

fof(c_0_2810,plain,
    ! [X10,X11,X12,X13,X14] : c_Datatype__Universe_OScons(X12,X11,X14,X13) != c_Datatype__Universe_OAtom(X10,X14,X13),
    inference(variable_rename,[status(thm)],[c_0_1449]) ).

fof(c_0_2811,plain,
    ! [X11,X12,X13,X14,X15] : c_Datatype__Universe_ONumb(X11,X15,X14) != c_Datatype__Universe_OScons(X13,X12,X15,X14),
    inference(variable_rename,[status(thm)],[c_0_1450]) ).

fof(c_0_2812,plain,
    ! [X10,X11,X12,X13,X14] : c_Datatype__Universe_OLeaf(X10,X14,X13) != c_Datatype__Universe_OScons(X12,X11,X14,X13),
    inference(variable_rename,[status(thm)],[c_0_1451]) ).

fof(c_0_2813,plain,
    ! [X10,X11,X12,X13,X14] : c_Datatype__Universe_OAtom(X10,X14,X13) != c_Datatype__Universe_OScons(X12,X11,X14,X13),
    inference(variable_rename,[status(thm)],[c_0_1452]) ).

fof(c_0_2814,plain,
    ! [X24,X25,X26,X27] :
      ( ~ c_in(X24,c_List_Olists(X26,X27),tc_List_Olist(X27))
      | ~ c_in(X25,c_List_Olists(X26,X27),tc_List_Olist(X27))
      | c_in(c_append(X25,X24,X27),c_List_Olists(X26,X27),tc_List_Olist(X27)) ),
    inference(variable_rename,[status(thm)],[c_0_1453]) ).

fof(c_0_2815,plain,
    ! [X15,X16,X17] :
      ( ~ c_in(c_Relation_Oconverse(X15,X16,X17),c_Finite__Set_OFinites,tc_set(tc_prod(X17,X16)))
      | c_in(X15,c_Finite__Set_OFinites,tc_set(tc_prod(X16,X17))) ),
    inference(variable_rename,[status(thm)],[c_0_1454]) ).

fof(c_0_2816,plain,
    ! [X25,X26,X27] : c_List_Orev(c_append(c_List_Orev(X25,X27),c_List_Olist_OCons(X26,c_List_Olist_ONil,X27),X27),X27) = c_List_Olist_OCons(X26,X25,X27),
    inference(variable_rename,[status(thm)],[c_0_1455]) ).

fof(c_0_2817,plain,
    ! [X45,X46] :
      ( ~ c_in(X45,c_Relation_OId,tc_prod(X46,X46))
      | X45 = c_Pair(c_Main_OIdE__1(X45,X46),c_Main_OIdE__1(X45,X46),X46,X46) ),
    inference(variable_rename,[status(thm)],[c_0_1456]) ).

fof(c_0_2818,plain,
    ! [X44,X45,X46,X47] :
      ( ~ c_in(X45,X46,X47)
      | ~ c_in(X44,c_List_Olists(X46,X47),tc_List_Olist(X47))
      | c_in(c_List_Olist_OCons(X45,X44,X47),c_List_Olists(X46,X47),tc_List_Olist(X47)) ),
    inference(variable_rename,[status(thm)],[c_0_1457]) ).

fof(c_0_2819,plain,
    ! [X15,X16,X17] :
      ( ~ c_in(X15,c_Finite__Set_OFinites,tc_set(tc_prod(X16,X17)))
      | c_in(c_Relation_Oconverse(X15,X16,X17),c_Finite__Set_OFinites,tc_set(tc_prod(X17,X16))) ),
    inference(variable_rename,[status(thm)],[c_0_1458]) ).

fof(c_0_2820,plain,
    ! [X44,X45,X46,X47] :
      ( ~ c_in(c_List_Olist_OCons(X44,X45,X47),c_List_Olists(X46,X47),tc_List_Olist(X47))
      | c_in(X45,c_List_Olists(X46,X47),tc_List_Olist(X47)) ),
    inference(variable_rename,[status(thm)],[c_0_1459]) ).

fof(c_0_2821,plain,
    ! [X24,X25,X26,X27] :
      ( ~ c_in(c_append(X25,X24,X27),c_List_Olists(X26,X27),tc_List_Olist(X27))
      | c_in(X24,c_List_Olists(X26,X27),tc_List_Olist(X27)) ),
    inference(variable_rename,[status(thm)],[c_0_1460]) ).

fof(c_0_2822,plain,
    ! [X24,X25,X26,X27] :
      ( ~ c_in(c_append(X25,X24,X27),c_List_Olists(X26,X27),tc_List_Olist(X27))
      | c_in(X25,c_List_Olists(X26,X27),tc_List_Olist(X27)) ),
    inference(variable_rename,[status(thm)],[c_0_1461]) ).

fof(c_0_2823,plain,
    ! [X16,X17,X18] :
      ( ~ c_lessequals(X17,c_insert(X16,c_emptyset,X18),tc_set(X18))
      | c_insert(X16,c_emptyset,X18) = c_insert(X16,X17,X18) ),
    inference(variable_rename,[status(thm)],[c_0_1462]) ).

fof(c_0_2824,plain,
    ! [X16,X17,X18] :
      ( ~ c_lessequals(X17,c_insert(X16,c_emptyset,X18),tc_set(X18))
      | c_insert(X16,X17,X18) = c_insert(X16,c_emptyset,X18) ),
    inference(variable_rename,[status(thm)],[c_0_1463]) ).

fof(c_0_2825,plain,
    ! [X36,X37,X38,X39] :
      ( ~ c_in(X36,c_union(X38,X37,X39),X39)
      | c_in(X36,X37,X39)
      | c_in(X36,X38,X39) ),
    inference(variable_rename,[status(thm)],[c_0_1464]) ).

fof(c_0_2826,plain,
    ! [X36,X37,X38,X39] :
      ( ~ c_in(X36,X37,X39)
      | ~ c_in(X36,c_minus(X38,X37,tc_set(X39)),X39) ),
    inference(variable_rename,[status(thm)],[c_0_1465]) ).

fof(c_0_2827,plain,
    ! [X44,X45,X46,X47] :
      ( ~ c_in(c_List_Olist_OCons(X44,X45,X47),c_List_Olists(X46,X47),tc_List_Olist(X47))
      | c_in(X44,X46,X47) ),
    inference(variable_rename,[status(thm)],[c_0_1466]) ).

fof(c_0_2828,plain,
    ! [X19,X20,X21] :
      ( ~ c_in(X19,c_Finite__Set_OFinites,tc_set(X21))
      | ~ c_in(X20,c_Finite__Set_OFinites,tc_set(X21))
      | c_in(c_union(X20,X19,X21),c_Finite__Set_OFinites,tc_set(X21)) ),
    inference(variable_rename,[status(thm)],[c_0_1467]) ).

fof(c_0_2829,plain,
    ! [X20,X21] :
      ( ~ c_less(c_0,c_plus(X21,X20,tc_nat),tc_nat)
      | c_less(c_0,X20,tc_nat)
      | c_less(c_0,X21,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_1468]) ).

fof(c_0_2830,plain,
    ! [X23,X24,X25] :
      ( ~ c_in(c_Main_Oin__listsI__1(X24,X23,X25),X24,X25)
      | c_in(X23,c_List_Olists(X24,X25),tc_List_Olist(X25)) ),
    inference(variable_rename,[status(thm)],[c_0_1469]) ).

fof(c_0_2831,plain,
    ! [X38,X39,X40] :
      ( ~ c_in(X39,c_Main_OInterI__1(X39,X38,X40),X40)
      | c_in(X39,c_Inter(X38,X40),X40) ),
    inference(variable_rename,[status(thm)],[c_0_1470]) ).

fof(c_0_2832,plain,
    ! [X36,X37,X38,X39] :
      ( ~ c_in(X36,X37,X39)
      | ~ c_in(X36,X38,X39)
      | c_in(X36,c_inter(X38,X37,X39),X39) ),
    inference(variable_rename,[status(thm)],[c_0_1471]) ).

fof(c_0_2833,plain,
    ! [X16,X17,X18,X19] :
      ( c_insert(X16,c_emptyset,X19) != c_insert(X17,X18,X19)
      | c_lessequals(X18,c_insert(X16,c_emptyset,X19),tc_set(X19)) ),
    inference(variable_rename,[status(thm)],[c_0_1472]) ).

fof(c_0_2834,plain,
    ! [X16,X17,X18,X19] :
      ( c_insert(X17,X18,X19) != c_insert(X16,c_emptyset,X19)
      | c_lessequals(X18,c_insert(X16,c_emptyset,X19),tc_set(X19)) ),
    inference(variable_rename,[status(thm)],[c_0_1473]) ).

fof(c_0_2835,plain,
    ! [X16,X17] :
      ( ~ c_in(X16,c_Finite__Set_OFinites,tc_set(tc_set(X17)))
      | ~ c_in(c_Main_Ofinite__Union__1(X16,X17),c_Finite__Set_OFinites,tc_set(X17))
      | c_in(c_Union(X16,X17),c_Finite__Set_OFinites,tc_set(X17)) ),
    inference(variable_rename,[status(thm)],[c_0_1474]) ).

fof(c_0_2836,plain,
    ! [X36,X37,X38] :
      ( ~ c_in(X36,c_Relation_Odiag(X37,X38),tc_prod(X38,X38))
      | c_in(c_Main_OdiagE__1(X37,X36,X38),X37,X38) ),
    inference(variable_rename,[status(thm)],[c_0_1475]) ).

fof(c_0_2837,plain,
    ! [X36,X37,X38,X39] :
      ( ~ c_in(X36,c_minus(X38,X37,tc_set(X39)),X39)
      | c_in(X36,X38,X39) ),
    inference(variable_rename,[status(thm)],[c_0_1476]) ).

fof(c_0_2838,plain,
    ! [X19,X20,X21] :
      ( ~ c_in(c_union(X20,X19,X21),c_Finite__Set_OFinites,tc_set(X21))
      | c_in(X19,c_Finite__Set_OFinites,tc_set(X21)) ),
    inference(variable_rename,[status(thm)],[c_0_1477]) ).

fof(c_0_2839,plain,
    ! [X19,X20,X21] :
      ( ~ c_in(c_union(X20,X19,X21),c_Finite__Set_OFinites,tc_set(X21))
      | c_in(X20,c_Finite__Set_OFinites,tc_set(X21)) ),
    inference(variable_rename,[status(thm)],[c_0_1478]) ).

fof(c_0_2840,plain,
    ! [X43,X44,X45,X46] :
      ( ~ c_in(X43,c_List_Olists(X45,X46),tc_List_Olist(X46))
      | ~ c_in(X44,c_List_Oset(X43,X46),X46)
      | c_in(X44,X45,X46) ),
    inference(variable_rename,[status(thm)],[c_0_1479]) ).

fof(c_0_2841,plain,
    ! [X17,X18,X19] :
      ( ~ c_in(c_Main_OsubsetI__1(X18,X17,X19),X17,X19)
      | c_lessequals(X18,X17,tc_set(X19)) ),
    inference(variable_rename,[status(thm)],[c_0_1480]) ).

fof(c_0_2842,plain,
    ! [X36,X37,X38,X39] :
      ( ~ c_in(X36,X38,X39)
      | c_in(X36,X37,X39)
      | c_in(X36,c_minus(X38,X37,tc_set(X39)),X39) ),
    inference(variable_rename,[status(thm)],[c_0_1481]) ).

fof(c_0_2843,plain,
    ! [X16,X17,X18,X19] :
      ( ~ c_in(X17,c_insert(X16,X18,X19),X19)
      | c_in(X17,X18,X19)
      | X17 = X16 ),
    inference(variable_rename,[status(thm)],[c_0_1482]) ).

fof(c_0_2844,plain,
    ! [X36,X37,X38,X39] :
      ( ~ c_in(X36,c_inter(X38,X37,X39),X39)
      | c_in(X36,X38,X39) ),
    inference(variable_rename,[status(thm)],[c_0_1483]) ).

fof(c_0_2845,plain,
    ! [X36,X37,X38,X39] :
      ( ~ c_in(X36,c_inter(X38,X37,X39),X39)
      | c_in(X36,X37,X39) ),
    inference(variable_rename,[status(thm)],[c_0_1484]) ).

fof(c_0_2846,plain,
    ! [X42,X43,X44,X45] :
      ( ~ c_lessequals(X43,X42,tc_set(tc_set(X45)))
      | c_lessequals(X43,c_Zorn_Osucc(X44,X42,X45),tc_set(tc_set(X45))) ),
    inference(variable_rename,[status(thm)],[c_0_1485]) ).

fof(c_0_2847,plain,
    ! [X38,X39,X40] :
      ( ~ c_in(X39,c_Union(X38,X40),X40)
      | c_in(c_Main_OUnionE__1(X39,X38,X40),X38,tc_set(X40)) ),
    inference(variable_rename,[status(thm)],[c_0_1486]) ).

fof(c_0_2848,plain,
    ! [X25,X26,X27,X28] :
      ( c_List_Orev(X27,X28) != c_List_Olist_OCons(X26,X25,X28)
      | X27 = c_append(c_List_Orev(X25,X28),c_List_Olist_OCons(X26,c_List_Olist_ONil,X28),X28) ),
    inference(variable_rename,[status(thm)],[c_0_1487]) ).

fof(c_0_2849,plain,
    ! [X38,X39,X40] :
      ( ~ c_in(X39,c_Union(X38,X40),X40)
      | c_in(X39,c_Main_OUnionE__1(X39,X38,X40),X40) ),
    inference(variable_rename,[status(thm)],[c_0_1488]) ).

fof(c_0_2850,plain,
    ! [X16,X17] :
      ( ~ c_in(X16,c_Finite__Set_OFinites,tc_set(tc_set(X17)))
      | c_in(c_Main_Ofinite__Union__1(X16,X17),X16,tc_set(X17))
      | c_in(c_Union(X16,X17),c_Finite__Set_OFinites,tc_set(X17)) ),
    inference(variable_rename,[status(thm)],[c_0_1489]) ).

fof(c_0_2851,plain,
    ! [X38,X39,X40,X41] :
      ( ~ c_in(X38,X39,tc_set(X41))
      | ~ c_in(X40,c_Inter(X39,X41),X41)
      | c_in(X40,X38,X41) ),
    inference(variable_rename,[status(thm)],[c_0_1490]) ).

fof(c_0_2852,plain,
    ! [X17,X18,X19] :
      ( ~ c_lessequals(c_uminus(X18,tc_set(X19)),c_uminus(X17,tc_set(X19)),tc_set(X19))
      | c_lessequals(X17,X18,tc_set(X19)) ),
    inference(variable_rename,[status(thm)],[c_0_1491]) ).

fof(c_0_2853,plain,
    ! [X23,X24,X25] :
      ( c_in(X23,c_List_Olists(X24,X25),tc_List_Olist(X25))
      | c_in(c_Main_Oin__listsI__1(X24,X23,X25),c_List_Oset(X23,X25),X25) ),
    inference(variable_rename,[status(thm)],[c_0_1492]) ).

fof(c_0_2854,plain,
    ! [X38,X39,X40,X41] :
      ( ~ c_in(X40,X38,X41)
      | ~ c_in(X38,X39,tc_set(X41))
      | c_in(X40,c_Union(X39,X41),X41) ),
    inference(variable_rename,[status(thm)],[c_0_1493]) ).

fof(c_0_2855,plain,
    ! [X19,X20,X21] :
      ( ~ c_in(X19,c_Finite__Set_OFinites,tc_set(X21))
      | c_in(c_inter(X20,X19,X21),c_Finite__Set_OFinites,tc_set(X21)) ),
    inference(variable_rename,[status(thm)],[c_0_1494]) ).

fof(c_0_2856,plain,
    ! [X19,X20,X21] :
      ( ~ c_in(X20,c_Finite__Set_OFinites,tc_set(X21))
      | c_in(c_inter(X20,X19,X21),c_Finite__Set_OFinites,tc_set(X21)) ),
    inference(variable_rename,[status(thm)],[c_0_1495]) ).

fof(c_0_2857,plain,
    ! [X16,X17,X18] :
      ( ~ c_in(X17,c_Finite__Set_OFinites,tc_set(X18))
      | c_in(c_insert(X16,X17,X18),c_Finite__Set_OFinites,tc_set(X18)) ),
    inference(variable_rename,[status(thm)],[c_0_1496]) ).

fof(c_0_2858,plain,
    ! [X7,X8,X9] :
      ( ~ c_in(X7,c_insert(X8,c_emptyset,X9),X9)
      | X7 = X8 ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1497])])]) ).

fof(c_0_2859,plain,
    ! [X38,X39,X40] :
      ( c_in(X39,c_Inter(X38,X40),X40)
      | c_in(c_Main_OInterI__1(X39,X38,X40),X38,tc_set(X40)) ),
    inference(variable_rename,[status(thm)],[c_0_1498]) ).

fof(c_0_2860,plain,
    ! [X17,X18,X19,X20] :
      ( ~ c_in(X18,X19,X20)
      | c_in(X18,c_insert(X17,X19,X20),X20) ),
    inference(variable_rename,[status(thm)],[c_0_1499]) ).

fof(c_0_2861,plain,
    ! [X36,X37,X38,X39] :
      ( ~ c_in(X36,X38,X39)
      | c_in(X36,c_union(X38,X37,X39),X39) ),
    inference(variable_rename,[status(thm)],[c_0_1500]) ).

fof(c_0_2862,plain,
    ! [X36,X37,X38,X39] :
      ( ~ c_in(X36,X37,X39)
      | c_in(X36,c_union(X38,X37,X39),X39) ),
    inference(variable_rename,[status(thm)],[c_0_1501]) ).

fof(c_0_2863,plain,
    ! [X34,X35] : ~ c_less(c_plus(X34,X35,tc_nat),X35,tc_nat),
    inference(variable_rename,[status(thm)],[c_0_1502]) ).

fof(c_0_2864,plain,
    ! [X34,X35] : ~ c_less(c_plus(X35,X34,tc_nat),X35,tc_nat),
    inference(variable_rename,[status(thm)],[c_0_1503]) ).

fof(c_0_2865,plain,
    ! [X25,X26,X27] :
      ( ~ class_Orderings_Olinorder(X27)
      | ~ c_lessequals(c_SetInterval_OlessThan(X26,X27),c_SetInterval_OlessThan(X25,X27),tc_set(X27))
      | c_lessequals(X26,X25,X27) ),
    inference(variable_rename,[status(thm)],[c_0_1504]) ).

fof(c_0_2866,plain,
    ! [X25,X26,X27] :
      ( ~ class_Orderings_Olinorder(X27)
      | ~ c_lessequals(c_SetInterval_OgreaterThan(X26,X27),c_SetInterval_OgreaterThan(X25,X27),tc_set(X27))
      | c_lessequals(X25,X26,X27) ),
    inference(variable_rename,[status(thm)],[c_0_1505]) ).

fof(c_0_2867,plain,
    ! [X25,X26,X27] :
      ( ~ class_Orderings_Oorder(X27)
      | ~ c_lessequals(c_SetInterval_OatMost(X26,X27),c_SetInterval_OatMost(X25,X27),tc_set(X27))
      | c_lessequals(X26,X25,X27) ),
    inference(variable_rename,[status(thm)],[c_0_1506]) ).

fof(c_0_2868,plain,
    ! [X25,X26,X27] :
      ( ~ class_Orderings_Oorder(X27)
      | ~ c_lessequals(c_SetInterval_OatLeast(X26,X27),c_SetInterval_OatLeast(X25,X27),tc_set(X27))
      | c_lessequals(X25,X26,X27) ),
    inference(variable_rename,[status(thm)],[c_0_1507]) ).

fof(c_0_2869,plain,
    ! [X36,X37,X38,X39] :
      ( ~ c_in(X36,X38,X39)
      | ~ c_lessequals(X38,X37,tc_set(X39))
      | c_in(X36,X37,X39) ),
    inference(variable_rename,[status(thm)],[c_0_1508]) ).

fof(c_0_2870,plain,
    ! [X20,X21] :
      ( ~ c_less(c_0,X20,tc_nat)
      | c_less(c_0,c_plus(X21,X20,tc_nat),tc_nat) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1509])])]) ).

fof(c_0_2871,plain,
    ! [X20,X21] :
      ( ~ c_less(c_0,X21,tc_nat)
      | c_less(c_0,c_plus(X21,X20,tc_nat),tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_1510]) ).

fof(c_0_2872,plain,
    ! [X45,X46,X47] :
      ( ~ c_in(X46,X45,tc_prod(X47,X47))
      | c_in(X46,c_Transitive__Closure_Ortrancl(X45,X47),tc_prod(X47,X47)) ),
    inference(variable_rename,[status(thm)],[c_0_1511]) ).

fof(c_0_2873,plain,
    ! [X17,X18,X19] :
      ( ~ c_lessequals(X17,X18,tc_set(X19))
      | c_lessequals(c_uminus(X18,tc_set(X19)),c_uminus(X17,tc_set(X19)),tc_set(X19)) ),
    inference(variable_rename,[status(thm)],[c_0_1512]) ).

fof(c_0_2874,plain,
    ! [X36,X37,X38] :
      ( ~ c_in(X36,X37,X38)
      | ~ c_in(X36,c_uminus(X37,tc_set(X38)),X38) ),
    inference(variable_rename,[status(thm)],[c_0_1513]) ).

fof(c_0_2875,plain,
    ! [X17,X18,X19] :
      ( c_in(c_Main_OsubsetI__1(X18,X17,X19),X18,X19)
      | c_lessequals(X18,X17,tc_set(X19)) ),
    inference(variable_rename,[status(thm)],[c_0_1514]) ).

fof(c_0_2876,plain,
    ! [X16,X17] :
      ( ~ c_in(c_Pow(X16,X17),c_Finite__Set_OFinites,tc_set(tc_set(X17)))
      | c_in(X16,c_Finite__Set_OFinites,tc_set(X17)) ),
    inference(variable_rename,[status(thm)],[c_0_1515]) ).

fof(c_0_2877,plain,
    ! [X25,X26,X27] :
      ( ~ class_Orderings_Olinorder(X27)
      | ~ c_lessequals(X26,X25,X27)
      | c_lessequals(c_SetInterval_OlessThan(X26,X27),c_SetInterval_OlessThan(X25,X27),tc_set(X27)) ),
    inference(variable_rename,[status(thm)],[c_0_1516]) ).

fof(c_0_2878,plain,
    ! [X25,X26,X27] :
      ( ~ class_Orderings_Olinorder(X27)
      | ~ c_lessequals(X25,X26,X27)
      | c_lessequals(c_SetInterval_OgreaterThan(X26,X27),c_SetInterval_OgreaterThan(X25,X27),tc_set(X27)) ),
    inference(variable_rename,[status(thm)],[c_0_1517]) ).

fof(c_0_2879,plain,
    ! [X25,X26,X27] :
      ( ~ class_Orderings_Oorder(X27)
      | ~ c_lessequals(X26,X25,X27)
      | c_lessequals(c_SetInterval_OatMost(X26,X27),c_SetInterval_OatMost(X25,X27),tc_set(X27)) ),
    inference(variable_rename,[status(thm)],[c_0_1518]) ).

fof(c_0_2880,plain,
    ! [X25,X26,X27] :
      ( ~ class_Orderings_Oorder(X27)
      | ~ c_lessequals(X25,X26,X27)
      | c_lessequals(c_SetInterval_OatLeast(X26,X27),c_SetInterval_OatLeast(X25,X27),tc_set(X27)) ),
    inference(variable_rename,[status(thm)],[c_0_1519]) ).

fof(c_0_2881,plain,
    ! [X15,X16] :
      ( ~ c_Wellfounded__Recursion_Oacyclic(c_Relation_Oconverse(X15,X16,X16),X16)
      | c_Wellfounded__Recursion_Oacyclic(X15,X16) ),
    inference(variable_rename,[status(thm)],[c_0_1520]) ).

fof(c_0_2882,plain,
    ! [X42,X43,X44,X45] :
      ( ~ c_Infinite__Set_Oatmost__one(X44,X45)
      | ~ c_in(X42,X44,X45)
      | ~ c_in(X43,X44,X45)
      | X42 = X43 ),
    inference(variable_rename,[status(thm)],[c_0_1521]) ).

fof(c_0_2883,plain,
    ! [X17,X18,X19] :
      ( ~ c_in(X18,c_Pow(X17,X19),tc_set(X19))
      | c_lessequals(X18,X17,tc_set(X19)) ),
    inference(variable_rename,[status(thm)],[c_0_1522]) ).

fof(c_0_2884,plain,
    ! [X17,X18,X19] :
      ( ~ c_lessequals(X17,X18,tc_set(X19))
      | ~ c_lessequals(X18,X17,tc_set(X19))
      | X18 = X17 ),
    inference(variable_rename,[status(thm)],[c_0_1523]) ).

fof(c_0_2885,plain,
    ! [X17,X18,X19] :
      ( ~ c_less(X18,X17,tc_set(X19))
      | ~ c_lessequals(X17,X18,tc_set(X19)) ),
    inference(variable_rename,[status(thm)],[c_0_1524]) ).

fof(c_0_2886,plain,
    ! [X16,X17] :
      ( ~ c_in(X16,c_Finite__Set_OFinites,tc_set(X17))
      | c_in(c_Pow(X16,X17),c_Finite__Set_OFinites,tc_set(tc_set(X17))) ),
    inference(variable_rename,[status(thm)],[c_0_1525]) ).

fof(c_0_2887,plain,
    ! [X33,X34,X35] :
      ( ~ class_Orderings_Oord(X35)
      | ~ c_in(X34,c_SetInterval_OlessThan(X33,X35),X35)
      | c_less(X34,X33,X35) ),
    inference(variable_rename,[status(thm)],[c_0_1526]) ).

fof(c_0_2888,plain,
    ! [X33,X34,X35] :
      ( ~ class_Orderings_Oord(X35)
      | ~ c_in(X34,c_SetInterval_OgreaterThan(X33,X35),X35)
      | c_less(X33,X34,X35) ),
    inference(variable_rename,[status(thm)],[c_0_1527]) ).

fof(c_0_2889,plain,
    ! [X33,X34,X35] :
      ( ~ class_Orderings_Oord(X35)
      | ~ c_in(X34,c_SetInterval_OatMost(X33,X35),X35)
      | c_lessequals(X34,X33,X35) ),
    inference(variable_rename,[status(thm)],[c_0_1528]) ).

fof(c_0_2890,plain,
    ! [X33,X34,X35] :
      ( ~ class_Orderings_Oord(X35)
      | ~ c_in(X34,c_SetInterval_OatLeast(X33,X35),X35)
      | c_lessequals(X33,X34,X35) ),
    inference(variable_rename,[status(thm)],[c_0_1529]) ).

fof(c_0_2891,plain,
    ! [X17,X18,X19] :
      ( ~ c_lessequals(X18,X17,tc_set(X19))
      | c_in(X18,c_Pow(X17,X19),tc_set(X19)) ),
    inference(variable_rename,[status(thm)],[c_0_1530]) ).

fof(c_0_2892,plain,
    ! [X23,X24] : c_lessequals(c_Nat_Osize(c_List_Oremdups(X23,X24),tc_List_Olist(X24)),c_Nat_Osize(X23,tc_List_Olist(X24)),tc_nat),
    inference(variable_rename,[status(thm)],[c_0_1531]) ).

fof(c_0_2893,plain,
    ! [X33,X34,X35] :
      ( ~ class_Orderings_Oord(X35)
      | ~ c_less(X34,X33,X35)
      | c_in(X34,c_SetInterval_OlessThan(X33,X35),X35) ),
    inference(variable_rename,[status(thm)],[c_0_1532]) ).

fof(c_0_2894,plain,
    ! [X33,X34,X35] :
      ( ~ class_Orderings_Oord(X35)
      | ~ c_less(X33,X34,X35)
      | c_in(X34,c_SetInterval_OgreaterThan(X33,X35),X35) ),
    inference(variable_rename,[status(thm)],[c_0_1533]) ).

fof(c_0_2895,plain,
    ! [X33,X34,X35] :
      ( ~ class_Orderings_Oord(X35)
      | ~ c_lessequals(X34,X33,X35)
      | c_in(X34,c_SetInterval_OatMost(X33,X35),X35) ),
    inference(variable_rename,[status(thm)],[c_0_1534]) ).

fof(c_0_2896,plain,
    ! [X33,X34,X35] :
      ( ~ class_Orderings_Oord(X35)
      | ~ c_lessequals(X33,X34,X35)
      | c_in(X34,c_SetInterval_OatLeast(X33,X35),X35) ),
    inference(variable_rename,[status(thm)],[c_0_1535]) ).

fof(c_0_2897,plain,
    ! [X25,X26,X27,X28] :
      ( c_Datatype__Universe_ONumb(X26,X28,X27) != c_Datatype__Universe_ONumb(X25,X28,X27)
      | X26 = X25 ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1536])])]) ).

fof(c_0_2898,plain,
    ! [X25,X26,X27,X28] :
      ( c_Datatype__Universe_OLeaf(X26,X28,X27) != c_Datatype__Universe_OLeaf(X25,X28,X27)
      | X26 = X25 ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1537])])]) ).

fof(c_0_2899,plain,
    ! [X25,X26,X27,X28] :
      ( c_Sum__Type_OInr(X26,X27,X28) != c_Sum__Type_OInr(X25,X27,X28)
      | X26 = X25 ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1538])])]) ).

fof(c_0_2900,plain,
    ! [X25,X26,X27,X28] :
      ( c_Sum__Type_OInl(X26,X28,X27) != c_Sum__Type_OInl(X25,X28,X27)
      | X26 = X25 ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1539])])]) ).

fof(c_0_2901,plain,
    ! [X26,X27,X28,X29] :
      ( c_append(X28,X27,X29) != c_append(X28,X26,X29)
      | X27 = X26 ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1540])])]) ).

fof(c_0_2902,plain,
    ! [X32,X33,X34,X35,X36] :
      ( c_List_Olist_OCons(X35,X33,X36) != c_List_Olist_OCons(X34,X32,X36)
      | X33 = X32 ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1541])])]) ).

fof(c_0_2903,plain,
    ! [X32,X33,X34,X35,X36] :
      ( c_List_Olist_OCons(X35,X33,X36) != c_List_Olist_OCons(X34,X32,X36)
      | X35 = X34 ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1542])])]) ).

fof(c_0_2904,plain,
    ! [X26,X27,X28,X29] :
      ( c_append(X27,X28,X29) != c_append(X26,X28,X29)
      | X27 = X26 ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1543])])]) ).

fof(c_0_2905,plain,
    ! [X10,X11,X12,X13] :
      ( c_Datatype__Universe_OIn1(X11,X13,X12) != c_Datatype__Universe_OIn1(X10,X13,X12)
      | X11 = X10 ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1544])])]) ).

fof(c_0_2906,plain,
    ! [X10,X11,X12,X13] :
      ( c_Datatype__Universe_OIn0(X11,X13,X12) != c_Datatype__Universe_OIn0(X10,X13,X12)
      | X11 = X10 ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1545])])]) ).

fof(c_0_2907,plain,
    ! [X8,X9,X10,X11] :
      ( c_Datatype__Universe_OAtom(X9,X11,X10) != c_Datatype__Universe_OAtom(X8,X11,X10)
      | X9 = X8 ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1546])])]) ).

fof(c_0_2908,plain,
    ! [X22,X23] :
      ( ~ c_Divides_Oop_Advd(c_uminus(X22,tc_IntDef_Oint),X23,tc_IntDef_Oint)
      | c_Divides_Oop_Advd(X22,X23,tc_IntDef_Oint) ),
    inference(variable_rename,[status(thm)],[c_0_1547]) ).

fof(c_0_2909,plain,
    ! [X22,X23] :
      ( ~ c_Divides_Oop_Advd(X22,c_uminus(X23,tc_IntDef_Oint),tc_IntDef_Oint)
      | c_Divides_Oop_Advd(X22,X23,tc_IntDef_Oint) ),
    inference(variable_rename,[status(thm)],[c_0_1548]) ).

fof(c_0_2910,plain,
    ! [X8,X9,X10,X11] : c_Sum__Type_OInr(X8,X10,X11) != c_Sum__Type_OInl(X9,X11,X10),
    inference(variable_rename,[status(thm)],[c_0_1549]) ).

fof(c_0_2911,plain,
    ! [X8,X9,X10,X11] : c_Sum__Type_OInl(X9,X11,X10) != c_Sum__Type_OInr(X8,X10,X11),
    inference(variable_rename,[status(thm)],[c_0_1550]) ).

fof(c_0_2912,plain,
    ! [X11,X12,X13,X14] : c_Datatype__Universe_ONumb(X11,X14,X13) != c_Datatype__Universe_OLeaf(X12,X14,X13),
    inference(variable_rename,[status(thm)],[c_0_1551]) ).

fof(c_0_2913,plain,
    ! [X11,X12,X13,X14] : c_Datatype__Universe_OLeaf(X12,X14,X13) != c_Datatype__Universe_ONumb(X11,X14,X13),
    inference(variable_rename,[status(thm)],[c_0_1552]) ).

fof(c_0_2914,plain,
    ! [X10,X11,X12,X13] : c_Datatype__Universe_OIn1(X10,X13,X12) != c_Datatype__Universe_OIn0(X11,X13,X12),
    inference(variable_rename,[status(thm)],[c_0_1553]) ).

fof(c_0_2915,plain,
    ! [X10,X11,X12,X13] : c_Datatype__Universe_OIn0(X11,X13,X12) != c_Datatype__Universe_OIn1(X10,X13,X12),
    inference(variable_rename,[status(thm)],[c_0_1554]) ).

fof(c_0_2916,plain,
    ! [X16,X17,X18,X19] :
      ( c_insert(X16,c_emptyset,X19) != c_insert(X17,X18,X19)
      | X17 = X16 ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1555])])]) ).

fof(c_0_2917,plain,
    ! [X16,X17,X18,X19] :
      ( c_insert(X17,X18,X19) != c_insert(X16,c_emptyset,X19)
      | X17 = X16 ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1556])])]) ).

fof(c_0_2918,plain,
    ! [X7,X8,X9] :
      ( c_insert(X8,c_emptyset,X9) != c_insert(X7,c_emptyset,X9)
      | X8 = X7 ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1557])])]) ).

fof(c_0_2919,plain,
    ! [X41,X42] :
      ( c_Divides_Oop_Amod(X41,X42,tc_IntDef_Oint) != c_0
      | X41 = c_times(X42,c_Main_Ozmod__eq__0D__dest__1(X42,X41),tc_IntDef_Oint) ),
    inference(variable_rename,[status(thm)],[c_0_1558]) ).

fof(c_0_2920,plain,
    ! [X41,X42] :
      ( c_Divides_Oop_Amod(X41,X42,tc_nat) != c_0
      | X41 = c_times(X42,c_Main_Omod__eq__0D__dest__1(X42,X41),tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_1559]) ).

fof(c_0_2921,plain,
    ! [X17,X18,X19] : c_in(X17,c_insert(X17,X18,X19),X19),
    inference(variable_rename,[status(thm)],[c_0_1560]) ).

fof(c_0_2922,plain,
    ! [X44,X45] : c_in(c_SetInterval_OgreaterThanLessThan(X45,X44,tc_IntDef_Oint),c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)),
    inference(variable_rename,[status(thm)],[c_0_1561]) ).

fof(c_0_2923,plain,
    ! [X44,X45] : c_in(c_SetInterval_OgreaterThanLessThan(X45,X44,tc_nat),c_Finite__Set_OFinites,tc_set(tc_nat)),
    inference(variable_rename,[status(thm)],[c_0_1562]) ).

fof(c_0_2924,plain,
    ! [X44,X45] : c_in(c_SetInterval_OgreaterThanAtMost(X45,X44,tc_IntDef_Oint),c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)),
    inference(variable_rename,[status(thm)],[c_0_1563]) ).

fof(c_0_2925,plain,
    ! [X44,X45] : c_in(c_SetInterval_OgreaterThanAtMost(X45,X44,tc_nat),c_Finite__Set_OFinites,tc_set(tc_nat)),
    inference(variable_rename,[status(thm)],[c_0_1564]) ).

fof(c_0_2926,plain,
    ! [X44,X45] : c_in(c_SetInterval_OatLeastLessThan(X45,X44,tc_IntDef_Oint),c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)),
    inference(variable_rename,[status(thm)],[c_0_1565]) ).

fof(c_0_2927,plain,
    ! [X44,X45] : c_in(c_SetInterval_OatLeastLessThan(X45,X44,tc_nat),c_Finite__Set_OFinites,tc_set(tc_nat)),
    inference(variable_rename,[status(thm)],[c_0_1566]) ).

fof(c_0_2928,plain,
    ! [X44,X45] : c_in(c_SetInterval_OatLeastAtMost(X45,X44,tc_IntDef_Oint),c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)),
    inference(variable_rename,[status(thm)],[c_0_1567]) ).

fof(c_0_2929,plain,
    ! [X44,X45] : c_in(c_SetInterval_OatLeastAtMost(X45,X44,tc_nat),c_Finite__Set_OFinites,tc_set(tc_nat)),
    inference(variable_rename,[status(thm)],[c_0_1568]) ).

fof(c_0_2930,plain,
    ! [X22,X23] :
      ( ~ c_Divides_Oop_Advd(X22,X23,tc_IntDef_Oint)
      | c_Divides_Oop_Advd(c_uminus(X22,tc_IntDef_Oint),X23,tc_IntDef_Oint) ),
    inference(variable_rename,[status(thm)],[c_0_1569]) ).

fof(c_0_2931,plain,
    ! [X22,X23] :
      ( ~ c_Divides_Oop_Advd(X22,X23,tc_IntDef_Oint)
      | c_Divides_Oop_Advd(X22,c_uminus(X23,tc_IntDef_Oint),tc_IntDef_Oint) ),
    inference(variable_rename,[status(thm)],[c_0_1570]) ).

fof(c_0_2932,plain,
    ! [X17,X18,X19] :
      ( ~ c_lessequals(X18,X17,tc_set(X19))
      | c_less(X18,X17,tc_set(X19))
      | X18 = X17 ),
    inference(variable_rename,[status(thm)],[c_0_1571]) ).

fof(c_0_2933,plain,
    ! [X6,X7] : c_in(X6,c_insert(X6,c_emptyset,X7),X7),
    inference(variable_rename,[status(thm)],[c_0_1572]) ).

fof(c_0_2934,plain,
    ! [X14,X15] : c_Divides_Oop_Advd(X15,c_times(X14,X15,tc_IntDef_Oint),tc_IntDef_Oint),
    inference(variable_rename,[status(thm)],[c_0_1573]) ).

fof(c_0_2935,plain,
    ! [X14,X15] : c_Divides_Oop_Advd(X15,c_times(X15,X14,tc_IntDef_Oint),tc_IntDef_Oint),
    inference(variable_rename,[status(thm)],[c_0_1574]) ).

fof(c_0_2936,plain,
    ! [X14,X15] : c_Divides_Oop_Advd(X15,c_times(X14,X15,tc_nat),tc_nat),
    inference(variable_rename,[status(thm)],[c_0_1575]) ).

fof(c_0_2937,plain,
    ! [X14,X15] : c_Divides_Oop_Advd(X15,c_times(X15,X14,tc_nat),tc_nat),
    inference(variable_rename,[status(thm)],[c_0_1576]) ).

fof(c_0_2938,plain,
    ! [X17,X18,X19] :
      ( ~ c_less(X18,X17,tc_set(X19))
      | c_lessequals(X18,X17,tc_set(X19)) ),
    inference(variable_rename,[status(thm)],[c_0_1577]) ).

fof(c_0_2939,plain,
    ! [X20,X21] :
      ( ~ c_less(c_Suc(X21),c_Suc(X20),tc_nat)
      | c_less(X21,X20,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_1578]) ).

fof(c_0_2940,plain,
    ! [X20,X21] :
      ( ~ c_lessequals(c_Suc(X20),c_Suc(X21),tc_nat)
      | c_lessequals(X20,X21,tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_1579]) ).

fof(c_0_2941,plain,
    ! [X20,X21] :
      ( ~ c_less(X21,X20,tc_nat)
      | c_less(c_Suc(X21),c_Suc(X20),tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_1580]) ).

fof(c_0_2942,plain,
    ! [X20,X21] :
      ( ~ c_lessequals(X20,X21,tc_nat)
      | c_lessequals(c_Suc(X20),c_Suc(X21),tc_nat) ),
    inference(variable_rename,[status(thm)],[c_0_1581]) ).

fof(c_0_2943,plain,
    ! [X36,X37,X38] :
      ( c_in(X36,X37,X38)
      | c_in(X36,c_uminus(X37,tc_set(X38)),X38) ),
    inference(variable_rename,[status(thm)],[c_0_1582]) ).

fof(c_0_2944,plain,
    ! [X15,X16] :
      ( ~ c_Wellfounded__Recursion_Oacyclic(X15,X16)
      | c_Wellfounded__Recursion_Oacyclic(c_Relation_Oconverse(X15,X16,X16),X16) ),
    inference(variable_rename,[status(thm)],[c_0_1583]) ).

fof(c_0_2945,plain,
    ! [X4,X5,X6] :
      ( ~ c_in(X5,c_Datatype_Oo2s(X4,X6),X6)
      | X4 = c_Datatype_Ooption_OSome(X5,X6) ),
    inference(variable_rename,[status(thm)],[c_0_1584]) ).

fof(c_0_2946,plain,
    ! [X4] : ~ c_less(c_0,c_Nat_Osize(c_List_Olist_ONil,tc_List_Olist(X4)),tc_nat),
    inference(variable_rename,[status(thm)],[c_0_1585]) ).

fof(c_0_2947,plain,
    ! [X4,X5] : c_in(X4,c_Datatype_Oo2s(c_Datatype_Ooption_OSome(X4,X5),X5),X5),
    inference(variable_rename,[status(thm)],[c_0_1586]) ).

fof(c_0_2948,plain,
    ! [X23,X24] :
      ( c_Nat_Osize(c_List_Oremdups(X23,X24),tc_List_Olist(X24)) != c_Nat_Osize(X23,tc_List_Olist(X24))
      | c_List_Oremdups(X23,X24) = X23 ),
    inference(variable_rename,[status(thm)],[c_0_1587]) ).

fof(c_0_2949,plain,
    ! [X20,X21] : c_less(c_uminus(c_IntDef_Oint(c_Suc(X20)),tc_IntDef_Oint),c_IntDef_Oint(X21),tc_IntDef_Oint),
    inference(variable_rename,[status(thm)],[c_0_1588]) ).

fof(c_0_2950,plain,
    ! [X20,X21] : c_lessequals(c_uminus(c_IntDef_Oint(X20),tc_IntDef_Oint),c_IntDef_Oint(X21),tc_IntDef_Oint),
    inference(variable_rename,[status(thm)],[c_0_1589]) ).

fof(c_0_2951,plain,
    ! [X16,X17] : ~ c_less(X16,c_emptyset,tc_set(X17)),
    inference(variable_rename,[status(thm)],[c_0_1590]) ).

fof(c_0_2952,plain,
    ! [X4,X5] :
      ( ~ class_Orderings_Oorder(X5)
      | ~ c_less(X4,X4,X5) ),
    inference(variable_rename,[status(thm)],[c_0_1591]) ).

fof(c_0_2953,plain,
    ! [X23,X24] :
      ( c_less(c_0,c_Nat_Osize(X23,tc_List_Olist(X24)),tc_nat)
      | X23 = c_List_Olist_ONil ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1592])])]) ).

fof(c_0_2954,plain,
    ! [X23,X24] :
      ( c_List_Oremdups(X23,X24) != X23
      | c_Nat_Osize(c_List_Oremdups(X23,X24),tc_List_Olist(X24)) = c_Nat_Osize(X23,tc_List_Olist(X24)) ),
    inference(variable_rename,[status(thm)],[c_0_1593]) ).

fof(c_0_2955,plain,
    ! [X20] :
      ( ~ c_less(X20,c_Suc(c_0),tc_nat)
      | X20 = c_0 ),
    inference(variable_rename,[status(thm)],[c_0_1594]) ).

fof(c_0_2956,plain,
    ! [X24,X25,X26] :
      ( X25 != c_append(X25,X24,X26)
      | X24 = c_List_Olist_ONil ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1595])])]) ).

fof(c_0_2957,plain,
    ! [X24,X25,X26] :
      ( X24 != c_append(X25,X24,X26)
      | X25 = c_List_Olist_ONil ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1596])])]) ).

fof(c_0_2958,plain,
    ! [X24,X25,X26] :
      ( c_append(X25,X24,X26) != X25
      | X24 = c_List_Olist_ONil ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1597])])]) ).

fof(c_0_2959,plain,
    ! [X24,X25,X26] :
      ( c_append(X25,X24,X26) != X24
      | X25 = c_List_Olist_ONil ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1598])])]) ).

fof(c_0_2960,plain,
    ! [X17,X18,X19] :
      ( c_union(X18,X17,X19) != c_emptyset
      | X17 = c_emptyset ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1599])])]) ).

fof(c_0_2961,plain,
    ! [X17,X18,X19] :
      ( c_union(X18,X17,X19) != c_emptyset
      | X18 = c_emptyset ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1600])])]) ).

fof(c_0_2962,plain,
    ! [X24,X25,X26] :
      ( c_append(X25,X24,X26) != c_List_Olist_ONil
      | X24 = c_List_Olist_ONil ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1601])])]) ).

fof(c_0_2963,plain,
    ! [X24,X25,X26] :
      ( c_append(X25,X24,X26) != c_List_Olist_ONil
      | X25 = c_List_Olist_ONil ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1602])])]) ).

fof(c_0_2964,plain,
    ! [X24,X25,X26] :
      ( c_List_Olist_ONil != c_append(X25,X24,X26)
      | X24 = c_List_Olist_ONil ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1603])])]) ).

fof(c_0_2965,plain,
    ! [X24,X25,X26] :
      ( c_List_Olist_ONil != c_append(X25,X24,X26)
      | X25 = c_List_Olist_ONil ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1604])])]) ).

fof(c_0_2966,plain,
    ! [X16,X17,X18] :
      ( c_Equiv__Relations_Oquotient(X17,X16,X18) != c_emptyset
      | X17 = c_emptyset ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1605])])]) ).

fof(c_0_2967,plain,
    ! [X16,X17,X18] :
      ( c_emptyset != c_Equiv__Relations_Oquotient(X17,X16,X18)
      | X17 = c_emptyset ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1606])])]) ).

fof(c_0_2968,plain,
    ! [X31,X32,X33] : c_List_Olist_OCons(X32,X31,X33) != c_List_Olist_ONil,
    inference(variable_rename,[status(thm)],[c_0_1607]) ).

fof(c_0_2969,plain,
    ! [X31,X32,X33] : c_List_Olist_ONil != c_List_Olist_OCons(X32,X31,X33),
    inference(variable_rename,[status(thm)],[c_0_1608]) ).

fof(c_0_2970,plain,
    ~ c_in(c_UNIV,c_Finite__Set_OFinites,tc_set(tc_nat)),
    c_0_1609 ).

fof(c_0_2971,plain,
    ! [X16,X17] : c_in(c_List_Olist_ONil,c_List_Olists(X16,X17),tc_List_Olist(X17)),
    inference(variable_rename,[status(thm)],[c_0_1610]) ).

fof(c_0_2972,plain,
    ! [X23,X24] : c_in(c_List_Oset(X23,X24),c_Finite__Set_OFinites,tc_set(X24)),
    inference(variable_rename,[status(thm)],[c_0_1611]) ).

fof(c_0_2973,plain,
    ! [X20,X21] :
      ( c_plus(X21,X20,tc_nat) != c_0
      | X20 = c_0 ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1612])])]) ).

fof(c_0_2974,plain,
    ! [X20,X21] :
      ( c_plus(X21,X20,tc_nat) != c_0
      | X21 = c_0 ),
    inference(variable_rename,[status(thm)],[c_0_1613]) ).

fof(c_0_2975,plain,
    ! [X20] : ~ c_less(X20,X20,tc_nat),
    inference(variable_rename,[status(thm)],[c_0_1614]) ).

fof(c_0_2976,plain,
    ! [X6,X7] : ~ c_in(X6,c_emptyset,X7),
    inference(variable_rename,[status(thm)],[c_0_1615]) ).

fof(c_0_2977,plain,
    ! [X20] :
      ( ~ c_less(X20,c_1,tc_nat)
      | X20 = c_0 ),
    inference(variable_rename,[status(thm)],[c_0_1616]) ).

fof(c_0_2978,plain,
    ! [X33] :
      ( ~ c_lessequals(X33,c_0,tc_nat)
      | X33 = c_0 ),
    inference(variable_rename,[status(thm)],[c_0_1617]) ).

fof(c_0_2979,plain,
    ! [X14] :
      ( ~ c_Divides_Oop_Advd(c_0,X14,tc_IntDef_Oint)
      | X14 = c_0 ),
    inference(variable_rename,[status(thm)],[c_0_1618]) ).

fof(c_0_2980,plain,
    ! [X14] :
      ( ~ c_Divides_Oop_Advd(c_0,X14,tc_nat)
      | X14 = c_0 ),
    inference(variable_rename,[status(thm)],[c_0_1619]) ).

fof(c_0_2981,plain,
    ! [X20] : ~ c_less(X20,c_0,tc_nat),
    inference(variable_rename,[status(thm)],[c_0_1620]) ).

fof(c_0_2982,plain,
    ! [X11] : c_in(c_SetInterval_OlessThan(X11,tc_nat),c_Finite__Set_OFinites,tc_set(tc_nat)),
    inference(variable_rename,[status(thm)],[c_0_1621]) ).

fof(c_0_2983,plain,
    ! [X11] : c_in(c_SetInterval_OatMost(X11,tc_nat),c_Finite__Set_OFinites,tc_set(tc_nat)),
    inference(variable_rename,[status(thm)],[c_0_1622]) ).

fof(c_0_2984,plain,
    ~ c_less(c_0,c_0,tc_nat),
    c_0_1623 ).

fof(c_0_2985,plain,
    ! [X15,X16] :
      ( ~ c_Wellfounded__Recursion_Owf(X15,X16)
      | c_Wellfounded__Recursion_Owf(c_List_Olex(X15,X16),tc_List_Olist(X16)) ),
    inference(variable_rename,[status(thm)],[c_0_1624]) ).

fof(c_0_2986,plain,
    ! [X15,X16] :
      ( ~ c_Wellfounded__Recursion_Owf(X15,X16)
      | c_Wellfounded__Recursion_Owf(c_List_Olenlex(X15,X16),tc_List_Olist(X16)) ),
    inference(variable_rename,[status(thm)],[c_0_1625]) ).

fof(c_0_2987,plain,
    ! [X17,X18,X19] :
      ( c_uminus(X18,tc_set(X19)) != c_uminus(X17,tc_set(X19))
      | X18 = X17 ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1626])])]) ).

fof(c_0_2988,plain,
    ! [X4,X5] :
      ( ~ class_Orderings_Oorder(X5)
      | c_lessequals(X4,X4,X5) ),
    inference(variable_rename,[status(thm)],[c_0_1627]) ).

fof(c_0_2989,plain,
    ! [X16,X17] : c_lessequals(X16,X16,tc_set(X17)),
    inference(variable_rename,[status(thm)],[c_0_1628]) ).

fof(c_0_2990,plain,
    ! [X16,X17] : c_lessequals(c_emptyset,X16,tc_set(X17)),
    inference(variable_rename,[status(thm)],[c_0_1629]) ).

fof(c_0_2991,plain,
    ! [X20] : c_less(X20,c_Suc(X20),tc_nat),
    inference(variable_rename,[status(thm)],[c_0_1630]) ).

fof(c_0_2992,plain,
    ! [X20] : c_less(c_0,c_Suc(X20),tc_nat),
    inference(variable_rename,[status(thm)],[c_0_1631]) ).

fof(c_0_2993,plain,
    ! [X4] : c_in(c_emptyset,c_Finite__Set_OFinites,tc_set(X4)),
    inference(variable_rename,[status(thm)],[c_0_1632]) ).

fof(c_0_2994,plain,
    ! [X11] : c_Divides_Oop_Advd(c_Suc(c_0),X11,tc_nat),
    inference(variable_rename,[status(thm)],[c_0_1633]) ).

fof(c_0_2995,axiom,
    c_less(c_0,c_Suc(c_0),tc_nat),
    c_0_1634 ).

fof(c_0_2996,plain,
    ! [X23,X24] : X23 = c_append(X23,c_List_Olist_ONil,X24),
    inference(variable_rename,[status(thm)],[c_0_1635]) ).

fof(c_0_2997,plain,
    ! [X24,X25] : X24 = c_append(c_List_Olist_ONil,X24,X25),
    inference(variable_rename,[status(thm)],[c_0_1636]) ).

fof(c_0_2998,plain,
    ! [X23,X24] : c_append(X23,c_List_Olist_ONil,X24) = X23,
    inference(variable_rename,[status(thm)],[c_0_1637]) ).

fof(c_0_2999,plain,
    ! [X24,X25] : c_append(c_List_Olist_ONil,X24,X25) = X24,
    inference(variable_rename,[status(thm)],[c_0_1638]) ).

fof(c_0_3000,plain,
    ! [X25,X26,X27] :
      ( ~ class_Orderings_Olinorder(X27)
      | c_SetInterval_OlessThan(X26,X27) != c_SetInterval_OlessThan(X25,X27)
      | X26 = X25 ),
    inference(variable_rename,[status(thm)],[c_0_1639]) ).

fof(c_0_3001,plain,
    ! [X25,X26,X27] :
      ( ~ class_Orderings_Olinorder(X27)
      | c_SetInterval_OgreaterThan(X26,X27) != c_SetInterval_OgreaterThan(X25,X27)
      | X26 = X25 ),
    inference(variable_rename,[status(thm)],[c_0_1640]) ).

fof(c_0_3002,plain,
    ! [X25,X26,X27] :
      ( ~ class_Orderings_Olinorder(X27)
      | c_SetInterval_OatMost(X26,X27) != c_SetInterval_OatMost(X25,X27)
      | X26 = X25 ),
    inference(variable_rename,[status(thm)],[c_0_1641]) ).

fof(c_0_3003,plain,
    ! [X25,X26,X27] :
      ( ~ class_Orderings_Olinorder(X27)
      | c_SetInterval_OatLeast(X26,X27) != c_SetInterval_OatLeast(X25,X27)
      | X26 = X25 ),
    inference(variable_rename,[status(thm)],[c_0_1642]) ).

fof(c_0_3004,plain,
    ! [X4,X5] : c_in(X4,c_UNIV,X5),
    inference(variable_rename,[status(thm)],[c_0_1643]) ).

fof(c_0_3005,plain,
    ! [X20] :
      ( c_less(c_0,X20,tc_nat)
      | X20 = c_0 ),
    inference(variable_rename,[status(thm)],[c_0_1644]) ).

fof(c_0_3006,plain,
    ! [X15,X16] : c_Equiv__Relations_Oquotient(c_emptyset,X15,X16) = c_emptyset,
    inference(variable_rename,[status(thm)],[c_0_1645]) ).

fof(c_0_3007,plain,
    ! [X15,X16] : c_emptyset = c_Equiv__Relations_Oquotient(c_emptyset,X15,X16),
    inference(variable_rename,[status(thm)],[c_0_1646]) ).

fof(c_0_3008,plain,
    ! [X20] : c_lessequals(c_0,X20,tc_nat),
    inference(variable_rename,[status(thm)],[c_0_1647]) ).

fof(c_0_3009,plain,
    ! [X14] : c_Divides_Oop_Advd(c_1,X14,tc_IntDef_Oint),
    inference(variable_rename,[status(thm)],[c_0_1648]) ).

fof(c_0_3010,plain,
    ! [X14] : c_Divides_Oop_Advd(X14,c_0,tc_IntDef_Oint),
    inference(variable_rename,[status(thm)],[c_0_1649]) ).

fof(c_0_3011,plain,
    ! [X14] : c_Divides_Oop_Advd(X14,c_0,tc_nat),
    inference(variable_rename,[status(thm)],[c_0_1650]) ).

fof(c_0_3012,plain,
    ! [X4] : c_union(c_emptyset,c_emptyset,X4) = c_emptyset,
    inference(variable_rename,[status(thm)],[c_0_1651]) ).

fof(c_0_3013,plain,
    ! [X4] : c_append(c_List_Olist_ONil,c_List_Olist_ONil,X4) = c_List_Olist_ONil,
    inference(variable_rename,[status(thm)],[c_0_1652]) ).

fof(c_0_3014,plain,
    ! [X4] : c_List_Olist_ONil = c_append(c_List_Olist_ONil,c_List_Olist_ONil,X4),
    inference(variable_rename,[status(thm)],[c_0_1653]) ).

fof(c_0_3015,axiom,
    c_less(c_0,c_1,tc_nat),
    c_0_1654 ).

fof(c_0_3016,axiom,
    c_lessequals(c_0,c_0,tc_nat),
    c_0_1655 ).

fof(c_0_3017,axiom,
    c_plus(c_0,c_0,tc_nat) = c_0,
    c_0_1656 ).

fof(c_0_3018,axiom,
    c_Divides_Oop_Advd(c_0,c_0,tc_IntDef_Oint),
    c_0_1657 ).

fof(c_0_3019,axiom,
    c_Divides_Oop_Advd(c_0,c_0,tc_nat),
    c_0_1658 ).

fof(c_0_3020,plain,
    ! [X24,X25,X26] :
      ( c_List_Orev(X25,X26) != c_List_Orev(X24,X26)
      | X25 = X24 ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1659])])]) ).

fof(c_0_3021,plain,
    ! [X30,X31,X32,X33] :
      ( c_List_Ochar_OChar(X33,X31) != c_List_Ochar_OChar(X32,X30)
      | X31 = X30 ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1660])])]) ).

fof(c_0_3022,plain,
    ! [X30,X31,X32,X33] :
      ( c_List_Ochar_OChar(X33,X31) != c_List_Ochar_OChar(X32,X30)
      | X33 = X32 ),
    inference(variable_rename,[status(thm)],[c_0_1661]) ).

fof(c_0_3023,plain,
    ! [X6,X7,X8] :
      ( c_Datatype_Ooption_OSome(X7,X8) != c_Datatype_Ooption_OSome(X6,X8)
      | X7 = X6 ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1662])])]) ).

fof(c_0_3024,plain,
    ! [X54,X55] :
      ( class_Finite__Set_Ofinite(tc_sum(X54,X55))
      | ~ class_Finite__Set_Ofinite(X55)
      | ~ class_Finite__Set_Ofinite(X54) ),
    inference(variable_rename,[status(thm)],[c_0_1663]) ).

fof(c_0_3025,plain,
    ! [X54,X55] :
      ( class_Finite__Set_Ofinite(tc_prod(X54,X55))
      | ~ class_Finite__Set_Ofinite(X55)
      | ~ class_Finite__Set_Ofinite(X54) ),
    inference(variable_rename,[status(thm)],[c_0_1664]) ).

fof(c_0_3026,plain,
    ! [X54,X55] :
      ( class_Finite__Set_Ofinite(tc_fun(X54,X55))
      | ~ class_Finite__Set_Ofinite(X55)
      | ~ class_Finite__Set_Ofinite(X54) ),
    inference(variable_rename,[status(thm)],[c_0_1665]) ).

fof(c_0_3027,plain,
    ! [X4,X5] :
      ( X4 = c_Datatype_Ooption_ONone
      | X4 = c_Datatype_Ooption_OSome(c_Main_Onot__Some__eq__iff1__1(X4,X5),X5) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1666])])]) ).

fof(c_0_3028,plain,
    ! [X4,X5] :
      ( X4 = c_Datatype_Ooption_ONone
      | X4 = c_Datatype_Ooption_OSome(c_Main_Onot__None__eq__iff1__1(X4,X5),X5) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1667])])]) ).

fof(c_0_3029,plain,
    ! [X23,X24] : c_List_Odistinct(c_List_Oremdups(X23,X24),X24),
    inference(variable_rename,[status(thm)],[c_0_1668]) ).

fof(c_0_3030,plain,
    ! [X23,X24] :
      ( c_Nat_Osize(X23,tc_List_Olist(X24)) != c_0
      | X23 = c_List_Olist_ONil ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1669])])]) ).

fof(c_0_3031,plain,
    ! [X54,X55] : class_Nat_Opower(tc_fun(X54,X55)),
    inference(variable_rename,[status(thm)],[c_0_1670]) ).

fof(c_0_3032,plain,
    ! [X23,X24] :
      ( c_List_Oset(X23,X24) != c_emptyset
      | X23 = c_List_Olist_ONil ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1671])])]) ).

fof(c_0_3033,plain,
    ! [X23,X24] :
      ( c_emptyset != c_List_Oset(X23,X24)
      | X23 = c_List_Olist_ONil ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1672])])]) ).

fof(c_0_3034,plain,
    ! [X23,X24] :
      ( c_List_Orev(X23,X24) != c_List_Olist_ONil
      | X23 = c_List_Olist_ONil ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1673])])]) ).

fof(c_0_3035,plain,
    ! [X23,X24] :
      ( c_List_Olist_ONil != c_List_Orev(X23,X24)
      | X23 = c_List_Olist_ONil ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1674])])]) ).

fof(c_0_3036,plain,
    ! [X5,X6] : c_Datatype_Ooption_OSome(X5,X6) != c_Datatype_Ooption_ONone,
    inference(variable_rename,[status(thm)],[c_0_1675]) ).

fof(c_0_3037,plain,
    ! [X5,X6] : c_Datatype_Ooption_ONone != c_Datatype_Ooption_OSome(X5,X6),
    inference(variable_rename,[status(thm)],[c_0_1676]) ).

fof(c_0_3038,plain,
    ! [X4] : c_Nat_Osize(c_List_Olist_ONil,tc_List_Olist(X4)) = c_0,
    inference(variable_rename,[status(thm)],[c_0_1677]) ).

fof(c_0_3039,plain,
    ! [X53] :
      ( class_Finite__Set_Ofinite(tc_set(X53))
      | ~ class_Finite__Set_Ofinite(X53) ),
    inference(variable_rename,[status(thm)],[c_0_1678]) ).

fof(c_0_3040,plain,
    ! [X53] :
      ( class_Finite__Set_Ofinite(tc_Datatype_Ooption(X53))
      | ~ class_Finite__Set_Ofinite(X53) ),
    inference(variable_rename,[status(thm)],[c_0_1679]) ).

fof(c_0_3041,plain,
    ! [X20,X21] :
      ( c_Suc(X21) != c_Suc(X20)
      | X21 = X20 ),
    inference(variable_rename,[status(thm)],[c_0_1680]) ).

fof(c_0_3042,plain,
    ! [X20,X21] :
      ( c_IntDef_Oint(X21) != c_IntDef_Oint(X20)
      | X21 = X20 ),
    inference(variable_rename,[status(thm)],[c_0_1681]) ).

fof(c_0_3043,plain,
    ! [X4] : c_Wellfounded__Recursion_Owf(c_emptyset,X4),
    inference(variable_rename,[status(thm)],[c_0_1682]) ).

fof(c_0_3044,plain,
    ! [X4] : c_List_Oset(c_List_Olist_ONil,X4) = c_emptyset,
    inference(variable_rename,[status(thm)],[c_0_1683]) ).

fof(c_0_3045,plain,
    ! [X4] : c_emptyset = c_List_Oset(c_List_Olist_ONil,X4),
    inference(variable_rename,[status(thm)],[c_0_1684]) ).

fof(c_0_3046,plain,
    ! [X4] : c_List_Orev(c_List_Olist_ONil,X4) = c_List_Olist_ONil,
    inference(variable_rename,[status(thm)],[c_0_1685]) ).

fof(c_0_3047,plain,
    ! [X4] : c_List_Olist_ONil = c_List_Orev(c_List_Olist_ONil,X4),
    inference(variable_rename,[status(thm)],[c_0_1686]) ).

fof(c_0_3048,plain,
    ! [X55] :
      ( ~ class_Wellfounded__Recursion_Owellorder(X55)
      | class_Orderings_Olinorder(X55) ),
    inference(variable_rename,[status(thm)],[c_0_1687]) ).

fof(c_0_3049,plain,
    ! [X55] :
      ( ~ class_Wellfounded__Recursion_Owellorder(X55)
      | class_LOrder_Olorder(X55) ),
    inference(variable_rename,[status(thm)],[c_0_1688]) ).

fof(c_0_3050,plain,
    ! [X55] :
      ( ~ class_Wellfounded__Recursion_Owellorder(X55)
      | class_LOrder_Ojoin__semilorder(X55) ),
    inference(variable_rename,[status(thm)],[c_0_1689]) ).

fof(c_0_3051,plain,
    ! [X55] :
      ( ~ class_Wellfounded__Recursion_Owellorder(X55)
      | class_LOrder_Omeet__semilorder(X55) ),
    inference(variable_rename,[status(thm)],[c_0_1690]) ).

fof(c_0_3052,plain,
    ! [X55] :
      ( ~ class_Wellfounded__Recursion_Owellorder(X55)
      | class_Orderings_Oorder(X55) ),
    inference(variable_rename,[status(thm)],[c_0_1691]) ).

fof(c_0_3053,plain,
    ! [X55] :
      ( ~ class_Wellfounded__Recursion_Owellorder(X55)
      | class_Orderings_Oord(X55) ),
    inference(variable_rename,[status(thm)],[c_0_1692]) ).

fof(c_0_3054,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Osemiring__1__cancel(X55)
      | class_OrderedGroup_Omonoid__mult(X55) ),
    inference(variable_rename,[status(thm)],[c_0_1693]) ).

fof(c_0_3055,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Osemiring__1__cancel(X55)
      | class_HOL_Oplus(X55) ),
    inference(variable_rename,[status(thm)],[c_0_1694]) ).

fof(c_0_3056,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Osemiring__1__cancel(X55)
      | class_OrderedGroup_Osemigroup__add(X55) ),
    inference(variable_rename,[status(thm)],[c_0_1695]) ).

fof(c_0_3057,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Osemiring__1__cancel(X55)
      | class_OrderedGroup_Oab__semigroup__add(X55) ),
    inference(variable_rename,[status(thm)],[c_0_1696]) ).

fof(c_0_3058,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Osemiring__1__cancel(X55)
      | class_HOL_Ozero(X55) ),
    inference(variable_rename,[status(thm)],[c_0_1697]) ).

fof(c_0_3059,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Osemiring__1__cancel(X55)
      | class_OrderedGroup_Ocomm__monoid__add(X55) ),
    inference(variable_rename,[status(thm)],[c_0_1698]) ).

fof(c_0_3060,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Osemiring__1__cancel(X55)
      | class_Ring__and__Field_Osemiring(X55) ),
    inference(variable_rename,[status(thm)],[c_0_1699]) ).

fof(c_0_3061,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Osemiring__1__cancel(X55)
      | class_Ring__and__Field_Osemiring__0(X55) ),
    inference(variable_rename,[status(thm)],[c_0_1700]) ).

fof(c_0_3062,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Osemiring__1__cancel(X55)
      | class_Ring__and__Field_Osemiring__0__cancel(X55) ),
    inference(variable_rename,[status(thm)],[c_0_1701]) ).

fof(c_0_3063,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Osemiring__1__cancel(X55)
      | class_OrderedGroup_Ocancel__semigroup__add(X55) ),
    inference(variable_rename,[status(thm)],[c_0_1702]) ).

fof(c_0_3064,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Osemiring__1__cancel(X55)
      | class_OrderedGroup_Ocancel__ab__semigroup__add(X55) ),
    inference(variable_rename,[status(thm)],[c_0_1703]) ).

fof(c_0_3065,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Osemiring__1__cancel(X55)
      | class_HOL_Otimes(X55) ),
    inference(variable_rename,[status(thm)],[c_0_1704]) ).

fof(c_0_3066,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Osemiring__1__cancel(X55)
      | class_OrderedGroup_Osemigroup__mult(X55) ),
    inference(variable_rename,[status(thm)],[c_0_1705]) ).

fof(c_0_3067,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Osemiring__1__cancel(X55)
      | class_HOL_Oone(X55) ),
    inference(variable_rename,[status(thm)],[c_0_1706]) ).

fof(c_0_3068,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Osemiring__1__cancel(X55)
      | class_Ring__and__Field_Oaxclass__0__neq__1(X55) ),
    inference(variable_rename,[status(thm)],[c_0_1707]) ).

fof(c_0_3069,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Osemiring__1__cancel(X55)
      | class_Ring__and__Field_Osemiring__1(X55) ),
    inference(variable_rename,[status(thm)],[c_0_1708]) ).

fof(c_0_3070,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Osemiring__1(X55)
      | class_OrderedGroup_Osemigroup__add(X55) ),
    inference(variable_rename,[status(thm)],[c_0_1709]) ).

fof(c_0_3071,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Osemiring__1(X55)
      | class_OrderedGroup_Oab__semigroup__add(X55) ),
    inference(variable_rename,[status(thm)],[c_0_1710]) ).

fof(c_0_3072,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Osemiring__1(X55)
      | class_OrderedGroup_Ocomm__monoid__add(X55) ),
    inference(variable_rename,[status(thm)],[c_0_1711]) ).

fof(c_0_3073,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Osemiring__1(X55)
      | class_HOL_Otimes(X55) ),
    inference(variable_rename,[status(thm)],[c_0_1712]) ).

fof(c_0_3074,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Osemiring__1(X55)
      | class_OrderedGroup_Osemigroup__mult(X55) ),
    inference(variable_rename,[status(thm)],[c_0_1713]) ).

fof(c_0_3075,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Osemiring__1(X55)
      | class_Ring__and__Field_Osemiring(X55) ),
    inference(variable_rename,[status(thm)],[c_0_1714]) ).

fof(c_0_3076,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Osemiring__1(X55)
      | class_Ring__and__Field_Osemiring__0(X55) ),
    inference(variable_rename,[status(thm)],[c_0_1715]) ).

fof(c_0_3077,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Osemiring__1(X55)
      | class_HOL_Oone(X55) ),
    inference(variable_rename,[status(thm)],[c_0_1716]) ).

fof(c_0_3078,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Osemiring__1(X55)
      | class_OrderedGroup_Omonoid__mult(X55) ),
    inference(variable_rename,[status(thm)],[c_0_1717]) ).

fof(c_0_3079,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Osemiring__1(X55)
      | class_HOL_Oplus(X55) ),
    inference(variable_rename,[status(thm)],[c_0_1718]) ).

fof(c_0_3080,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Osemiring__1(X55)
      | class_HOL_Ozero(X55) ),
    inference(variable_rename,[status(thm)],[c_0_1719]) ).

fof(c_0_3081,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Osemiring__1(X55)
      | class_Ring__and__Field_Oaxclass__0__neq__1(X55) ),
    inference(variable_rename,[status(thm)],[c_0_1720]) ).

fof(c_0_3082,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Osemiring__0__cancel(X55)
      | class_OrderedGroup_Ocancel__ab__semigroup__add(X55) ),
    inference(variable_rename,[status(thm)],[c_0_1721]) ).

fof(c_0_3083,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Osemiring__0__cancel(X55)
      | class_HOL_Ozero(X55) ),
    inference(variable_rename,[status(thm)],[c_0_1722]) ).

fof(c_0_3084,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Osemiring__0__cancel(X55)
      | class_HOL_Oplus(X55) ),
    inference(variable_rename,[status(thm)],[c_0_1723]) ).

fof(c_0_3085,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Osemiring__0__cancel(X55)
      | class_OrderedGroup_Osemigroup__add(X55) ),
    inference(variable_rename,[status(thm)],[c_0_1724]) ).

fof(c_0_3086,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Osemiring__0__cancel(X55)
      | class_OrderedGroup_Oab__semigroup__add(X55) ),
    inference(variable_rename,[status(thm)],[c_0_1725]) ).

fof(c_0_3087,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Osemiring__0__cancel(X55)
      | class_OrderedGroup_Ocomm__monoid__add(X55) ),
    inference(variable_rename,[status(thm)],[c_0_1726]) ).

fof(c_0_3088,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Osemiring__0__cancel(X55)
      | class_HOL_Otimes(X55) ),
    inference(variable_rename,[status(thm)],[c_0_1727]) ).

fof(c_0_3089,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Osemiring__0__cancel(X55)
      | class_OrderedGroup_Osemigroup__mult(X55) ),
    inference(variable_rename,[status(thm)],[c_0_1728]) ).

fof(c_0_3090,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Osemiring__0__cancel(X55)
      | class_OrderedGroup_Ocancel__semigroup__add(X55) ),
    inference(variable_rename,[status(thm)],[c_0_1729]) ).

fof(c_0_3091,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Osemiring__0__cancel(X55)
      | class_Ring__and__Field_Osemiring(X55) ),
    inference(variable_rename,[status(thm)],[c_0_1730]) ).

fof(c_0_3092,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Osemiring__0__cancel(X55)
      | class_Ring__and__Field_Osemiring__0(X55) ),
    inference(variable_rename,[status(thm)],[c_0_1731]) ).

fof(c_0_3093,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Osemiring__0(X55)
      | class_HOL_Ozero(X55) ),
    inference(variable_rename,[status(thm)],[c_0_1732]) ).

fof(c_0_3094,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Osemiring__0(X55)
      | class_OrderedGroup_Ocomm__monoid__add(X55) ),
    inference(variable_rename,[status(thm)],[c_0_1733]) ).

fof(c_0_3095,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Osemiring__0(X55)
      | class_HOL_Otimes(X55) ),
    inference(variable_rename,[status(thm)],[c_0_1734]) ).

fof(c_0_3096,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Osemiring__0(X55)
      | class_OrderedGroup_Osemigroup__mult(X55) ),
    inference(variable_rename,[status(thm)],[c_0_1735]) ).

fof(c_0_3097,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Osemiring__0(X55)
      | class_HOL_Oplus(X55) ),
    inference(variable_rename,[status(thm)],[c_0_1736]) ).

fof(c_0_3098,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Osemiring__0(X55)
      | class_OrderedGroup_Osemigroup__add(X55) ),
    inference(variable_rename,[status(thm)],[c_0_1737]) ).

fof(c_0_3099,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Osemiring__0(X55)
      | class_OrderedGroup_Oab__semigroup__add(X55) ),
    inference(variable_rename,[status(thm)],[c_0_1738]) ).

fof(c_0_3100,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Osemiring__0(X55)
      | class_Ring__and__Field_Osemiring(X55) ),
    inference(variable_rename,[status(thm)],[c_0_1739]) ).

fof(c_0_3101,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Osemiring(X55)
      | class_HOL_Otimes(X55) ),
    inference(variable_rename,[status(thm)],[c_0_1740]) ).

fof(c_0_3102,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Osemiring(X55)
      | class_OrderedGroup_Osemigroup__mult(X55) ),
    inference(variable_rename,[status(thm)],[c_0_1741]) ).

fof(c_0_3103,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Osemiring(X55)
      | class_HOL_Oplus(X55) ),
    inference(variable_rename,[status(thm)],[c_0_1742]) ).

fof(c_0_3104,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Osemiring(X55)
      | class_OrderedGroup_Osemigroup__add(X55) ),
    inference(variable_rename,[status(thm)],[c_0_1743]) ).

fof(c_0_3105,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Osemiring(X55)
      | class_OrderedGroup_Oab__semigroup__add(X55) ),
    inference(variable_rename,[status(thm)],[c_0_1744]) ).

fof(c_0_3106,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oring__1(X55)
      | class_HOL_Otimes(X55) ),
    inference(variable_rename,[status(thm)],[c_0_1745]) ).

fof(c_0_3107,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oring__1(X55)
      | class_OrderedGroup_Osemigroup__mult(X55) ),
    inference(variable_rename,[status(thm)],[c_0_1746]) ).

fof(c_0_3108,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oring__1(X55)
      | class_Ring__and__Field_Osemiring(X55) ),
    inference(variable_rename,[status(thm)],[c_0_1747]) ).

fof(c_0_3109,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oring__1(X55)
      | class_Ring__and__Field_Osemiring__0(X55) ),
    inference(variable_rename,[status(thm)],[c_0_1748]) ).

fof(c_0_3110,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oring__1(X55)
      | class_OrderedGroup_Ocancel__semigroup__add(X55) ),
    inference(variable_rename,[status(thm)],[c_0_1749]) ).

fof(c_0_3111,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oring__1(X55)
      | class_OrderedGroup_Ocancel__ab__semigroup__add(X55) ),
    inference(variable_rename,[status(thm)],[c_0_1750]) ).

fof(c_0_3112,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oring__1(X55)
      | class_Ring__and__Field_Osemiring__0__cancel(X55) ),
    inference(variable_rename,[status(thm)],[c_0_1751]) ).

fof(c_0_3113,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oring__1(X55)
      | class_HOL_Ominus(X55) ),
    inference(variable_rename,[status(thm)],[c_0_1752]) ).

fof(c_0_3114,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oring__1(X55)
      | class_Ring__and__Field_Osemiring__1__cancel(X55) ),
    inference(variable_rename,[status(thm)],[c_0_1753]) ).

fof(c_0_3115,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oring__1(X55)
      | class_HOL_Oone(X55) ),
    inference(variable_rename,[status(thm)],[c_0_1754]) ).

fof(c_0_3116,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oring__1(X55)
      | class_OrderedGroup_Omonoid__mult(X55) ),
    inference(variable_rename,[status(thm)],[c_0_1755]) ).

fof(c_0_3117,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oring__1(X55)
      | class_Ring__and__Field_Oaxclass__0__neq__1(X55) ),
    inference(variable_rename,[status(thm)],[c_0_1756]) ).

fof(c_0_3118,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oring__1(X55)
      | class_Ring__and__Field_Osemiring__1(X55) ),
    inference(variable_rename,[status(thm)],[c_0_1757]) ).

fof(c_0_3119,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oring__1(X55)
      | class_HOL_Ozero(X55) ),
    inference(variable_rename,[status(thm)],[c_0_1758]) ).

fof(c_0_3120,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oring__1(X55)
      | class_HOL_Oplus(X55) ),
    inference(variable_rename,[status(thm)],[c_0_1759]) ).

fof(c_0_3121,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oring__1(X55)
      | class_OrderedGroup_Osemigroup__add(X55) ),
    inference(variable_rename,[status(thm)],[c_0_1760]) ).

fof(c_0_3122,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oring__1(X55)
      | class_OrderedGroup_Oab__semigroup__add(X55) ),
    inference(variable_rename,[status(thm)],[c_0_1761]) ).

fof(c_0_3123,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oring__1(X55)
      | class_OrderedGroup_Ocomm__monoid__add(X55) ),
    inference(variable_rename,[status(thm)],[c_0_1762]) ).

fof(c_0_3124,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oring__1(X55)
      | class_OrderedGroup_Oab__group__add(X55) ),
    inference(variable_rename,[status(thm)],[c_0_1763]) ).

fof(c_0_3125,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oring__1(X55)
      | class_Ring__and__Field_Oring(X55) ),
    inference(variable_rename,[status(thm)],[c_0_1764]) ).

fof(c_0_3126,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oring(X55)
      | class_HOL_Ozero(X55) ),
    inference(variable_rename,[status(thm)],[c_0_1765]) ).

fof(c_0_3127,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oring(X55)
      | class_OrderedGroup_Ocomm__monoid__add(X55) ),
    inference(variable_rename,[status(thm)],[c_0_1766]) ).

fof(c_0_3128,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oring(X55)
      | class_HOL_Ominus(X55) ),
    inference(variable_rename,[status(thm)],[c_0_1767]) ).

fof(c_0_3129,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oring(X55)
      | class_OrderedGroup_Oab__group__add(X55) ),
    inference(variable_rename,[status(thm)],[c_0_1768]) ).

fof(c_0_3130,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oring(X55)
      | class_HOL_Otimes(X55) ),
    inference(variable_rename,[status(thm)],[c_0_1769]) ).

fof(c_0_3131,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oring(X55)
      | class_OrderedGroup_Osemigroup__mult(X55) ),
    inference(variable_rename,[status(thm)],[c_0_1770]) ).

fof(c_0_3132,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oring(X55)
      | class_HOL_Oplus(X55) ),
    inference(variable_rename,[status(thm)],[c_0_1771]) ).

fof(c_0_3133,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oring(X55)
      | class_OrderedGroup_Osemigroup__add(X55) ),
    inference(variable_rename,[status(thm)],[c_0_1772]) ).

fof(c_0_3134,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oring(X55)
      | class_Ring__and__Field_Osemiring__0(X55) ),
    inference(variable_rename,[status(thm)],[c_0_1773]) ).

fof(c_0_3135,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oring(X55)
      | class_Ring__and__Field_Osemiring__0__cancel(X55) ),
    inference(variable_rename,[status(thm)],[c_0_1774]) ).

fof(c_0_3136,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oring(X55)
      | class_OrderedGroup_Ocancel__semigroup__add(X55) ),
    inference(variable_rename,[status(thm)],[c_0_1775]) ).

fof(c_0_3137,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oring(X55)
      | class_OrderedGroup_Ocancel__ab__semigroup__add(X55) ),
    inference(variable_rename,[status(thm)],[c_0_1776]) ).

fof(c_0_3138,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oring(X55)
      | class_OrderedGroup_Oab__semigroup__add(X55) ),
    inference(variable_rename,[status(thm)],[c_0_1777]) ).

fof(c_0_3139,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oring(X55)
      | class_Ring__and__Field_Osemiring(X55) ),
    inference(variable_rename,[status(thm)],[c_0_1778]) ).

fof(c_0_3140,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Opordered__semiring(X55)
      | class_OrderedGroup_Opordered__ab__semigroup__add(X55) ),
    inference(variable_rename,[status(thm)],[c_0_1779]) ).

fof(c_0_3141,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Opordered__semiring(X55)
      | class_HOL_Ozero(X55) ),
    inference(variable_rename,[status(thm)],[c_0_1780]) ).

fof(c_0_3142,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Opordered__semiring(X55)
      | class_HOL_Oplus(X55) ),
    inference(variable_rename,[status(thm)],[c_0_1781]) ).

fof(c_0_3143,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Opordered__semiring(X55)
      | class_OrderedGroup_Osemigroup__add(X55) ),
    inference(variable_rename,[status(thm)],[c_0_1782]) ).

fof(c_0_3144,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Opordered__semiring(X55)
      | class_OrderedGroup_Oab__semigroup__add(X55) ),
    inference(variable_rename,[status(thm)],[c_0_1783]) ).

fof(c_0_3145,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Opordered__semiring(X55)
      | class_OrderedGroup_Ocomm__monoid__add(X55) ),
    inference(variable_rename,[status(thm)],[c_0_1784]) ).

fof(c_0_3146,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Opordered__semiring(X55)
      | class_HOL_Otimes(X55) ),
    inference(variable_rename,[status(thm)],[c_0_1785]) ).

fof(c_0_3147,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Opordered__semiring(X55)
      | class_OrderedGroup_Osemigroup__mult(X55) ),
    inference(variable_rename,[status(thm)],[c_0_1786]) ).

fof(c_0_3148,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Opordered__semiring(X55)
      | class_Orderings_Oord(X55) ),
    inference(variable_rename,[status(thm)],[c_0_1787]) ).

fof(c_0_3149,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Opordered__semiring(X55)
      | class_Orderings_Oorder(X55) ),
    inference(variable_rename,[status(thm)],[c_0_1788]) ).

fof(c_0_3150,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Opordered__semiring(X55)
      | class_Ring__and__Field_Osemiring(X55) ),
    inference(variable_rename,[status(thm)],[c_0_1789]) ).

fof(c_0_3151,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Opordered__semiring(X55)
      | class_Ring__and__Field_Osemiring__0(X55) ),
    inference(variable_rename,[status(thm)],[c_0_1790]) ).

fof(c_0_3152,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Opordered__ring(X55)
      | class_HOL_Otimes(X55) ),
    inference(variable_rename,[status(thm)],[c_0_1791]) ).

fof(c_0_3153,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Opordered__ring(X55)
      | class_OrderedGroup_Osemigroup__mult(X55) ),
    inference(variable_rename,[status(thm)],[c_0_1792]) ).

fof(c_0_3154,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Opordered__ring(X55)
      | class_Ring__and__Field_Osemiring(X55) ),
    inference(variable_rename,[status(thm)],[c_0_1793]) ).

fof(c_0_3155,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Opordered__ring(X55)
      | class_Ring__and__Field_Osemiring__0(X55) ),
    inference(variable_rename,[status(thm)],[c_0_1794]) ).

fof(c_0_3156,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Opordered__ring(X55)
      | class_OrderedGroup_Ocancel__semigroup__add(X55) ),
    inference(variable_rename,[status(thm)],[c_0_1795]) ).

fof(c_0_3157,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Opordered__ring(X55)
      | class_OrderedGroup_Ocancel__ab__semigroup__add(X55) ),
    inference(variable_rename,[status(thm)],[c_0_1796]) ).

fof(c_0_3158,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Opordered__ring(X55)
      | class_Ring__and__Field_Osemiring__0__cancel(X55) ),
    inference(variable_rename,[status(thm)],[c_0_1797]) ).

fof(c_0_3159,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Opordered__ring(X55)
      | class_Ring__and__Field_Opordered__cancel__semiring(X55) ),
    inference(variable_rename,[status(thm)],[c_0_1798]) ).

fof(c_0_3160,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Opordered__ring(X55)
      | class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X55) ),
    inference(variable_rename,[status(thm)],[c_0_1799]) ).

fof(c_0_3161,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Opordered__ring(X55)
      | class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X55) ),
    inference(variable_rename,[status(thm)],[c_0_1800]) ).

fof(c_0_3162,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Opordered__ring(X55)
      | class_HOL_Ominus(X55) ),
    inference(variable_rename,[status(thm)],[c_0_1801]) ).

fof(c_0_3163,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Opordered__ring(X55)
      | class_OrderedGroup_Opordered__ab__group__add(X55) ),
    inference(variable_rename,[status(thm)],[c_0_1802]) ).

fof(c_0_3164,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Opordered__ring(X55)
      | class_Orderings_Oord(X55) ),
    inference(variable_rename,[status(thm)],[c_0_1803]) ).

fof(c_0_3165,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Opordered__ring(X55)
      | class_Orderings_Oorder(X55) ),
    inference(variable_rename,[status(thm)],[c_0_1804]) ).

fof(c_0_3166,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Opordered__ring(X55)
      | class_OrderedGroup_Opordered__ab__semigroup__add(X55) ),
    inference(variable_rename,[status(thm)],[c_0_1805]) ).

fof(c_0_3167,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Opordered__ring(X55)
      | class_Ring__and__Field_Opordered__semiring(X55) ),
    inference(variable_rename,[status(thm)],[c_0_1806]) ).

fof(c_0_3168,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Opordered__ring(X55)
      | class_HOL_Ozero(X55) ),
    inference(variable_rename,[status(thm)],[c_0_1807]) ).

fof(c_0_3169,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Opordered__ring(X55)
      | class_HOL_Oplus(X55) ),
    inference(variable_rename,[status(thm)],[c_0_1808]) ).

fof(c_0_3170,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Opordered__ring(X55)
      | class_OrderedGroup_Osemigroup__add(X55) ),
    inference(variable_rename,[status(thm)],[c_0_1809]) ).

fof(c_0_3171,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Opordered__ring(X55)
      | class_OrderedGroup_Oab__semigroup__add(X55) ),
    inference(variable_rename,[status(thm)],[c_0_1810]) ).

fof(c_0_3172,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Opordered__ring(X55)
      | class_OrderedGroup_Ocomm__monoid__add(X55) ),
    inference(variable_rename,[status(thm)],[c_0_1811]) ).

fof(c_0_3173,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Opordered__ring(X55)
      | class_OrderedGroup_Oab__group__add(X55) ),
    inference(variable_rename,[status(thm)],[c_0_1812]) ).

fof(c_0_3174,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Opordered__ring(X55)
      | class_Ring__and__Field_Oring(X55) ),
    inference(variable_rename,[status(thm)],[c_0_1813]) ).

fof(c_0_3175,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Opordered__comm__semiring(X55)
      | class_OrderedGroup_Osemigroup__add(X55) ),
    inference(variable_rename,[status(thm)],[c_0_1814]) ).

fof(c_0_3176,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Opordered__comm__semiring(X55)
      | class_OrderedGroup_Oab__semigroup__add(X55) ),
    inference(variable_rename,[status(thm)],[c_0_1815]) ).

fof(c_0_3177,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Opordered__comm__semiring(X55)
      | class_OrderedGroup_Ocomm__monoid__add(X55) ),
    inference(variable_rename,[status(thm)],[c_0_1816]) ).

fof(c_0_3178,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Opordered__comm__semiring(X55)
      | class_HOL_Otimes(X55) ),
    inference(variable_rename,[status(thm)],[c_0_1817]) ).

fof(c_0_3179,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Opordered__comm__semiring(X55)
      | class_OrderedGroup_Osemigroup__mult(X55) ),
    inference(variable_rename,[status(thm)],[c_0_1818]) ).

fof(c_0_3180,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Opordered__comm__semiring(X55)
      | class_Ring__and__Field_Osemiring(X55) ),
    inference(variable_rename,[status(thm)],[c_0_1819]) ).

fof(c_0_3181,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Opordered__comm__semiring(X55)
      | class_Ring__and__Field_Osemiring__0(X55) ),
    inference(variable_rename,[status(thm)],[c_0_1820]) ).

fof(c_0_3182,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Opordered__comm__semiring(X55)
      | class_OrderedGroup_Oab__semigroup__mult(X55) ),
    inference(variable_rename,[status(thm)],[c_0_1821]) ).

fof(c_0_3183,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Opordered__comm__semiring(X55)
      | class_Ring__and__Field_Opordered__semiring(X55) ),
    inference(variable_rename,[status(thm)],[c_0_1822]) ).

fof(c_0_3184,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Opordered__comm__semiring(X55)
      | class_Orderings_Oord(X55) ),
    inference(variable_rename,[status(thm)],[c_0_1823]) ).

fof(c_0_3185,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Opordered__comm__semiring(X55)
      | class_Orderings_Oorder(X55) ),
    inference(variable_rename,[status(thm)],[c_0_1824]) ).

fof(c_0_3186,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Opordered__comm__semiring(X55)
      | class_OrderedGroup_Opordered__ab__semigroup__add(X55) ),
    inference(variable_rename,[status(thm)],[c_0_1825]) ).

fof(c_0_3187,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Opordered__comm__semiring(X55)
      | class_HOL_Ozero(X55) ),
    inference(variable_rename,[status(thm)],[c_0_1826]) ).

fof(c_0_3188,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Opordered__comm__semiring(X55)
      | class_HOL_Oplus(X55) ),
    inference(variable_rename,[status(thm)],[c_0_1827]) ).

fof(c_0_3189,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Opordered__comm__semiring(X55)
      | class_Ring__and__Field_Ocomm__semiring(X55) ),
    inference(variable_rename,[status(thm)],[c_0_1828]) ).

fof(c_0_3190,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Opordered__comm__semiring(X55)
      | class_Ring__and__Field_Ocomm__semiring__0(X55) ),
    inference(variable_rename,[status(thm)],[c_0_1829]) ).

fof(c_0_3191,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Opordered__comm__ring(X55)
      | class_Ring__and__Field_Osemiring__0(X55) ),
    inference(variable_rename,[status(thm)],[c_0_1830]) ).

fof(c_0_3192,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Opordered__comm__ring(X55)
      | class_Ring__and__Field_Osemiring__0__cancel(X55) ),
    inference(variable_rename,[status(thm)],[c_0_1831]) ).

fof(c_0_3193,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Opordered__comm__ring(X55)
      | class_OrderedGroup_Oab__semigroup__mult(X55) ),
    inference(variable_rename,[status(thm)],[c_0_1832]) ).

fof(c_0_3194,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Opordered__comm__ring(X55)
      | class_Ring__and__Field_Ocomm__semiring(X55) ),
    inference(variable_rename,[status(thm)],[c_0_1833]) ).

fof(c_0_3195,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Opordered__comm__ring(X55)
      | class_Ring__and__Field_Ocomm__semiring__0(X55) ),
    inference(variable_rename,[status(thm)],[c_0_1834]) ).

fof(c_0_3196,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Opordered__comm__ring(X55)
      | class_Ring__and__Field_Ocomm__semiring__0__cancel(X55) ),
    inference(variable_rename,[status(thm)],[c_0_1835]) ).

fof(c_0_3197,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Opordered__comm__ring(X55)
      | class_HOL_Ominus(X55) ),
    inference(variable_rename,[status(thm)],[c_0_1836]) ).

fof(c_0_3198,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Opordered__comm__ring(X55)
      | class_Orderings_Oord(X55) ),
    inference(variable_rename,[status(thm)],[c_0_1837]) ).

fof(c_0_3199,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Opordered__comm__ring(X55)
      | class_Orderings_Oorder(X55) ),
    inference(variable_rename,[status(thm)],[c_0_1838]) ).

fof(c_0_3200,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Opordered__comm__ring(X55)
      | class_OrderedGroup_Opordered__ab__semigroup__add(X55) ),
    inference(variable_rename,[status(thm)],[c_0_1839]) ).

fof(c_0_3201,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Opordered__comm__ring(X55)
      | class_Ring__and__Field_Opordered__semiring(X55) ),
    inference(variable_rename,[status(thm)],[c_0_1840]) ).

fof(c_0_3202,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Opordered__comm__ring(X55)
      | class_Ring__and__Field_Opordered__comm__semiring(X55) ),
    inference(variable_rename,[status(thm)],[c_0_1841]) ).

fof(c_0_3203,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Opordered__comm__ring(X55)
      | class_OrderedGroup_Oab__group__add(X55) ),
    inference(variable_rename,[status(thm)],[c_0_1842]) ).

fof(c_0_3204,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Opordered__comm__ring(X55)
      | class_HOL_Oplus(X55) ),
    inference(variable_rename,[status(thm)],[c_0_1843]) ).

fof(c_0_3205,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Opordered__comm__ring(X55)
      | class_OrderedGroup_Osemigroup__add(X55) ),
    inference(variable_rename,[status(thm)],[c_0_1844]) ).

fof(c_0_3206,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Opordered__comm__ring(X55)
      | class_OrderedGroup_Ocancel__semigroup__add(X55) ),
    inference(variable_rename,[status(thm)],[c_0_1845]) ).

fof(c_0_3207,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Opordered__comm__ring(X55)
      | class_OrderedGroup_Oab__semigroup__add(X55) ),
    inference(variable_rename,[status(thm)],[c_0_1846]) ).

fof(c_0_3208,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Opordered__comm__ring(X55)
      | class_OrderedGroup_Ocancel__ab__semigroup__add(X55) ),
    inference(variable_rename,[status(thm)],[c_0_1847]) ).

fof(c_0_3209,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Opordered__comm__ring(X55)
      | class_HOL_Ozero(X55) ),
    inference(variable_rename,[status(thm)],[c_0_1848]) ).

fof(c_0_3210,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Opordered__comm__ring(X55)
      | class_OrderedGroup_Ocomm__monoid__add(X55) ),
    inference(variable_rename,[status(thm)],[c_0_1849]) ).

fof(c_0_3211,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Opordered__comm__ring(X55)
      | class_HOL_Otimes(X55) ),
    inference(variable_rename,[status(thm)],[c_0_1850]) ).

fof(c_0_3212,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Opordered__comm__ring(X55)
      | class_OrderedGroup_Osemigroup__mult(X55) ),
    inference(variable_rename,[status(thm)],[c_0_1851]) ).

fof(c_0_3213,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Opordered__comm__ring(X55)
      | class_Ring__and__Field_Osemiring(X55) ),
    inference(variable_rename,[status(thm)],[c_0_1852]) ).

fof(c_0_3214,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Opordered__comm__ring(X55)
      | class_Ring__and__Field_Oring(X55) ),
    inference(variable_rename,[status(thm)],[c_0_1853]) ).

fof(c_0_3215,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Opordered__comm__ring(X55)
      | class_Ring__and__Field_Ocomm__ring(X55) ),
    inference(variable_rename,[status(thm)],[c_0_1854]) ).

fof(c_0_3216,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Opordered__cancel__semiring(X55)
      | class_OrderedGroup_Osemigroup__add(X55) ),
    inference(variable_rename,[status(thm)],[c_0_1855]) ).

fof(c_0_3217,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Opordered__cancel__semiring(X55)
      | class_OrderedGroup_Oab__semigroup__add(X55) ),
    inference(variable_rename,[status(thm)],[c_0_1856]) ).

fof(c_0_3218,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Opordered__cancel__semiring(X55)
      | class_OrderedGroup_Opordered__ab__semigroup__add(X55) ),
    inference(variable_rename,[status(thm)],[c_0_1857]) ).

fof(c_0_3219,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Opordered__cancel__semiring(X55)
      | class_HOL_Ozero(X55) ),
    inference(variable_rename,[status(thm)],[c_0_1858]) ).

fof(c_0_3220,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Opordered__cancel__semiring(X55)
      | class_OrderedGroup_Ocomm__monoid__add(X55) ),
    inference(variable_rename,[status(thm)],[c_0_1859]) ).

fof(c_0_3221,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Opordered__cancel__semiring(X55)
      | class_HOL_Otimes(X55) ),
    inference(variable_rename,[status(thm)],[c_0_1860]) ).

fof(c_0_3222,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Opordered__cancel__semiring(X55)
      | class_OrderedGroup_Osemigroup__mult(X55) ),
    inference(variable_rename,[status(thm)],[c_0_1861]) ).

fof(c_0_3223,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Opordered__cancel__semiring(X55)
      | class_Ring__and__Field_Osemiring(X55) ),
    inference(variable_rename,[status(thm)],[c_0_1862]) ).

fof(c_0_3224,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Opordered__cancel__semiring(X55)
      | class_Ring__and__Field_Osemiring__0__cancel(X55) ),
    inference(variable_rename,[status(thm)],[c_0_1863]) ).

fof(c_0_3225,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Opordered__cancel__semiring(X55)
      | class_OrderedGroup_Ocancel__semigroup__add(X55) ),
    inference(variable_rename,[status(thm)],[c_0_1864]) ).

fof(c_0_3226,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Opordered__cancel__semiring(X55)
      | class_OrderedGroup_Ocancel__ab__semigroup__add(X55) ),
    inference(variable_rename,[status(thm)],[c_0_1865]) ).

fof(c_0_3227,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Opordered__cancel__semiring(X55)
      | class_Orderings_Oord(X55) ),
    inference(variable_rename,[status(thm)],[c_0_1866]) ).

fof(c_0_3228,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Opordered__cancel__semiring(X55)
      | class_Orderings_Oorder(X55) ),
    inference(variable_rename,[status(thm)],[c_0_1867]) ).

fof(c_0_3229,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Opordered__cancel__semiring(X55)
      | class_HOL_Oplus(X55) ),
    inference(variable_rename,[status(thm)],[c_0_1868]) ).

fof(c_0_3230,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Opordered__cancel__semiring(X55)
      | class_Ring__and__Field_Osemiring__0(X55) ),
    inference(variable_rename,[status(thm)],[c_0_1869]) ).

fof(c_0_3231,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Opordered__cancel__semiring(X55)
      | class_Ring__and__Field_Opordered__semiring(X55) ),
    inference(variable_rename,[status(thm)],[c_0_1870]) ).

fof(c_0_3232,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X55)
      | class_HOL_Ozero(X55) ),
    inference(variable_rename,[status(thm)],[c_0_1871]) ).

fof(c_0_3233,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X55)
      | class_OrderedGroup_Ocomm__monoid__add(X55) ),
    inference(variable_rename,[status(thm)],[c_0_1872]) ).

fof(c_0_3234,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X55)
      | class_HOL_Otimes(X55) ),
    inference(variable_rename,[status(thm)],[c_0_1873]) ).

fof(c_0_3235,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X55)
      | class_OrderedGroup_Osemigroup__mult(X55) ),
    inference(variable_rename,[status(thm)],[c_0_1874]) ).

fof(c_0_3236,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X55)
      | class_Ring__and__Field_Osemiring(X55) ),
    inference(variable_rename,[status(thm)],[c_0_1875]) ).

fof(c_0_3237,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X55)
      | class_Ring__and__Field_Osemiring__0(X55) ),
    inference(variable_rename,[status(thm)],[c_0_1876]) ).

fof(c_0_3238,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X55)
      | class_OrderedGroup_Oab__semigroup__mult(X55) ),
    inference(variable_rename,[status(thm)],[c_0_1877]) ).

fof(c_0_3239,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X55)
      | class_Ring__and__Field_Osemiring__0__cancel(X55) ),
    inference(variable_rename,[status(thm)],[c_0_1878]) ).

fof(c_0_3240,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X55)
      | class_Ring__and__Field_Ocomm__semiring(X55) ),
    inference(variable_rename,[status(thm)],[c_0_1879]) ).

fof(c_0_3241,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X55)
      | class_Ring__and__Field_Opordered__cancel__semiring(X55) ),
    inference(variable_rename,[status(thm)],[c_0_1880]) ).

fof(c_0_3242,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X55)
      | class_Ring__and__Field_Opordered__semiring(X55) ),
    inference(variable_rename,[status(thm)],[c_0_1881]) ).

fof(c_0_3243,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X55)
      | class_OrderedGroup_Ocancel__semigroup__add(X55) ),
    inference(variable_rename,[status(thm)],[c_0_1882]) ).

fof(c_0_3244,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X55)
      | class_OrderedGroup_Ocancel__ab__semigroup__add(X55) ),
    inference(variable_rename,[status(thm)],[c_0_1883]) ).

fof(c_0_3245,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X55)
      | class_Orderings_Oord(X55) ),
    inference(variable_rename,[status(thm)],[c_0_1884]) ).

fof(c_0_3246,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X55)
      | class_Orderings_Oorder(X55) ),
    inference(variable_rename,[status(thm)],[c_0_1885]) ).

fof(c_0_3247,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X55)
      | class_HOL_Oplus(X55) ),
    inference(variable_rename,[status(thm)],[c_0_1886]) ).

fof(c_0_3248,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X55)
      | class_OrderedGroup_Osemigroup__add(X55) ),
    inference(variable_rename,[status(thm)],[c_0_1887]) ).

fof(c_0_3249,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X55)
      | class_OrderedGroup_Oab__semigroup__add(X55) ),
    inference(variable_rename,[status(thm)],[c_0_1888]) ).

fof(c_0_3250,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X55)
      | class_OrderedGroup_Opordered__ab__semigroup__add(X55) ),
    inference(variable_rename,[status(thm)],[c_0_1889]) ).

fof(c_0_3251,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X55)
      | class_Ring__and__Field_Ocomm__semiring__0(X55) ),
    inference(variable_rename,[status(thm)],[c_0_1890]) ).

fof(c_0_3252,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X55)
      | class_Ring__and__Field_Opordered__comm__semiring(X55) ),
    inference(variable_rename,[status(thm)],[c_0_1891]) ).

fof(c_0_3253,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X55)
      | class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X55) ),
    inference(variable_rename,[status(thm)],[c_0_1892]) ).

fof(c_0_3254,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X55)
      | class_HOL_Ozero(X55) ),
    inference(variable_rename,[status(thm)],[c_0_1893]) ).

fof(c_0_3255,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X55)
      | class_HOL_Oplus(X55) ),
    inference(variable_rename,[status(thm)],[c_0_1894]) ).

fof(c_0_3256,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X55)
      | class_OrderedGroup_Osemigroup__add(X55) ),
    inference(variable_rename,[status(thm)],[c_0_1895]) ).

fof(c_0_3257,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X55)
      | class_OrderedGroup_Oab__semigroup__add(X55) ),
    inference(variable_rename,[status(thm)],[c_0_1896]) ).

fof(c_0_3258,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X55)
      | class_OrderedGroup_Ocomm__monoid__add(X55) ),
    inference(variable_rename,[status(thm)],[c_0_1897]) ).

fof(c_0_3259,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X55)
      | class_HOL_Otimes(X55) ),
    inference(variable_rename,[status(thm)],[c_0_1898]) ).

fof(c_0_3260,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X55)
      | class_Ring__and__Field_Opordered__semiring(X55) ),
    inference(variable_rename,[status(thm)],[c_0_1899]) ).

fof(c_0_3261,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X55)
      | class_Ring__and__Field_Opordered__cancel__semiring(X55) ),
    inference(variable_rename,[status(thm)],[c_0_1900]) ).

fof(c_0_3262,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X55)
      | class_Ring__and__Field_Osemiring__0__cancel(X55) ),
    inference(variable_rename,[status(thm)],[c_0_1901]) ).

fof(c_0_3263,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X55)
      | class_OrderedGroup_Ocancel__semigroup__add(X55) ),
    inference(variable_rename,[status(thm)],[c_0_1902]) ).

fof(c_0_3264,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X55)
      | class_OrderedGroup_Osemigroup__mult(X55) ),
    inference(variable_rename,[status(thm)],[c_0_1903]) ).

fof(c_0_3265,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X55)
      | class_OrderedGroup_Ocancel__ab__semigroup__add(X55) ),
    inference(variable_rename,[status(thm)],[c_0_1904]) ).

fof(c_0_3266,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X55)
      | class_Orderings_Oord(X55) ),
    inference(variable_rename,[status(thm)],[c_0_1905]) ).

fof(c_0_3267,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X55)
      | class_Orderings_Oorder(X55) ),
    inference(variable_rename,[status(thm)],[c_0_1906]) ).

fof(c_0_3268,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X55)
      | class_OrderedGroup_Opordered__ab__semigroup__add(X55) ),
    inference(variable_rename,[status(thm)],[c_0_1907]) ).

fof(c_0_3269,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X55)
      | class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X55) ),
    inference(variable_rename,[status(thm)],[c_0_1908]) ).

fof(c_0_3270,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X55)
      | class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X55) ),
    inference(variable_rename,[status(thm)],[c_0_1909]) ).

fof(c_0_3271,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X55)
      | class_LOrder_Omeet__semilorder(X55) ),
    inference(variable_rename,[status(thm)],[c_0_1910]) ).

fof(c_0_3272,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X55)
      | class_LOrder_Ojoin__semilorder(X55) ),
    inference(variable_rename,[status(thm)],[c_0_1911]) ).

fof(c_0_3273,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X55)
      | class_LOrder_Olorder(X55) ),
    inference(variable_rename,[status(thm)],[c_0_1912]) ).

fof(c_0_3274,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X55)
      | class_Orderings_Olinorder(X55) ),
    inference(variable_rename,[status(thm)],[c_0_1913]) ).

fof(c_0_3275,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X55)
      | class_Ring__and__Field_Osemiring(X55) ),
    inference(variable_rename,[status(thm)],[c_0_1914]) ).

fof(c_0_3276,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X55)
      | class_Ring__and__Field_Osemiring__0(X55) ),
    inference(variable_rename,[status(thm)],[c_0_1915]) ).

fof(c_0_3277,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X55)
      | class_Ring__and__Field_Ocomm__semiring__0(X55) ),
    inference(variable_rename,[status(thm)],[c_0_1916]) ).

fof(c_0_3278,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X55)
      | class_Ring__and__Field_Ocomm__semiring__0__cancel(X55) ),
    inference(variable_rename,[status(thm)],[c_0_1917]) ).

fof(c_0_3279,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X55)
      | class_HOL_Oone(X55) ),
    inference(variable_rename,[status(thm)],[c_0_1918]) ).

fof(c_0_3280,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X55)
      | class_OrderedGroup_Omonoid__mult(X55) ),
    inference(variable_rename,[status(thm)],[c_0_1919]) ).

fof(c_0_3281,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X55)
      | class_Ring__and__Field_Oaxclass__0__neq__1(X55) ),
    inference(variable_rename,[status(thm)],[c_0_1920]) ).

fof(c_0_3282,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X55)
      | class_Ring__and__Field_Osemiring__1(X55) ),
    inference(variable_rename,[status(thm)],[c_0_1921]) ).

fof(c_0_3283,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X55)
      | class_Orderings_Oord(X55) ),
    inference(variable_rename,[status(thm)],[c_0_1922]) ).

fof(c_0_3284,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X55)
      | class_Orderings_Oorder(X55) ),
    inference(variable_rename,[status(thm)],[c_0_1923]) ).

fof(c_0_3285,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X55)
      | class_OrderedGroup_Opordered__ab__semigroup__add(X55) ),
    inference(variable_rename,[status(thm)],[c_0_1924]) ).

fof(c_0_3286,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X55)
      | class_Ring__and__Field_Opordered__semiring(X55) ),
    inference(variable_rename,[status(thm)],[c_0_1925]) ).

fof(c_0_3287,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X55)
      | class_Ring__and__Field_Opordered__comm__semiring(X55) ),
    inference(variable_rename,[status(thm)],[c_0_1926]) ).

fof(c_0_3288,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X55)
      | class_Ring__and__Field_Opordered__cancel__semiring(X55) ),
    inference(variable_rename,[status(thm)],[c_0_1927]) ).

fof(c_0_3289,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X55)
      | class_Ring__and__Field_Opordered__cancel__comm__semiring(X55) ),
    inference(variable_rename,[status(thm)],[c_0_1928]) ).

fof(c_0_3290,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X55)
      | class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X55) ),
    inference(variable_rename,[status(thm)],[c_0_1929]) ).

fof(c_0_3291,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X55)
      | class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X55) ),
    inference(variable_rename,[status(thm)],[c_0_1930]) ).

fof(c_0_3292,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X55)
      | class_LOrder_Omeet__semilorder(X55) ),
    inference(variable_rename,[status(thm)],[c_0_1931]) ).

fof(c_0_3293,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X55)
      | class_Ring__and__Field_Osemiring__1__cancel(X55) ),
    inference(variable_rename,[status(thm)],[c_0_1932]) ).

fof(c_0_3294,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X55)
      | class_LOrder_Ojoin__semilorder(X55) ),
    inference(variable_rename,[status(thm)],[c_0_1933]) ).

fof(c_0_3295,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X55)
      | class_LOrder_Olorder(X55) ),
    inference(variable_rename,[status(thm)],[c_0_1934]) ).

fof(c_0_3296,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X55)
      | class_Orderings_Olinorder(X55) ),
    inference(variable_rename,[status(thm)],[c_0_1935]) ).

fof(c_0_3297,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X55)
      | class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X55) ),
    inference(variable_rename,[status(thm)],[c_0_1936]) ).

fof(c_0_3298,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X55)
      | class_Ring__and__Field_Oordered__semiring__strict(X55) ),
    inference(variable_rename,[status(thm)],[c_0_1937]) ).

fof(c_0_3299,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X55)
      | class_Ring__and__Field_Oordered__comm__semiring__strict(X55) ),
    inference(variable_rename,[status(thm)],[c_0_1938]) ).

fof(c_0_3300,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X55)
      | class_HOL_Oplus(X55) ),
    inference(variable_rename,[status(thm)],[c_0_1939]) ).

fof(c_0_3301,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X55)
      | class_OrderedGroup_Osemigroup__add(X55) ),
    inference(variable_rename,[status(thm)],[c_0_1940]) ).

fof(c_0_3302,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X55)
      | class_OrderedGroup_Ocancel__semigroup__add(X55) ),
    inference(variable_rename,[status(thm)],[c_0_1941]) ).

fof(c_0_3303,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X55)
      | class_OrderedGroup_Oab__semigroup__add(X55) ),
    inference(variable_rename,[status(thm)],[c_0_1942]) ).

fof(c_0_3304,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X55)
      | class_OrderedGroup_Ocomm__monoid__mult(X55) ),
    inference(variable_rename,[status(thm)],[c_0_1943]) ).

fof(c_0_3305,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X55)
      | class_OrderedGroup_Ocancel__ab__semigroup__add(X55) ),
    inference(variable_rename,[status(thm)],[c_0_1944]) ).

fof(c_0_3306,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X55)
      | class_HOL_Ozero(X55) ),
    inference(variable_rename,[status(thm)],[c_0_1945]) ).

fof(c_0_3307,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X55)
      | class_OrderedGroup_Ocomm__monoid__add(X55) ),
    inference(variable_rename,[status(thm)],[c_0_1946]) ).

fof(c_0_3308,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X55)
      | class_HOL_Otimes(X55) ),
    inference(variable_rename,[status(thm)],[c_0_1947]) ).

fof(c_0_3309,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X55)
      | class_OrderedGroup_Osemigroup__mult(X55) ),
    inference(variable_rename,[status(thm)],[c_0_1948]) ).

fof(c_0_3310,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X55)
      | class_Ring__and__Field_Osemiring(X55) ),
    inference(variable_rename,[status(thm)],[c_0_1949]) ).

fof(c_0_3311,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X55)
      | class_Ring__and__Field_Osemiring__0(X55) ),
    inference(variable_rename,[status(thm)],[c_0_1950]) ).

fof(c_0_3312,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X55)
      | class_Ring__and__Field_Osemiring__0__cancel(X55) ),
    inference(variable_rename,[status(thm)],[c_0_1951]) ).

fof(c_0_3313,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X55)
      | class_OrderedGroup_Oab__semigroup__mult(X55) ),
    inference(variable_rename,[status(thm)],[c_0_1952]) ).

fof(c_0_3314,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X55)
      | class_Ring__and__Field_Ocomm__semiring(X55) ),
    inference(variable_rename,[status(thm)],[c_0_1953]) ).

fof(c_0_3315,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X55)
      | class_Ring__and__Field_Ocomm__semiring__1(X55) ),
    inference(variable_rename,[status(thm)],[c_0_1954]) ).

fof(c_0_3316,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X55)
      | class_Ring__and__Field_Ocomm__semiring__1__cancel(X55) ),
    inference(variable_rename,[status(thm)],[c_0_1955]) ).

fof(c_0_3317,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X55)
      | class_HOL_Otimes(X55) ),
    inference(variable_rename,[status(thm)],[c_0_1956]) ).

fof(c_0_3318,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X55)
      | class_OrderedGroup_Osemigroup__mult(X55) ),
    inference(variable_rename,[status(thm)],[c_0_1957]) ).

fof(c_0_3319,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X55)
      | class_Ring__and__Field_Osemiring(X55) ),
    inference(variable_rename,[status(thm)],[c_0_1958]) ).

fof(c_0_3320,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X55)
      | class_Ring__and__Field_Osemiring__0(X55) ),
    inference(variable_rename,[status(thm)],[c_0_1959]) ).

fof(c_0_3321,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X55)
      | class_OrderedGroup_Ocancel__semigroup__add(X55) ),
    inference(variable_rename,[status(thm)],[c_0_1960]) ).

fof(c_0_3322,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X55)
      | class_OrderedGroup_Ocancel__ab__semigroup__add(X55) ),
    inference(variable_rename,[status(thm)],[c_0_1961]) ).

fof(c_0_3323,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X55)
      | class_Ring__and__Field_Oaxclass__no__zero__divisors(X55) ),
    inference(variable_rename,[status(thm)],[c_0_1962]) ).

fof(c_0_3324,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X55)
      | class_OrderedGroup_Olordered__ab__group__join(X55) ),
    inference(variable_rename,[status(thm)],[c_0_1963]) ).

fof(c_0_3325,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X55)
      | class_OrderedGroup_Olordered__ab__group__meet(X55) ),
    inference(variable_rename,[status(thm)],[c_0_1964]) ).

fof(c_0_3326,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X55)
      | class_OrderedGroup_Olordered__ab__group__abs(X55) ),
    inference(variable_rename,[status(thm)],[c_0_1965]) ).

fof(c_0_3327,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X55)
      | class_Ring__and__Field_Opordered__ring(X55) ),
    inference(variable_rename,[status(thm)],[c_0_1966]) ).

fof(c_0_3328,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X55)
      | class_Ring__and__Field_Olordered__ring(X55) ),
    inference(variable_rename,[status(thm)],[c_0_1967]) ).

fof(c_0_3329,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X55)
      | class_OrderedGroup_Opordered__ab__group__add(X55) ),
    inference(variable_rename,[status(thm)],[c_0_1968]) ).

fof(c_0_3330,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X55)
      | class_Ring__and__Field_Osemiring__0__cancel(X55) ),
    inference(variable_rename,[status(thm)],[c_0_1969]) ).

fof(c_0_3331,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X55)
      | class_OrderedGroup_Olordered__ab__group(X55) ),
    inference(variable_rename,[status(thm)],[c_0_1970]) ).

fof(c_0_3332,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X55)
      | class_Ring__and__Field_Oaxclass__abs__if(X55) ),
    inference(variable_rename,[status(thm)],[c_0_1971]) ).

fof(c_0_3333,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X55)
      | class_Orderings_Oord(X55) ),
    inference(variable_rename,[status(thm)],[c_0_1972]) ).

fof(c_0_3334,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X55)
      | class_Orderings_Oorder(X55) ),
    inference(variable_rename,[status(thm)],[c_0_1973]) ).

fof(c_0_3335,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X55)
      | class_OrderedGroup_Opordered__ab__semigroup__add(X55) ),
    inference(variable_rename,[status(thm)],[c_0_1974]) ).

fof(c_0_3336,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X55)
      | class_Ring__and__Field_Opordered__semiring(X55) ),
    inference(variable_rename,[status(thm)],[c_0_1975]) ).

fof(c_0_3337,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X55)
      | class_Ring__and__Field_Opordered__cancel__semiring(X55) ),
    inference(variable_rename,[status(thm)],[c_0_1976]) ).

fof(c_0_3338,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X55)
      | class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X55) ),
    inference(variable_rename,[status(thm)],[c_0_1977]) ).

fof(c_0_3339,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X55)
      | class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X55) ),
    inference(variable_rename,[status(thm)],[c_0_1978]) ).

fof(c_0_3340,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X55)
      | class_LOrder_Omeet__semilorder(X55) ),
    inference(variable_rename,[status(thm)],[c_0_1979]) ).

fof(c_0_3341,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X55)
      | class_HOL_Ominus(X55) ),
    inference(variable_rename,[status(thm)],[c_0_1980]) ).

fof(c_0_3342,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X55)
      | class_LOrder_Ojoin__semilorder(X55) ),
    inference(variable_rename,[status(thm)],[c_0_1981]) ).

fof(c_0_3343,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X55)
      | class_LOrder_Olorder(X55) ),
    inference(variable_rename,[status(thm)],[c_0_1982]) ).

fof(c_0_3344,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X55)
      | class_Orderings_Olinorder(X55) ),
    inference(variable_rename,[status(thm)],[c_0_1983]) ).

fof(c_0_3345,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X55)
      | class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X55) ),
    inference(variable_rename,[status(thm)],[c_0_1984]) ).

fof(c_0_3346,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X55)
      | class_Ring__and__Field_Oordered__semiring__strict(X55) ),
    inference(variable_rename,[status(thm)],[c_0_1985]) ).

fof(c_0_3347,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X55)
      | class_HOL_Ozero(X55) ),
    inference(variable_rename,[status(thm)],[c_0_1986]) ).

fof(c_0_3348,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X55)
      | class_HOL_Oplus(X55) ),
    inference(variable_rename,[status(thm)],[c_0_1987]) ).

fof(c_0_3349,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X55)
      | class_OrderedGroup_Osemigroup__add(X55) ),
    inference(variable_rename,[status(thm)],[c_0_1988]) ).

fof(c_0_3350,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X55)
      | class_OrderedGroup_Oab__semigroup__add(X55) ),
    inference(variable_rename,[status(thm)],[c_0_1989]) ).

fof(c_0_3351,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X55)
      | class_OrderedGroup_Ocomm__monoid__add(X55) ),
    inference(variable_rename,[status(thm)],[c_0_1990]) ).

fof(c_0_3352,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X55)
      | class_OrderedGroup_Oab__group__add(X55) ),
    inference(variable_rename,[status(thm)],[c_0_1991]) ).

fof(c_0_3353,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X55)
      | class_Ring__and__Field_Oring(X55) ),
    inference(variable_rename,[status(thm)],[c_0_1992]) ).

fof(c_0_3354,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oordered__idom(X55)
      | class_Ring__and__Field_Osemiring__1__cancel(X55) ),
    inference(variable_rename,[status(thm)],[c_0_1993]) ).

fof(c_0_3355,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oordered__idom(X55)
      | class_OrderedGroup_Ocomm__monoid__mult(X55) ),
    inference(variable_rename,[status(thm)],[c_0_1994]) ).

fof(c_0_3356,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oordered__idom(X55)
      | class_Ring__and__Field_Ocomm__semiring__1(X55) ),
    inference(variable_rename,[status(thm)],[c_0_1995]) ).

fof(c_0_3357,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oordered__idom(X55)
      | class_Ring__and__Field_Ocomm__semiring__1__cancel(X55) ),
    inference(variable_rename,[status(thm)],[c_0_1996]) ).

fof(c_0_3358,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oordered__idom(X55)
      | class_Ring__and__Field_Oidom(X55) ),
    inference(variable_rename,[status(thm)],[c_0_1997]) ).

fof(c_0_3359,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oordered__idom(X55)
      | class_Ring__and__Field_Oaxclass__no__zero__divisors(X55) ),
    inference(variable_rename,[status(thm)],[c_0_1998]) ).

fof(c_0_3360,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oordered__idom(X55)
      | class_Ring__and__Field_Oordered__semidom(X55) ),
    inference(variable_rename,[status(thm)],[c_0_1999]) ).

fof(c_0_3361,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oordered__idom(X55)
      | class_OrderedGroup_Opordered__ab__group__add(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2000]) ).

fof(c_0_3362,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oordered__idom(X55)
      | class_OrderedGroup_Olordered__ab__group(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2001]) ).

fof(c_0_3363,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oordered__idom(X55)
      | class_OrderedGroup_Olordered__ab__group__join(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2002]) ).

fof(c_0_3364,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oordered__idom(X55)
      | class_OrderedGroup_Olordered__ab__group__meet(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2003]) ).

fof(c_0_3365,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oordered__idom(X55)
      | class_OrderedGroup_Olordered__ab__group__abs(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2004]) ).

fof(c_0_3366,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oordered__idom(X55)
      | class_HOL_Ominus(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2005]) ).

fof(c_0_3367,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oordered__idom(X55)
      | class_Ring__and__Field_Opordered__ring(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2006]) ).

fof(c_0_3368,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oordered__idom(X55)
      | class_Ring__and__Field_Olordered__ring(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2007]) ).

fof(c_0_3369,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oordered__idom(X55)
      | class_Ring__and__Field_Oordered__ring__strict(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2008]) ).

fof(c_0_3370,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oordered__idom(X55)
      | class_Ring__and__Field_Oaxclass__abs__if(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2009]) ).

fof(c_0_3371,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oordered__idom(X55)
      | class_Orderings_Oord(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2010]) ).

fof(c_0_3372,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oordered__idom(X55)
      | class_Orderings_Oorder(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2011]) ).

fof(c_0_3373,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oordered__idom(X55)
      | class_OrderedGroup_Opordered__ab__semigroup__add(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2012]) ).

fof(c_0_3374,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oordered__idom(X55)
      | class_Ring__and__Field_Opordered__semiring(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2013]) ).

fof(c_0_3375,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oordered__idom(X55)
      | class_Ring__and__Field_Opordered__comm__semiring(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2014]) ).

fof(c_0_3376,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oordered__idom(X55)
      | class_Ring__and__Field_Opordered__cancel__semiring(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2015]) ).

fof(c_0_3377,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oordered__idom(X55)
      | class_OrderedGroup_Oab__group__add(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2016]) ).

fof(c_0_3378,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oordered__idom(X55)
      | class_Ring__and__Field_Opordered__cancel__comm__semiring(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2017]) ).

fof(c_0_3379,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oordered__idom(X55)
      | class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2018]) ).

fof(c_0_3380,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oordered__idom(X55)
      | class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2019]) ).

fof(c_0_3381,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oordered__idom(X55)
      | class_LOrder_Omeet__semilorder(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2020]) ).

fof(c_0_3382,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oordered__idom(X55)
      | class_LOrder_Ojoin__semilorder(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2021]) ).

fof(c_0_3383,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oordered__idom(X55)
      | class_LOrder_Olorder(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2022]) ).

fof(c_0_3384,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oordered__idom(X55)
      | class_Orderings_Olinorder(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2023]) ).

fof(c_0_3385,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oordered__idom(X55)
      | class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2024]) ).

fof(c_0_3386,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oordered__idom(X55)
      | class_Ring__and__Field_Oordered__semiring__strict(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2025]) ).

fof(c_0_3387,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oordered__idom(X55)
      | class_Ring__and__Field_Oordered__comm__semiring__strict(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2026]) ).

fof(c_0_3388,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oordered__idom(X55)
      | class_Ring__and__Field_Oring(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2027]) ).

fof(c_0_3389,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oordered__idom(X55)
      | class_HOL_Oplus(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2028]) ).

fof(c_0_3390,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oordered__idom(X55)
      | class_OrderedGroup_Osemigroup__add(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2029]) ).

fof(c_0_3391,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oordered__idom(X55)
      | class_OrderedGroup_Ocancel__semigroup__add(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2030]) ).

fof(c_0_3392,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oordered__idom(X55)
      | class_OrderedGroup_Oab__semigroup__add(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2031]) ).

fof(c_0_3393,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oordered__idom(X55)
      | class_OrderedGroup_Ocancel__ab__semigroup__add(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2032]) ).

fof(c_0_3394,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oordered__idom(X55)
      | class_HOL_Ozero(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2033]) ).

fof(c_0_3395,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oordered__idom(X55)
      | class_OrderedGroup_Ocomm__monoid__add(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2034]) ).

fof(c_0_3396,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oordered__idom(X55)
      | class_HOL_Otimes(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2035]) ).

fof(c_0_3397,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oordered__idom(X55)
      | class_OrderedGroup_Osemigroup__mult(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2036]) ).

fof(c_0_3398,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oordered__idom(X55)
      | class_Ring__and__Field_Osemiring(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2037]) ).

fof(c_0_3399,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oordered__idom(X55)
      | class_Ring__and__Field_Oring__1(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2038]) ).

fof(c_0_3400,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oordered__idom(X55)
      | class_Ring__and__Field_Osemiring__0(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2039]) ).

fof(c_0_3401,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oordered__idom(X55)
      | class_Ring__and__Field_Osemiring__0__cancel(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2040]) ).

fof(c_0_3402,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oordered__idom(X55)
      | class_OrderedGroup_Oab__semigroup__mult(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2041]) ).

fof(c_0_3403,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oordered__idom(X55)
      | class_Ring__and__Field_Ocomm__semiring(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2042]) ).

fof(c_0_3404,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oordered__idom(X55)
      | class_Ring__and__Field_Ocomm__semiring__0(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2043]) ).

fof(c_0_3405,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oordered__idom(X55)
      | class_Ring__and__Field_Ocomm__semiring__0__cancel(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2044]) ).

fof(c_0_3406,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oordered__idom(X55)
      | class_HOL_Oone(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2045]) ).

fof(c_0_3407,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oordered__idom(X55)
      | class_OrderedGroup_Omonoid__mult(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2046]) ).

fof(c_0_3408,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oordered__idom(X55)
      | class_Ring__and__Field_Oaxclass__0__neq__1(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2047]) ).

fof(c_0_3409,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oordered__idom(X55)
      | class_Ring__and__Field_Osemiring__1(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2048]) ).

fof(c_0_3410,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oordered__idom(X55)
      | class_Ring__and__Field_Ocomm__ring(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2049]) ).

fof(c_0_3411,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oordered__idom(X55)
      | class_Ring__and__Field_Ocomm__ring__1(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2050]) ).

fof(c_0_3412,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oordered__field(X55)
      | class_Ring__and__Field_Ocomm__semiring__1__cancel(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2051]) ).

fof(c_0_3413,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oordered__field(X55)
      | class_HOL_Ominus(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2052]) ).

fof(c_0_3414,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oordered__field(X55)
      | class_OrderedGroup_Oab__group__add(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2053]) ).

fof(c_0_3415,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oordered__field(X55)
      | class_Ring__and__Field_Oordered__semidom(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2054]) ).

fof(c_0_3416,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oordered__field(X55)
      | class_Ring__and__Field_Oring(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2055]) ).

fof(c_0_3417,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oordered__field(X55)
      | class_Orderings_Oord(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2056]) ).

fof(c_0_3418,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oordered__field(X55)
      | class_Orderings_Oorder(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2057]) ).

fof(c_0_3419,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oordered__field(X55)
      | class_OrderedGroup_Opordered__ab__semigroup__add(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2058]) ).

fof(c_0_3420,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oordered__field(X55)
      | class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2059]) ).

fof(c_0_3421,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oordered__field(X55)
      | class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2060]) ).

fof(c_0_3422,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oordered__field(X55)
      | class_OrderedGroup_Opordered__ab__group__add(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2061]) ).

fof(c_0_3423,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oordered__field(X55)
      | class_LOrder_Omeet__semilorder(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2062]) ).

fof(c_0_3424,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oordered__field(X55)
      | class_LOrder_Ojoin__semilorder(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2063]) ).

fof(c_0_3425,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oordered__field(X55)
      | class_LOrder_Olorder(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2064]) ).

fof(c_0_3426,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oordered__field(X55)
      | class_OrderedGroup_Olordered__ab__group(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2065]) ).

fof(c_0_3427,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oordered__field(X55)
      | class_Ring__and__Field_Oring__1(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2066]) ).

fof(c_0_3428,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oordered__field(X55)
      | class_OrderedGroup_Olordered__ab__group__join(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2067]) ).

fof(c_0_3429,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oordered__field(X55)
      | class_OrderedGroup_Olordered__ab__group__meet(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2068]) ).

fof(c_0_3430,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oordered__field(X55)
      | class_OrderedGroup_Olordered__ab__group__abs(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2069]) ).

fof(c_0_3431,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oordered__field(X55)
      | class_Ring__and__Field_Opordered__semiring(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2070]) ).

fof(c_0_3432,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oordered__field(X55)
      | class_Ring__and__Field_Opordered__cancel__semiring(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2071]) ).

fof(c_0_3433,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oordered__field(X55)
      | class_Ring__and__Field_Opordered__ring(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2072]) ).

fof(c_0_3434,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oordered__field(X55)
      | class_Ring__and__Field_Olordered__ring(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2073]) ).

fof(c_0_3435,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oordered__field(X55)
      | class_Ring__and__Field_Oaxclass__abs__if(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2074]) ).

fof(c_0_3436,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oordered__field(X55)
      | class_Orderings_Olinorder(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2075]) ).

fof(c_0_3437,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oordered__field(X55)
      | class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2076]) ).

fof(c_0_3438,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oordered__field(X55)
      | class_Ring__and__Field_Ocomm__ring(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2077]) ).

fof(c_0_3439,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oordered__field(X55)
      | class_Ring__and__Field_Oordered__semiring__strict(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2078]) ).

fof(c_0_3440,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oordered__field(X55)
      | class_Ring__and__Field_Oordered__ring__strict(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2079]) ).

fof(c_0_3441,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oordered__field(X55)
      | class_Ring__and__Field_Opordered__comm__semiring(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2080]) ).

fof(c_0_3442,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oordered__field(X55)
      | class_Ring__and__Field_Opordered__cancel__comm__semiring(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2081]) ).

fof(c_0_3443,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oordered__field(X55)
      | class_Ring__and__Field_Oordered__comm__semiring__strict(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2082]) ).

fof(c_0_3444,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oordered__field(X55)
      | class_Ring__and__Field_Oordered__idom(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2083]) ).

fof(c_0_3445,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oordered__field(X55)
      | class_HOL_Otimes(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2084]) ).

fof(c_0_3446,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oordered__field(X55)
      | class_HOL_Ozero(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2085]) ).

fof(c_0_3447,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oordered__field(X55)
      | class_Ring__and__Field_Oaxclass__no__zero__divisors(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2086]) ).

fof(c_0_3448,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oordered__field(X55)
      | class_HOL_Oplus(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2087]) ).

fof(c_0_3449,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oordered__field(X55)
      | class_Ring__and__Field_Ocomm__ring__1(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2088]) ).

fof(c_0_3450,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oordered__field(X55)
      | class_OrderedGroup_Osemigroup__add(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2089]) ).

fof(c_0_3451,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oordered__field(X55)
      | class_OrderedGroup_Ocancel__semigroup__add(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2090]) ).

fof(c_0_3452,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oordered__field(X55)
      | class_OrderedGroup_Oab__semigroup__add(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2091]) ).

fof(c_0_3453,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oordered__field(X55)
      | class_OrderedGroup_Ocancel__ab__semigroup__add(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2092]) ).

fof(c_0_3454,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oordered__field(X55)
      | class_OrderedGroup_Ocomm__monoid__add(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2093]) ).

fof(c_0_3455,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oordered__field(X55)
      | class_OrderedGroup_Osemigroup__mult(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2094]) ).

fof(c_0_3456,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oordered__field(X55)
      | class_Ring__and__Field_Osemiring(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2095]) ).

fof(c_0_3457,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oordered__field(X55)
      | class_Ring__and__Field_Osemiring__0(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2096]) ).

fof(c_0_3458,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oordered__field(X55)
      | class_Ring__and__Field_Osemiring__0__cancel(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2097]) ).

fof(c_0_3459,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oordered__field(X55)
      | class_OrderedGroup_Oab__semigroup__mult(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2098]) ).

fof(c_0_3460,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oordered__field(X55)
      | class_Ring__and__Field_Oidom(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2099]) ).

fof(c_0_3461,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oordered__field(X55)
      | class_Ring__and__Field_Ocomm__semiring(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2100]) ).

fof(c_0_3462,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oordered__field(X55)
      | class_Ring__and__Field_Ocomm__semiring__0(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2101]) ).

fof(c_0_3463,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oordered__field(X55)
      | class_Ring__and__Field_Ocomm__semiring__0__cancel(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2102]) ).

fof(c_0_3464,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oordered__field(X55)
      | class_HOL_Oone(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2103]) ).

fof(c_0_3465,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oordered__field(X55)
      | class_OrderedGroup_Omonoid__mult(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2104]) ).

fof(c_0_3466,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oordered__field(X55)
      | class_Ring__and__Field_Oaxclass__0__neq__1(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2105]) ).

fof(c_0_3467,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oordered__field(X55)
      | class_Ring__and__Field_Osemiring__1(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2106]) ).

fof(c_0_3468,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oordered__field(X55)
      | class_Ring__and__Field_Osemiring__1__cancel(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2107]) ).

fof(c_0_3469,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oordered__field(X55)
      | class_OrderedGroup_Ocomm__monoid__mult(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2108]) ).

fof(c_0_3470,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oordered__field(X55)
      | class_Ring__and__Field_Ocomm__semiring__1(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2109]) ).

fof(c_0_3471,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oordered__field(X55)
      | class_HOL_Oinverse(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2110]) ).

fof(c_0_3472,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oordered__field(X55)
      | class_Ring__and__Field_Ofield(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2111]) ).

fof(c_0_3473,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X55)
      | class_OrderedGroup_Osemigroup__add(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2112]) ).

fof(c_0_3474,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X55)
      | class_OrderedGroup_Oab__semigroup__add(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2113]) ).

fof(c_0_3475,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X55)
      | class_OrderedGroup_Ocomm__monoid__add(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2114]) ).

fof(c_0_3476,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X55)
      | class_HOL_Otimes(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2115]) ).

fof(c_0_3477,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X55)
      | class_OrderedGroup_Osemigroup__mult(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2116]) ).

fof(c_0_3478,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X55)
      | class_Ring__and__Field_Osemiring(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2117]) ).

fof(c_0_3479,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X55)
      | class_Ring__and__Field_Osemiring__0(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2118]) ).

fof(c_0_3480,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X55)
      | class_Ring__and__Field_Opordered__comm__semiring(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2119]) ).

fof(c_0_3481,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X55)
      | class_Ring__and__Field_Opordered__cancel__comm__semiring(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2120]) ).

fof(c_0_3482,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X55)
      | class_Ring__and__Field_Opordered__semiring(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2121]) ).

fof(c_0_3483,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X55)
      | class_Ring__and__Field_Osemiring__0__cancel(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2122]) ).

fof(c_0_3484,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X55)
      | class_Ring__and__Field_Opordered__cancel__semiring(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2123]) ).

fof(c_0_3485,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X55)
      | class_Ring__and__Field_Oordered__semiring__strict(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2124]) ).

fof(c_0_3486,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X55)
      | class_OrderedGroup_Ocancel__semigroup__add(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2125]) ).

fof(c_0_3487,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X55)
      | class_OrderedGroup_Ocancel__ab__semigroup__add(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2126]) ).

fof(c_0_3488,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X55)
      | class_Orderings_Oord(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2127]) ).

fof(c_0_3489,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X55)
      | class_Orderings_Oorder(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2128]) ).

fof(c_0_3490,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X55)
      | class_OrderedGroup_Oab__semigroup__mult(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2129]) ).

fof(c_0_3491,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X55)
      | class_OrderedGroup_Opordered__ab__semigroup__add(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2130]) ).

fof(c_0_3492,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X55)
      | class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2131]) ).

fof(c_0_3493,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X55)
      | class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2132]) ).

fof(c_0_3494,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X55)
      | class_LOrder_Omeet__semilorder(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2133]) ).

fof(c_0_3495,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X55)
      | class_LOrder_Ojoin__semilorder(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2134]) ).

fof(c_0_3496,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X55)
      | class_LOrder_Olorder(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2135]) ).

fof(c_0_3497,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X55)
      | class_Orderings_Olinorder(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2136]) ).

fof(c_0_3498,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X55)
      | class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2137]) ).

fof(c_0_3499,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X55)
      | class_HOL_Ozero(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2138]) ).

fof(c_0_3500,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X55)
      | class_HOL_Oplus(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2139]) ).

fof(c_0_3501,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X55)
      | class_Ring__and__Field_Ocomm__semiring(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2140]) ).

fof(c_0_3502,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X55)
      | class_Ring__and__Field_Ocomm__semiring__0(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2141]) ).

fof(c_0_3503,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Olordered__ring(X55)
      | class_OrderedGroup_Opordered__ab__semigroup__add(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2142]) ).

fof(c_0_3504,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Olordered__ring(X55)
      | class_Ring__and__Field_Opordered__semiring(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2143]) ).

fof(c_0_3505,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Olordered__ring(X55)
      | class_Ring__and__Field_Opordered__cancel__semiring(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2144]) ).

fof(c_0_3506,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Olordered__ring(X55)
      | class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2145]) ).

fof(c_0_3507,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Olordered__ring(X55)
      | class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2146]) ).

fof(c_0_3508,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Olordered__ring(X55)
      | class_HOL_Ominus(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2147]) ).

fof(c_0_3509,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Olordered__ring(X55)
      | class_OrderedGroup_Olordered__ab__group__join(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2148]) ).

fof(c_0_3510,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Olordered__ring(X55)
      | class_OrderedGroup_Oab__group__add(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2149]) ).

fof(c_0_3511,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Olordered__ring(X55)
      | class_OrderedGroup_Olordered__ab__group__meet(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2150]) ).

fof(c_0_3512,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Olordered__ring(X55)
      | class_LOrder_Omeet__semilorder(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2151]) ).

fof(c_0_3513,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Olordered__ring(X55)
      | class_LOrder_Ojoin__semilorder(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2152]) ).

fof(c_0_3514,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Olordered__ring(X55)
      | class_LOrder_Olorder(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2153]) ).

fof(c_0_3515,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Olordered__ring(X55)
      | class_OrderedGroup_Olordered__ab__group(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2154]) ).

fof(c_0_3516,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Olordered__ring(X55)
      | class_OrderedGroup_Olordered__ab__group__abs(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2155]) ).

fof(c_0_3517,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Olordered__ring(X55)
      | class_HOL_Oplus(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2156]) ).

fof(c_0_3518,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Olordered__ring(X55)
      | class_OrderedGroup_Osemigroup__add(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2157]) ).

fof(c_0_3519,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Olordered__ring(X55)
      | class_OrderedGroup_Ocancel__semigroup__add(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2158]) ).

fof(c_0_3520,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Olordered__ring(X55)
      | class_OrderedGroup_Oab__semigroup__add(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2159]) ).

fof(c_0_3521,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Olordered__ring(X55)
      | class_OrderedGroup_Opordered__ab__group__add(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2160]) ).

fof(c_0_3522,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Olordered__ring(X55)
      | class_OrderedGroup_Ocancel__ab__semigroup__add(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2161]) ).

fof(c_0_3523,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Olordered__ring(X55)
      | class_HOL_Ozero(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2162]) ).

fof(c_0_3524,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Olordered__ring(X55)
      | class_OrderedGroup_Ocomm__monoid__add(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2163]) ).

fof(c_0_3525,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Olordered__ring(X55)
      | class_HOL_Otimes(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2164]) ).

fof(c_0_3526,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Olordered__ring(X55)
      | class_OrderedGroup_Osemigroup__mult(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2165]) ).

fof(c_0_3527,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Olordered__ring(X55)
      | class_Ring__and__Field_Osemiring(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2166]) ).

fof(c_0_3528,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Olordered__ring(X55)
      | class_Ring__and__Field_Osemiring__0(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2167]) ).

fof(c_0_3529,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Olordered__ring(X55)
      | class_Ring__and__Field_Osemiring__0__cancel(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2168]) ).

fof(c_0_3530,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Olordered__ring(X55)
      | class_Orderings_Oord(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2169]) ).

fof(c_0_3531,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Olordered__ring(X55)
      | class_Orderings_Oorder(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2170]) ).

fof(c_0_3532,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Olordered__ring(X55)
      | class_Ring__and__Field_Oring(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2171]) ).

fof(c_0_3533,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Olordered__ring(X55)
      | class_Ring__and__Field_Opordered__ring(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2172]) ).

fof(c_0_3534,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oidom(X55)
      | class_Ring__and__Field_Osemiring__1__cancel(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2173]) ).

fof(c_0_3535,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oidom(X55)
      | class_OrderedGroup_Ocomm__monoid__mult(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2174]) ).

fof(c_0_3536,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oidom(X55)
      | class_Ring__and__Field_Ocomm__semiring__1(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2175]) ).

fof(c_0_3537,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oidom(X55)
      | class_Ring__and__Field_Ocomm__semiring__1__cancel(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2176]) ).

fof(c_0_3538,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oidom(X55)
      | class_HOL_Ominus(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2177]) ).

fof(c_0_3539,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oidom(X55)
      | class_OrderedGroup_Oab__group__add(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2178]) ).

fof(c_0_3540,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oidom(X55)
      | class_Ring__and__Field_Oaxclass__no__zero__divisors(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2179]) ).

fof(c_0_3541,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oidom(X55)
      | class_Ring__and__Field_Oring(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2180]) ).

fof(c_0_3542,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oidom(X55)
      | class_HOL_Oplus(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2181]) ).

fof(c_0_3543,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oidom(X55)
      | class_OrderedGroup_Osemigroup__add(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2182]) ).

fof(c_0_3544,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oidom(X55)
      | class_OrderedGroup_Ocancel__semigroup__add(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2183]) ).

fof(c_0_3545,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oidom(X55)
      | class_OrderedGroup_Oab__semigroup__add(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2184]) ).

fof(c_0_3546,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oidom(X55)
      | class_OrderedGroup_Ocancel__ab__semigroup__add(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2185]) ).

fof(c_0_3547,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oidom(X55)
      | class_HOL_Ozero(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2186]) ).

fof(c_0_3548,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oidom(X55)
      | class_OrderedGroup_Ocomm__monoid__add(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2187]) ).

fof(c_0_3549,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oidom(X55)
      | class_HOL_Otimes(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2188]) ).

fof(c_0_3550,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oidom(X55)
      | class_OrderedGroup_Osemigroup__mult(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2189]) ).

fof(c_0_3551,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oidom(X55)
      | class_Ring__and__Field_Osemiring(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2190]) ).

fof(c_0_3552,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oidom(X55)
      | class_Ring__and__Field_Oring__1(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2191]) ).

fof(c_0_3553,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oidom(X55)
      | class_Ring__and__Field_Osemiring__0(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2192]) ).

fof(c_0_3554,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oidom(X55)
      | class_Ring__and__Field_Osemiring__0__cancel(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2193]) ).

fof(c_0_3555,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oidom(X55)
      | class_OrderedGroup_Oab__semigroup__mult(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2194]) ).

fof(c_0_3556,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oidom(X55)
      | class_Ring__and__Field_Ocomm__semiring(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2195]) ).

fof(c_0_3557,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oidom(X55)
      | class_Ring__and__Field_Ocomm__semiring__0(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2196]) ).

fof(c_0_3558,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oidom(X55)
      | class_Ring__and__Field_Ocomm__semiring__0__cancel(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2197]) ).

fof(c_0_3559,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oidom(X55)
      | class_HOL_Oone(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2198]) ).

fof(c_0_3560,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oidom(X55)
      | class_OrderedGroup_Omonoid__mult(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2199]) ).

fof(c_0_3561,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oidom(X55)
      | class_Ring__and__Field_Oaxclass__0__neq__1(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2200]) ).

fof(c_0_3562,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oidom(X55)
      | class_Ring__and__Field_Osemiring__1(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2201]) ).

fof(c_0_3563,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oidom(X55)
      | class_Ring__and__Field_Ocomm__ring(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2202]) ).

fof(c_0_3564,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oidom(X55)
      | class_Ring__and__Field_Ocomm__ring__1(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2203]) ).

fof(c_0_3565,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Ofield(X55)
      | class_Ring__and__Field_Osemiring__1__cancel(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2204]) ).

fof(c_0_3566,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Ofield(X55)
      | class_OrderedGroup_Ocomm__monoid__mult(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2205]) ).

fof(c_0_3567,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Ofield(X55)
      | class_Ring__and__Field_Ocomm__semiring__1(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2206]) ).

fof(c_0_3568,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Ofield(X55)
      | class_Ring__and__Field_Ocomm__semiring__1__cancel(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2207]) ).

fof(c_0_3569,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Ofield(X55)
      | class_HOL_Ominus(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2208]) ).

fof(c_0_3570,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Ofield(X55)
      | class_OrderedGroup_Oab__group__add(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2209]) ).

fof(c_0_3571,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Ofield(X55)
      | class_Ring__and__Field_Oaxclass__no__zero__divisors(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2210]) ).

fof(c_0_3572,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Ofield(X55)
      | class_Ring__and__Field_Oidom(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2211]) ).

fof(c_0_3573,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Ofield(X55)
      | class_HOL_Oinverse(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2212]) ).

fof(c_0_3574,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Ofield(X55)
      | class_Ring__and__Field_Oring(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2213]) ).

fof(c_0_3575,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Ofield(X55)
      | class_HOL_Oplus(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2214]) ).

fof(c_0_3576,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Ofield(X55)
      | class_OrderedGroup_Osemigroup__add(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2215]) ).

fof(c_0_3577,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Ofield(X55)
      | class_OrderedGroup_Ocancel__semigroup__add(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2216]) ).

fof(c_0_3578,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Ofield(X55)
      | class_OrderedGroup_Oab__semigroup__add(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2217]) ).

fof(c_0_3579,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Ofield(X55)
      | class_OrderedGroup_Ocancel__ab__semigroup__add(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2218]) ).

fof(c_0_3580,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Ofield(X55)
      | class_HOL_Ozero(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2219]) ).

fof(c_0_3581,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Ofield(X55)
      | class_OrderedGroup_Ocomm__monoid__add(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2220]) ).

fof(c_0_3582,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Ofield(X55)
      | class_HOL_Otimes(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2221]) ).

fof(c_0_3583,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Ofield(X55)
      | class_OrderedGroup_Osemigroup__mult(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2222]) ).

fof(c_0_3584,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Ofield(X55)
      | class_Ring__and__Field_Osemiring(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2223]) ).

fof(c_0_3585,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Ofield(X55)
      | class_Ring__and__Field_Oring__1(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2224]) ).

fof(c_0_3586,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Ofield(X55)
      | class_Ring__and__Field_Osemiring__0(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2225]) ).

fof(c_0_3587,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Ofield(X55)
      | class_Ring__and__Field_Osemiring__0__cancel(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2226]) ).

fof(c_0_3588,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Ofield(X55)
      | class_OrderedGroup_Oab__semigroup__mult(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2227]) ).

fof(c_0_3589,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Ofield(X55)
      | class_Ring__and__Field_Ocomm__semiring(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2228]) ).

fof(c_0_3590,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Ofield(X55)
      | class_Ring__and__Field_Ocomm__semiring__0(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2229]) ).

fof(c_0_3591,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Ofield(X55)
      | class_Ring__and__Field_Ocomm__semiring__0__cancel(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2230]) ).

fof(c_0_3592,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Ofield(X55)
      | class_HOL_Oone(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2231]) ).

fof(c_0_3593,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Ofield(X55)
      | class_OrderedGroup_Omonoid__mult(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2232]) ).

fof(c_0_3594,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Ofield(X55)
      | class_Ring__and__Field_Oaxclass__0__neq__1(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2233]) ).

fof(c_0_3595,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Ofield(X55)
      | class_Ring__and__Field_Osemiring__1(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2234]) ).

fof(c_0_3596,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Ofield(X55)
      | class_Ring__and__Field_Ocomm__ring(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2235]) ).

fof(c_0_3597,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Ofield(X55)
      | class_Ring__and__Field_Ocomm__ring__1(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2236]) ).

fof(c_0_3598,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Odivision__by__zero(X55)
      | class_HOL_Oinverse(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2237]) ).

fof(c_0_3599,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Odivision__by__zero(X55)
      | class_HOL_Ozero(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2238]) ).

fof(c_0_3600,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X55)
      | class_OrderedGroup_Ocomm__monoid__add(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2239]) ).

fof(c_0_3601,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X55)
      | class_Ring__and__Field_Osemiring(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2240]) ).

fof(c_0_3602,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X55)
      | class_Ring__and__Field_Osemiring__0(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2241]) ).

fof(c_0_3603,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X55)
      | class_Ring__and__Field_Oaxclass__0__neq__1(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2242]) ).

fof(c_0_3604,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X55)
      | class_Ring__and__Field_Osemiring__1(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2243]) ).

fof(c_0_3605,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X55)
      | class_OrderedGroup_Oab__semigroup__mult(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2244]) ).

fof(c_0_3606,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X55)
      | class_OrderedGroup_Ocomm__monoid__mult(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2245]) ).

fof(c_0_3607,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X55)
      | class_Ring__and__Field_Ocomm__semiring__0__cancel(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2246]) ).

fof(c_0_3608,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X55)
      | class_Ring__and__Field_Osemiring__0__cancel(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2247]) ).

fof(c_0_3609,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X55)
      | class_Ring__and__Field_Osemiring__1__cancel(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2248]) ).

fof(c_0_3610,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X55)
      | class_Ring__and__Field_Ocomm__semiring(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2249]) ).

fof(c_0_3611,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X55)
      | class_OrderedGroup_Ocancel__semigroup__add(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2250]) ).

fof(c_0_3612,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X55)
      | class_OrderedGroup_Ocancel__ab__semigroup__add(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2251]) ).

fof(c_0_3613,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X55)
      | class_HOL_Otimes(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2252]) ).

fof(c_0_3614,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X55)
      | class_OrderedGroup_Osemigroup__mult(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2253]) ).

fof(c_0_3615,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X55)
      | class_HOL_Oone(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2254]) ).

fof(c_0_3616,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X55)
      | class_OrderedGroup_Omonoid__mult(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2255]) ).

fof(c_0_3617,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X55)
      | class_HOL_Oplus(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2256]) ).

fof(c_0_3618,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X55)
      | class_OrderedGroup_Osemigroup__add(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2257]) ).

fof(c_0_3619,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X55)
      | class_OrderedGroup_Oab__semigroup__add(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2258]) ).

fof(c_0_3620,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X55)
      | class_HOL_Ozero(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2259]) ).

fof(c_0_3621,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X55)
      | class_Ring__and__Field_Ocomm__semiring__0(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2260]) ).

fof(c_0_3622,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X55)
      | class_Ring__and__Field_Ocomm__semiring__1(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2261]) ).

fof(c_0_3623,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X55)
      | class_HOL_Otimes(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2262]) ).

fof(c_0_3624,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X55)
      | class_OrderedGroup_Osemigroup__mult(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2263]) ).

fof(c_0_3625,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X55)
      | class_Ring__and__Field_Osemiring(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2264]) ).

fof(c_0_3626,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X55)
      | class_Ring__and__Field_Osemiring__0(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2265]) ).

fof(c_0_3627,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X55)
      | class_OrderedGroup_Oab__semigroup__mult(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2266]) ).

fof(c_0_3628,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X55)
      | class_Ring__and__Field_Ocomm__semiring(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2267]) ).

fof(c_0_3629,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X55)
      | class_Ring__and__Field_Ocomm__semiring__0(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2268]) ).

fof(c_0_3630,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X55)
      | class_HOL_Oone(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2269]) ).

fof(c_0_3631,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X55)
      | class_Ring__and__Field_Osemiring__1(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2270]) ).

fof(c_0_3632,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X55)
      | class_OrderedGroup_Omonoid__mult(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2271]) ).

fof(c_0_3633,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X55)
      | class_OrderedGroup_Ocomm__monoid__mult(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2272]) ).

fof(c_0_3634,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X55)
      | class_HOL_Oplus(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2273]) ).

fof(c_0_3635,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X55)
      | class_OrderedGroup_Osemigroup__add(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2274]) ).

fof(c_0_3636,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X55)
      | class_OrderedGroup_Oab__semigroup__add(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2275]) ).

fof(c_0_3637,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X55)
      | class_OrderedGroup_Ocomm__monoid__add(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2276]) ).

fof(c_0_3638,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X55)
      | class_HOL_Ozero(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2277]) ).

fof(c_0_3639,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X55)
      | class_Ring__and__Field_Oaxclass__0__neq__1(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2278]) ).

fof(c_0_3640,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X55)
      | class_OrderedGroup_Osemigroup__add(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2279]) ).

fof(c_0_3641,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X55)
      | class_OrderedGroup_Oab__semigroup__add(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2280]) ).

fof(c_0_3642,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X55)
      | class_OrderedGroup_Ocomm__monoid__add(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2281]) ).

fof(c_0_3643,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X55)
      | class_HOL_Otimes(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2282]) ).

fof(c_0_3644,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X55)
      | class_OrderedGroup_Osemigroup__mult(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2283]) ).

fof(c_0_3645,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X55)
      | class_Ring__and__Field_Osemiring(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2284]) ).

fof(c_0_3646,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X55)
      | class_Ring__and__Field_Osemiring__0(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2285]) ).

fof(c_0_3647,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X55)
      | class_OrderedGroup_Oab__semigroup__mult(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2286]) ).

fof(c_0_3648,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X55)
      | class_Ring__and__Field_Osemiring__0__cancel(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2287]) ).

fof(c_0_3649,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X55)
      | class_OrderedGroup_Ocancel__semigroup__add(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2288]) ).

fof(c_0_3650,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X55)
      | class_OrderedGroup_Ocancel__ab__semigroup__add(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2289]) ).

fof(c_0_3651,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X55)
      | class_HOL_Ozero(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2290]) ).

fof(c_0_3652,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X55)
      | class_HOL_Oplus(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2291]) ).

fof(c_0_3653,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X55)
      | class_Ring__and__Field_Ocomm__semiring(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2292]) ).

fof(c_0_3654,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X55)
      | class_Ring__and__Field_Ocomm__semiring__0(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2293]) ).

fof(c_0_3655,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__0(X55)
      | class_HOL_Ozero(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2294]) ).

fof(c_0_3656,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__0(X55)
      | class_OrderedGroup_Ocomm__monoid__add(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2295]) ).

fof(c_0_3657,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__0(X55)
      | class_HOL_Otimes(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2296]) ).

fof(c_0_3658,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__0(X55)
      | class_OrderedGroup_Osemigroup__mult(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2297]) ).

fof(c_0_3659,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__0(X55)
      | class_HOL_Oplus(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2298]) ).

fof(c_0_3660,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__0(X55)
      | class_OrderedGroup_Osemigroup__add(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2299]) ).

fof(c_0_3661,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__0(X55)
      | class_OrderedGroup_Oab__semigroup__add(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2300]) ).

fof(c_0_3662,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__0(X55)
      | class_Ring__and__Field_Osemiring(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2301]) ).

fof(c_0_3663,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__0(X55)
      | class_Ring__and__Field_Osemiring__0(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2302]) ).

fof(c_0_3664,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__0(X55)
      | class_OrderedGroup_Oab__semigroup__mult(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2303]) ).

fof(c_0_3665,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__0(X55)
      | class_Ring__and__Field_Ocomm__semiring(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2304]) ).

fof(c_0_3666,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Ocomm__semiring(X55)
      | class_Ring__and__Field_Osemiring(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2305]) ).

fof(c_0_3667,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Ocomm__semiring(X55)
      | class_HOL_Otimes(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2306]) ).

fof(c_0_3668,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Ocomm__semiring(X55)
      | class_OrderedGroup_Osemigroup__mult(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2307]) ).

fof(c_0_3669,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Ocomm__semiring(X55)
      | class_OrderedGroup_Oab__semigroup__mult(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2308]) ).

fof(c_0_3670,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Ocomm__semiring(X55)
      | class_HOL_Oplus(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2309]) ).

fof(c_0_3671,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Ocomm__semiring(X55)
      | class_OrderedGroup_Osemigroup__add(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2310]) ).

fof(c_0_3672,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Ocomm__semiring(X55)
      | class_OrderedGroup_Oab__semigroup__add(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2311]) ).

fof(c_0_3673,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Ocomm__ring__1(X55)
      | class_Ring__and__Field_Osemiring__0(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2312]) ).

fof(c_0_3674,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Ocomm__ring__1(X55)
      | class_Ring__and__Field_Osemiring__0__cancel(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2313]) ).

fof(c_0_3675,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Ocomm__ring__1(X55)
      | class_OrderedGroup_Oab__semigroup__mult(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2314]) ).

fof(c_0_3676,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Ocomm__ring__1(X55)
      | class_Ring__and__Field_Ocomm__semiring(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2315]) ).

fof(c_0_3677,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Ocomm__ring__1(X55)
      | class_Ring__and__Field_Ocomm__semiring__0(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2316]) ).

fof(c_0_3678,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Ocomm__ring__1(X55)
      | class_Ring__and__Field_Ocomm__semiring__0__cancel(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2317]) ).

fof(c_0_3679,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Ocomm__ring__1(X55)
      | class_HOL_Ominus(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2318]) ).

fof(c_0_3680,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Ocomm__ring__1(X55)
      | class_Ring__and__Field_Ocomm__semiring__1__cancel(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2319]) ).

fof(c_0_3681,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Ocomm__ring__1(X55)
      | class_Ring__and__Field_Osemiring__1__cancel(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2320]) ).

fof(c_0_3682,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Ocomm__ring__1(X55)
      | class_Ring__and__Field_Oring__1(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2321]) ).

fof(c_0_3683,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Ocomm__ring__1(X55)
      | class_HOL_Oone(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2322]) ).

fof(c_0_3684,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Ocomm__ring__1(X55)
      | class_OrderedGroup_Omonoid__mult(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2323]) ).

fof(c_0_3685,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Ocomm__ring__1(X55)
      | class_Ring__and__Field_Oaxclass__0__neq__1(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2324]) ).

fof(c_0_3686,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Ocomm__ring__1(X55)
      | class_Ring__and__Field_Osemiring__1(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2325]) ).

fof(c_0_3687,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Ocomm__ring__1(X55)
      | class_OrderedGroup_Ocomm__monoid__mult(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2326]) ).

fof(c_0_3688,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Ocomm__ring__1(X55)
      | class_Ring__and__Field_Ocomm__semiring__1(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2327]) ).

fof(c_0_3689,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Ocomm__ring__1(X55)
      | class_OrderedGroup_Oab__group__add(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2328]) ).

fof(c_0_3690,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Ocomm__ring__1(X55)
      | class_HOL_Oplus(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2329]) ).

fof(c_0_3691,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Ocomm__ring__1(X55)
      | class_OrderedGroup_Osemigroup__add(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2330]) ).

fof(c_0_3692,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Ocomm__ring__1(X55)
      | class_OrderedGroup_Ocancel__semigroup__add(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2331]) ).

fof(c_0_3693,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Ocomm__ring__1(X55)
      | class_OrderedGroup_Oab__semigroup__add(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2332]) ).

fof(c_0_3694,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Ocomm__ring__1(X55)
      | class_OrderedGroup_Ocancel__ab__semigroup__add(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2333]) ).

fof(c_0_3695,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Ocomm__ring__1(X55)
      | class_HOL_Ozero(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2334]) ).

fof(c_0_3696,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Ocomm__ring__1(X55)
      | class_OrderedGroup_Ocomm__monoid__add(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2335]) ).

fof(c_0_3697,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Ocomm__ring__1(X55)
      | class_HOL_Otimes(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2336]) ).

fof(c_0_3698,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Ocomm__ring__1(X55)
      | class_OrderedGroup_Osemigroup__mult(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2337]) ).

fof(c_0_3699,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Ocomm__ring__1(X55)
      | class_Ring__and__Field_Osemiring(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2338]) ).

fof(c_0_3700,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Ocomm__ring__1(X55)
      | class_Ring__and__Field_Oring(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2339]) ).

fof(c_0_3701,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Ocomm__ring__1(X55)
      | class_Ring__and__Field_Ocomm__ring(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2340]) ).

fof(c_0_3702,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Ocomm__ring(X55)
      | class_OrderedGroup_Osemigroup__add(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2341]) ).

fof(c_0_3703,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Ocomm__ring(X55)
      | class_OrderedGroup_Oab__semigroup__add(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2342]) ).

fof(c_0_3704,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Ocomm__ring(X55)
      | class_OrderedGroup_Ocomm__monoid__add(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2343]) ).

fof(c_0_3705,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Ocomm__ring(X55)
      | class_HOL_Otimes(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2344]) ).

fof(c_0_3706,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Ocomm__ring(X55)
      | class_OrderedGroup_Osemigroup__mult(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2345]) ).

fof(c_0_3707,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Ocomm__ring(X55)
      | class_Ring__and__Field_Osemiring(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2346]) ).

fof(c_0_3708,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Ocomm__ring(X55)
      | class_Ring__and__Field_Osemiring__0(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2347]) ).

fof(c_0_3709,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Ocomm__ring(X55)
      | class_OrderedGroup_Oab__semigroup__mult(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2348]) ).

fof(c_0_3710,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Ocomm__ring(X55)
      | class_Ring__and__Field_Ocomm__semiring__0__cancel(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2349]) ).

fof(c_0_3711,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Ocomm__ring(X55)
      | class_Ring__and__Field_Osemiring__0__cancel(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2350]) ).

fof(c_0_3712,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Ocomm__ring(X55)
      | class_Ring__and__Field_Oring(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2351]) ).

fof(c_0_3713,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Ocomm__ring(X55)
      | class_OrderedGroup_Ocancel__semigroup__add(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2352]) ).

fof(c_0_3714,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Ocomm__ring(X55)
      | class_OrderedGroup_Ocancel__ab__semigroup__add(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2353]) ).

fof(c_0_3715,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Ocomm__ring(X55)
      | class_HOL_Ominus(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2354]) ).

fof(c_0_3716,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Ocomm__ring(X55)
      | class_OrderedGroup_Oab__group__add(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2355]) ).

fof(c_0_3717,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Ocomm__ring(X55)
      | class_HOL_Ozero(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2356]) ).

fof(c_0_3718,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Ocomm__ring(X55)
      | class_HOL_Oplus(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2357]) ).

fof(c_0_3719,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Ocomm__ring(X55)
      | class_Ring__and__Field_Ocomm__semiring(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2358]) ).

fof(c_0_3720,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Ocomm__ring(X55)
      | class_Ring__and__Field_Ocomm__semiring__0(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2359]) ).

fof(c_0_3721,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oaxclass__no__zero__divisors(X55)
      | class_HOL_Otimes(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2360]) ).

fof(c_0_3722,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oaxclass__no__zero__divisors(X55)
      | class_HOL_Ozero(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2361]) ).

fof(c_0_3723,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oaxclass__abs__if(X55)
      | class_HOL_Ozero(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2362]) ).

fof(c_0_3724,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oaxclass__abs__if(X55)
      | class_Orderings_Oord(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2363]) ).

fof(c_0_3725,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oaxclass__abs__if(X55)
      | class_HOL_Ominus(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2364]) ).

fof(c_0_3726,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oaxclass__0__neq__1(X55)
      | class_HOL_Oone(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2365]) ).

fof(c_0_3727,plain,
    ! [X55] :
      ( ~ class_Ring__and__Field_Oaxclass__0__neq__1(X55)
      | class_HOL_Ozero(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2366]) ).

fof(c_0_3728,plain,
    ! [X55] :
      ( ~ class_Power_Orecpower(X55)
      | class_OrderedGroup_Oab__semigroup__mult(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2367]) ).

fof(c_0_3729,plain,
    ! [X55] :
      ( ~ class_Power_Orecpower(X55)
      | class_OrderedGroup_Osemigroup__mult(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2368]) ).

fof(c_0_3730,plain,
    ! [X55] :
      ( ~ class_Power_Orecpower(X55)
      | class_HOL_Otimes(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2369]) ).

fof(c_0_3731,plain,
    ! [X55] :
      ( ~ class_Power_Orecpower(X55)
      | class_OrderedGroup_Oab__semigroup__add(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2370]) ).

fof(c_0_3732,plain,
    ! [X55] :
      ( ~ class_Power_Orecpower(X55)
      | class_OrderedGroup_Osemigroup__add(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2371]) ).

fof(c_0_3733,plain,
    ! [X55] :
      ( ~ class_Power_Orecpower(X55)
      | class_HOL_Oplus(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2372]) ).

fof(c_0_3734,plain,
    ! [X55] :
      ( ~ class_Power_Orecpower(X55)
      | class_Ring__and__Field_Oaxclass__0__neq__1(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2373]) ).

fof(c_0_3735,plain,
    ! [X55] :
      ( ~ class_Power_Orecpower(X55)
      | class_Ring__and__Field_Ocomm__semiring__1__cancel(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2374]) ).

fof(c_0_3736,plain,
    ! [X55] :
      ( ~ class_Power_Orecpower(X55)
      | class_Ring__and__Field_Ocomm__semiring__0__cancel(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2375]) ).

fof(c_0_3737,plain,
    ! [X55] :
      ( ~ class_Power_Orecpower(X55)
      | class_Ring__and__Field_Osemiring__1__cancel(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2376]) ).

fof(c_0_3738,plain,
    ! [X55] :
      ( ~ class_Power_Orecpower(X55)
      | class_Ring__and__Field_Osemiring__0__cancel(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2377]) ).

fof(c_0_3739,plain,
    ! [X55] :
      ( ~ class_Power_Orecpower(X55)
      | class_OrderedGroup_Ocancel__ab__semigroup__add(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2378]) ).

fof(c_0_3740,plain,
    ! [X55] :
      ( ~ class_Power_Orecpower(X55)
      | class_HOL_Oone(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2379]) ).

fof(c_0_3741,plain,
    ! [X55] :
      ( ~ class_Power_Orecpower(X55)
      | class_OrderedGroup_Ocancel__semigroup__add(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2380]) ).

fof(c_0_3742,plain,
    ! [X55] :
      ( ~ class_Power_Orecpower(X55)
      | class_Ring__and__Field_Ocomm__semiring__1(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2381]) ).

fof(c_0_3743,plain,
    ! [X55] :
      ( ~ class_Power_Orecpower(X55)
      | class_Ring__and__Field_Osemiring__1(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2382]) ).

fof(c_0_3744,plain,
    ! [X55] :
      ( ~ class_Power_Orecpower(X55)
      | class_OrderedGroup_Ocomm__monoid__mult(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2383]) ).

fof(c_0_3745,plain,
    ! [X55] :
      ( ~ class_Power_Orecpower(X55)
      | class_OrderedGroup_Omonoid__mult(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2384]) ).

fof(c_0_3746,plain,
    ! [X55] :
      ( ~ class_Power_Orecpower(X55)
      | class_Ring__and__Field_Ocomm__semiring__0(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2385]) ).

fof(c_0_3747,plain,
    ! [X55] :
      ( ~ class_Power_Orecpower(X55)
      | class_Ring__and__Field_Osemiring__0(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2386]) ).

fof(c_0_3748,plain,
    ! [X55] :
      ( ~ class_Power_Orecpower(X55)
      | class_OrderedGroup_Ocomm__monoid__add(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2387]) ).

fof(c_0_3749,plain,
    ! [X55] :
      ( ~ class_Power_Orecpower(X55)
      | class_Ring__and__Field_Ocomm__semiring(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2388]) ).

fof(c_0_3750,plain,
    ! [X55] :
      ( ~ class_Power_Orecpower(X55)
      | class_Ring__and__Field_Osemiring(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2389]) ).

fof(c_0_3751,plain,
    ! [X55] :
      ( ~ class_Power_Orecpower(X55)
      | class_HOL_Ozero(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2390]) ).

fof(c_0_3752,plain,
    ! [X55] :
      ( ~ class_Power_Orecpower(X55)
      | class_Nat_Opower(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2391]) ).

fof(c_0_3753,plain,
    ! [X55] :
      ( ~ class_Orderings_Oorder(X55)
      | class_Orderings_Oord(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2392]) ).

fof(c_0_3754,plain,
    ! [X55] :
      ( ~ class_Orderings_Olinorder(X55)
      | class_Orderings_Oorder(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2393]) ).

fof(c_0_3755,plain,
    ! [X55] :
      ( ~ class_Orderings_Olinorder(X55)
      | class_Orderings_Oord(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2394]) ).

fof(c_0_3756,plain,
    ! [X55] :
      ( ~ class_Orderings_Olinorder(X55)
      | class_LOrder_Omeet__semilorder(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2395]) ).

fof(c_0_3757,plain,
    ! [X55] :
      ( ~ class_Orderings_Olinorder(X55)
      | class_LOrder_Ojoin__semilorder(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2396]) ).

fof(c_0_3758,plain,
    ! [X55] :
      ( ~ class_Orderings_Olinorder(X55)
      | class_LOrder_Olorder(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2397]) ).

fof(c_0_3759,plain,
    ! [X55] :
      ( ~ class_OrderedGroup_Osemigroup__mult(X55)
      | class_HOL_Otimes(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2398]) ).

fof(c_0_3760,plain,
    ! [X55] :
      ( ~ class_OrderedGroup_Osemigroup__add(X55)
      | class_HOL_Oplus(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2399]) ).

fof(c_0_3761,plain,
    ! [X55] :
      ( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X55)
      | class_OrderedGroup_Ocancel__semigroup__add(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2400]) ).

fof(c_0_3762,plain,
    ! [X55] :
      ( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X55)
      | class_OrderedGroup_Ocancel__ab__semigroup__add(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2401]) ).

fof(c_0_3763,plain,
    ! [X55] :
      ( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X55)
      | class_HOL_Oplus(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2402]) ).

fof(c_0_3764,plain,
    ! [X55] :
      ( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X55)
      | class_OrderedGroup_Osemigroup__add(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2403]) ).

fof(c_0_3765,plain,
    ! [X55] :
      ( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X55)
      | class_OrderedGroup_Oab__semigroup__add(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2404]) ).

fof(c_0_3766,plain,
    ! [X55] :
      ( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X55)
      | class_Orderings_Oord(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2405]) ).

fof(c_0_3767,plain,
    ! [X55] :
      ( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X55)
      | class_Orderings_Oorder(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2406]) ).

fof(c_0_3768,plain,
    ! [X55] :
      ( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X55)
      | class_OrderedGroup_Opordered__ab__semigroup__add(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2407]) ).

fof(c_0_3769,plain,
    ! [X55] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X55)
      | class_HOL_Oplus(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2408]) ).

fof(c_0_3770,plain,
    ! [X55] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X55)
      | class_OrderedGroup_Osemigroup__add(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2409]) ).

fof(c_0_3771,plain,
    ! [X55] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X55)
      | class_OrderedGroup_Ocancel__semigroup__add(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2410]) ).

fof(c_0_3772,plain,
    ! [X55] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X55)
      | class_OrderedGroup_Oab__semigroup__add(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2411]) ).

fof(c_0_3773,plain,
    ! [X55] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X55)
      | class_OrderedGroup_Ocancel__ab__semigroup__add(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2412]) ).

fof(c_0_3774,plain,
    ! [X55] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X55)
      | class_Orderings_Oord(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2413]) ).

fof(c_0_3775,plain,
    ! [X55] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X55)
      | class_Orderings_Oorder(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2414]) ).

fof(c_0_3776,plain,
    ! [X55] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X55)
      | class_OrderedGroup_Opordered__ab__semigroup__add(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2415]) ).

fof(c_0_3777,plain,
    ! [X55] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X55)
      | class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2416]) ).

fof(c_0_3778,plain,
    ! [X55] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X55)
      | class_HOL_Oplus(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2417]) ).

fof(c_0_3779,plain,
    ! [X55] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X55)
      | class_OrderedGroup_Osemigroup__add(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2418]) ).

fof(c_0_3780,plain,
    ! [X55] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X55)
      | class_OrderedGroup_Oab__semigroup__add(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2419]) ).

fof(c_0_3781,plain,
    ! [X55] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X55)
      | class_Orderings_Oord(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2420]) ).

fof(c_0_3782,plain,
    ! [X55] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X55)
      | class_Orderings_Oorder(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2421]) ).

fof(c_0_3783,plain,
    ! [X55] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add(X55)
      | class_OrderedGroup_Opordered__ab__semigroup__add(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2422]) ).

fof(c_0_3784,plain,
    ! [X55] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add(X55)
      | class_HOL_Oplus(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2423]) ).

fof(c_0_3785,plain,
    ! [X55] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add(X55)
      | class_OrderedGroup_Osemigroup__add(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2424]) ).

fof(c_0_3786,plain,
    ! [X55] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add(X55)
      | class_OrderedGroup_Ocancel__semigroup__add(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2425]) ).

fof(c_0_3787,plain,
    ! [X55] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add(X55)
      | class_OrderedGroup_Oab__semigroup__add(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2426]) ).

fof(c_0_3788,plain,
    ! [X55] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add(X55)
      | class_OrderedGroup_Ocancel__ab__semigroup__add(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2427]) ).

fof(c_0_3789,plain,
    ! [X55] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add(X55)
      | class_HOL_Ozero(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2428]) ).

fof(c_0_3790,plain,
    ! [X55] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add(X55)
      | class_OrderedGroup_Ocomm__monoid__add(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2429]) ).

fof(c_0_3791,plain,
    ! [X55] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add(X55)
      | class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2430]) ).

fof(c_0_3792,plain,
    ! [X55] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add(X55)
      | class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2431]) ).

fof(c_0_3793,plain,
    ! [X55] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add(X55)
      | class_Orderings_Oord(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2432]) ).

fof(c_0_3794,plain,
    ! [X55] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add(X55)
      | class_Orderings_Oorder(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2433]) ).

fof(c_0_3795,plain,
    ! [X55] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add(X55)
      | class_HOL_Ominus(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2434]) ).

fof(c_0_3796,plain,
    ! [X55] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add(X55)
      | class_OrderedGroup_Oab__group__add(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2435]) ).

fof(c_0_3797,plain,
    ! [X55] :
      ( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X55)
      | class_Orderings_Olinorder(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2436]) ).

fof(c_0_3798,plain,
    ! [X55] :
      ( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X55)
      | class_HOL_Oplus(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2437]) ).

fof(c_0_3799,plain,
    ! [X55] :
      ( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X55)
      | class_OrderedGroup_Osemigroup__add(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2438]) ).

fof(c_0_3800,plain,
    ! [X55] :
      ( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X55)
      | class_OrderedGroup_Ocancel__semigroup__add(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2439]) ).

fof(c_0_3801,plain,
    ! [X55] :
      ( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X55)
      | class_OrderedGroup_Oab__semigroup__add(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2440]) ).

fof(c_0_3802,plain,
    ! [X55] :
      ( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X55)
      | class_OrderedGroup_Ocancel__ab__semigroup__add(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2441]) ).

fof(c_0_3803,plain,
    ! [X55] :
      ( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X55)
      | class_Orderings_Oord(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2442]) ).

fof(c_0_3804,plain,
    ! [X55] :
      ( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X55)
      | class_Orderings_Oorder(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2443]) ).

fof(c_0_3805,plain,
    ! [X55] :
      ( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X55)
      | class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2444]) ).

fof(c_0_3806,plain,
    ! [X55] :
      ( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X55)
      | class_LOrder_Omeet__semilorder(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2445]) ).

fof(c_0_3807,plain,
    ! [X55] :
      ( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X55)
      | class_LOrder_Ojoin__semilorder(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2446]) ).

fof(c_0_3808,plain,
    ! [X55] :
      ( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X55)
      | class_LOrder_Olorder(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2447]) ).

fof(c_0_3809,plain,
    ! [X55] :
      ( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X55)
      | class_OrderedGroup_Opordered__ab__semigroup__add(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2448]) ).

fof(c_0_3810,plain,
    ! [X55] :
      ( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X55)
      | class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2449]) ).

fof(c_0_3811,plain,
    ! [X55] :
      ( ~ class_OrderedGroup_Omonoid__mult(X55)
      | class_HOL_Otimes(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2450]) ).

fof(c_0_3812,plain,
    ! [X55] :
      ( ~ class_OrderedGroup_Omonoid__mult(X55)
      | class_OrderedGroup_Osemigroup__mult(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2451]) ).

fof(c_0_3813,plain,
    ! [X55] :
      ( ~ class_OrderedGroup_Omonoid__mult(X55)
      | class_HOL_Oone(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2452]) ).

fof(c_0_3814,plain,
    ! [X55] :
      ( ~ class_OrderedGroup_Olordered__ab__group__meet(X55)
      | class_Orderings_Oord(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2453]) ).

fof(c_0_3815,plain,
    ! [X55] :
      ( ~ class_OrderedGroup_Olordered__ab__group__meet(X55)
      | class_Orderings_Oorder(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2454]) ).

fof(c_0_3816,plain,
    ! [X55] :
      ( ~ class_OrderedGroup_Olordered__ab__group__meet(X55)
      | class_OrderedGroup_Opordered__ab__semigroup__add(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2455]) ).

fof(c_0_3817,plain,
    ! [X55] :
      ( ~ class_OrderedGroup_Olordered__ab__group__meet(X55)
      | class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2456]) ).

fof(c_0_3818,plain,
    ! [X55] :
      ( ~ class_OrderedGroup_Olordered__ab__group__meet(X55)
      | class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2457]) ).

fof(c_0_3819,plain,
    ! [X55] :
      ( ~ class_OrderedGroup_Olordered__ab__group__meet(X55)
      | class_HOL_Ozero(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2458]) ).

fof(c_0_3820,plain,
    ! [X55] :
      ( ~ class_OrderedGroup_Olordered__ab__group__meet(X55)
      | class_OrderedGroup_Ocomm__monoid__add(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2459]) ).

fof(c_0_3821,plain,
    ! [X55] :
      ( ~ class_OrderedGroup_Olordered__ab__group__meet(X55)
      | class_HOL_Ominus(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2460]) ).

fof(c_0_3822,plain,
    ! [X55] :
      ( ~ class_OrderedGroup_Olordered__ab__group__meet(X55)
      | class_LOrder_Ojoin__semilorder(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2461]) ).

fof(c_0_3823,plain,
    ! [X55] :
      ( ~ class_OrderedGroup_Olordered__ab__group__meet(X55)
      | class_LOrder_Olorder(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2462]) ).

fof(c_0_3824,plain,
    ! [X55] :
      ( ~ class_OrderedGroup_Olordered__ab__group__meet(X55)
      | class_OrderedGroup_Olordered__ab__group(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2463]) ).

fof(c_0_3825,plain,
    ! [X55] :
      ( ~ class_OrderedGroup_Olordered__ab__group__meet(X55)
      | class_LOrder_Omeet__semilorder(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2464]) ).

fof(c_0_3826,plain,
    ! [X55] :
      ( ~ class_OrderedGroup_Olordered__ab__group__meet(X55)
      | class_HOL_Oplus(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2465]) ).

fof(c_0_3827,plain,
    ! [X55] :
      ( ~ class_OrderedGroup_Olordered__ab__group__meet(X55)
      | class_OrderedGroup_Osemigroup__add(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2466]) ).

fof(c_0_3828,plain,
    ! [X55] :
      ( ~ class_OrderedGroup_Olordered__ab__group__meet(X55)
      | class_OrderedGroup_Ocancel__semigroup__add(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2467]) ).

fof(c_0_3829,plain,
    ! [X55] :
      ( ~ class_OrderedGroup_Olordered__ab__group__meet(X55)
      | class_OrderedGroup_Oab__semigroup__add(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2468]) ).

fof(c_0_3830,plain,
    ! [X55] :
      ( ~ class_OrderedGroup_Olordered__ab__group__meet(X55)
      | class_OrderedGroup_Ocancel__ab__semigroup__add(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2469]) ).

fof(c_0_3831,plain,
    ! [X55] :
      ( ~ class_OrderedGroup_Olordered__ab__group__meet(X55)
      | class_OrderedGroup_Oab__group__add(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2470]) ).

fof(c_0_3832,plain,
    ! [X55] :
      ( ~ class_OrderedGroup_Olordered__ab__group__meet(X55)
      | class_OrderedGroup_Opordered__ab__group__add(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2471]) ).

fof(c_0_3833,plain,
    ! [X55] :
      ( ~ class_OrderedGroup_Olordered__ab__group__join(X55)
      | class_Orderings_Oord(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2472]) ).

fof(c_0_3834,plain,
    ! [X55] :
      ( ~ class_OrderedGroup_Olordered__ab__group__join(X55)
      | class_Orderings_Oorder(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2473]) ).

fof(c_0_3835,plain,
    ! [X55] :
      ( ~ class_OrderedGroup_Olordered__ab__group__join(X55)
      | class_OrderedGroup_Opordered__ab__semigroup__add(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2474]) ).

fof(c_0_3836,plain,
    ! [X55] :
      ( ~ class_OrderedGroup_Olordered__ab__group__join(X55)
      | class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2475]) ).

fof(c_0_3837,plain,
    ! [X55] :
      ( ~ class_OrderedGroup_Olordered__ab__group__join(X55)
      | class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2476]) ).

fof(c_0_3838,plain,
    ! [X55] :
      ( ~ class_OrderedGroup_Olordered__ab__group__join(X55)
      | class_HOL_Ozero(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2477]) ).

fof(c_0_3839,plain,
    ! [X55] :
      ( ~ class_OrderedGroup_Olordered__ab__group__join(X55)
      | class_OrderedGroup_Ocomm__monoid__add(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2478]) ).

fof(c_0_3840,plain,
    ! [X55] :
      ( ~ class_OrderedGroup_Olordered__ab__group__join(X55)
      | class_HOL_Ominus(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2479]) ).

fof(c_0_3841,plain,
    ! [X55] :
      ( ~ class_OrderedGroup_Olordered__ab__group__join(X55)
      | class_LOrder_Omeet__semilorder(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2480]) ).

fof(c_0_3842,plain,
    ! [X55] :
      ( ~ class_OrderedGroup_Olordered__ab__group__join(X55)
      | class_LOrder_Olorder(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2481]) ).

fof(c_0_3843,plain,
    ! [X55] :
      ( ~ class_OrderedGroup_Olordered__ab__group__join(X55)
      | class_OrderedGroup_Olordered__ab__group(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2482]) ).

fof(c_0_3844,plain,
    ! [X55] :
      ( ~ class_OrderedGroup_Olordered__ab__group__join(X55)
      | class_LOrder_Ojoin__semilorder(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2483]) ).

fof(c_0_3845,plain,
    ! [X55] :
      ( ~ class_OrderedGroup_Olordered__ab__group__join(X55)
      | class_HOL_Oplus(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2484]) ).

fof(c_0_3846,plain,
    ! [X55] :
      ( ~ class_OrderedGroup_Olordered__ab__group__join(X55)
      | class_OrderedGroup_Osemigroup__add(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2485]) ).

fof(c_0_3847,plain,
    ! [X55] :
      ( ~ class_OrderedGroup_Olordered__ab__group__join(X55)
      | class_OrderedGroup_Ocancel__semigroup__add(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2486]) ).

fof(c_0_3848,plain,
    ! [X55] :
      ( ~ class_OrderedGroup_Olordered__ab__group__join(X55)
      | class_OrderedGroup_Oab__semigroup__add(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2487]) ).

fof(c_0_3849,plain,
    ! [X55] :
      ( ~ class_OrderedGroup_Olordered__ab__group__join(X55)
      | class_OrderedGroup_Ocancel__ab__semigroup__add(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2488]) ).

fof(c_0_3850,plain,
    ! [X55] :
      ( ~ class_OrderedGroup_Olordered__ab__group__join(X55)
      | class_OrderedGroup_Oab__group__add(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2489]) ).

fof(c_0_3851,plain,
    ! [X55] :
      ( ~ class_OrderedGroup_Olordered__ab__group__join(X55)
      | class_OrderedGroup_Opordered__ab__group__add(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2490]) ).

fof(c_0_3852,plain,
    ! [X55] :
      ( ~ class_OrderedGroup_Olordered__ab__group__abs(X55)
      | class_OrderedGroup_Ocancel__ab__semigroup__add(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2491]) ).

fof(c_0_3853,plain,
    ! [X55] :
      ( ~ class_OrderedGroup_Olordered__ab__group__abs(X55)
      | class_OrderedGroup_Opordered__ab__semigroup__add(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2492]) ).

fof(c_0_3854,plain,
    ! [X55] :
      ( ~ class_OrderedGroup_Olordered__ab__group__abs(X55)
      | class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2493]) ).

fof(c_0_3855,plain,
    ! [X55] :
      ( ~ class_OrderedGroup_Olordered__ab__group__abs(X55)
      | class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2494]) ).

fof(c_0_3856,plain,
    ! [X55] :
      ( ~ class_OrderedGroup_Olordered__ab__group__abs(X55)
      | class_HOL_Ozero(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2495]) ).

fof(c_0_3857,plain,
    ! [X55] :
      ( ~ class_OrderedGroup_Olordered__ab__group__abs(X55)
      | class_OrderedGroup_Ocomm__monoid__add(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2496]) ).

fof(c_0_3858,plain,
    ! [X55] :
      ( ~ class_OrderedGroup_Olordered__ab__group__abs(X55)
      | class_HOL_Ominus(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2497]) ).

fof(c_0_3859,plain,
    ! [X55] :
      ( ~ class_OrderedGroup_Olordered__ab__group__abs(X55)
      | class_OrderedGroup_Oab__group__add(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2498]) ).

fof(c_0_3860,plain,
    ! [X55] :
      ( ~ class_OrderedGroup_Olordered__ab__group__abs(X55)
      | class_Orderings_Oord(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2499]) ).

fof(c_0_3861,plain,
    ! [X55] :
      ( ~ class_OrderedGroup_Olordered__ab__group__abs(X55)
      | class_Orderings_Oorder(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2500]) ).

fof(c_0_3862,plain,
    ! [X55] :
      ( ~ class_OrderedGroup_Olordered__ab__group__abs(X55)
      | class_LOrder_Omeet__semilorder(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2501]) ).

fof(c_0_3863,plain,
    ! [X55] :
      ( ~ class_OrderedGroup_Olordered__ab__group__abs(X55)
      | class_LOrder_Ojoin__semilorder(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2502]) ).

fof(c_0_3864,plain,
    ! [X55] :
      ( ~ class_OrderedGroup_Olordered__ab__group__abs(X55)
      | class_LOrder_Olorder(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2503]) ).

fof(c_0_3865,plain,
    ! [X55] :
      ( ~ class_OrderedGroup_Olordered__ab__group__abs(X55)
      | class_HOL_Oplus(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2504]) ).

fof(c_0_3866,plain,
    ! [X55] :
      ( ~ class_OrderedGroup_Olordered__ab__group__abs(X55)
      | class_OrderedGroup_Osemigroup__add(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2505]) ).

fof(c_0_3867,plain,
    ! [X55] :
      ( ~ class_OrderedGroup_Olordered__ab__group__abs(X55)
      | class_OrderedGroup_Ocancel__semigroup__add(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2506]) ).

fof(c_0_3868,plain,
    ! [X55] :
      ( ~ class_OrderedGroup_Olordered__ab__group__abs(X55)
      | class_OrderedGroup_Oab__semigroup__add(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2507]) ).

fof(c_0_3869,plain,
    ! [X55] :
      ( ~ class_OrderedGroup_Olordered__ab__group__abs(X55)
      | class_OrderedGroup_Opordered__ab__group__add(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2508]) ).

fof(c_0_3870,plain,
    ! [X55] :
      ( ~ class_OrderedGroup_Olordered__ab__group__abs(X55)
      | class_OrderedGroup_Olordered__ab__group(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2509]) ).

fof(c_0_3871,plain,
    ! [X55] :
      ( ~ class_OrderedGroup_Olordered__ab__group(X55)
      | class_Orderings_Oord(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2510]) ).

fof(c_0_3872,plain,
    ! [X55] :
      ( ~ class_OrderedGroup_Olordered__ab__group(X55)
      | class_Orderings_Oorder(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2511]) ).

fof(c_0_3873,plain,
    ! [X55] :
      ( ~ class_OrderedGroup_Olordered__ab__group(X55)
      | class_OrderedGroup_Opordered__ab__semigroup__add(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2512]) ).

fof(c_0_3874,plain,
    ! [X55] :
      ( ~ class_OrderedGroup_Olordered__ab__group(X55)
      | class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2513]) ).

fof(c_0_3875,plain,
    ! [X55] :
      ( ~ class_OrderedGroup_Olordered__ab__group(X55)
      | class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2514]) ).

fof(c_0_3876,plain,
    ! [X55] :
      ( ~ class_OrderedGroup_Olordered__ab__group(X55)
      | class_HOL_Ozero(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2515]) ).

fof(c_0_3877,plain,
    ! [X55] :
      ( ~ class_OrderedGroup_Olordered__ab__group(X55)
      | class_OrderedGroup_Ocomm__monoid__add(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2516]) ).

fof(c_0_3878,plain,
    ! [X55] :
      ( ~ class_OrderedGroup_Olordered__ab__group(X55)
      | class_HOL_Ominus(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2517]) ).

fof(c_0_3879,plain,
    ! [X55] :
      ( ~ class_OrderedGroup_Olordered__ab__group(X55)
      | class_LOrder_Omeet__semilorder(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2518]) ).

fof(c_0_3880,plain,
    ! [X55] :
      ( ~ class_OrderedGroup_Olordered__ab__group(X55)
      | class_LOrder_Ojoin__semilorder(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2519]) ).

fof(c_0_3881,plain,
    ! [X55] :
      ( ~ class_OrderedGroup_Olordered__ab__group(X55)
      | class_LOrder_Olorder(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2520]) ).

fof(c_0_3882,plain,
    ! [X55] :
      ( ~ class_OrderedGroup_Olordered__ab__group(X55)
      | class_HOL_Oplus(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2521]) ).

fof(c_0_3883,plain,
    ! [X55] :
      ( ~ class_OrderedGroup_Olordered__ab__group(X55)
      | class_OrderedGroup_Osemigroup__add(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2522]) ).

fof(c_0_3884,plain,
    ! [X55] :
      ( ~ class_OrderedGroup_Olordered__ab__group(X55)
      | class_OrderedGroup_Ocancel__semigroup__add(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2523]) ).

fof(c_0_3885,plain,
    ! [X55] :
      ( ~ class_OrderedGroup_Olordered__ab__group(X55)
      | class_OrderedGroup_Oab__semigroup__add(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2524]) ).

fof(c_0_3886,plain,
    ! [X55] :
      ( ~ class_OrderedGroup_Olordered__ab__group(X55)
      | class_OrderedGroup_Ocancel__ab__semigroup__add(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2525]) ).

fof(c_0_3887,plain,
    ! [X55] :
      ( ~ class_OrderedGroup_Olordered__ab__group(X55)
      | class_OrderedGroup_Oab__group__add(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2526]) ).

fof(c_0_3888,plain,
    ! [X55] :
      ( ~ class_OrderedGroup_Olordered__ab__group(X55)
      | class_OrderedGroup_Opordered__ab__group__add(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2527]) ).

fof(c_0_3889,plain,
    ! [X55] :
      ( ~ class_OrderedGroup_Ocomm__monoid__mult(X55)
      | class_OrderedGroup_Omonoid__mult(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2528]) ).

fof(c_0_3890,plain,
    ! [X55] :
      ( ~ class_OrderedGroup_Ocomm__monoid__mult(X55)
      | class_HOL_Otimes(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2529]) ).

fof(c_0_3891,plain,
    ! [X55] :
      ( ~ class_OrderedGroup_Ocomm__monoid__mult(X55)
      | class_OrderedGroup_Osemigroup__mult(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2530]) ).

fof(c_0_3892,plain,
    ! [X55] :
      ( ~ class_OrderedGroup_Ocomm__monoid__mult(X55)
      | class_OrderedGroup_Oab__semigroup__mult(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2531]) ).

fof(c_0_3893,plain,
    ! [X55] :
      ( ~ class_OrderedGroup_Ocomm__monoid__mult(X55)
      | class_HOL_Oone(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2532]) ).

fof(c_0_3894,plain,
    ! [X55] :
      ( ~ class_OrderedGroup_Ocomm__monoid__add(X55)
      | class_HOL_Oplus(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2533]) ).

fof(c_0_3895,plain,
    ! [X55] :
      ( ~ class_OrderedGroup_Ocomm__monoid__add(X55)
      | class_OrderedGroup_Osemigroup__add(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2534]) ).

fof(c_0_3896,plain,
    ! [X55] :
      ( ~ class_OrderedGroup_Ocomm__monoid__add(X55)
      | class_OrderedGroup_Oab__semigroup__add(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2535]) ).

fof(c_0_3897,plain,
    ! [X55] :
      ( ~ class_OrderedGroup_Ocomm__monoid__add(X55)
      | class_HOL_Ozero(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2536]) ).

fof(c_0_3898,plain,
    ! [X55] :
      ( ~ class_OrderedGroup_Ocancel__semigroup__add(X55)
      | class_HOL_Oplus(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2537]) ).

fof(c_0_3899,plain,
    ! [X55] :
      ( ~ class_OrderedGroup_Ocancel__semigroup__add(X55)
      | class_OrderedGroup_Osemigroup__add(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2538]) ).

fof(c_0_3900,plain,
    ! [X55] :
      ( ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X55)
      | class_OrderedGroup_Ocancel__semigroup__add(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2539]) ).

fof(c_0_3901,plain,
    ! [X55] :
      ( ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X55)
      | class_HOL_Oplus(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2540]) ).

fof(c_0_3902,plain,
    ! [X55] :
      ( ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X55)
      | class_OrderedGroup_Osemigroup__add(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2541]) ).

fof(c_0_3903,plain,
    ! [X55] :
      ( ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X55)
      | class_OrderedGroup_Oab__semigroup__add(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2542]) ).

fof(c_0_3904,plain,
    ! [X55] :
      ( ~ class_OrderedGroup_Oab__semigroup__mult(X55)
      | class_HOL_Otimes(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2543]) ).

fof(c_0_3905,plain,
    ! [X55] :
      ( ~ class_OrderedGroup_Oab__semigroup__mult(X55)
      | class_OrderedGroup_Osemigroup__mult(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2544]) ).

fof(c_0_3906,plain,
    ! [X55] :
      ( ~ class_OrderedGroup_Oab__semigroup__add(X55)
      | class_HOL_Oplus(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2545]) ).

fof(c_0_3907,plain,
    ! [X55] :
      ( ~ class_OrderedGroup_Oab__semigroup__add(X55)
      | class_OrderedGroup_Osemigroup__add(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2546]) ).

fof(c_0_3908,plain,
    ! [X55] :
      ( ~ class_OrderedGroup_Oab__group__add(X55)
      | class_OrderedGroup_Ocancel__semigroup__add(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2547]) ).

fof(c_0_3909,plain,
    ! [X55] :
      ( ~ class_OrderedGroup_Oab__group__add(X55)
      | class_OrderedGroup_Ocancel__ab__semigroup__add(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2548]) ).

fof(c_0_3910,plain,
    ! [X55] :
      ( ~ class_OrderedGroup_Oab__group__add(X55)
      | class_HOL_Oplus(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2549]) ).

fof(c_0_3911,plain,
    ! [X55] :
      ( ~ class_OrderedGroup_Oab__group__add(X55)
      | class_OrderedGroup_Osemigroup__add(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2550]) ).

fof(c_0_3912,plain,
    ! [X55] :
      ( ~ class_OrderedGroup_Oab__group__add(X55)
      | class_OrderedGroup_Oab__semigroup__add(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2551]) ).

fof(c_0_3913,plain,
    ! [X55] :
      ( ~ class_OrderedGroup_Oab__group__add(X55)
      | class_HOL_Ozero(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2552]) ).

fof(c_0_3914,plain,
    ! [X55] :
      ( ~ class_OrderedGroup_Oab__group__add(X55)
      | class_OrderedGroup_Ocomm__monoid__add(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2553]) ).

fof(c_0_3915,plain,
    ! [X55] :
      ( ~ class_OrderedGroup_Oab__group__add(X55)
      | class_HOL_Ominus(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2554]) ).

fof(c_0_3916,plain,
    ! [X55] :
      ( ~ class_Numeral_Onumber__ring(X55)
      | class_OrderedGroup_Ocomm__monoid__add(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2555]) ).

fof(c_0_3917,plain,
    ! [X55] :
      ( ~ class_Numeral_Onumber__ring(X55)
      | class_HOL_Ozero(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2556]) ).

fof(c_0_3918,plain,
    ! [X55] :
      ( ~ class_Numeral_Onumber__ring(X55)
      | class_Ring__and__Field_Ocomm__semiring(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2557]) ).

fof(c_0_3919,plain,
    ! [X55] :
      ( ~ class_Numeral_Onumber__ring(X55)
      | class_Ring__and__Field_Osemiring(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2558]) ).

fof(c_0_3920,plain,
    ! [X55] :
      ( ~ class_Numeral_Onumber__ring(X55)
      | class_OrderedGroup_Oab__semigroup__mult(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2559]) ).

fof(c_0_3921,plain,
    ! [X55] :
      ( ~ class_Numeral_Onumber__ring(X55)
      | class_OrderedGroup_Osemigroup__mult(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2560]) ).

fof(c_0_3922,plain,
    ! [X55] :
      ( ~ class_Numeral_Onumber__ring(X55)
      | class_Numeral_Onumber(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2561]) ).

fof(c_0_3923,plain,
    ! [X55] :
      ( ~ class_Numeral_Onumber__ring(X55)
      | class_HOL_Otimes(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2562]) ).

fof(c_0_3924,plain,
    ! [X55] :
      ( ~ class_Numeral_Onumber__ring(X55)
      | class_Ring__and__Field_Ocomm__ring__1(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2563]) ).

fof(c_0_3925,plain,
    ! [X55] :
      ( ~ class_Numeral_Onumber__ring(X55)
      | class_Ring__and__Field_Ocomm__semiring__1__cancel(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2564]) ).

fof(c_0_3926,plain,
    ! [X55] :
      ( ~ class_Numeral_Onumber__ring(X55)
      | class_Ring__and__Field_Oring__1(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2565]) ).

fof(c_0_3927,plain,
    ! [X55] :
      ( ~ class_Numeral_Onumber__ring(X55)
      | class_Ring__and__Field_Osemiring__1__cancel(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2566]) ).

fof(c_0_3928,plain,
    ! [X55] :
      ( ~ class_Numeral_Onumber__ring(X55)
      | class_Ring__and__Field_Ocomm__semiring__1(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2567]) ).

fof(c_0_3929,plain,
    ! [X55] :
      ( ~ class_Numeral_Onumber__ring(X55)
      | class_Ring__and__Field_Osemiring__1(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2568]) ).

fof(c_0_3930,plain,
    ! [X55] :
      ( ~ class_Numeral_Onumber__ring(X55)
      | class_OrderedGroup_Ocomm__monoid__mult(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2569]) ).

fof(c_0_3931,plain,
    ! [X55] :
      ( ~ class_Numeral_Onumber__ring(X55)
      | class_OrderedGroup_Omonoid__mult(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2570]) ).

fof(c_0_3932,plain,
    ! [X55] :
      ( ~ class_Numeral_Onumber__ring(X55)
      | class_Ring__and__Field_Oaxclass__0__neq__1(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2571]) ).

fof(c_0_3933,plain,
    ! [X55] :
      ( ~ class_Numeral_Onumber__ring(X55)
      | class_HOL_Oone(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2572]) ).

fof(c_0_3934,plain,
    ! [X55] :
      ( ~ class_Numeral_Onumber__ring(X55)
      | class_OrderedGroup_Oab__semigroup__add(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2573]) ).

fof(c_0_3935,plain,
    ! [X55] :
      ( ~ class_Numeral_Onumber__ring(X55)
      | class_Ring__and__Field_Ocomm__ring(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2574]) ).

fof(c_0_3936,plain,
    ! [X55] :
      ( ~ class_Numeral_Onumber__ring(X55)
      | class_Ring__and__Field_Ocomm__semiring__0__cancel(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2575]) ).

fof(c_0_3937,plain,
    ! [X55] :
      ( ~ class_Numeral_Onumber__ring(X55)
      | class_Ring__and__Field_Oring(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2576]) ).

fof(c_0_3938,plain,
    ! [X55] :
      ( ~ class_Numeral_Onumber__ring(X55)
      | class_Ring__and__Field_Osemiring__0__cancel(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2577]) ).

fof(c_0_3939,plain,
    ! [X55] :
      ( ~ class_Numeral_Onumber__ring(X55)
      | class_OrderedGroup_Oab__group__add(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2578]) ).

fof(c_0_3940,plain,
    ! [X55] :
      ( ~ class_Numeral_Onumber__ring(X55)
      | class_OrderedGroup_Ocancel__ab__semigroup__add(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2579]) ).

fof(c_0_3941,plain,
    ! [X55] :
      ( ~ class_Numeral_Onumber__ring(X55)
      | class_OrderedGroup_Ocancel__semigroup__add(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2580]) ).

fof(c_0_3942,plain,
    ! [X55] :
      ( ~ class_Numeral_Onumber__ring(X55)
      | class_HOL_Ominus(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2581]) ).

fof(c_0_3943,plain,
    ! [X55] :
      ( ~ class_Numeral_Onumber__ring(X55)
      | class_Ring__and__Field_Ocomm__semiring__0(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2582]) ).

fof(c_0_3944,plain,
    ! [X55] :
      ( ~ class_Numeral_Onumber__ring(X55)
      | class_Ring__and__Field_Osemiring__0(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2583]) ).

fof(c_0_3945,plain,
    ! [X55] :
      ( ~ class_Numeral_Onumber__ring(X55)
      | class_OrderedGroup_Osemigroup__add(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2584]) ).

fof(c_0_3946,plain,
    ! [X55] :
      ( ~ class_Numeral_Onumber__ring(X55)
      | class_HOL_Oplus(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2585]) ).

fof(c_0_3947,plain,
    ! [X55] :
      ( ~ class_LOrder_Omeet__semilorder(X55)
      | class_Orderings_Oorder(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2586]) ).

fof(c_0_3948,plain,
    ! [X55] :
      ( ~ class_LOrder_Omeet__semilorder(X55)
      | class_Orderings_Oord(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2587]) ).

fof(c_0_3949,plain,
    ! [X55] :
      ( ~ class_LOrder_Olorder(X55)
      | class_LOrder_Ojoin__semilorder(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2588]) ).

fof(c_0_3950,plain,
    ! [X55] :
      ( ~ class_LOrder_Olorder(X55)
      | class_Orderings_Oorder(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2589]) ).

fof(c_0_3951,plain,
    ! [X55] :
      ( ~ class_LOrder_Olorder(X55)
      | class_Orderings_Oord(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2590]) ).

fof(c_0_3952,plain,
    ! [X55] :
      ( ~ class_LOrder_Olorder(X55)
      | class_LOrder_Omeet__semilorder(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2591]) ).

fof(c_0_3953,plain,
    ! [X55] :
      ( ~ class_LOrder_Ojoin__semilorder(X55)
      | class_Orderings_Oorder(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2592]) ).

fof(c_0_3954,plain,
    ! [X55] :
      ( ~ class_LOrder_Ojoin__semilorder(X55)
      | class_Orderings_Oord(X55) ),
    inference(variable_rename,[status(thm)],[c_0_2593]) ).

fof(c_0_3955,axiom,
    c_Wellfounded__Recursion_Owf(c_Wellfounded__Relations_Oless__than,tc_nat),
    c_0_2594 ).

fof(c_0_3956,axiom,
    c_Relation_Otrans(c_Wellfounded__Relations_Oless__than,tc_nat),
    c_0_2595 ).

fof(c_0_3957,plain,
    ! [X53] : class_Nat_Opower(tc_set(X53)),
    inference(variable_rename,[status(thm)],[c_0_2596]) ).

fof(c_0_3958,plain,
    ! [X53] : class_Orderings_Oorder(tc_set(X53)),
    inference(variable_rename,[status(thm)],[c_0_2597]) ).

fof(c_0_3959,plain,
    ! [X53] : class_Orderings_Oord(tc_set(X53)),
    inference(variable_rename,[status(thm)],[c_0_2598]) ).

fof(c_0_3960,plain,
    ! [X53] : class_HOL_Ominus(tc_set(X53)),
    inference(variable_rename,[status(thm)],[c_0_2599]) ).

fof(c_0_3961,plain,
    ! [X14] : c_0 != c_Suc(X14),
    inference(variable_rename,[status(thm)],[c_0_2600]) ).

fof(c_0_3962,plain,
    ! [X14] : c_Suc(X14) != c_0,
    inference(variable_rename,[status(thm)],[c_0_2601]) ).

fof(c_0_3963,axiom,
    class_HOL_Ominus(tc_nat),
    c_0_2602 ).

fof(c_0_3964,axiom,
    class_Wellfounded__Recursion_Owellorder(tc_nat),
    c_0_2603 ).

fof(c_0_3965,axiom,
    class_Orderings_Olinorder(tc_nat),
    c_0_2604 ).

fof(c_0_3966,axiom,
    class_LOrder_Olorder(tc_nat),
    c_0_2605 ).

fof(c_0_3967,axiom,
    class_LOrder_Ojoin__semilorder(tc_nat),
    c_0_2606 ).

fof(c_0_3968,axiom,
    class_Parity_Oeven__odd(tc_nat),
    c_0_2607 ).

fof(c_0_3969,axiom,
    class_Numeral_Onumber(tc_nat),
    c_0_2608 ).

fof(c_0_3970,axiom,
    class_Power_Orecpower(tc_nat),
    c_0_2609 ).

fof(c_0_3971,axiom,
    class_Divides_Odiv(tc_nat),
    c_0_2610 ).

fof(c_0_3972,axiom,
    class_Ring__and__Field_Oordered__semidom(tc_nat),
    c_0_2611 ).

fof(c_0_3973,axiom,
    class_Ring__and__Field_Oordered__comm__semiring__strict(tc_nat),
    c_0_2612 ).

fof(c_0_3974,axiom,
    class_Ring__and__Field_Opordered__cancel__comm__semiring(tc_nat),
    c_0_2613 ).

fof(c_0_3975,axiom,
    class_Ring__and__Field_Opordered__comm__semiring(tc_nat),
    c_0_2614 ).

fof(c_0_3976,axiom,
    class_LOrder_Omeet__semilorder(tc_nat),
    c_0_2615 ).

fof(c_0_3977,axiom,
    class_Ring__and__Field_Oordered__semiring__strict(tc_nat),
    c_0_2616 ).

fof(c_0_3978,axiom,
    class_Ring__and__Field_Opordered__cancel__semiring(tc_nat),
    c_0_2617 ).

fof(c_0_3979,axiom,
    class_Ring__and__Field_Opordered__semiring(tc_nat),
    c_0_2618 ).

fof(c_0_3980,axiom,
    class_OrderedGroup_Oordered__cancel__ab__semigroup__add(tc_nat),
    c_0_2619 ).

fof(c_0_3981,axiom,
    class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat),
    c_0_2620 ).

fof(c_0_3982,axiom,
    class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat),
    c_0_2621 ).

fof(c_0_3983,axiom,
    class_OrderedGroup_Opordered__ab__semigroup__add(tc_nat),
    c_0_2622 ).

fof(c_0_3984,axiom,
    class_Ring__and__Field_Ocomm__semiring__1__cancel(tc_nat),
    c_0_2623 ).

fof(c_0_3985,axiom,
    class_Ring__and__Field_Ocomm__semiring__0__cancel(tc_nat),
    c_0_2624 ).

fof(c_0_3986,axiom,
    class_Ring__and__Field_Osemiring__1__cancel(tc_nat),
    c_0_2625 ).

fof(c_0_3987,axiom,
    class_Orderings_Oorder(tc_nat),
    c_0_2626 ).

fof(c_0_3988,axiom,
    class_Ring__and__Field_Osemiring__0__cancel(tc_nat),
    c_0_2627 ).

fof(c_0_3989,axiom,
    class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat),
    c_0_2628 ).

fof(c_0_3990,axiom,
    class_OrderedGroup_Ocancel__semigroup__add(tc_nat),
    c_0_2629 ).

fof(c_0_3991,axiom,
    class_Ring__and__Field_Ocomm__semiring__1(tc_nat),
    c_0_2630 ).

fof(c_0_3992,axiom,
    class_Ring__and__Field_Osemiring__1(tc_nat),
    c_0_2631 ).

fof(c_0_3993,axiom,
    class_OrderedGroup_Ocomm__monoid__mult(tc_nat),
    c_0_2632 ).

fof(c_0_3994,axiom,
    class_OrderedGroup_Omonoid__mult(tc_nat),
    c_0_2633 ).

fof(c_0_3995,axiom,
    class_Ring__and__Field_Ocomm__semiring__0(tc_nat),
    c_0_2634 ).

fof(c_0_3996,axiom,
    class_Ring__and__Field_Osemiring__0(tc_nat),
    c_0_2635 ).

fof(c_0_3997,axiom,
    class_OrderedGroup_Ocomm__monoid__add(tc_nat),
    c_0_2636 ).

fof(c_0_3998,axiom,
    class_Orderings_Oord(tc_nat),
    c_0_2637 ).

fof(c_0_3999,axiom,
    class_Ring__and__Field_Ocomm__semiring(tc_nat),
    c_0_2638 ).

fof(c_0_4000,axiom,
    class_Ring__and__Field_Osemiring(tc_nat),
    c_0_2639 ).

fof(c_0_4001,axiom,
    class_OrderedGroup_Oab__semigroup__mult(tc_nat),
    c_0_2640 ).

fof(c_0_4002,axiom,
    class_OrderedGroup_Osemigroup__mult(tc_nat),
    c_0_2641 ).

fof(c_0_4003,axiom,
    class_OrderedGroup_Oab__semigroup__add(tc_nat),
    c_0_2642 ).

fof(c_0_4004,axiom,
    class_OrderedGroup_Osemigroup__add(tc_nat),
    c_0_2643 ).

fof(c_0_4005,axiom,
    class_Ring__and__Field_Oaxclass__0__neq__1(tc_nat),
    c_0_2644 ).

fof(c_0_4006,axiom,
    class_Nat_Opower(tc_nat),
    c_0_2645 ).

fof(c_0_4007,axiom,
    class_HOL_Otimes(tc_nat),
    c_0_2646 ).

fof(c_0_4008,axiom,
    class_HOL_Oplus(tc_nat),
    c_0_2647 ).

fof(c_0_4009,axiom,
    class_HOL_Ozero(tc_nat),
    c_0_2648 ).

fof(c_0_4010,axiom,
    class_HOL_Oone(tc_nat),
    c_0_2649 ).

fof(c_0_4011,axiom,
    class_Finite__Set_Ofinite(tc_bool),
    c_0_2650 ).

fof(c_0_4012,axiom,
    class_Finite__Set_Ofinite(tc_Product__Type_Ounit),
    c_0_2651 ).

fof(c_0_4013,axiom,
    class_OrderedGroup_Oab__semigroup__mult(tc_IntDef_Oint),
    c_0_2652 ).

fof(c_0_4014,axiom,
    class_OrderedGroup_Osemigroup__mult(tc_IntDef_Oint),
    c_0_2653 ).

fof(c_0_4015,axiom,
    class_OrderedGroup_Oab__semigroup__add(tc_IntDef_Oint),
    c_0_2654 ).

fof(c_0_4016,axiom,
    class_Parity_Oeven__odd(tc_IntDef_Oint),
    c_0_2655 ).

fof(c_0_4017,axiom,
    class_Power_Orecpower(tc_IntDef_Oint),
    c_0_2656 ).

fof(c_0_4018,axiom,
    class_Nat_Opower(tc_IntDef_Oint),
    c_0_2657 ).

fof(c_0_4019,axiom,
    class_Divides_Odiv(tc_IntDef_Oint),
    c_0_2658 ).

fof(c_0_4020,axiom,
    class_Numeral_Onumber__ring(tc_IntDef_Oint),
    c_0_2659 ).

fof(c_0_4021,axiom,
    class_OrderedGroup_Osemigroup__add(tc_IntDef_Oint),
    c_0_2660 ).

fof(c_0_4022,axiom,
    class_Numeral_Onumber(tc_IntDef_Oint),
    c_0_2661 ).

fof(c_0_4023,axiom,
    class_Ring__and__Field_Oordered__idom(tc_IntDef_Oint),
    c_0_2662 ).

fof(c_0_4024,axiom,
    class_Ring__and__Field_Oidom(tc_IntDef_Oint),
    c_0_2663 ).

fof(c_0_4025,axiom,
    class_Ring__and__Field_Oordered__semidom(tc_IntDef_Oint),
    c_0_2664 ).

fof(c_0_4026,axiom,
    class_Ring__and__Field_Oordered__ring__strict(tc_IntDef_Oint),
    c_0_2665 ).

fof(c_0_4027,axiom,
    class_Ring__and__Field_Oaxclass__no__zero__divisors(tc_IntDef_Oint),
    c_0_2666 ).

fof(c_0_4028,axiom,
    class_Ring__and__Field_Olordered__ring(tc_IntDef_Oint),
    c_0_2667 ).

fof(c_0_4029,axiom,
    class_OrderedGroup_Olordered__ab__group__join(tc_IntDef_Oint),
    c_0_2668 ).

fof(c_0_4030,axiom,
    class_OrderedGroup_Olordered__ab__group__meet(tc_IntDef_Oint),
    c_0_2669 ).

fof(c_0_4031,axiom,
    class_OrderedGroup_Olordered__ab__group__abs(tc_IntDef_Oint),
    c_0_2670 ).

fof(c_0_4032,axiom,
    class_Orderings_Oord(tc_IntDef_Oint),
    c_0_2671 ).

fof(c_0_4033,axiom,
    class_Ring__and__Field_Opordered__ring(tc_IntDef_Oint),
    c_0_2672 ).

fof(c_0_4034,axiom,
    class_OrderedGroup_Olordered__ab__group(tc_IntDef_Oint),
    c_0_2673 ).

fof(c_0_4035,axiom,
    class_OrderedGroup_Opordered__ab__group__add(tc_IntDef_Oint),
    c_0_2674 ).

fof(c_0_4036,axiom,
    class_Ring__and__Field_Oaxclass__abs__if(tc_IntDef_Oint),
    c_0_2675 ).

fof(c_0_4037,axiom,
    class_Ring__and__Field_Oordered__comm__semiring__strict(tc_IntDef_Oint),
    c_0_2676 ).

fof(c_0_4038,axiom,
    class_Ring__and__Field_Opordered__cancel__comm__semiring(tc_IntDef_Oint),
    c_0_2677 ).

fof(c_0_4039,axiom,
    class_Ring__and__Field_Opordered__comm__semiring(tc_IntDef_Oint),
    c_0_2678 ).

fof(c_0_4040,axiom,
    class_Ring__and__Field_Oordered__semiring__strict(tc_IntDef_Oint),
    c_0_2679 ).

fof(c_0_4041,axiom,
    class_Ring__and__Field_Opordered__cancel__semiring(tc_IntDef_Oint),
    c_0_2680 ).

fof(c_0_4042,axiom,
    class_Ring__and__Field_Opordered__semiring(tc_IntDef_Oint),
    c_0_2681 ).

fof(c_0_4043,axiom,
    class_HOL_Ozero(tc_IntDef_Oint),
    c_0_2682 ).

fof(c_0_4044,axiom,
    class_OrderedGroup_Oordered__cancel__ab__semigroup__add(tc_IntDef_Oint),
    c_0_2683 ).

fof(c_0_4045,axiom,
    class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_IntDef_Oint),
    c_0_2684 ).

fof(c_0_4046,axiom,
    class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_IntDef_Oint),
    c_0_2685 ).

fof(c_0_4047,axiom,
    class_OrderedGroup_Opordered__ab__semigroup__add(tc_IntDef_Oint),
    c_0_2686 ).

fof(c_0_4048,axiom,
    class_Orderings_Olinorder(tc_IntDef_Oint),
    c_0_2687 ).

fof(c_0_4049,axiom,
    class_LOrder_Olorder(tc_IntDef_Oint),
    c_0_2688 ).

fof(c_0_4050,axiom,
    class_LOrder_Ojoin__semilorder(tc_IntDef_Oint),
    c_0_2689 ).

fof(c_0_4051,axiom,
    class_LOrder_Omeet__semilorder(tc_IntDef_Oint),
    c_0_2690 ).

fof(c_0_4052,axiom,
    class_Orderings_Oorder(tc_IntDef_Oint),
    c_0_2691 ).

fof(c_0_4053,axiom,
    class_Ring__and__Field_Ocomm__ring__1(tc_IntDef_Oint),
    c_0_2692 ).

fof(c_0_4054,axiom,
    class_HOL_Otimes(tc_IntDef_Oint),
    c_0_2693 ).

fof(c_0_4055,axiom,
    class_Ring__and__Field_Ocomm__semiring__1__cancel(tc_IntDef_Oint),
    c_0_2694 ).

fof(c_0_4056,axiom,
    class_Ring__and__Field_Oring__1(tc_IntDef_Oint),
    c_0_2695 ).

fof(c_0_4057,axiom,
    class_Ring__and__Field_Osemiring__1__cancel(tc_IntDef_Oint),
    c_0_2696 ).

fof(c_0_4058,axiom,
    class_Ring__and__Field_Ocomm__semiring__1(tc_IntDef_Oint),
    c_0_2697 ).

fof(c_0_4059,axiom,
    class_Ring__and__Field_Osemiring__1(tc_IntDef_Oint),
    c_0_2698 ).

fof(c_0_4060,axiom,
    class_OrderedGroup_Ocomm__monoid__mult(tc_IntDef_Oint),
    c_0_2699 ).

fof(c_0_4061,axiom,
    class_OrderedGroup_Omonoid__mult(tc_IntDef_Oint),
    c_0_2700 ).

fof(c_0_4062,axiom,
    class_Ring__and__Field_Oaxclass__0__neq__1(tc_IntDef_Oint),
    c_0_2701 ).

fof(c_0_4063,axiom,
    class_Ring__and__Field_Ocomm__ring(tc_IntDef_Oint),
    c_0_2702 ).

fof(c_0_4064,axiom,
    class_Ring__and__Field_Ocomm__semiring__0__cancel(tc_IntDef_Oint),
    c_0_2703 ).

fof(c_0_4065,axiom,
    class_HOL_Oplus(tc_IntDef_Oint),
    c_0_2704 ).

fof(c_0_4066,axiom,
    class_Ring__and__Field_Oring(tc_IntDef_Oint),
    c_0_2705 ).

fof(c_0_4067,axiom,
    class_Ring__and__Field_Osemiring__0__cancel(tc_IntDef_Oint),
    c_0_2706 ).

fof(c_0_4068,axiom,
    class_OrderedGroup_Oab__group__add(tc_IntDef_Oint),
    c_0_2707 ).

fof(c_0_4069,axiom,
    class_OrderedGroup_Ocancel__ab__semigroup__add(tc_IntDef_Oint),
    c_0_2708 ).

fof(c_0_4070,axiom,
    class_OrderedGroup_Ocancel__semigroup__add(tc_IntDef_Oint),
    c_0_2709 ).

fof(c_0_4071,axiom,
    class_Ring__and__Field_Ocomm__semiring__0(tc_IntDef_Oint),
    c_0_2710 ).

fof(c_0_4072,axiom,
    class_Ring__and__Field_Osemiring__0(tc_IntDef_Oint),
    c_0_2711 ).

fof(c_0_4073,axiom,
    class_OrderedGroup_Ocomm__monoid__add(tc_IntDef_Oint),
    c_0_2712 ).

fof(c_0_4074,axiom,
    class_Ring__and__Field_Ocomm__semiring(tc_IntDef_Oint),
    c_0_2713 ).

fof(c_0_4075,axiom,
    class_Ring__and__Field_Osemiring(tc_IntDef_Oint),
    c_0_2714 ).

fof(c_0_4076,axiom,
    class_HOL_Oone(tc_IntDef_Oint),
    c_0_2715 ).

fof(c_0_4077,axiom,
    class_HOL_Ominus(tc_IntDef_Oint),
    c_0_2716 ).

fof(c_0_4078,axiom,
    c_UNIV != c_emptyset,
    c_0_2717 ).

fof(c_0_4079,axiom,
    c_Numeral_Obit_OB1 != c_Numeral_Obit_OB0,
    c_0_2718 ).

fof(c_0_4080,axiom,
    c_Numeral_Obit_OB0 != c_Numeral_Obit_OB1,
    c_0_2719 ).

fof(c_0_4081,axiom,
    c_Extraction_Osumbool_ORight != c_Extraction_Osumbool_OLeft,
    c_0_2720 ).

fof(c_0_4082,axiom,
    c_Extraction_Osumbool_OLeft != c_Extraction_Osumbool_ORight,
    c_0_2721 ).

cnf(c_0_4083,plain,
    ( c_in(c_Pair(c_Main_Orel__compE__1(X1,X2,X3,X4,X5,X6),c_Main_Orel__compE__2(X1,X2,X3,X4,X5,X6),X6,X4),X2,tc_prod(X6,X4))
    | ~ c_in(X3,c_Relation_Orel__comp(X1,X2,X4,X5,X6),tc_prod(X6,X5)) ),
    inference(split_conjunct,[status(thm)],[c_0_2722]) ).

cnf(c_0_4084,plain,
    ( c_in(c_Pair(c_Main_Orel__compE__2(X1,X2,X3,X4,X5,X6),c_Main_Orel__compE__3(X1,X2,X3,X4,X5,X6),X4,X5),X1,tc_prod(X4,X5))
    | ~ c_in(X3,c_Relation_Orel__comp(X1,X2,X4,X5,X6),tc_prod(X6,X5)) ),
    inference(split_conjunct,[status(thm)],[c_0_2723]) ).

cnf(c_0_4085,plain,
    ( X1 = c_Pair(c_Main_Orel__compE__1(X2,X3,X1,X4,X5,X6),c_Main_Orel__compE__3(X2,X3,X1,X4,X5,X6),X6,X5)
    | ~ c_in(X1,c_Relation_Orel__comp(X2,X3,X4,X5,X6),tc_prod(X6,X5)) ),
    inference(split_conjunct,[status(thm)],[c_0_2724]) ).

cnf(c_0_4086,plain,
    ( X1 = c_Pair(c_Datatype__Universe_OScons(c_Main_OdprodE__1(X1,X2,X3,X4,X5),c_Main_OdprodE__2(X1,X2,X3,X4,X5),X4,X5),c_Datatype__Universe_OScons(c_Main_OdprodE__3(X1,X2,X3,X4,X5),c_Main_OdprodE__4(X1,X2,X3,X4,X5),X4,X5),tc_set(tc_Datatype__Universe_Onode(X4,X5)),tc_set(tc_Datatype__Universe_Onode(X4,X5)))
    | ~ c_in(X1,c_Datatype__Universe_Odprod(X2,X3,X4,X5),tc_prod(tc_set(tc_Datatype__Universe_Onode(X4,X5)),tc_set(tc_Datatype__Universe_Onode(X4,X5)))) ),
    inference(split_conjunct,[status(thm)],[c_0_2725]) ).

cnf(c_0_4087,plain,
    ( c_in(c_Pair(c_Main_OdprodE__1(X1,X2,X3,X4,X5),c_Main_OdprodE__3(X1,X2,X3,X4,X5),tc_set(tc_Datatype__Universe_Onode(X4,X5)),tc_set(tc_Datatype__Universe_Onode(X4,X5))),X2,tc_prod(tc_set(tc_Datatype__Universe_Onode(X4,X5)),tc_set(tc_Datatype__Universe_Onode(X4,X5))))
    | ~ c_in(X1,c_Datatype__Universe_Odprod(X2,X3,X4,X5),tc_prod(tc_set(tc_Datatype__Universe_Onode(X4,X5)),tc_set(tc_Datatype__Universe_Onode(X4,X5)))) ),
    inference(split_conjunct,[status(thm)],[c_0_2726]) ).

cnf(c_0_4088,plain,
    ( c_in(c_Pair(c_Main_OdprodE__2(X1,X2,X3,X4,X5),c_Main_OdprodE__4(X1,X2,X3,X4,X5),tc_set(tc_Datatype__Universe_Onode(X4,X5)),tc_set(tc_Datatype__Universe_Onode(X4,X5))),X3,tc_prod(tc_set(tc_Datatype__Universe_Onode(X4,X5)),tc_set(tc_Datatype__Universe_Onode(X4,X5))))
    | ~ c_in(X1,c_Datatype__Universe_Odprod(X2,X3,X4,X5),tc_prod(tc_set(tc_Datatype__Universe_Onode(X4,X5)),tc_set(tc_Datatype__Universe_Onode(X4,X5)))) ),
    inference(split_conjunct,[status(thm)],[c_0_2727]) ).

cnf(c_0_4089,plain,
    ( c_in(c_Pair(c_Main_OdsumE__3(X1,X2,X3,X4),c_Main_OdsumE__4(X1,X2,X3,X4),tc_set(tc_Datatype__Universe_Onode(X3,X4)),tc_set(tc_Datatype__Universe_Onode(X3,X4))),X1,tc_prod(tc_set(tc_Datatype__Universe_Onode(X3,X4)),tc_set(tc_Datatype__Universe_Onode(X3,X4))))
    | c_in(c_Pair(c_Main_OdsumE__1(X5,X2,X3,X4),c_Main_OdsumE__2(X5,X2,X3,X4),tc_set(tc_Datatype__Universe_Onode(X3,X4)),tc_set(tc_Datatype__Universe_Onode(X3,X4))),X5,tc_prod(tc_set(tc_Datatype__Universe_Onode(X3,X4)),tc_set(tc_Datatype__Universe_Onode(X3,X4))))
    | ~ c_in(X2,c_Datatype__Universe_Odsum(X5,X1,X3,X4),tc_prod(tc_set(tc_Datatype__Universe_Onode(X3,X4)),tc_set(tc_Datatype__Universe_Onode(X3,X4)))) ),
    inference(split_conjunct,[status(thm)],[c_0_2728]) ).

cnf(c_0_4090,plain,
    ( X1 = c_Pair(c_Datatype__Universe_OIn1(c_Main_OdsumE__3(X2,X1,X3,X4),X3,X4),c_Datatype__Universe_OIn1(c_Main_OdsumE__4(X2,X1,X3,X4),X3,X4),tc_set(tc_Datatype__Universe_Onode(X3,X4)),tc_set(tc_Datatype__Universe_Onode(X3,X4)))
    | c_in(c_Pair(c_Main_OdsumE__1(X5,X1,X3,X4),c_Main_OdsumE__2(X5,X1,X3,X4),tc_set(tc_Datatype__Universe_Onode(X3,X4)),tc_set(tc_Datatype__Universe_Onode(X3,X4))),X5,tc_prod(tc_set(tc_Datatype__Universe_Onode(X3,X4)),tc_set(tc_Datatype__Universe_Onode(X3,X4))))
    | ~ c_in(X1,c_Datatype__Universe_Odsum(X5,X2,X3,X4),tc_prod(tc_set(tc_Datatype__Universe_Onode(X3,X4)),tc_set(tc_Datatype__Universe_Onode(X3,X4)))) ),
    inference(split_conjunct,[status(thm)],[c_0_2729]) ).

cnf(c_0_4091,plain,
    ( X1 = c_Pair(c_Datatype__Universe_OIn0(c_Main_OdsumE__1(X2,X1,X3,X4),X3,X4),c_Datatype__Universe_OIn0(c_Main_OdsumE__2(X2,X1,X3,X4),X3,X4),tc_set(tc_Datatype__Universe_Onode(X3,X4)),tc_set(tc_Datatype__Universe_Onode(X3,X4)))
    | c_in(c_Pair(c_Main_OdsumE__3(X5,X1,X3,X4),c_Main_OdsumE__4(X5,X1,X3,X4),tc_set(tc_Datatype__Universe_Onode(X3,X4)),tc_set(tc_Datatype__Universe_Onode(X3,X4))),X5,tc_prod(tc_set(tc_Datatype__Universe_Onode(X3,X4)),tc_set(tc_Datatype__Universe_Onode(X3,X4))))
    | ~ c_in(X1,c_Datatype__Universe_Odsum(X2,X5,X3,X4),tc_prod(tc_set(tc_Datatype__Universe_Onode(X3,X4)),tc_set(tc_Datatype__Universe_Onode(X3,X4)))) ),
    inference(split_conjunct,[status(thm)],[c_0_2730]) ).

cnf(c_0_4092,plain,
    ( c_in(c_Pair(c_Main_Olistrel__Cons2__2(X1,X2,X3,X4,X5),X4,tc_List_Olist(X5),tc_List_Olist(X5)),c_List_Olistrel(X1,X5),tc_prod(tc_List_Olist(X5),tc_List_Olist(X5)))
    | ~ c_in(c_Pair(X2,c_List_Olist_OCons(X3,X4,X5),tc_List_Olist(X5),tc_List_Olist(X5)),c_List_Olistrel(X1,X5),tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))) ),
    inference(split_conjunct,[status(thm)],[c_0_2731]) ).

cnf(c_0_4093,plain,
    ( c_in(c_Pair(X1,c_Main_Olistrel__Cons1__2(X2,X3,X4,X1,X5),tc_List_Olist(X5),tc_List_Olist(X5)),c_List_Olistrel(X2,X5),tc_prod(tc_List_Olist(X5),tc_List_Olist(X5)))
    | ~ c_in(c_Pair(c_List_Olist_OCons(X4,X1,X5),X3,tc_List_Olist(X5),tc_List_Olist(X5)),c_List_Olistrel(X2,X5),tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))) ),
    inference(split_conjunct,[status(thm)],[c_0_2732]) ).

cnf(c_0_4094,plain,
    ( c_in(c_Pair(c_Datatype__Universe_OScons(X1,X2,X3,X4),c_Datatype__Universe_OScons(X5,X6,X3,X4),tc_set(tc_Datatype__Universe_Onode(X3,X4)),tc_set(tc_Datatype__Universe_Onode(X3,X4))),c_Datatype__Universe_Odprod(X7,X8,X3,X4),tc_prod(tc_set(tc_Datatype__Universe_Onode(X3,X4)),tc_set(tc_Datatype__Universe_Onode(X3,X4))))
    | ~ c_in(c_Pair(X1,X5,tc_set(tc_Datatype__Universe_Onode(X3,X4)),tc_set(tc_Datatype__Universe_Onode(X3,X4))),X7,tc_prod(tc_set(tc_Datatype__Universe_Onode(X3,X4)),tc_set(tc_Datatype__Universe_Onode(X3,X4))))
    | ~ c_in(c_Pair(X2,X6,tc_set(tc_Datatype__Universe_Onode(X3,X4)),tc_set(tc_Datatype__Universe_Onode(X3,X4))),X8,tc_prod(tc_set(tc_Datatype__Universe_Onode(X3,X4)),tc_set(tc_Datatype__Universe_Onode(X3,X4)))) ),
    inference(split_conjunct,[status(thm)],[c_0_2733]) ).

cnf(c_0_4095,plain,
    ( c_in(c_Pair(c_Main_Olistrel__Cons2__1(X1,X2,X3,X4,X5),X3,X5,X5),X1,tc_prod(X5,X5))
    | ~ c_in(c_Pair(X2,c_List_Olist_OCons(X3,X4,X5),tc_List_Olist(X5),tc_List_Olist(X5)),c_List_Olistrel(X1,X5),tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))) ),
    inference(split_conjunct,[status(thm)],[c_0_2734]) ).

cnf(c_0_4096,plain,
    ( c_in(c_Pair(X1,c_Main_Olistrel__Cons1__1(X2,X3,X1,X4,X5),X5,X5),X2,tc_prod(X5,X5))
    | ~ c_in(c_Pair(c_List_Olist_OCons(X1,X4,X5),X3,tc_List_Olist(X5),tc_List_Olist(X5)),c_List_Olistrel(X2,X5),tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))) ),
    inference(split_conjunct,[status(thm)],[c_0_2735]) ).

cnf(c_0_4097,plain,
    ( X1 = c_Pair(c_Datatype__Universe_OIn1(c_Main_OdsumE__3(X2,X1,X3,X4),X3,X4),c_Datatype__Universe_OIn1(c_Main_OdsumE__4(X2,X1,X3,X4),X3,X4),tc_set(tc_Datatype__Universe_Onode(X3,X4)),tc_set(tc_Datatype__Universe_Onode(X3,X4)))
    | X1 = c_Pair(c_Datatype__Universe_OIn0(c_Main_OdsumE__1(X5,X1,X3,X4),X3,X4),c_Datatype__Universe_OIn0(c_Main_OdsumE__2(X5,X1,X3,X4),X3,X4),tc_set(tc_Datatype__Universe_Onode(X3,X4)),tc_set(tc_Datatype__Universe_Onode(X3,X4)))
    | ~ c_in(X1,c_Datatype__Universe_Odsum(X5,X2,X3,X4),tc_prod(tc_set(tc_Datatype__Universe_Onode(X3,X4)),tc_set(tc_Datatype__Universe_Onode(X3,X4)))) ),
    inference(split_conjunct,[status(thm)],[c_0_2736]) ).

cnf(c_0_4098,plain,
    ( c_in(c_Pair(c_Main_OImageE__1(X1,X2,X3,X4,X5),X2,X4,X5),X3,tc_prod(X4,X5))
    | ~ c_in(X2,c_Relation_OImage(X3,X1,X4,X5),X5) ),
    inference(split_conjunct,[status(thm)],[c_0_2737]) ).

cnf(c_0_4099,plain,
    ( X1 = c_List_Olist_OCons(c_Main_Olistrel__Cons2__1(X2,X1,X3,X4,X5),c_Main_Olistrel__Cons2__2(X2,X1,X3,X4,X5),X5)
    | ~ c_in(c_Pair(X1,c_List_Olist_OCons(X3,X4,X5),tc_List_Olist(X5),tc_List_Olist(X5)),c_List_Olistrel(X2,X5),tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))) ),
    inference(split_conjunct,[status(thm)],[c_0_2738]) ).

cnf(c_0_4100,plain,
    ( X1 = c_List_Olist_OCons(c_Main_Olistrel__Cons1__1(X2,X1,X3,X4,X5),c_Main_Olistrel__Cons1__2(X2,X1,X3,X4,X5),X5)
    | ~ c_in(c_Pair(c_List_Olist_OCons(X3,X4,X5),X1,tc_List_Olist(X5),tc_List_Olist(X5)),c_List_Olistrel(X2,X5),tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))) ),
    inference(split_conjunct,[status(thm)],[c_0_2739]) ).

cnf(c_0_4101,plain,
    ( X1 = c_Datatype__Universe_OScons(c_Main_OuprodE__1(X2,X3,X1,X4,X5),c_Main_OuprodE__2(X2,X3,X1,X4,X5),X4,X5)
    | ~ c_in(X1,c_Datatype__Universe_Ouprod(X2,X3,X4,X5),tc_set(tc_Datatype__Universe_Onode(X4,X5))) ),
    inference(split_conjunct,[status(thm)],[c_0_2740]) ).

cnf(c_0_4102,plain,
    ( c_in(c_Pair(X1,X2,X3,X4),c_Relation_Orel__comp(X5,X6,X7,X4,X3),tc_prod(X3,X4))
    | ~ c_in(c_Pair(X1,X8,X3,X7),X6,tc_prod(X3,X7))
    | ~ c_in(c_Pair(X8,X2,X7,X4),X5,tc_prod(X7,X4)) ),
    inference(split_conjunct,[status(thm)],[c_0_2741]) ).

cnf(c_0_4103,plain,
    ( c_in(c_Pair(c_Datatype__Universe_OIn1(X1,X2,X3),c_Datatype__Universe_OIn1(X4,X2,X3),tc_set(tc_Datatype__Universe_Onode(X2,X3)),tc_set(tc_Datatype__Universe_Onode(X2,X3))),c_Datatype__Universe_Odsum(X5,X6,X2,X3),tc_prod(tc_set(tc_Datatype__Universe_Onode(X2,X3)),tc_set(tc_Datatype__Universe_Onode(X2,X3))))
    | ~ c_in(c_Pair(X1,X4,tc_set(tc_Datatype__Universe_Onode(X2,X3)),tc_set(tc_Datatype__Universe_Onode(X2,X3))),X6,tc_prod(tc_set(tc_Datatype__Universe_Onode(X2,X3)),tc_set(tc_Datatype__Universe_Onode(X2,X3)))) ),
    inference(split_conjunct,[status(thm)],[c_0_2742]) ).

cnf(c_0_4104,plain,
    ( c_in(c_Pair(c_Datatype__Universe_OIn0(X1,X2,X3),c_Datatype__Universe_OIn0(X4,X2,X3),tc_set(tc_Datatype__Universe_Onode(X2,X3)),tc_set(tc_Datatype__Universe_Onode(X2,X3))),c_Datatype__Universe_Odsum(X5,X6,X2,X3),tc_prod(tc_set(tc_Datatype__Universe_Onode(X2,X3)),tc_set(tc_Datatype__Universe_Onode(X2,X3))))
    | ~ c_in(c_Pair(X1,X4,tc_set(tc_Datatype__Universe_Onode(X2,X3)),tc_set(tc_Datatype__Universe_Onode(X2,X3))),X5,tc_prod(tc_set(tc_Datatype__Universe_Onode(X2,X3)),tc_set(tc_Datatype__Universe_Onode(X2,X3)))) ),
    inference(split_conjunct,[status(thm)],[c_0_2743]) ).

cnf(c_0_4105,plain,
    ( c_in(c_Main_OuprodE__1(X1,X2,X3,X4,X5),X1,tc_set(tc_Datatype__Universe_Onode(X4,X5)))
    | ~ c_in(X3,c_Datatype__Universe_Ouprod(X1,X2,X4,X5),tc_set(tc_Datatype__Universe_Onode(X4,X5))) ),
    inference(split_conjunct,[status(thm)],[c_0_2744]) ).

cnf(c_0_4106,plain,
    ( c_in(c_Main_OuprodE__2(X1,X2,X3,X4,X5),X2,tc_set(tc_Datatype__Universe_Onode(X4,X5)))
    | ~ c_in(X3,c_Datatype__Universe_Ouprod(X1,X2,X4,X5),tc_set(tc_Datatype__Universe_Onode(X4,X5))) ),
    inference(split_conjunct,[status(thm)],[c_0_2745]) ).

cnf(c_0_4107,plain,
    ( c_in(c_Main_OImageE__1(X1,X2,X3,X4,X5),X1,X4)
    | ~ c_in(X2,c_Relation_OImage(X3,X1,X4,X5),X5) ),
    inference(split_conjunct,[status(thm)],[c_0_2746]) ).

cnf(c_0_4108,plain,
    ( c_in(c_Pair(c_Main_OconverseE__1(X1,X2,X3,X4),c_Main_OconverseE__2(X1,X2,X3,X4),X3,X4),X1,tc_prod(X3,X4))
    | ~ c_in(X2,c_Relation_Oconverse(X1,X3,X4),tc_prod(X4,X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_2747]) ).

cnf(c_0_4109,plain,
    ( ~ c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Ortrancl(X4,X3),tc_prod(X3,X3))
    | ~ c_Wellfounded__Recursion_Owf(c_insert(c_Pair(X2,X1,X3,X3),X4,tc_prod(X3,X3)),X3) ),
    inference(split_conjunct,[status(thm)],[c_0_2748]) ).

cnf(c_0_4110,plain,
    ( ~ c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Ortrancl(X4,X3),tc_prod(X3,X3))
    | ~ c_Wellfounded__Recursion_Oacyclic(c_insert(c_Pair(X2,X1,X3,X3),X4,tc_prod(X3,X3)),X3) ),
    inference(split_conjunct,[status(thm)],[c_0_2749]) ).

cnf(c_0_4111,plain,
    ( c_in(c_Main_OusumE__2(X1,X2,X3,X4),X1,tc_set(tc_Datatype__Universe_Onode(X3,X4)))
    | c_in(c_Main_OusumE__1(X5,X2,X3,X4),X5,tc_set(tc_Datatype__Universe_Onode(X3,X4)))
    | ~ c_in(X2,c_Datatype__Universe_Ousum(X5,X1,X3,X4),tc_set(tc_Datatype__Universe_Onode(X3,X4))) ),
    inference(split_conjunct,[status(thm)],[c_0_2750]) ).

cnf(c_0_4112,plain,
    ( X1 = c_Datatype__Universe_OIn1(c_Main_OusumE__2(X2,X1,X3,X4),X3,X4)
    | c_in(c_Main_OusumE__1(X5,X1,X3,X4),X5,tc_set(tc_Datatype__Universe_Onode(X3,X4)))
    | ~ c_in(X1,c_Datatype__Universe_Ousum(X5,X2,X3,X4),tc_set(tc_Datatype__Universe_Onode(X3,X4))) ),
    inference(split_conjunct,[status(thm)],[c_0_2751]) ).

cnf(c_0_4113,plain,
    ( X1 = c_Datatype__Universe_OIn0(c_Main_OusumE__1(X2,X1,X3,X4),X3,X4)
    | c_in(c_Main_OusumE__2(X5,X1,X3,X4),X5,tc_set(tc_Datatype__Universe_Onode(X3,X4)))
    | ~ c_in(X1,c_Datatype__Universe_Ousum(X2,X5,X3,X4),tc_set(tc_Datatype__Universe_Onode(X3,X4))) ),
    inference(split_conjunct,[status(thm)],[c_0_2752]) ).

cnf(c_0_4114,plain,
    ( X1 = c_Datatype__Universe_OIn1(c_Main_OusumE__2(X2,X1,X3,X4),X3,X4)
    | X1 = c_Datatype__Universe_OIn0(c_Main_OusumE__1(X5,X1,X3,X4),X3,X4)
    | ~ c_in(X1,c_Datatype__Universe_Ousum(X5,X2,X3,X4),tc_set(tc_Datatype__Universe_Onode(X3,X4))) ),
    inference(split_conjunct,[status(thm)],[c_0_2753]) ).

cnf(c_0_4115,plain,
    ( X1 = c_Sum__Type_OInr(c_Main_OPlusE__2(X2,X1,X3,X4),X3,X4)
    | X1 = c_Sum__Type_OInl(c_Main_OPlusE__1(X5,X1,X4,X3),X4,X3)
    | ~ c_in(X1,c_Sum__Type_OPlus(X5,X2,X4,X3),tc_sum(X4,X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_2754]) ).

cnf(c_0_4116,plain,
    ( X1 = c_Sum__Type_OInr(c_Main_OPlusE__2(X2,X1,X3,X4),X3,X4)
    | c_in(c_Main_OPlusE__1(X5,X1,X4,X3),X5,X4)
    | ~ c_in(X1,c_Sum__Type_OPlus(X5,X2,X4,X3),tc_sum(X4,X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_2755]) ).

cnf(c_0_4117,plain,
    ( X1 = c_Sum__Type_OInl(c_Main_OPlusE__1(X2,X1,X3,X4),X3,X4)
    | c_in(c_Main_OPlusE__2(X5,X1,X4,X3),X5,X4)
    | ~ c_in(X1,c_Sum__Type_OPlus(X2,X5,X3,X4),tc_sum(X3,X4)) ),
    inference(split_conjunct,[status(thm)],[c_0_2756]) ).

cnf(c_0_4118,plain,
    ( c_in(c_Main_OPlusE__2(X1,X2,X3,X4),X1,X3)
    | c_in(c_Main_OPlusE__1(X5,X2,X4,X3),X5,X4)
    | ~ c_in(X2,c_Sum__Type_OPlus(X5,X1,X4,X3),tc_sum(X4,X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_2757]) ).

cnf(c_0_4119,plain,
    ( c_Wellfounded__Recursion_Owf(X1,X2)
    | ~ c_Wellfounded__Recursion_Owf(c_insert(c_Pair(X3,X4,X2,X2),X1,tc_prod(X2,X2)),X2) ),
    inference(split_conjunct,[status(thm)],[c_0_2758]) ).

cnf(c_0_4120,plain,
    ( c_Wellfounded__Recursion_Oacyclic(X1,X2)
    | ~ c_Wellfounded__Recursion_Oacyclic(c_insert(c_Pair(X3,X4,X2,X2),X1,tc_prod(X2,X2)),X2) ),
    inference(split_conjunct,[status(thm)],[c_0_2759]) ).

cnf(c_0_4121,plain,
    ( c_in(c_Pair(c_Main_ORangeE__1(X1,X2,X3,X4),X1,X4,X3),X2,tc_prod(X4,X3))
    | ~ c_in(X1,c_Relation_ORange(X2,X4,X3),X3) ),
    inference(split_conjunct,[status(thm)],[c_0_2760]) ).

cnf(c_0_4122,plain,
    ( c_in(c_Pair(X1,c_Main_ODomainE__1(X1,X2,X3,X4),X3,X4),X2,tc_prod(X3,X4))
    | ~ c_in(X1,c_Relation_ODomain(X2,X3,X4),X3) ),
    inference(split_conjunct,[status(thm)],[c_0_2761]) ).

cnf(c_0_4123,plain,
    ( c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Ortrancl(X4,X3),tc_prod(X3,X3))
    | c_Wellfounded__Recursion_Owf(c_insert(c_Pair(X2,X1,X3,X3),X4,tc_prod(X3,X3)),X3)
    | ~ c_Wellfounded__Recursion_Owf(X4,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_2762]) ).

cnf(c_0_4124,plain,
    ( c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Ortrancl(X4,X3),tc_prod(X3,X3))
    | c_Wellfounded__Recursion_Oacyclic(c_insert(c_Pair(X2,X1,X3,X3),X4,tc_prod(X3,X3)),X3)
    | ~ c_Wellfounded__Recursion_Oacyclic(X4,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_2763]) ).

cnf(c_0_4125,plain,
    ( c_in(c_Pair(X1,X2,X3,X4),X5,tc_prod(X3,X4))
    | ~ c_in(X2,c_Relation_OImage(X5,c_insert(X1,c_emptyset,X3),X3,X4),X4) ),
    inference(split_conjunct,[status(thm)],[c_0_2764]) ).

cnf(c_0_4126,plain,
    ( c_Divides_Oop_Advd(X1,X2,tc_nat)
    | ~ c_Divides_Oop_Advd(X1,c_GCD_Ogcd(c_Pair(X3,X2,tc_nat,tc_nat)),tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_2765]) ).

cnf(c_0_4127,plain,
    ( c_Divides_Oop_Advd(X1,X2,tc_nat)
    | ~ c_Divides_Oop_Advd(X1,c_GCD_Ogcd(c_Pair(X2,X3,tc_nat,tc_nat)),tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_2766]) ).

cnf(c_0_4128,plain,
    ( c_in(X1,c_Relation_OImage(X2,c_insert(X3,c_emptyset,X4),X4,X5),X5)
    | ~ c_in(c_Pair(X3,X1,X4,X5),X2,tc_prod(X4,X5)) ),
    inference(split_conjunct,[status(thm)],[c_0_2767]) ).

cnf(c_0_4129,plain,
    ( c_in(c_Pair(X1,X2,X3,X4),X5,tc_prod(X3,X4))
    | ~ c_in(c_Pair(X2,X1,X4,X3),c_Relation_Oconverse(X5,X3,X4),tc_prod(X4,X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_2768]) ).

cnf(c_0_4130,plain,
    ( c_in(c_Pair(X1,X2,X3,X4),c_Relation_Oconverse(X5,X4,X3),tc_prod(X3,X4))
    | ~ c_in(c_Pair(X2,X1,X4,X3),X5,tc_prod(X4,X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_2769]) ).

cnf(c_0_4131,plain,
    ( c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Ortrancl(X4,X3),tc_prod(X3,X3))
    | ~ c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Otrancl(X4,X3),tc_prod(X3,X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_2770]) ).

cnf(c_0_4132,plain,
    ( c_in(X1,c_Relation_OImage(X2,X3,X4,X5),X5)
    | ~ c_in(c_Pair(X6,X1,X4,X5),X2,tc_prod(X4,X5))
    | ~ c_in(X6,X3,X4) ),
    inference(split_conjunct,[status(thm)],[c_0_2771]) ).

cnf(c_0_4133,plain,
    ( X1 = c_Pair(c_Main_OconverseE__2(X2,X1,X3,X4),c_Main_OconverseE__1(X2,X1,X3,X4),X4,X3)
    | ~ c_in(X1,c_Relation_Oconverse(X2,X3,X4),tc_prod(X4,X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_2772]) ).

cnf(c_0_4134,plain,
    ( c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Otrancl(X4,X3),tc_prod(X3,X3))
    | ~ c_in(c_Pair(X1,X2,X3,X3),X4,tc_prod(X3,X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_2773]) ).

cnf(c_0_4135,plain,
    ( c_in(c_Datatype__Universe_OScons(X1,X2,X3,X4),c_Datatype__Universe_Ouprod(X5,X6,X3,X4),tc_set(tc_Datatype__Universe_Onode(X3,X4)))
    | ~ c_in(X1,X5,tc_set(tc_Datatype__Universe_Onode(X3,X4)))
    | ~ c_in(X2,X6,tc_set(tc_Datatype__Universe_Onode(X3,X4))) ),
    inference(split_conjunct,[status(thm)],[c_0_2774]) ).

cnf(c_0_4136,plain,
    ( c_Divides_Oop_Advd(X1,c_GCD_Ogcd(c_Pair(X2,X3,tc_nat,tc_nat)),tc_nat)
    | ~ c_Divides_Oop_Advd(X1,X2,tc_nat)
    | ~ c_Divides_Oop_Advd(X1,X3,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_2775]) ).

cnf(c_0_4137,plain,
    ( c_in(X1,c_Relation_ORange(X2,X3,X4),X4)
    | ~ c_in(c_Pair(X5,X1,X3,X4),X2,tc_prod(X3,X4)) ),
    inference(split_conjunct,[status(thm)],[c_0_2776]) ).

cnf(c_0_4138,plain,
    ( c_in(X1,c_Relation_ODomain(X2,X3,X4),X3)
    | ~ c_in(c_Pair(X1,X5,X3,X4),X2,tc_prod(X3,X4)) ),
    inference(split_conjunct,[status(thm)],[c_0_2777]) ).

cnf(c_0_4139,plain,
    ( c_lessequals(c_Union(X1,X2),X3,tc_set(X2))
    | c_lessequals(X4,c_Union(X1,X2),tc_set(X2))
    | ~ c_lessequals(X4,c_Zorn_OUnion__lemma0__1(X3,X4,X1,X2),tc_set(X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_2778]) ).

cnf(c_0_4140,plain,
    ( c_lessequals(c_Union(X1,X2),X3,tc_set(X2))
    | c_lessequals(X4,c_Union(X1,X2),tc_set(X2))
    | ~ c_lessequals(c_Zorn_OUnion__lemma0__1(X3,X4,X1,X2),X3,tc_set(X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_2779]) ).

cnf(c_0_4141,plain,
    c_Divides_Oop_Advd(c_GCD_Ogcd(c_Pair(X1,X2,tc_nat,tc_nat)),X2,tc_nat),
    inference(split_conjunct,[status(thm)],[c_0_2780]) ).

cnf(c_0_4142,plain,
    c_Divides_Oop_Advd(c_GCD_Ogcd(c_Pair(X1,X2,tc_nat,tc_nat)),X1,tc_nat),
    inference(split_conjunct,[status(thm)],[c_0_2781]) ).

cnf(c_0_4143,plain,
    ( X1 = c_List_Olist_ONil
    | ~ c_in(c_Pair(X1,c_List_Olist_ONil,tc_List_Olist(X2),tc_List_Olist(X2)),c_List_Olistrel(X3,X2),tc_prod(tc_List_Olist(X2),tc_List_Olist(X2))) ),
    inference(split_conjunct,[status(thm)],[c_0_2782]) ).

cnf(c_0_4144,plain,
    ( X1 = c_List_Olist_ONil
    | ~ c_in(c_Pair(c_List_Olist_ONil,X1,tc_List_Olist(X2),tc_List_Olist(X2)),c_List_Olistrel(X3,X2),tc_prod(tc_List_Olist(X2),tc_List_Olist(X2))) ),
    inference(split_conjunct,[status(thm)],[c_0_2783]) ).

cnf(c_0_4145,plain,
    ~ c_in(c_Pair(c_List_Olist_ONil,X1,tc_List_Olist(X2),tc_List_Olist(X2)),c_List_Olex(X3,X2),tc_prod(tc_List_Olist(X2),tc_List_Olist(X2))),
    inference(split_conjunct,[status(thm)],[c_0_2784]) ).

cnf(c_0_4146,plain,
    ~ c_in(c_Pair(X1,c_List_Olist_ONil,tc_List_Olist(X2),tc_List_Olist(X2)),c_List_Olex(X3,X2),tc_prod(tc_List_Olist(X2),tc_List_Olist(X2))),
    inference(split_conjunct,[status(thm)],[c_0_2785]) ).

cnf(c_0_4147,plain,
    ( c_less(X1,X2,tc_nat)
    | ~ c_in(c_Pair(X1,X2,tc_nat,tc_nat),c_Wellfounded__Relations_Oless__than,tc_prod(tc_nat,tc_nat)) ),
    inference(split_conjunct,[status(thm)],[c_0_2786]) ).

cnf(c_0_4148,plain,
    ( X1 = X2
    | ~ c_in(c_Pair(X1,X2,X3,X3),c_Relation_OId,tc_prod(X3,X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_2787]) ).

cnf(c_0_4149,plain,
    ( c_in(c_Datatype__Universe_OIn1(X1,X2,X3),c_Datatype__Universe_Ousum(X4,X5,X2,X3),tc_set(tc_Datatype__Universe_Onode(X2,X3)))
    | ~ c_in(X1,X5,tc_set(tc_Datatype__Universe_Onode(X2,X3))) ),
    inference(split_conjunct,[status(thm)],[c_0_2788]) ).

cnf(c_0_4150,plain,
    ( c_in(c_Datatype__Universe_OIn0(X1,X2,X3),c_Datatype__Universe_Ousum(X4,X5,X2,X3),tc_set(tc_Datatype__Universe_Onode(X2,X3)))
    | ~ c_in(X1,X4,tc_set(tc_Datatype__Universe_Onode(X2,X3))) ),
    inference(split_conjunct,[status(thm)],[c_0_2789]) ).

cnf(c_0_4151,plain,
    ( c_in(c_minus(X1,X2,tc_set(X3)),c_Finite__Set_OFinites,tc_set(X3))
    | ~ c_in(c_minus(X1,c_insert(X4,X2,X3),tc_set(X3)),c_Finite__Set_OFinites,tc_set(X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_2790]) ).

cnf(c_0_4152,plain,
    ( X1 = X2
    | c_Pair(X3,X1,X4,X5) != c_Pair(X6,X2,X4,X5) ),
    inference(split_conjunct,[status(thm)],[c_0_2791]) ).

cnf(c_0_4153,plain,
    ( X1 = X2
    | c_Pair(X1,X3,X4,X5) != c_Pair(X2,X6,X4,X5) ),
    inference(split_conjunct,[status(thm)],[c_0_2792]) ).

cnf(c_0_4154,plain,
    ( X1 = X2
    | c_Datatype__Universe_OScons(X3,X1,X4,X5) != c_Datatype__Universe_OScons(X6,X2,X4,X5) ),
    inference(split_conjunct,[status(thm)],[c_0_2793]) ).

cnf(c_0_4155,plain,
    ( X1 = X2
    | c_Datatype__Universe_OScons(X1,X3,X4,X5) != c_Datatype__Universe_OScons(X2,X6,X4,X5) ),
    inference(split_conjunct,[status(thm)],[c_0_2794]) ).

cnf(c_0_4156,plain,
    ( c_in(c_Sum__Type_OInr(X1,X2,X3),c_Sum__Type_OPlus(X4,X5,X3,X2),tc_sum(X3,X2))
    | ~ c_in(X1,X5,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_2795]) ).

cnf(c_0_4157,plain,
    ( c_in(c_Sum__Type_OInl(X1,X2,X3),c_Sum__Type_OPlus(X4,X5,X2,X3),tc_sum(X2,X3))
    | ~ c_in(X1,X4,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_2796]) ).

cnf(c_0_4158,plain,
    ( c_lessequals(c_Union(X1,X2),X3,tc_set(X2))
    | c_lessequals(X4,c_Union(X1,X2),tc_set(X2))
    | c_in(c_Zorn_OUnion__lemma0__1(X3,X4,X1,X2),X1,tc_set(X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_2797]) ).

cnf(c_0_4159,plain,
    ( c_in(c_Pair(X1,X1,X2,X2),c_Relation_Odiag(X3,X2),tc_prod(X2,X2))
    | ~ c_in(X1,X3,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_2798]) ).

cnf(c_0_4160,plain,
    ( c_in(c_minus(X1,c_insert(X2,X3,X4),tc_set(X4)),c_Finite__Set_OFinites,tc_set(X4))
    | ~ c_in(c_minus(X1,X3,tc_set(X4)),c_Finite__Set_OFinites,tc_set(X4)) ),
    inference(split_conjunct,[status(thm)],[c_0_2799]) ).

cnf(c_0_4161,plain,
    ( c_in(c_Pair(X1,X2,tc_nat,tc_nat),c_Wellfounded__Relations_Oless__than,tc_prod(tc_nat,tc_nat))
    | ~ c_less(X1,X2,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_2800]) ).

cnf(c_0_4162,plain,
    ( X1 = c_Pair(c_Main_OdiagE__1(X2,X1,X3),c_Main_OdiagE__1(X2,X1,X3),X3,X3)
    | ~ c_in(X1,c_Relation_Odiag(X2,X3),tc_prod(X3,X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_2801]) ).

cnf(c_0_4163,plain,
    c_in(c_Pair(X1,X1,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2)),
    inference(split_conjunct,[status(thm)],[c_0_2802]) ).

cnf(c_0_4164,plain,
    ( c_Wellfounded__Recursion_Owf(c_Wellfounded__Relations_Olex__prod(X1,X2,X3,X4),tc_prod(X3,X4))
    | ~ c_Wellfounded__Recursion_Owf(X1,X3)
    | ~ c_Wellfounded__Recursion_Owf(X2,X4) ),
    inference(split_conjunct,[status(thm)],[c_0_2803]) ).

cnf(c_0_4165,plain,
    ( c_Relation_Otrans(c_Wellfounded__Relations_Olex__prod(X1,X2,X3,X4),tc_prod(X3,X4))
    | ~ c_Relation_Otrans(X1,X3)
    | ~ c_Relation_Otrans(X2,X4) ),
    inference(split_conjunct,[status(thm)],[c_0_2804]) ).

cnf(c_0_4166,plain,
    c_in(c_Pair(X1,X1,X2,X2),c_Relation_OId,tc_prod(X2,X2)),
    inference(split_conjunct,[status(thm)],[c_0_2805]) ).

cnf(c_0_4167,plain,
    ( X1 = X2
    | c_append(X3,c_List_Olist_OCons(X1,c_List_Olist_ONil,X4),X4) != c_append(X5,c_List_Olist_OCons(X2,c_List_Olist_ONil,X4),X4) ),
    inference(split_conjunct,[status(thm)],[c_0_2806]) ).

cnf(c_0_4168,plain,
    ( X1 = X2
    | c_append(X1,c_List_Olist_OCons(X3,c_List_Olist_ONil,X4),X4) != c_append(X2,c_List_Olist_OCons(X5,c_List_Olist_ONil,X4),X4) ),
    inference(split_conjunct,[status(thm)],[c_0_2807]) ).

cnf(c_0_4169,plain,
    c_Datatype__Universe_OScons(X1,X2,X3,X4) != c_Datatype__Universe_ONumb(X5,X3,X4),
    inference(split_conjunct,[status(thm)],[c_0_2808]) ).

cnf(c_0_4170,plain,
    c_Datatype__Universe_OScons(X1,X2,X3,X4) != c_Datatype__Universe_OLeaf(X5,X3,X4),
    inference(split_conjunct,[status(thm)],[c_0_2809]) ).

cnf(c_0_4171,plain,
    c_Datatype__Universe_OScons(X1,X2,X3,X4) != c_Datatype__Universe_OAtom(X5,X3,X4),
    inference(split_conjunct,[status(thm)],[c_0_2810]) ).

cnf(c_0_4172,plain,
    c_Datatype__Universe_ONumb(X1,X2,X3) != c_Datatype__Universe_OScons(X4,X5,X2,X3),
    inference(split_conjunct,[status(thm)],[c_0_2811]) ).

cnf(c_0_4173,plain,
    c_Datatype__Universe_OLeaf(X1,X2,X3) != c_Datatype__Universe_OScons(X4,X5,X2,X3),
    inference(split_conjunct,[status(thm)],[c_0_2812]) ).

cnf(c_0_4174,plain,
    c_Datatype__Universe_OAtom(X1,X2,X3) != c_Datatype__Universe_OScons(X4,X5,X2,X3),
    inference(split_conjunct,[status(thm)],[c_0_2813]) ).

cnf(c_0_4175,plain,
    ( c_in(c_append(X1,X2,X3),c_List_Olists(X4,X3),tc_List_Olist(X3))
    | ~ c_in(X1,c_List_Olists(X4,X3),tc_List_Olist(X3))
    | ~ c_in(X2,c_List_Olists(X4,X3),tc_List_Olist(X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_2814]) ).

cnf(c_0_4176,plain,
    ( c_in(X1,c_Finite__Set_OFinites,tc_set(tc_prod(X2,X3)))
    | ~ c_in(c_Relation_Oconverse(X1,X2,X3),c_Finite__Set_OFinites,tc_set(tc_prod(X3,X2))) ),
    inference(split_conjunct,[status(thm)],[c_0_2815]) ).

cnf(c_0_4177,plain,
    c_List_Orev(c_append(c_List_Orev(X1,X2),c_List_Olist_OCons(X3,c_List_Olist_ONil,X2),X2),X2) = c_List_Olist_OCons(X3,X1,X2),
    inference(split_conjunct,[status(thm)],[c_0_2816]) ).

cnf(c_0_4178,plain,
    ( X1 = c_Pair(c_Main_OIdE__1(X1,X2),c_Main_OIdE__1(X1,X2),X2,X2)
    | ~ c_in(X1,c_Relation_OId,tc_prod(X2,X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_2817]) ).

cnf(c_0_4179,plain,
    ( c_in(c_List_Olist_OCons(X1,X2,X3),c_List_Olists(X4,X3),tc_List_Olist(X3))
    | ~ c_in(X2,c_List_Olists(X4,X3),tc_List_Olist(X3))
    | ~ c_in(X1,X4,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_2818]) ).

cnf(c_0_4180,plain,
    ( c_in(c_Relation_Oconverse(X1,X2,X3),c_Finite__Set_OFinites,tc_set(tc_prod(X3,X2)))
    | ~ c_in(X1,c_Finite__Set_OFinites,tc_set(tc_prod(X2,X3))) ),
    inference(split_conjunct,[status(thm)],[c_0_2819]) ).

cnf(c_0_4181,plain,
    ( c_in(X1,c_List_Olists(X2,X3),tc_List_Olist(X3))
    | ~ c_in(c_List_Olist_OCons(X4,X1,X3),c_List_Olists(X2,X3),tc_List_Olist(X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_2820]) ).

cnf(c_0_4182,plain,
    ( c_in(X1,c_List_Olists(X2,X3),tc_List_Olist(X3))
    | ~ c_in(c_append(X4,X1,X3),c_List_Olists(X2,X3),tc_List_Olist(X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_2821]) ).

cnf(c_0_4183,plain,
    ( c_in(X1,c_List_Olists(X2,X3),tc_List_Olist(X3))
    | ~ c_in(c_append(X1,X4,X3),c_List_Olists(X2,X3),tc_List_Olist(X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_2822]) ).

cnf(c_0_4184,plain,
    ( c_insert(X1,c_emptyset,X2) = c_insert(X1,X3,X2)
    | ~ c_lessequals(X3,c_insert(X1,c_emptyset,X2),tc_set(X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_2823]) ).

cnf(c_0_4185,plain,
    ( c_insert(X1,X2,X3) = c_insert(X1,c_emptyset,X3)
    | ~ c_lessequals(X2,c_insert(X1,c_emptyset,X3),tc_set(X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_2824]) ).

cnf(c_0_4186,plain,
    ( c_in(X1,X2,X3)
    | c_in(X1,X4,X3)
    | ~ c_in(X1,c_union(X2,X4,X3),X3) ),
    inference(split_conjunct,[status(thm)],[c_0_2825]) ).

cnf(c_0_4187,plain,
    ( ~ c_in(X1,c_minus(X2,X3,tc_set(X4)),X4)
    | ~ c_in(X1,X3,X4) ),
    inference(split_conjunct,[status(thm)],[c_0_2826]) ).

cnf(c_0_4188,plain,
    ( c_in(X1,X2,X3)
    | ~ c_in(c_List_Olist_OCons(X1,X4,X3),c_List_Olists(X2,X3),tc_List_Olist(X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_2827]) ).

cnf(c_0_4189,plain,
    ( c_in(c_union(X1,X2,X3),c_Finite__Set_OFinites,tc_set(X3))
    | ~ c_in(X1,c_Finite__Set_OFinites,tc_set(X3))
    | ~ c_in(X2,c_Finite__Set_OFinites,tc_set(X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_2828]) ).

cnf(c_0_4190,plain,
    ( c_less(c_0,X1,tc_nat)
    | c_less(c_0,X2,tc_nat)
    | ~ c_less(c_0,c_plus(X1,X2,tc_nat),tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_2829]) ).

cnf(c_0_4191,plain,
    ( c_in(X1,c_List_Olists(X2,X3),tc_List_Olist(X3))
    | ~ c_in(c_Main_Oin__listsI__1(X2,X1,X3),X2,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_2830]) ).

cnf(c_0_4192,plain,
    ( c_in(X1,c_Inter(X2,X3),X3)
    | ~ c_in(X1,c_Main_OInterI__1(X1,X2,X3),X3) ),
    inference(split_conjunct,[status(thm)],[c_0_2831]) ).

cnf(c_0_4193,plain,
    ( c_in(X1,c_inter(X2,X3,X4),X4)
    | ~ c_in(X1,X2,X4)
    | ~ c_in(X1,X3,X4) ),
    inference(split_conjunct,[status(thm)],[c_0_2832]) ).

cnf(c_0_4194,plain,
    ( c_lessequals(X1,c_insert(X2,c_emptyset,X3),tc_set(X3))
    | c_insert(X2,c_emptyset,X3) != c_insert(X4,X1,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_2833]) ).

cnf(c_0_4195,plain,
    ( c_lessequals(X1,c_insert(X2,c_emptyset,X3),tc_set(X3))
    | c_insert(X4,X1,X3) != c_insert(X2,c_emptyset,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_2834]) ).

cnf(c_0_4196,plain,
    ( c_in(c_Union(X1,X2),c_Finite__Set_OFinites,tc_set(X2))
    | ~ c_in(c_Main_Ofinite__Union__1(X1,X2),c_Finite__Set_OFinites,tc_set(X2))
    | ~ c_in(X1,c_Finite__Set_OFinites,tc_set(tc_set(X2))) ),
    inference(split_conjunct,[status(thm)],[c_0_2835]) ).

cnf(c_0_4197,plain,
    ( c_in(c_Main_OdiagE__1(X1,X2,X3),X1,X3)
    | ~ c_in(X2,c_Relation_Odiag(X1,X3),tc_prod(X3,X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_2836]) ).

cnf(c_0_4198,plain,
    ( c_in(X1,X2,X3)
    | ~ c_in(X1,c_minus(X2,X4,tc_set(X3)),X3) ),
    inference(split_conjunct,[status(thm)],[c_0_2837]) ).

cnf(c_0_4199,plain,
    ( c_in(X1,c_Finite__Set_OFinites,tc_set(X2))
    | ~ c_in(c_union(X3,X1,X2),c_Finite__Set_OFinites,tc_set(X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_2838]) ).

cnf(c_0_4200,plain,
    ( c_in(X1,c_Finite__Set_OFinites,tc_set(X2))
    | ~ c_in(c_union(X1,X3,X2),c_Finite__Set_OFinites,tc_set(X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_2839]) ).

cnf(c_0_4201,plain,
    ( c_in(X1,X2,X3)
    | ~ c_in(X1,c_List_Oset(X4,X3),X3)
    | ~ c_in(X4,c_List_Olists(X2,X3),tc_List_Olist(X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_2840]) ).

cnf(c_0_4202,plain,
    ( c_lessequals(X1,X2,tc_set(X3))
    | ~ c_in(c_Main_OsubsetI__1(X1,X2,X3),X2,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_2841]) ).

cnf(c_0_4203,plain,
    ( c_in(X1,c_minus(X2,X3,tc_set(X4)),X4)
    | c_in(X1,X3,X4)
    | ~ c_in(X1,X2,X4) ),
    inference(split_conjunct,[status(thm)],[c_0_2842]) ).

cnf(c_0_4204,plain,
    ( X1 = X2
    | c_in(X1,X3,X4)
    | ~ c_in(X1,c_insert(X2,X3,X4),X4) ),
    inference(split_conjunct,[status(thm)],[c_0_2843]) ).

cnf(c_0_4205,plain,
    ( c_in(X1,X2,X3)
    | ~ c_in(X1,c_inter(X2,X4,X3),X3) ),
    inference(split_conjunct,[status(thm)],[c_0_2844]) ).

cnf(c_0_4206,plain,
    ( c_in(X1,X2,X3)
    | ~ c_in(X1,c_inter(X4,X2,X3),X3) ),
    inference(split_conjunct,[status(thm)],[c_0_2845]) ).

cnf(c_0_4207,plain,
    ( c_lessequals(X1,c_Zorn_Osucc(X2,X3,X4),tc_set(tc_set(X4)))
    | ~ c_lessequals(X1,X3,tc_set(tc_set(X4))) ),
    inference(split_conjunct,[status(thm)],[c_0_2846]) ).

cnf(c_0_4208,plain,
    ( c_in(c_Main_OUnionE__1(X1,X2,X3),X2,tc_set(X3))
    | ~ c_in(X1,c_Union(X2,X3),X3) ),
    inference(split_conjunct,[status(thm)],[c_0_2847]) ).

cnf(c_0_4209,plain,
    ( X1 = c_append(c_List_Orev(X2,X3),c_List_Olist_OCons(X4,c_List_Olist_ONil,X3),X3)
    | c_List_Orev(X1,X3) != c_List_Olist_OCons(X4,X2,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_2848]) ).

cnf(c_0_4210,plain,
    ( c_in(X1,c_Main_OUnionE__1(X1,X2,X3),X3)
    | ~ c_in(X1,c_Union(X2,X3),X3) ),
    inference(split_conjunct,[status(thm)],[c_0_2849]) ).

cnf(c_0_4211,plain,
    ( c_in(c_Union(X1,X2),c_Finite__Set_OFinites,tc_set(X2))
    | c_in(c_Main_Ofinite__Union__1(X1,X2),X1,tc_set(X2))
    | ~ c_in(X1,c_Finite__Set_OFinites,tc_set(tc_set(X2))) ),
    inference(split_conjunct,[status(thm)],[c_0_2850]) ).

cnf(c_0_4212,plain,
    ( c_in(X1,X2,X3)
    | ~ c_in(X1,c_Inter(X4,X3),X3)
    | ~ c_in(X2,X4,tc_set(X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_2851]) ).

cnf(c_0_4213,plain,
    ( c_lessequals(X1,X2,tc_set(X3))
    | ~ c_lessequals(c_uminus(X2,tc_set(X3)),c_uminus(X1,tc_set(X3)),tc_set(X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_2852]) ).

cnf(c_0_4214,plain,
    ( c_in(c_Main_Oin__listsI__1(X1,X2,X3),c_List_Oset(X2,X3),X3)
    | c_in(X2,c_List_Olists(X1,X3),tc_List_Olist(X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_2853]) ).

cnf(c_0_4215,plain,
    ( c_in(X1,c_Union(X2,X3),X3)
    | ~ c_in(X4,X2,tc_set(X3))
    | ~ c_in(X1,X4,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_2854]) ).

cnf(c_0_4216,plain,
    ( c_in(c_inter(X1,X2,X3),c_Finite__Set_OFinites,tc_set(X3))
    | ~ c_in(X2,c_Finite__Set_OFinites,tc_set(X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_2855]) ).

cnf(c_0_4217,plain,
    ( c_in(c_inter(X1,X2,X3),c_Finite__Set_OFinites,tc_set(X3))
    | ~ c_in(X1,c_Finite__Set_OFinites,tc_set(X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_2856]) ).

cnf(c_0_4218,plain,
    ( c_in(c_insert(X1,X2,X3),c_Finite__Set_OFinites,tc_set(X3))
    | ~ c_in(X2,c_Finite__Set_OFinites,tc_set(X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_2857]) ).

cnf(c_0_4219,plain,
    ( X1 = X2
    | ~ c_in(X1,c_insert(X2,c_emptyset,X3),X3) ),
    inference(split_conjunct,[status(thm)],[c_0_2858]) ).

cnf(c_0_4220,plain,
    ( c_in(c_Main_OInterI__1(X1,X2,X3),X2,tc_set(X3))
    | c_in(X1,c_Inter(X2,X3),X3) ),
    inference(split_conjunct,[status(thm)],[c_0_2859]) ).

cnf(c_0_4221,plain,
    ( c_in(X1,c_insert(X2,X3,X4),X4)
    | ~ c_in(X1,X3,X4) ),
    inference(split_conjunct,[status(thm)],[c_0_2860]) ).

cnf(c_0_4222,plain,
    ( c_in(X1,c_union(X2,X3,X4),X4)
    | ~ c_in(X1,X2,X4) ),
    inference(split_conjunct,[status(thm)],[c_0_2861]) ).

cnf(c_0_4223,plain,
    ( c_in(X1,c_union(X2,X3,X4),X4)
    | ~ c_in(X1,X3,X4) ),
    inference(split_conjunct,[status(thm)],[c_0_2862]) ).

cnf(c_0_4224,plain,
    ~ c_less(c_plus(X1,X2,tc_nat),X2,tc_nat),
    inference(split_conjunct,[status(thm)],[c_0_2863]) ).

cnf(c_0_4225,plain,
    ~ c_less(c_plus(X1,X2,tc_nat),X1,tc_nat),
    inference(split_conjunct,[status(thm)],[c_0_2864]) ).

cnf(c_0_4226,plain,
    ( c_lessequals(X1,X2,X3)
    | ~ c_lessequals(c_SetInterval_OlessThan(X1,X3),c_SetInterval_OlessThan(X2,X3),tc_set(X3))
    | ~ class_Orderings_Olinorder(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_2865]) ).

cnf(c_0_4227,plain,
    ( c_lessequals(X1,X2,X3)
    | ~ c_lessequals(c_SetInterval_OgreaterThan(X2,X3),c_SetInterval_OgreaterThan(X1,X3),tc_set(X3))
    | ~ class_Orderings_Olinorder(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_2866]) ).

cnf(c_0_4228,plain,
    ( c_lessequals(X1,X2,X3)
    | ~ c_lessequals(c_SetInterval_OatMost(X1,X3),c_SetInterval_OatMost(X2,X3),tc_set(X3))
    | ~ class_Orderings_Oorder(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_2867]) ).

cnf(c_0_4229,plain,
    ( c_lessequals(X1,X2,X3)
    | ~ c_lessequals(c_SetInterval_OatLeast(X2,X3),c_SetInterval_OatLeast(X1,X3),tc_set(X3))
    | ~ class_Orderings_Oorder(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_2868]) ).

cnf(c_0_4230,plain,
    ( c_in(X1,X2,X3)
    | ~ c_lessequals(X4,X2,tc_set(X3))
    | ~ c_in(X1,X4,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_2869]) ).

cnf(c_0_4231,plain,
    ( c_less(c_0,c_plus(X1,X2,tc_nat),tc_nat)
    | ~ c_less(c_0,X2,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_2870]) ).

cnf(c_0_4232,plain,
    ( c_less(c_0,c_plus(X1,X2,tc_nat),tc_nat)
    | ~ c_less(c_0,X1,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_2871]) ).

cnf(c_0_4233,plain,
    ( c_in(X1,c_Transitive__Closure_Ortrancl(X2,X3),tc_prod(X3,X3))
    | ~ c_in(X1,X2,tc_prod(X3,X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_2872]) ).

cnf(c_0_4234,plain,
    ( c_lessequals(c_uminus(X1,tc_set(X2)),c_uminus(X3,tc_set(X2)),tc_set(X2))
    | ~ c_lessequals(X3,X1,tc_set(X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_2873]) ).

cnf(c_0_4235,plain,
    ( ~ c_in(X1,c_uminus(X2,tc_set(X3)),X3)
    | ~ c_in(X1,X2,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_2874]) ).

cnf(c_0_4236,plain,
    ( c_lessequals(X1,X2,tc_set(X3))
    | c_in(c_Main_OsubsetI__1(X1,X2,X3),X1,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_2875]) ).

cnf(c_0_4237,plain,
    ( c_in(X1,c_Finite__Set_OFinites,tc_set(X2))
    | ~ c_in(c_Pow(X1,X2),c_Finite__Set_OFinites,tc_set(tc_set(X2))) ),
    inference(split_conjunct,[status(thm)],[c_0_2876]) ).

cnf(c_0_4238,plain,
    ( c_lessequals(c_SetInterval_OlessThan(X1,X2),c_SetInterval_OlessThan(X3,X2),tc_set(X2))
    | ~ c_lessequals(X1,X3,X2)
    | ~ class_Orderings_Olinorder(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_2877]) ).

cnf(c_0_4239,plain,
    ( c_lessequals(c_SetInterval_OgreaterThan(X1,X2),c_SetInterval_OgreaterThan(X3,X2),tc_set(X2))
    | ~ c_lessequals(X3,X1,X2)
    | ~ class_Orderings_Olinorder(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_2878]) ).

cnf(c_0_4240,plain,
    ( c_lessequals(c_SetInterval_OatMost(X1,X2),c_SetInterval_OatMost(X3,X2),tc_set(X2))
    | ~ c_lessequals(X1,X3,X2)
    | ~ class_Orderings_Oorder(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_2879]) ).

cnf(c_0_4241,plain,
    ( c_lessequals(c_SetInterval_OatLeast(X1,X2),c_SetInterval_OatLeast(X3,X2),tc_set(X2))
    | ~ c_lessequals(X3,X1,X2)
    | ~ class_Orderings_Oorder(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_2880]) ).

cnf(c_0_4242,plain,
    ( c_Wellfounded__Recursion_Oacyclic(X1,X2)
    | ~ c_Wellfounded__Recursion_Oacyclic(c_Relation_Oconverse(X1,X2,X2),X2) ),
    inference(split_conjunct,[status(thm)],[c_0_2881]) ).

cnf(c_0_4243,plain,
    ( X1 = X2
    | ~ c_in(X2,X3,X4)
    | ~ c_in(X1,X3,X4)
    | ~ c_Infinite__Set_Oatmost__one(X3,X4) ),
    inference(split_conjunct,[status(thm)],[c_0_2882]) ).

cnf(c_0_4244,plain,
    ( c_lessequals(X1,X2,tc_set(X3))
    | ~ c_in(X1,c_Pow(X2,X3),tc_set(X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_2883]) ).

cnf(c_0_4245,plain,
    ( X1 = X2
    | ~ c_lessequals(X1,X2,tc_set(X3))
    | ~ c_lessequals(X2,X1,tc_set(X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_2884]) ).

cnf(c_0_4246,plain,
    ( ~ c_lessequals(X1,X2,tc_set(X3))
    | ~ c_less(X2,X1,tc_set(X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_2885]) ).

cnf(c_0_4247,plain,
    ( c_in(c_Pow(X1,X2),c_Finite__Set_OFinites,tc_set(tc_set(X2)))
    | ~ c_in(X1,c_Finite__Set_OFinites,tc_set(X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_2886]) ).

cnf(c_0_4248,plain,
    ( c_less(X1,X2,X3)
    | ~ c_in(X1,c_SetInterval_OlessThan(X2,X3),X3)
    | ~ class_Orderings_Oord(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_2887]) ).

cnf(c_0_4249,plain,
    ( c_less(X1,X2,X3)
    | ~ c_in(X2,c_SetInterval_OgreaterThan(X1,X3),X3)
    | ~ class_Orderings_Oord(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_2888]) ).

cnf(c_0_4250,plain,
    ( c_lessequals(X1,X2,X3)
    | ~ c_in(X1,c_SetInterval_OatMost(X2,X3),X3)
    | ~ class_Orderings_Oord(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_2889]) ).

cnf(c_0_4251,plain,
    ( c_lessequals(X1,X2,X3)
    | ~ c_in(X2,c_SetInterval_OatLeast(X1,X3),X3)
    | ~ class_Orderings_Oord(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_2890]) ).

cnf(c_0_4252,plain,
    ( c_in(X1,c_Pow(X2,X3),tc_set(X3))
    | ~ c_lessequals(X1,X2,tc_set(X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_2891]) ).

cnf(c_0_4253,plain,
    c_lessequals(c_Nat_Osize(c_List_Oremdups(X1,X2),tc_List_Olist(X2)),c_Nat_Osize(X1,tc_List_Olist(X2)),tc_nat),
    inference(split_conjunct,[status(thm)],[c_0_2892]) ).

cnf(c_0_4254,plain,
    ( c_in(X1,c_SetInterval_OlessThan(X2,X3),X3)
    | ~ c_less(X1,X2,X3)
    | ~ class_Orderings_Oord(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_2893]) ).

cnf(c_0_4255,plain,
    ( c_in(X1,c_SetInterval_OgreaterThan(X2,X3),X3)
    | ~ c_less(X2,X1,X3)
    | ~ class_Orderings_Oord(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_2894]) ).

cnf(c_0_4256,plain,
    ( c_in(X1,c_SetInterval_OatMost(X2,X3),X3)
    | ~ c_lessequals(X1,X2,X3)
    | ~ class_Orderings_Oord(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_2895]) ).

cnf(c_0_4257,plain,
    ( c_in(X1,c_SetInterval_OatLeast(X2,X3),X3)
    | ~ c_lessequals(X2,X1,X3)
    | ~ class_Orderings_Oord(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_2896]) ).

cnf(c_0_4258,plain,
    ( X1 = X2
    | c_Datatype__Universe_ONumb(X1,X3,X4) != c_Datatype__Universe_ONumb(X2,X3,X4) ),
    inference(split_conjunct,[status(thm)],[c_0_2897]) ).

cnf(c_0_4259,plain,
    ( X1 = X2
    | c_Datatype__Universe_OLeaf(X1,X3,X4) != c_Datatype__Universe_OLeaf(X2,X3,X4) ),
    inference(split_conjunct,[status(thm)],[c_0_2898]) ).

cnf(c_0_4260,plain,
    ( X1 = X2
    | c_Sum__Type_OInr(X1,X3,X4) != c_Sum__Type_OInr(X2,X3,X4) ),
    inference(split_conjunct,[status(thm)],[c_0_2899]) ).

cnf(c_0_4261,plain,
    ( X1 = X2
    | c_Sum__Type_OInl(X1,X3,X4) != c_Sum__Type_OInl(X2,X3,X4) ),
    inference(split_conjunct,[status(thm)],[c_0_2900]) ).

cnf(c_0_4262,plain,
    ( X1 = X2
    | c_append(X3,X1,X4) != c_append(X3,X2,X4) ),
    inference(split_conjunct,[status(thm)],[c_0_2901]) ).

cnf(c_0_4263,plain,
    ( X1 = X2
    | c_List_Olist_OCons(X3,X1,X4) != c_List_Olist_OCons(X5,X2,X4) ),
    inference(split_conjunct,[status(thm)],[c_0_2902]) ).

cnf(c_0_4264,plain,
    ( X1 = X2
    | c_List_Olist_OCons(X1,X3,X4) != c_List_Olist_OCons(X2,X5,X4) ),
    inference(split_conjunct,[status(thm)],[c_0_2903]) ).

cnf(c_0_4265,plain,
    ( X1 = X2
    | c_append(X1,X3,X4) != c_append(X2,X3,X4) ),
    inference(split_conjunct,[status(thm)],[c_0_2904]) ).

cnf(c_0_4266,plain,
    ( X1 = X2
    | c_Datatype__Universe_OIn1(X1,X3,X4) != c_Datatype__Universe_OIn1(X2,X3,X4) ),
    inference(split_conjunct,[status(thm)],[c_0_2905]) ).

cnf(c_0_4267,plain,
    ( X1 = X2
    | c_Datatype__Universe_OIn0(X1,X3,X4) != c_Datatype__Universe_OIn0(X2,X3,X4) ),
    inference(split_conjunct,[status(thm)],[c_0_2906]) ).

cnf(c_0_4268,plain,
    ( X1 = X2
    | c_Datatype__Universe_OAtom(X1,X3,X4) != c_Datatype__Universe_OAtom(X2,X3,X4) ),
    inference(split_conjunct,[status(thm)],[c_0_2907]) ).

cnf(c_0_4269,plain,
    ( c_Divides_Oop_Advd(X1,X2,tc_IntDef_Oint)
    | ~ c_Divides_Oop_Advd(c_uminus(X1,tc_IntDef_Oint),X2,tc_IntDef_Oint) ),
    inference(split_conjunct,[status(thm)],[c_0_2908]) ).

cnf(c_0_4270,plain,
    ( c_Divides_Oop_Advd(X1,X2,tc_IntDef_Oint)
    | ~ c_Divides_Oop_Advd(X1,c_uminus(X2,tc_IntDef_Oint),tc_IntDef_Oint) ),
    inference(split_conjunct,[status(thm)],[c_0_2909]) ).

cnf(c_0_4271,plain,
    c_Sum__Type_OInr(X1,X2,X3) != c_Sum__Type_OInl(X4,X3,X2),
    inference(split_conjunct,[status(thm)],[c_0_2910]) ).

cnf(c_0_4272,plain,
    c_Sum__Type_OInl(X1,X2,X3) != c_Sum__Type_OInr(X4,X3,X2),
    inference(split_conjunct,[status(thm)],[c_0_2911]) ).

cnf(c_0_4273,plain,
    c_Datatype__Universe_ONumb(X1,X2,X3) != c_Datatype__Universe_OLeaf(X4,X2,X3),
    inference(split_conjunct,[status(thm)],[c_0_2912]) ).

cnf(c_0_4274,plain,
    c_Datatype__Universe_OLeaf(X1,X2,X3) != c_Datatype__Universe_ONumb(X4,X2,X3),
    inference(split_conjunct,[status(thm)],[c_0_2913]) ).

cnf(c_0_4275,plain,
    c_Datatype__Universe_OIn1(X1,X2,X3) != c_Datatype__Universe_OIn0(X4,X2,X3),
    inference(split_conjunct,[status(thm)],[c_0_2914]) ).

cnf(c_0_4276,plain,
    c_Datatype__Universe_OIn0(X1,X2,X3) != c_Datatype__Universe_OIn1(X4,X2,X3),
    inference(split_conjunct,[status(thm)],[c_0_2915]) ).

cnf(c_0_4277,plain,
    ( X1 = X2
    | c_insert(X2,c_emptyset,X3) != c_insert(X1,X4,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_2916]) ).

cnf(c_0_4278,plain,
    ( X1 = X2
    | c_insert(X1,X3,X4) != c_insert(X2,c_emptyset,X4) ),
    inference(split_conjunct,[status(thm)],[c_0_2917]) ).

cnf(c_0_4279,plain,
    ( X1 = X2
    | c_insert(X1,c_emptyset,X3) != c_insert(X2,c_emptyset,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_2918]) ).

cnf(c_0_4280,plain,
    ( X1 = c_times(X2,c_Main_Ozmod__eq__0D__dest__1(X2,X1),tc_IntDef_Oint)
    | c_Divides_Oop_Amod(X1,X2,tc_IntDef_Oint) != c_0 ),
    inference(split_conjunct,[status(thm)],[c_0_2919]) ).

cnf(c_0_4281,plain,
    ( X1 = c_times(X2,c_Main_Omod__eq__0D__dest__1(X2,X1),tc_nat)
    | c_Divides_Oop_Amod(X1,X2,tc_nat) != c_0 ),
    inference(split_conjunct,[status(thm)],[c_0_2920]) ).

cnf(c_0_4282,plain,
    c_in(X1,c_insert(X1,X2,X3),X3),
    inference(split_conjunct,[status(thm)],[c_0_2921]) ).

cnf(c_0_4283,plain,
    c_in(c_SetInterval_OgreaterThanLessThan(X1,X2,tc_IntDef_Oint),c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)),
    inference(split_conjunct,[status(thm)],[c_0_2922]) ).

cnf(c_0_4284,plain,
    c_in(c_SetInterval_OgreaterThanLessThan(X1,X2,tc_nat),c_Finite__Set_OFinites,tc_set(tc_nat)),
    inference(split_conjunct,[status(thm)],[c_0_2923]) ).

cnf(c_0_4285,plain,
    c_in(c_SetInterval_OgreaterThanAtMost(X1,X2,tc_IntDef_Oint),c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)),
    inference(split_conjunct,[status(thm)],[c_0_2924]) ).

cnf(c_0_4286,plain,
    c_in(c_SetInterval_OgreaterThanAtMost(X1,X2,tc_nat),c_Finite__Set_OFinites,tc_set(tc_nat)),
    inference(split_conjunct,[status(thm)],[c_0_2925]) ).

cnf(c_0_4287,plain,
    c_in(c_SetInterval_OatLeastLessThan(X1,X2,tc_IntDef_Oint),c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)),
    inference(split_conjunct,[status(thm)],[c_0_2926]) ).

cnf(c_0_4288,plain,
    c_in(c_SetInterval_OatLeastLessThan(X1,X2,tc_nat),c_Finite__Set_OFinites,tc_set(tc_nat)),
    inference(split_conjunct,[status(thm)],[c_0_2927]) ).

cnf(c_0_4289,plain,
    c_in(c_SetInterval_OatLeastAtMost(X1,X2,tc_IntDef_Oint),c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)),
    inference(split_conjunct,[status(thm)],[c_0_2928]) ).

cnf(c_0_4290,plain,
    c_in(c_SetInterval_OatLeastAtMost(X1,X2,tc_nat),c_Finite__Set_OFinites,tc_set(tc_nat)),
    inference(split_conjunct,[status(thm)],[c_0_2929]) ).

cnf(c_0_4291,plain,
    ( c_Divides_Oop_Advd(c_uminus(X1,tc_IntDef_Oint),X2,tc_IntDef_Oint)
    | ~ c_Divides_Oop_Advd(X1,X2,tc_IntDef_Oint) ),
    inference(split_conjunct,[status(thm)],[c_0_2930]) ).

cnf(c_0_4292,plain,
    ( c_Divides_Oop_Advd(X1,c_uminus(X2,tc_IntDef_Oint),tc_IntDef_Oint)
    | ~ c_Divides_Oop_Advd(X1,X2,tc_IntDef_Oint) ),
    inference(split_conjunct,[status(thm)],[c_0_2931]) ).

cnf(c_0_4293,plain,
    ( X1 = X2
    | c_less(X1,X2,tc_set(X3))
    | ~ c_lessequals(X1,X2,tc_set(X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_2932]) ).

cnf(c_0_4294,plain,
    c_in(X1,c_insert(X1,c_emptyset,X2),X2),
    inference(split_conjunct,[status(thm)],[c_0_2933]) ).

cnf(c_0_4295,plain,
    c_Divides_Oop_Advd(X1,c_times(X2,X1,tc_IntDef_Oint),tc_IntDef_Oint),
    inference(split_conjunct,[status(thm)],[c_0_2934]) ).

cnf(c_0_4296,plain,
    c_Divides_Oop_Advd(X1,c_times(X1,X2,tc_IntDef_Oint),tc_IntDef_Oint),
    inference(split_conjunct,[status(thm)],[c_0_2935]) ).

cnf(c_0_4297,plain,
    c_Divides_Oop_Advd(X1,c_times(X2,X1,tc_nat),tc_nat),
    inference(split_conjunct,[status(thm)],[c_0_2936]) ).

cnf(c_0_4298,plain,
    c_Divides_Oop_Advd(X1,c_times(X1,X2,tc_nat),tc_nat),
    inference(split_conjunct,[status(thm)],[c_0_2937]) ).

cnf(c_0_4299,plain,
    ( c_lessequals(X1,X2,tc_set(X3))
    | ~ c_less(X1,X2,tc_set(X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_2938]) ).

cnf(c_0_4300,plain,
    ( c_less(X1,X2,tc_nat)
    | ~ c_less(c_Suc(X1),c_Suc(X2),tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_2939]) ).

cnf(c_0_4301,plain,
    ( c_lessequals(X1,X2,tc_nat)
    | ~ c_lessequals(c_Suc(X1),c_Suc(X2),tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_2940]) ).

cnf(c_0_4302,plain,
    ( c_less(c_Suc(X1),c_Suc(X2),tc_nat)
    | ~ c_less(X1,X2,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_2941]) ).

cnf(c_0_4303,plain,
    ( c_lessequals(c_Suc(X1),c_Suc(X2),tc_nat)
    | ~ c_lessequals(X1,X2,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_2942]) ).

cnf(c_0_4304,plain,
    ( c_in(X1,c_uminus(X2,tc_set(X3)),X3)
    | c_in(X1,X2,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_2943]) ).

cnf(c_0_4305,plain,
    ( c_Wellfounded__Recursion_Oacyclic(c_Relation_Oconverse(X1,X2,X2),X2)
    | ~ c_Wellfounded__Recursion_Oacyclic(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_2944]) ).

cnf(c_0_4306,plain,
    ( X1 = c_Datatype_Ooption_OSome(X2,X3)
    | ~ c_in(X2,c_Datatype_Oo2s(X1,X3),X3) ),
    inference(split_conjunct,[status(thm)],[c_0_2945]) ).

cnf(c_0_4307,plain,
    ~ c_less(c_0,c_Nat_Osize(c_List_Olist_ONil,tc_List_Olist(X1)),tc_nat),
    inference(split_conjunct,[status(thm)],[c_0_2946]) ).

cnf(c_0_4308,plain,
    c_in(X1,c_Datatype_Oo2s(c_Datatype_Ooption_OSome(X1,X2),X2),X2),
    inference(split_conjunct,[status(thm)],[c_0_2947]) ).

cnf(c_0_4309,plain,
    ( c_List_Oremdups(X1,X2) = X1
    | c_Nat_Osize(c_List_Oremdups(X1,X2),tc_List_Olist(X2)) != c_Nat_Osize(X1,tc_List_Olist(X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_2948]) ).

cnf(c_0_4310,plain,
    c_less(c_uminus(c_IntDef_Oint(c_Suc(X1)),tc_IntDef_Oint),c_IntDef_Oint(X2),tc_IntDef_Oint),
    inference(split_conjunct,[status(thm)],[c_0_2949]) ).

cnf(c_0_4311,plain,
    c_lessequals(c_uminus(c_IntDef_Oint(X1),tc_IntDef_Oint),c_IntDef_Oint(X2),tc_IntDef_Oint),
    inference(split_conjunct,[status(thm)],[c_0_2950]) ).

cnf(c_0_4312,plain,
    ~ c_less(X1,c_emptyset,tc_set(X2)),
    inference(split_conjunct,[status(thm)],[c_0_2951]) ).

cnf(c_0_4313,plain,
    ( ~ c_less(X1,X1,X2)
    | ~ class_Orderings_Oorder(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_2952]) ).

cnf(c_0_4314,plain,
    ( X1 = c_List_Olist_ONil
    | c_less(c_0,c_Nat_Osize(X1,tc_List_Olist(X2)),tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_2953]) ).

cnf(c_0_4315,plain,
    ( c_Nat_Osize(c_List_Oremdups(X1,X2),tc_List_Olist(X2)) = c_Nat_Osize(X1,tc_List_Olist(X2))
    | c_List_Oremdups(X1,X2) != X1 ),
    inference(split_conjunct,[status(thm)],[c_0_2954]) ).

cnf(c_0_4316,plain,
    ( X1 = c_0
    | ~ c_less(X1,c_Suc(c_0),tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_2955]) ).

cnf(c_0_4317,plain,
    ( X1 = c_List_Olist_ONil
    | X2 != c_append(X2,X1,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_2956]) ).

cnf(c_0_4318,plain,
    ( X1 = c_List_Olist_ONil
    | X2 != c_append(X1,X2,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_2957]) ).

cnf(c_0_4319,plain,
    ( X1 = c_List_Olist_ONil
    | c_append(X2,X1,X3) != X2 ),
    inference(split_conjunct,[status(thm)],[c_0_2958]) ).

cnf(c_0_4320,plain,
    ( X1 = c_List_Olist_ONil
    | c_append(X1,X2,X3) != X2 ),
    inference(split_conjunct,[status(thm)],[c_0_2959]) ).

cnf(c_0_4321,plain,
    ( X1 = c_emptyset
    | c_union(X2,X1,X3) != c_emptyset ),
    inference(split_conjunct,[status(thm)],[c_0_2960]) ).

cnf(c_0_4322,plain,
    ( X1 = c_emptyset
    | c_union(X1,X2,X3) != c_emptyset ),
    inference(split_conjunct,[status(thm)],[c_0_2961]) ).

cnf(c_0_4323,plain,
    ( X1 = c_List_Olist_ONil
    | c_append(X2,X1,X3) != c_List_Olist_ONil ),
    inference(split_conjunct,[status(thm)],[c_0_2962]) ).

cnf(c_0_4324,plain,
    ( X1 = c_List_Olist_ONil
    | c_append(X1,X2,X3) != c_List_Olist_ONil ),
    inference(split_conjunct,[status(thm)],[c_0_2963]) ).

cnf(c_0_4325,plain,
    ( X1 = c_List_Olist_ONil
    | c_List_Olist_ONil != c_append(X2,X1,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_2964]) ).

cnf(c_0_4326,plain,
    ( X1 = c_List_Olist_ONil
    | c_List_Olist_ONil != c_append(X1,X2,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_2965]) ).

cnf(c_0_4327,plain,
    ( X1 = c_emptyset
    | c_Equiv__Relations_Oquotient(X1,X2,X3) != c_emptyset ),
    inference(split_conjunct,[status(thm)],[c_0_2966]) ).

cnf(c_0_4328,plain,
    ( X1 = c_emptyset
    | c_emptyset != c_Equiv__Relations_Oquotient(X1,X2,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_2967]) ).

cnf(c_0_4329,plain,
    c_List_Olist_OCons(X1,X2,X3) != c_List_Olist_ONil,
    inference(split_conjunct,[status(thm)],[c_0_2968]) ).

cnf(c_0_4330,plain,
    c_List_Olist_ONil != c_List_Olist_OCons(X1,X2,X3),
    inference(split_conjunct,[status(thm)],[c_0_2969]) ).

cnf(c_0_4331,plain,
    ~ c_in(c_UNIV,c_Finite__Set_OFinites,tc_set(tc_nat)),
    inference(split_conjunct,[status(thm)],[c_0_2970]) ).

cnf(c_0_4332,plain,
    c_in(c_List_Olist_ONil,c_List_Olists(X1,X2),tc_List_Olist(X2)),
    inference(split_conjunct,[status(thm)],[c_0_2971]) ).

cnf(c_0_4333,plain,
    c_in(c_List_Oset(X1,X2),c_Finite__Set_OFinites,tc_set(X2)),
    inference(split_conjunct,[status(thm)],[c_0_2972]) ).

cnf(c_0_4334,plain,
    ( X1 = c_0
    | c_plus(X2,X1,tc_nat) != c_0 ),
    inference(split_conjunct,[status(thm)],[c_0_2973]) ).

cnf(c_0_4335,plain,
    ( X1 = c_0
    | c_plus(X1,X2,tc_nat) != c_0 ),
    inference(split_conjunct,[status(thm)],[c_0_2974]) ).

cnf(c_0_4336,plain,
    ~ c_less(X1,X1,tc_nat),
    inference(split_conjunct,[status(thm)],[c_0_2975]) ).

cnf(c_0_4337,plain,
    ~ c_in(X1,c_emptyset,X2),
    inference(split_conjunct,[status(thm)],[c_0_2976]) ).

cnf(c_0_4338,plain,
    ( X1 = c_0
    | ~ c_less(X1,c_1,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_2977]) ).

cnf(c_0_4339,plain,
    ( X1 = c_0
    | ~ c_lessequals(X1,c_0,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_2978]) ).

cnf(c_0_4340,plain,
    ( X1 = c_0
    | ~ c_Divides_Oop_Advd(c_0,X1,tc_IntDef_Oint) ),
    inference(split_conjunct,[status(thm)],[c_0_2979]) ).

cnf(c_0_4341,plain,
    ( X1 = c_0
    | ~ c_Divides_Oop_Advd(c_0,X1,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_2980]) ).

cnf(c_0_4342,plain,
    ~ c_less(X1,c_0,tc_nat),
    inference(split_conjunct,[status(thm)],[c_0_2981]) ).

cnf(c_0_4343,plain,
    c_in(c_SetInterval_OlessThan(X1,tc_nat),c_Finite__Set_OFinites,tc_set(tc_nat)),
    inference(split_conjunct,[status(thm)],[c_0_2982]) ).

cnf(c_0_4344,plain,
    c_in(c_SetInterval_OatMost(X1,tc_nat),c_Finite__Set_OFinites,tc_set(tc_nat)),
    inference(split_conjunct,[status(thm)],[c_0_2983]) ).

cnf(c_0_4345,plain,
    ~ c_less(c_0,c_0,tc_nat),
    inference(split_conjunct,[status(thm)],[c_0_2984]) ).

cnf(c_0_4346,plain,
    ( c_Wellfounded__Recursion_Owf(c_List_Olex(X1,X2),tc_List_Olist(X2))
    | ~ c_Wellfounded__Recursion_Owf(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_2985]) ).

cnf(c_0_4347,plain,
    ( c_Wellfounded__Recursion_Owf(c_List_Olenlex(X1,X2),tc_List_Olist(X2))
    | ~ c_Wellfounded__Recursion_Owf(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_2986]) ).

cnf(c_0_4348,plain,
    ( X1 = X2
    | c_uminus(X1,tc_set(X3)) != c_uminus(X2,tc_set(X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_2987]) ).

cnf(c_0_4349,plain,
    ( c_lessequals(X1,X1,X2)
    | ~ class_Orderings_Oorder(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_2988]) ).

cnf(c_0_4350,plain,
    c_lessequals(X1,X1,tc_set(X2)),
    inference(split_conjunct,[status(thm)],[c_0_2989]) ).

cnf(c_0_4351,plain,
    c_lessequals(c_emptyset,X1,tc_set(X2)),
    inference(split_conjunct,[status(thm)],[c_0_2990]) ).

cnf(c_0_4352,plain,
    c_less(X1,c_Suc(X1),tc_nat),
    inference(split_conjunct,[status(thm)],[c_0_2991]) ).

cnf(c_0_4353,plain,
    c_less(c_0,c_Suc(X1),tc_nat),
    inference(split_conjunct,[status(thm)],[c_0_2992]) ).

cnf(c_0_4354,plain,
    c_in(c_emptyset,c_Finite__Set_OFinites,tc_set(X1)),
    inference(split_conjunct,[status(thm)],[c_0_2993]) ).

cnf(c_0_4355,plain,
    c_Divides_Oop_Advd(c_Suc(c_0),X1,tc_nat),
    inference(split_conjunct,[status(thm)],[c_0_2994]) ).

cnf(c_0_4356,plain,
    c_less(c_0,c_Suc(c_0),tc_nat),
    inference(split_conjunct,[status(thm)],[c_0_2995]) ).

cnf(c_0_4357,plain,
    X1 = c_append(X1,c_List_Olist_ONil,X2),
    inference(split_conjunct,[status(thm)],[c_0_2996]) ).

cnf(c_0_4358,plain,
    X1 = c_append(c_List_Olist_ONil,X1,X2),
    inference(split_conjunct,[status(thm)],[c_0_2997]) ).

cnf(c_0_4359,plain,
    c_append(X1,c_List_Olist_ONil,X2) = X1,
    inference(split_conjunct,[status(thm)],[c_0_2998]) ).

cnf(c_0_4360,plain,
    c_append(c_List_Olist_ONil,X1,X2) = X1,
    inference(split_conjunct,[status(thm)],[c_0_2999]) ).

cnf(c_0_4361,plain,
    ( X1 = X2
    | c_SetInterval_OlessThan(X1,X3) != c_SetInterval_OlessThan(X2,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_3000]) ).

cnf(c_0_4362,plain,
    ( X1 = X2
    | c_SetInterval_OgreaterThan(X1,X3) != c_SetInterval_OgreaterThan(X2,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_3001]) ).

cnf(c_0_4363,plain,
    ( X1 = X2
    | c_SetInterval_OatMost(X1,X3) != c_SetInterval_OatMost(X2,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_3002]) ).

cnf(c_0_4364,plain,
    ( X1 = X2
    | c_SetInterval_OatLeast(X1,X3) != c_SetInterval_OatLeast(X2,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_3003]) ).

cnf(c_0_4365,plain,
    c_in(X1,c_UNIV,X2),
    inference(split_conjunct,[status(thm)],[c_0_3004]) ).

cnf(c_0_4366,plain,
    ( X1 = c_0
    | c_less(c_0,X1,tc_nat) ),
    inference(split_conjunct,[status(thm)],[c_0_3005]) ).

cnf(c_0_4367,plain,
    c_Equiv__Relations_Oquotient(c_emptyset,X1,X2) = c_emptyset,
    inference(split_conjunct,[status(thm)],[c_0_3006]) ).

cnf(c_0_4368,plain,
    c_emptyset = c_Equiv__Relations_Oquotient(c_emptyset,X1,X2),
    inference(split_conjunct,[status(thm)],[c_0_3007]) ).

cnf(c_0_4369,plain,
    c_lessequals(c_0,X1,tc_nat),
    inference(split_conjunct,[status(thm)],[c_0_3008]) ).

cnf(c_0_4370,plain,
    c_Divides_Oop_Advd(c_1,X1,tc_IntDef_Oint),
    inference(split_conjunct,[status(thm)],[c_0_3009]) ).

cnf(c_0_4371,plain,
    c_Divides_Oop_Advd(X1,c_0,tc_IntDef_Oint),
    inference(split_conjunct,[status(thm)],[c_0_3010]) ).

cnf(c_0_4372,plain,
    c_Divides_Oop_Advd(X1,c_0,tc_nat),
    inference(split_conjunct,[status(thm)],[c_0_3011]) ).

cnf(c_0_4373,plain,
    c_union(c_emptyset,c_emptyset,X1) = c_emptyset,
    inference(split_conjunct,[status(thm)],[c_0_3012]) ).

cnf(c_0_4374,plain,
    c_append(c_List_Olist_ONil,c_List_Olist_ONil,X1) = c_List_Olist_ONil,
    inference(split_conjunct,[status(thm)],[c_0_3013]) ).

cnf(c_0_4375,plain,
    c_List_Olist_ONil = c_append(c_List_Olist_ONil,c_List_Olist_ONil,X1),
    inference(split_conjunct,[status(thm)],[c_0_3014]) ).

cnf(c_0_4376,plain,
    c_less(c_0,c_1,tc_nat),
    inference(split_conjunct,[status(thm)],[c_0_3015]) ).

cnf(c_0_4377,plain,
    c_lessequals(c_0,c_0,tc_nat),
    inference(split_conjunct,[status(thm)],[c_0_3016]) ).

cnf(c_0_4378,plain,
    c_plus(c_0,c_0,tc_nat) = c_0,
    inference(split_conjunct,[status(thm)],[c_0_3017]) ).

cnf(c_0_4379,plain,
    c_Divides_Oop_Advd(c_0,c_0,tc_IntDef_Oint),
    inference(split_conjunct,[status(thm)],[c_0_3018]) ).

cnf(c_0_4380,plain,
    c_Divides_Oop_Advd(c_0,c_0,tc_nat),
    inference(split_conjunct,[status(thm)],[c_0_3019]) ).

cnf(c_0_4381,plain,
    ( X1 = X2
    | c_List_Orev(X1,X3) != c_List_Orev(X2,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_3020]) ).

cnf(c_0_4382,plain,
    ( X1 = X2
    | c_List_Ochar_OChar(X3,X1) != c_List_Ochar_OChar(X4,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_3021]) ).

cnf(c_0_4383,plain,
    ( X1 = X2
    | c_List_Ochar_OChar(X1,X3) != c_List_Ochar_OChar(X2,X4) ),
    inference(split_conjunct,[status(thm)],[c_0_3022]) ).

cnf(c_0_4384,plain,
    ( X1 = X2
    | c_Datatype_Ooption_OSome(X1,X3) != c_Datatype_Ooption_OSome(X2,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_3023]) ).

cnf(c_0_4385,plain,
    ( class_Finite__Set_Ofinite(tc_sum(X1,X2))
    | ~ class_Finite__Set_Ofinite(X1)
    | ~ class_Finite__Set_Ofinite(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_3024]) ).

cnf(c_0_4386,plain,
    ( class_Finite__Set_Ofinite(tc_prod(X1,X2))
    | ~ class_Finite__Set_Ofinite(X1)
    | ~ class_Finite__Set_Ofinite(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_3025]) ).

cnf(c_0_4387,plain,
    ( class_Finite__Set_Ofinite(tc_fun(X1,X2))
    | ~ class_Finite__Set_Ofinite(X1)
    | ~ class_Finite__Set_Ofinite(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_3026]) ).

cnf(c_0_4388,plain,
    ( X1 = c_Datatype_Ooption_OSome(c_Main_Onot__Some__eq__iff1__1(X1,X2),X2)
    | X1 = c_Datatype_Ooption_ONone ),
    inference(split_conjunct,[status(thm)],[c_0_3027]) ).

cnf(c_0_4389,plain,
    ( X1 = c_Datatype_Ooption_OSome(c_Main_Onot__None__eq__iff1__1(X1,X2),X2)
    | X1 = c_Datatype_Ooption_ONone ),
    inference(split_conjunct,[status(thm)],[c_0_3028]) ).

cnf(c_0_4390,plain,
    c_List_Odistinct(c_List_Oremdups(X1,X2),X2),
    inference(split_conjunct,[status(thm)],[c_0_3029]) ).

cnf(c_0_4391,plain,
    ( X1 = c_List_Olist_ONil
    | c_Nat_Osize(X1,tc_List_Olist(X2)) != c_0 ),
    inference(split_conjunct,[status(thm)],[c_0_3030]) ).

cnf(c_0_4392,plain,
    class_Nat_Opower(tc_fun(X1,X2)),
    inference(split_conjunct,[status(thm)],[c_0_3031]) ).

cnf(c_0_4393,plain,
    ( X1 = c_List_Olist_ONil
    | c_List_Oset(X1,X2) != c_emptyset ),
    inference(split_conjunct,[status(thm)],[c_0_3032]) ).

cnf(c_0_4394,plain,
    ( X1 = c_List_Olist_ONil
    | c_emptyset != c_List_Oset(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_3033]) ).

cnf(c_0_4395,plain,
    ( X1 = c_List_Olist_ONil
    | c_List_Orev(X1,X2) != c_List_Olist_ONil ),
    inference(split_conjunct,[status(thm)],[c_0_3034]) ).

cnf(c_0_4396,plain,
    ( X1 = c_List_Olist_ONil
    | c_List_Olist_ONil != c_List_Orev(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_3035]) ).

cnf(c_0_4397,plain,
    c_Datatype_Ooption_OSome(X1,X2) != c_Datatype_Ooption_ONone,
    inference(split_conjunct,[status(thm)],[c_0_3036]) ).

cnf(c_0_4398,plain,
    c_Datatype_Ooption_ONone != c_Datatype_Ooption_OSome(X1,X2),
    inference(split_conjunct,[status(thm)],[c_0_3037]) ).

cnf(c_0_4399,plain,
    c_Nat_Osize(c_List_Olist_ONil,tc_List_Olist(X1)) = c_0,
    inference(split_conjunct,[status(thm)],[c_0_3038]) ).

cnf(c_0_4400,plain,
    ( class_Finite__Set_Ofinite(tc_set(X1))
    | ~ class_Finite__Set_Ofinite(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3039]) ).

cnf(c_0_4401,plain,
    ( class_Finite__Set_Ofinite(tc_Datatype_Ooption(X1))
    | ~ class_Finite__Set_Ofinite(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3040]) ).

cnf(c_0_4402,plain,
    ( X1 = X2
    | c_Suc(X1) != c_Suc(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_3041]) ).

cnf(c_0_4403,plain,
    ( X1 = X2
    | c_IntDef_Oint(X1) != c_IntDef_Oint(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_3042]) ).

cnf(c_0_4404,plain,
    c_Wellfounded__Recursion_Owf(c_emptyset,X1),
    inference(split_conjunct,[status(thm)],[c_0_3043]) ).

cnf(c_0_4405,plain,
    c_List_Oset(c_List_Olist_ONil,X1) = c_emptyset,
    inference(split_conjunct,[status(thm)],[c_0_3044]) ).

cnf(c_0_4406,plain,
    c_emptyset = c_List_Oset(c_List_Olist_ONil,X1),
    inference(split_conjunct,[status(thm)],[c_0_3045]) ).

cnf(c_0_4407,plain,
    c_List_Orev(c_List_Olist_ONil,X1) = c_List_Olist_ONil,
    inference(split_conjunct,[status(thm)],[c_0_3046]) ).

cnf(c_0_4408,plain,
    c_List_Olist_ONil = c_List_Orev(c_List_Olist_ONil,X1),
    inference(split_conjunct,[status(thm)],[c_0_3047]) ).

cnf(c_0_4409,plain,
    ( class_Orderings_Olinorder(X1)
    | ~ class_Wellfounded__Recursion_Owellorder(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3048]) ).

cnf(c_0_4410,plain,
    ( class_LOrder_Olorder(X1)
    | ~ class_Wellfounded__Recursion_Owellorder(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3049]) ).

cnf(c_0_4411,plain,
    ( class_LOrder_Ojoin__semilorder(X1)
    | ~ class_Wellfounded__Recursion_Owellorder(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3050]) ).

cnf(c_0_4412,plain,
    ( class_LOrder_Omeet__semilorder(X1)
    | ~ class_Wellfounded__Recursion_Owellorder(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3051]) ).

cnf(c_0_4413,plain,
    ( class_Orderings_Oorder(X1)
    | ~ class_Wellfounded__Recursion_Owellorder(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3052]) ).

cnf(c_0_4414,plain,
    ( class_Orderings_Oord(X1)
    | ~ class_Wellfounded__Recursion_Owellorder(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3053]) ).

cnf(c_0_4415,plain,
    ( class_OrderedGroup_Omonoid__mult(X1)
    | ~ class_Ring__and__Field_Osemiring__1__cancel(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3054]) ).

cnf(c_0_4416,plain,
    ( class_HOL_Oplus(X1)
    | ~ class_Ring__and__Field_Osemiring__1__cancel(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3055]) ).

cnf(c_0_4417,plain,
    ( class_OrderedGroup_Osemigroup__add(X1)
    | ~ class_Ring__and__Field_Osemiring__1__cancel(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3056]) ).

cnf(c_0_4418,plain,
    ( class_OrderedGroup_Oab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Osemiring__1__cancel(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3057]) ).

cnf(c_0_4419,plain,
    ( class_HOL_Ozero(X1)
    | ~ class_Ring__and__Field_Osemiring__1__cancel(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3058]) ).

cnf(c_0_4420,plain,
    ( class_OrderedGroup_Ocomm__monoid__add(X1)
    | ~ class_Ring__and__Field_Osemiring__1__cancel(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3059]) ).

cnf(c_0_4421,plain,
    ( class_Ring__and__Field_Osemiring(X1)
    | ~ class_Ring__and__Field_Osemiring__1__cancel(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3060]) ).

cnf(c_0_4422,plain,
    ( class_Ring__and__Field_Osemiring__0(X1)
    | ~ class_Ring__and__Field_Osemiring__1__cancel(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3061]) ).

cnf(c_0_4423,plain,
    ( class_Ring__and__Field_Osemiring__0__cancel(X1)
    | ~ class_Ring__and__Field_Osemiring__1__cancel(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3062]) ).

cnf(c_0_4424,plain,
    ( class_OrderedGroup_Ocancel__semigroup__add(X1)
    | ~ class_Ring__and__Field_Osemiring__1__cancel(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3063]) ).

cnf(c_0_4425,plain,
    ( class_OrderedGroup_Ocancel__ab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Osemiring__1__cancel(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3064]) ).

cnf(c_0_4426,plain,
    ( class_HOL_Otimes(X1)
    | ~ class_Ring__and__Field_Osemiring__1__cancel(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3065]) ).

cnf(c_0_4427,plain,
    ( class_OrderedGroup_Osemigroup__mult(X1)
    | ~ class_Ring__and__Field_Osemiring__1__cancel(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3066]) ).

cnf(c_0_4428,plain,
    ( class_HOL_Oone(X1)
    | ~ class_Ring__and__Field_Osemiring__1__cancel(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3067]) ).

cnf(c_0_4429,plain,
    ( class_Ring__and__Field_Oaxclass__0__neq__1(X1)
    | ~ class_Ring__and__Field_Osemiring__1__cancel(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3068]) ).

cnf(c_0_4430,plain,
    ( class_Ring__and__Field_Osemiring__1(X1)
    | ~ class_Ring__and__Field_Osemiring__1__cancel(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3069]) ).

cnf(c_0_4431,plain,
    ( class_OrderedGroup_Osemigroup__add(X1)
    | ~ class_Ring__and__Field_Osemiring__1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3070]) ).

cnf(c_0_4432,plain,
    ( class_OrderedGroup_Oab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Osemiring__1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3071]) ).

cnf(c_0_4433,plain,
    ( class_OrderedGroup_Ocomm__monoid__add(X1)
    | ~ class_Ring__and__Field_Osemiring__1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3072]) ).

cnf(c_0_4434,plain,
    ( class_HOL_Otimes(X1)
    | ~ class_Ring__and__Field_Osemiring__1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3073]) ).

cnf(c_0_4435,plain,
    ( class_OrderedGroup_Osemigroup__mult(X1)
    | ~ class_Ring__and__Field_Osemiring__1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3074]) ).

cnf(c_0_4436,plain,
    ( class_Ring__and__Field_Osemiring(X1)
    | ~ class_Ring__and__Field_Osemiring__1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3075]) ).

cnf(c_0_4437,plain,
    ( class_Ring__and__Field_Osemiring__0(X1)
    | ~ class_Ring__and__Field_Osemiring__1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3076]) ).

cnf(c_0_4438,plain,
    ( class_HOL_Oone(X1)
    | ~ class_Ring__and__Field_Osemiring__1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3077]) ).

cnf(c_0_4439,plain,
    ( class_OrderedGroup_Omonoid__mult(X1)
    | ~ class_Ring__and__Field_Osemiring__1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3078]) ).

cnf(c_0_4440,plain,
    ( class_HOL_Oplus(X1)
    | ~ class_Ring__and__Field_Osemiring__1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3079]) ).

cnf(c_0_4441,plain,
    ( class_HOL_Ozero(X1)
    | ~ class_Ring__and__Field_Osemiring__1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3080]) ).

cnf(c_0_4442,plain,
    ( class_Ring__and__Field_Oaxclass__0__neq__1(X1)
    | ~ class_Ring__and__Field_Osemiring__1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3081]) ).

cnf(c_0_4443,plain,
    ( class_OrderedGroup_Ocancel__ab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Osemiring__0__cancel(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3082]) ).

cnf(c_0_4444,plain,
    ( class_HOL_Ozero(X1)
    | ~ class_Ring__and__Field_Osemiring__0__cancel(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3083]) ).

cnf(c_0_4445,plain,
    ( class_HOL_Oplus(X1)
    | ~ class_Ring__and__Field_Osemiring__0__cancel(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3084]) ).

cnf(c_0_4446,plain,
    ( class_OrderedGroup_Osemigroup__add(X1)
    | ~ class_Ring__and__Field_Osemiring__0__cancel(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3085]) ).

cnf(c_0_4447,plain,
    ( class_OrderedGroup_Oab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Osemiring__0__cancel(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3086]) ).

cnf(c_0_4448,plain,
    ( class_OrderedGroup_Ocomm__monoid__add(X1)
    | ~ class_Ring__and__Field_Osemiring__0__cancel(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3087]) ).

cnf(c_0_4449,plain,
    ( class_HOL_Otimes(X1)
    | ~ class_Ring__and__Field_Osemiring__0__cancel(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3088]) ).

cnf(c_0_4450,plain,
    ( class_OrderedGroup_Osemigroup__mult(X1)
    | ~ class_Ring__and__Field_Osemiring__0__cancel(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3089]) ).

cnf(c_0_4451,plain,
    ( class_OrderedGroup_Ocancel__semigroup__add(X1)
    | ~ class_Ring__and__Field_Osemiring__0__cancel(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3090]) ).

cnf(c_0_4452,plain,
    ( class_Ring__and__Field_Osemiring(X1)
    | ~ class_Ring__and__Field_Osemiring__0__cancel(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3091]) ).

cnf(c_0_4453,plain,
    ( class_Ring__and__Field_Osemiring__0(X1)
    | ~ class_Ring__and__Field_Osemiring__0__cancel(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3092]) ).

cnf(c_0_4454,plain,
    ( class_HOL_Ozero(X1)
    | ~ class_Ring__and__Field_Osemiring__0(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3093]) ).

cnf(c_0_4455,plain,
    ( class_OrderedGroup_Ocomm__monoid__add(X1)
    | ~ class_Ring__and__Field_Osemiring__0(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3094]) ).

cnf(c_0_4456,plain,
    ( class_HOL_Otimes(X1)
    | ~ class_Ring__and__Field_Osemiring__0(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3095]) ).

cnf(c_0_4457,plain,
    ( class_OrderedGroup_Osemigroup__mult(X1)
    | ~ class_Ring__and__Field_Osemiring__0(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3096]) ).

cnf(c_0_4458,plain,
    ( class_HOL_Oplus(X1)
    | ~ class_Ring__and__Field_Osemiring__0(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3097]) ).

cnf(c_0_4459,plain,
    ( class_OrderedGroup_Osemigroup__add(X1)
    | ~ class_Ring__and__Field_Osemiring__0(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3098]) ).

cnf(c_0_4460,plain,
    ( class_OrderedGroup_Oab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Osemiring__0(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3099]) ).

cnf(c_0_4461,plain,
    ( class_Ring__and__Field_Osemiring(X1)
    | ~ class_Ring__and__Field_Osemiring__0(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3100]) ).

cnf(c_0_4462,plain,
    ( class_HOL_Otimes(X1)
    | ~ class_Ring__and__Field_Osemiring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3101]) ).

cnf(c_0_4463,plain,
    ( class_OrderedGroup_Osemigroup__mult(X1)
    | ~ class_Ring__and__Field_Osemiring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3102]) ).

cnf(c_0_4464,plain,
    ( class_HOL_Oplus(X1)
    | ~ class_Ring__and__Field_Osemiring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3103]) ).

cnf(c_0_4465,plain,
    ( class_OrderedGroup_Osemigroup__add(X1)
    | ~ class_Ring__and__Field_Osemiring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3104]) ).

cnf(c_0_4466,plain,
    ( class_OrderedGroup_Oab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Osemiring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3105]) ).

cnf(c_0_4467,plain,
    ( class_HOL_Otimes(X1)
    | ~ class_Ring__and__Field_Oring__1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3106]) ).

cnf(c_0_4468,plain,
    ( class_OrderedGroup_Osemigroup__mult(X1)
    | ~ class_Ring__and__Field_Oring__1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3107]) ).

cnf(c_0_4469,plain,
    ( class_Ring__and__Field_Osemiring(X1)
    | ~ class_Ring__and__Field_Oring__1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3108]) ).

cnf(c_0_4470,plain,
    ( class_Ring__and__Field_Osemiring__0(X1)
    | ~ class_Ring__and__Field_Oring__1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3109]) ).

cnf(c_0_4471,plain,
    ( class_OrderedGroup_Ocancel__semigroup__add(X1)
    | ~ class_Ring__and__Field_Oring__1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3110]) ).

cnf(c_0_4472,plain,
    ( class_OrderedGroup_Ocancel__ab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Oring__1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3111]) ).

cnf(c_0_4473,plain,
    ( class_Ring__and__Field_Osemiring__0__cancel(X1)
    | ~ class_Ring__and__Field_Oring__1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3112]) ).

cnf(c_0_4474,plain,
    ( class_HOL_Ominus(X1)
    | ~ class_Ring__and__Field_Oring__1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3113]) ).

cnf(c_0_4475,plain,
    ( class_Ring__and__Field_Osemiring__1__cancel(X1)
    | ~ class_Ring__and__Field_Oring__1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3114]) ).

cnf(c_0_4476,plain,
    ( class_HOL_Oone(X1)
    | ~ class_Ring__and__Field_Oring__1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3115]) ).

cnf(c_0_4477,plain,
    ( class_OrderedGroup_Omonoid__mult(X1)
    | ~ class_Ring__and__Field_Oring__1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3116]) ).

cnf(c_0_4478,plain,
    ( class_Ring__and__Field_Oaxclass__0__neq__1(X1)
    | ~ class_Ring__and__Field_Oring__1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3117]) ).

cnf(c_0_4479,plain,
    ( class_Ring__and__Field_Osemiring__1(X1)
    | ~ class_Ring__and__Field_Oring__1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3118]) ).

cnf(c_0_4480,plain,
    ( class_HOL_Ozero(X1)
    | ~ class_Ring__and__Field_Oring__1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3119]) ).

cnf(c_0_4481,plain,
    ( class_HOL_Oplus(X1)
    | ~ class_Ring__and__Field_Oring__1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3120]) ).

cnf(c_0_4482,plain,
    ( class_OrderedGroup_Osemigroup__add(X1)
    | ~ class_Ring__and__Field_Oring__1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3121]) ).

cnf(c_0_4483,plain,
    ( class_OrderedGroup_Oab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Oring__1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3122]) ).

cnf(c_0_4484,plain,
    ( class_OrderedGroup_Ocomm__monoid__add(X1)
    | ~ class_Ring__and__Field_Oring__1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3123]) ).

cnf(c_0_4485,plain,
    ( class_OrderedGroup_Oab__group__add(X1)
    | ~ class_Ring__and__Field_Oring__1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3124]) ).

cnf(c_0_4486,plain,
    ( class_Ring__and__Field_Oring(X1)
    | ~ class_Ring__and__Field_Oring__1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3125]) ).

cnf(c_0_4487,plain,
    ( class_HOL_Ozero(X1)
    | ~ class_Ring__and__Field_Oring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3126]) ).

cnf(c_0_4488,plain,
    ( class_OrderedGroup_Ocomm__monoid__add(X1)
    | ~ class_Ring__and__Field_Oring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3127]) ).

cnf(c_0_4489,plain,
    ( class_HOL_Ominus(X1)
    | ~ class_Ring__and__Field_Oring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3128]) ).

cnf(c_0_4490,plain,
    ( class_OrderedGroup_Oab__group__add(X1)
    | ~ class_Ring__and__Field_Oring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3129]) ).

cnf(c_0_4491,plain,
    ( class_HOL_Otimes(X1)
    | ~ class_Ring__and__Field_Oring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3130]) ).

cnf(c_0_4492,plain,
    ( class_OrderedGroup_Osemigroup__mult(X1)
    | ~ class_Ring__and__Field_Oring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3131]) ).

cnf(c_0_4493,plain,
    ( class_HOL_Oplus(X1)
    | ~ class_Ring__and__Field_Oring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3132]) ).

cnf(c_0_4494,plain,
    ( class_OrderedGroup_Osemigroup__add(X1)
    | ~ class_Ring__and__Field_Oring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3133]) ).

cnf(c_0_4495,plain,
    ( class_Ring__and__Field_Osemiring__0(X1)
    | ~ class_Ring__and__Field_Oring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3134]) ).

cnf(c_0_4496,plain,
    ( class_Ring__and__Field_Osemiring__0__cancel(X1)
    | ~ class_Ring__and__Field_Oring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3135]) ).

cnf(c_0_4497,plain,
    ( class_OrderedGroup_Ocancel__semigroup__add(X1)
    | ~ class_Ring__and__Field_Oring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3136]) ).

cnf(c_0_4498,plain,
    ( class_OrderedGroup_Ocancel__ab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Oring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3137]) ).

cnf(c_0_4499,plain,
    ( class_OrderedGroup_Oab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Oring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3138]) ).

cnf(c_0_4500,plain,
    ( class_Ring__and__Field_Osemiring(X1)
    | ~ class_Ring__and__Field_Oring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3139]) ).

cnf(c_0_4501,plain,
    ( class_OrderedGroup_Opordered__ab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Opordered__semiring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3140]) ).

cnf(c_0_4502,plain,
    ( class_HOL_Ozero(X1)
    | ~ class_Ring__and__Field_Opordered__semiring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3141]) ).

cnf(c_0_4503,plain,
    ( class_HOL_Oplus(X1)
    | ~ class_Ring__and__Field_Opordered__semiring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3142]) ).

cnf(c_0_4504,plain,
    ( class_OrderedGroup_Osemigroup__add(X1)
    | ~ class_Ring__and__Field_Opordered__semiring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3143]) ).

cnf(c_0_4505,plain,
    ( class_OrderedGroup_Oab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Opordered__semiring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3144]) ).

cnf(c_0_4506,plain,
    ( class_OrderedGroup_Ocomm__monoid__add(X1)
    | ~ class_Ring__and__Field_Opordered__semiring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3145]) ).

cnf(c_0_4507,plain,
    ( class_HOL_Otimes(X1)
    | ~ class_Ring__and__Field_Opordered__semiring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3146]) ).

cnf(c_0_4508,plain,
    ( class_OrderedGroup_Osemigroup__mult(X1)
    | ~ class_Ring__and__Field_Opordered__semiring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3147]) ).

cnf(c_0_4509,plain,
    ( class_Orderings_Oord(X1)
    | ~ class_Ring__and__Field_Opordered__semiring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3148]) ).

cnf(c_0_4510,plain,
    ( class_Orderings_Oorder(X1)
    | ~ class_Ring__and__Field_Opordered__semiring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3149]) ).

cnf(c_0_4511,plain,
    ( class_Ring__and__Field_Osemiring(X1)
    | ~ class_Ring__and__Field_Opordered__semiring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3150]) ).

cnf(c_0_4512,plain,
    ( class_Ring__and__Field_Osemiring__0(X1)
    | ~ class_Ring__and__Field_Opordered__semiring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3151]) ).

cnf(c_0_4513,plain,
    ( class_HOL_Otimes(X1)
    | ~ class_Ring__and__Field_Opordered__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3152]) ).

cnf(c_0_4514,plain,
    ( class_OrderedGroup_Osemigroup__mult(X1)
    | ~ class_Ring__and__Field_Opordered__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3153]) ).

cnf(c_0_4515,plain,
    ( class_Ring__and__Field_Osemiring(X1)
    | ~ class_Ring__and__Field_Opordered__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3154]) ).

cnf(c_0_4516,plain,
    ( class_Ring__and__Field_Osemiring__0(X1)
    | ~ class_Ring__and__Field_Opordered__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3155]) ).

cnf(c_0_4517,plain,
    ( class_OrderedGroup_Ocancel__semigroup__add(X1)
    | ~ class_Ring__and__Field_Opordered__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3156]) ).

cnf(c_0_4518,plain,
    ( class_OrderedGroup_Ocancel__ab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Opordered__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3157]) ).

cnf(c_0_4519,plain,
    ( class_Ring__and__Field_Osemiring__0__cancel(X1)
    | ~ class_Ring__and__Field_Opordered__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3158]) ).

cnf(c_0_4520,plain,
    ( class_Ring__and__Field_Opordered__cancel__semiring(X1)
    | ~ class_Ring__and__Field_Opordered__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3159]) ).

cnf(c_0_4521,plain,
    ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Opordered__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3160]) ).

cnf(c_0_4522,plain,
    ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
    | ~ class_Ring__and__Field_Opordered__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3161]) ).

cnf(c_0_4523,plain,
    ( class_HOL_Ominus(X1)
    | ~ class_Ring__and__Field_Opordered__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3162]) ).

cnf(c_0_4524,plain,
    ( class_OrderedGroup_Opordered__ab__group__add(X1)
    | ~ class_Ring__and__Field_Opordered__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3163]) ).

cnf(c_0_4525,plain,
    ( class_Orderings_Oord(X1)
    | ~ class_Ring__and__Field_Opordered__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3164]) ).

cnf(c_0_4526,plain,
    ( class_Orderings_Oorder(X1)
    | ~ class_Ring__and__Field_Opordered__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3165]) ).

cnf(c_0_4527,plain,
    ( class_OrderedGroup_Opordered__ab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Opordered__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3166]) ).

cnf(c_0_4528,plain,
    ( class_Ring__and__Field_Opordered__semiring(X1)
    | ~ class_Ring__and__Field_Opordered__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3167]) ).

cnf(c_0_4529,plain,
    ( class_HOL_Ozero(X1)
    | ~ class_Ring__and__Field_Opordered__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3168]) ).

cnf(c_0_4530,plain,
    ( class_HOL_Oplus(X1)
    | ~ class_Ring__and__Field_Opordered__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3169]) ).

cnf(c_0_4531,plain,
    ( class_OrderedGroup_Osemigroup__add(X1)
    | ~ class_Ring__and__Field_Opordered__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3170]) ).

cnf(c_0_4532,plain,
    ( class_OrderedGroup_Oab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Opordered__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3171]) ).

cnf(c_0_4533,plain,
    ( class_OrderedGroup_Ocomm__monoid__add(X1)
    | ~ class_Ring__and__Field_Opordered__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3172]) ).

cnf(c_0_4534,plain,
    ( class_OrderedGroup_Oab__group__add(X1)
    | ~ class_Ring__and__Field_Opordered__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3173]) ).

cnf(c_0_4535,plain,
    ( class_Ring__and__Field_Oring(X1)
    | ~ class_Ring__and__Field_Opordered__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3174]) ).

cnf(c_0_4536,plain,
    ( class_OrderedGroup_Osemigroup__add(X1)
    | ~ class_Ring__and__Field_Opordered__comm__semiring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3175]) ).

cnf(c_0_4537,plain,
    ( class_OrderedGroup_Oab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Opordered__comm__semiring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3176]) ).

cnf(c_0_4538,plain,
    ( class_OrderedGroup_Ocomm__monoid__add(X1)
    | ~ class_Ring__and__Field_Opordered__comm__semiring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3177]) ).

cnf(c_0_4539,plain,
    ( class_HOL_Otimes(X1)
    | ~ class_Ring__and__Field_Opordered__comm__semiring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3178]) ).

cnf(c_0_4540,plain,
    ( class_OrderedGroup_Osemigroup__mult(X1)
    | ~ class_Ring__and__Field_Opordered__comm__semiring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3179]) ).

cnf(c_0_4541,plain,
    ( class_Ring__and__Field_Osemiring(X1)
    | ~ class_Ring__and__Field_Opordered__comm__semiring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3180]) ).

cnf(c_0_4542,plain,
    ( class_Ring__and__Field_Osemiring__0(X1)
    | ~ class_Ring__and__Field_Opordered__comm__semiring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3181]) ).

cnf(c_0_4543,plain,
    ( class_OrderedGroup_Oab__semigroup__mult(X1)
    | ~ class_Ring__and__Field_Opordered__comm__semiring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3182]) ).

cnf(c_0_4544,plain,
    ( class_Ring__and__Field_Opordered__semiring(X1)
    | ~ class_Ring__and__Field_Opordered__comm__semiring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3183]) ).

cnf(c_0_4545,plain,
    ( class_Orderings_Oord(X1)
    | ~ class_Ring__and__Field_Opordered__comm__semiring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3184]) ).

cnf(c_0_4546,plain,
    ( class_Orderings_Oorder(X1)
    | ~ class_Ring__and__Field_Opordered__comm__semiring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3185]) ).

cnf(c_0_4547,plain,
    ( class_OrderedGroup_Opordered__ab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Opordered__comm__semiring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3186]) ).

cnf(c_0_4548,plain,
    ( class_HOL_Ozero(X1)
    | ~ class_Ring__and__Field_Opordered__comm__semiring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3187]) ).

cnf(c_0_4549,plain,
    ( class_HOL_Oplus(X1)
    | ~ class_Ring__and__Field_Opordered__comm__semiring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3188]) ).

cnf(c_0_4550,plain,
    ( class_Ring__and__Field_Ocomm__semiring(X1)
    | ~ class_Ring__and__Field_Opordered__comm__semiring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3189]) ).

cnf(c_0_4551,plain,
    ( class_Ring__and__Field_Ocomm__semiring__0(X1)
    | ~ class_Ring__and__Field_Opordered__comm__semiring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3190]) ).

cnf(c_0_4552,plain,
    ( class_Ring__and__Field_Osemiring__0(X1)
    | ~ class_Ring__and__Field_Opordered__comm__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3191]) ).

cnf(c_0_4553,plain,
    ( class_Ring__and__Field_Osemiring__0__cancel(X1)
    | ~ class_Ring__and__Field_Opordered__comm__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3192]) ).

cnf(c_0_4554,plain,
    ( class_OrderedGroup_Oab__semigroup__mult(X1)
    | ~ class_Ring__and__Field_Opordered__comm__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3193]) ).

cnf(c_0_4555,plain,
    ( class_Ring__and__Field_Ocomm__semiring(X1)
    | ~ class_Ring__and__Field_Opordered__comm__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3194]) ).

cnf(c_0_4556,plain,
    ( class_Ring__and__Field_Ocomm__semiring__0(X1)
    | ~ class_Ring__and__Field_Opordered__comm__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3195]) ).

cnf(c_0_4557,plain,
    ( class_Ring__and__Field_Ocomm__semiring__0__cancel(X1)
    | ~ class_Ring__and__Field_Opordered__comm__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3196]) ).

cnf(c_0_4558,plain,
    ( class_HOL_Ominus(X1)
    | ~ class_Ring__and__Field_Opordered__comm__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3197]) ).

cnf(c_0_4559,plain,
    ( class_Orderings_Oord(X1)
    | ~ class_Ring__and__Field_Opordered__comm__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3198]) ).

cnf(c_0_4560,plain,
    ( class_Orderings_Oorder(X1)
    | ~ class_Ring__and__Field_Opordered__comm__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3199]) ).

cnf(c_0_4561,plain,
    ( class_OrderedGroup_Opordered__ab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Opordered__comm__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3200]) ).

cnf(c_0_4562,plain,
    ( class_Ring__and__Field_Opordered__semiring(X1)
    | ~ class_Ring__and__Field_Opordered__comm__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3201]) ).

cnf(c_0_4563,plain,
    ( class_Ring__and__Field_Opordered__comm__semiring(X1)
    | ~ class_Ring__and__Field_Opordered__comm__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3202]) ).

cnf(c_0_4564,plain,
    ( class_OrderedGroup_Oab__group__add(X1)
    | ~ class_Ring__and__Field_Opordered__comm__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3203]) ).

cnf(c_0_4565,plain,
    ( class_HOL_Oplus(X1)
    | ~ class_Ring__and__Field_Opordered__comm__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3204]) ).

cnf(c_0_4566,plain,
    ( class_OrderedGroup_Osemigroup__add(X1)
    | ~ class_Ring__and__Field_Opordered__comm__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3205]) ).

cnf(c_0_4567,plain,
    ( class_OrderedGroup_Ocancel__semigroup__add(X1)
    | ~ class_Ring__and__Field_Opordered__comm__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3206]) ).

cnf(c_0_4568,plain,
    ( class_OrderedGroup_Oab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Opordered__comm__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3207]) ).

cnf(c_0_4569,plain,
    ( class_OrderedGroup_Ocancel__ab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Opordered__comm__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3208]) ).

cnf(c_0_4570,plain,
    ( class_HOL_Ozero(X1)
    | ~ class_Ring__and__Field_Opordered__comm__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3209]) ).

cnf(c_0_4571,plain,
    ( class_OrderedGroup_Ocomm__monoid__add(X1)
    | ~ class_Ring__and__Field_Opordered__comm__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3210]) ).

cnf(c_0_4572,plain,
    ( class_HOL_Otimes(X1)
    | ~ class_Ring__and__Field_Opordered__comm__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3211]) ).

cnf(c_0_4573,plain,
    ( class_OrderedGroup_Osemigroup__mult(X1)
    | ~ class_Ring__and__Field_Opordered__comm__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3212]) ).

cnf(c_0_4574,plain,
    ( class_Ring__and__Field_Osemiring(X1)
    | ~ class_Ring__and__Field_Opordered__comm__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3213]) ).

cnf(c_0_4575,plain,
    ( class_Ring__and__Field_Oring(X1)
    | ~ class_Ring__and__Field_Opordered__comm__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3214]) ).

cnf(c_0_4576,plain,
    ( class_Ring__and__Field_Ocomm__ring(X1)
    | ~ class_Ring__and__Field_Opordered__comm__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3215]) ).

cnf(c_0_4577,plain,
    ( class_OrderedGroup_Osemigroup__add(X1)
    | ~ class_Ring__and__Field_Opordered__cancel__semiring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3216]) ).

cnf(c_0_4578,plain,
    ( class_OrderedGroup_Oab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Opordered__cancel__semiring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3217]) ).

cnf(c_0_4579,plain,
    ( class_OrderedGroup_Opordered__ab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Opordered__cancel__semiring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3218]) ).

cnf(c_0_4580,plain,
    ( class_HOL_Ozero(X1)
    | ~ class_Ring__and__Field_Opordered__cancel__semiring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3219]) ).

cnf(c_0_4581,plain,
    ( class_OrderedGroup_Ocomm__monoid__add(X1)
    | ~ class_Ring__and__Field_Opordered__cancel__semiring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3220]) ).

cnf(c_0_4582,plain,
    ( class_HOL_Otimes(X1)
    | ~ class_Ring__and__Field_Opordered__cancel__semiring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3221]) ).

cnf(c_0_4583,plain,
    ( class_OrderedGroup_Osemigroup__mult(X1)
    | ~ class_Ring__and__Field_Opordered__cancel__semiring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3222]) ).

cnf(c_0_4584,plain,
    ( class_Ring__and__Field_Osemiring(X1)
    | ~ class_Ring__and__Field_Opordered__cancel__semiring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3223]) ).

cnf(c_0_4585,plain,
    ( class_Ring__and__Field_Osemiring__0__cancel(X1)
    | ~ class_Ring__and__Field_Opordered__cancel__semiring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3224]) ).

cnf(c_0_4586,plain,
    ( class_OrderedGroup_Ocancel__semigroup__add(X1)
    | ~ class_Ring__and__Field_Opordered__cancel__semiring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3225]) ).

cnf(c_0_4587,plain,
    ( class_OrderedGroup_Ocancel__ab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Opordered__cancel__semiring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3226]) ).

cnf(c_0_4588,plain,
    ( class_Orderings_Oord(X1)
    | ~ class_Ring__and__Field_Opordered__cancel__semiring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3227]) ).

cnf(c_0_4589,plain,
    ( class_Orderings_Oorder(X1)
    | ~ class_Ring__and__Field_Opordered__cancel__semiring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3228]) ).

cnf(c_0_4590,plain,
    ( class_HOL_Oplus(X1)
    | ~ class_Ring__and__Field_Opordered__cancel__semiring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3229]) ).

cnf(c_0_4591,plain,
    ( class_Ring__and__Field_Osemiring__0(X1)
    | ~ class_Ring__and__Field_Opordered__cancel__semiring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3230]) ).

cnf(c_0_4592,plain,
    ( class_Ring__and__Field_Opordered__semiring(X1)
    | ~ class_Ring__and__Field_Opordered__cancel__semiring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3231]) ).

cnf(c_0_4593,plain,
    ( class_HOL_Ozero(X1)
    | ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3232]) ).

cnf(c_0_4594,plain,
    ( class_OrderedGroup_Ocomm__monoid__add(X1)
    | ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3233]) ).

cnf(c_0_4595,plain,
    ( class_HOL_Otimes(X1)
    | ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3234]) ).

cnf(c_0_4596,plain,
    ( class_OrderedGroup_Osemigroup__mult(X1)
    | ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3235]) ).

cnf(c_0_4597,plain,
    ( class_Ring__and__Field_Osemiring(X1)
    | ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3236]) ).

cnf(c_0_4598,plain,
    ( class_Ring__and__Field_Osemiring__0(X1)
    | ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3237]) ).

cnf(c_0_4599,plain,
    ( class_OrderedGroup_Oab__semigroup__mult(X1)
    | ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3238]) ).

cnf(c_0_4600,plain,
    ( class_Ring__and__Field_Osemiring__0__cancel(X1)
    | ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3239]) ).

cnf(c_0_4601,plain,
    ( class_Ring__and__Field_Ocomm__semiring(X1)
    | ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3240]) ).

cnf(c_0_4602,plain,
    ( class_Ring__and__Field_Opordered__cancel__semiring(X1)
    | ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3241]) ).

cnf(c_0_4603,plain,
    ( class_Ring__and__Field_Opordered__semiring(X1)
    | ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3242]) ).

cnf(c_0_4604,plain,
    ( class_OrderedGroup_Ocancel__semigroup__add(X1)
    | ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3243]) ).

cnf(c_0_4605,plain,
    ( class_OrderedGroup_Ocancel__ab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3244]) ).

cnf(c_0_4606,plain,
    ( class_Orderings_Oord(X1)
    | ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3245]) ).

cnf(c_0_4607,plain,
    ( class_Orderings_Oorder(X1)
    | ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3246]) ).

cnf(c_0_4608,plain,
    ( class_HOL_Oplus(X1)
    | ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3247]) ).

cnf(c_0_4609,plain,
    ( class_OrderedGroup_Osemigroup__add(X1)
    | ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3248]) ).

cnf(c_0_4610,plain,
    ( class_OrderedGroup_Oab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3249]) ).

cnf(c_0_4611,plain,
    ( class_OrderedGroup_Opordered__ab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3250]) ).

cnf(c_0_4612,plain,
    ( class_Ring__and__Field_Ocomm__semiring__0(X1)
    | ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3251]) ).

cnf(c_0_4613,plain,
    ( class_Ring__and__Field_Opordered__comm__semiring(X1)
    | ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3252]) ).

cnf(c_0_4614,plain,
    ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3253]) ).

cnf(c_0_4615,plain,
    ( class_HOL_Ozero(X1)
    | ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3254]) ).

cnf(c_0_4616,plain,
    ( class_HOL_Oplus(X1)
    | ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3255]) ).

cnf(c_0_4617,plain,
    ( class_OrderedGroup_Osemigroup__add(X1)
    | ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3256]) ).

cnf(c_0_4618,plain,
    ( class_OrderedGroup_Oab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3257]) ).

cnf(c_0_4619,plain,
    ( class_OrderedGroup_Ocomm__monoid__add(X1)
    | ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3258]) ).

cnf(c_0_4620,plain,
    ( class_HOL_Otimes(X1)
    | ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3259]) ).

cnf(c_0_4621,plain,
    ( class_Ring__and__Field_Opordered__semiring(X1)
    | ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3260]) ).

cnf(c_0_4622,plain,
    ( class_Ring__and__Field_Opordered__cancel__semiring(X1)
    | ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3261]) ).

cnf(c_0_4623,plain,
    ( class_Ring__and__Field_Osemiring__0__cancel(X1)
    | ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3262]) ).

cnf(c_0_4624,plain,
    ( class_OrderedGroup_Ocancel__semigroup__add(X1)
    | ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3263]) ).

cnf(c_0_4625,plain,
    ( class_OrderedGroup_Osemigroup__mult(X1)
    | ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3264]) ).

cnf(c_0_4626,plain,
    ( class_OrderedGroup_Ocancel__ab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3265]) ).

cnf(c_0_4627,plain,
    ( class_Orderings_Oord(X1)
    | ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3266]) ).

cnf(c_0_4628,plain,
    ( class_Orderings_Oorder(X1)
    | ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3267]) ).

cnf(c_0_4629,plain,
    ( class_OrderedGroup_Opordered__ab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3268]) ).

cnf(c_0_4630,plain,
    ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3269]) ).

cnf(c_0_4631,plain,
    ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
    | ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3270]) ).

cnf(c_0_4632,plain,
    ( class_LOrder_Omeet__semilorder(X1)
    | ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3271]) ).

cnf(c_0_4633,plain,
    ( class_LOrder_Ojoin__semilorder(X1)
    | ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3272]) ).

cnf(c_0_4634,plain,
    ( class_LOrder_Olorder(X1)
    | ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3273]) ).

cnf(c_0_4635,plain,
    ( class_Orderings_Olinorder(X1)
    | ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3274]) ).

cnf(c_0_4636,plain,
    ( class_Ring__and__Field_Osemiring(X1)
    | ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3275]) ).

cnf(c_0_4637,plain,
    ( class_Ring__and__Field_Osemiring__0(X1)
    | ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3276]) ).

cnf(c_0_4638,plain,
    ( class_Ring__and__Field_Ocomm__semiring__0(X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3277]) ).

cnf(c_0_4639,plain,
    ( class_Ring__and__Field_Ocomm__semiring__0__cancel(X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3278]) ).

cnf(c_0_4640,plain,
    ( class_HOL_Oone(X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3279]) ).

cnf(c_0_4641,plain,
    ( class_OrderedGroup_Omonoid__mult(X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3280]) ).

cnf(c_0_4642,plain,
    ( class_Ring__and__Field_Oaxclass__0__neq__1(X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3281]) ).

cnf(c_0_4643,plain,
    ( class_Ring__and__Field_Osemiring__1(X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3282]) ).

cnf(c_0_4644,plain,
    ( class_Orderings_Oord(X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3283]) ).

cnf(c_0_4645,plain,
    ( class_Orderings_Oorder(X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3284]) ).

cnf(c_0_4646,plain,
    ( class_OrderedGroup_Opordered__ab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3285]) ).

cnf(c_0_4647,plain,
    ( class_Ring__and__Field_Opordered__semiring(X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3286]) ).

cnf(c_0_4648,plain,
    ( class_Ring__and__Field_Opordered__comm__semiring(X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3287]) ).

cnf(c_0_4649,plain,
    ( class_Ring__and__Field_Opordered__cancel__semiring(X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3288]) ).

cnf(c_0_4650,plain,
    ( class_Ring__and__Field_Opordered__cancel__comm__semiring(X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3289]) ).

cnf(c_0_4651,plain,
    ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3290]) ).

cnf(c_0_4652,plain,
    ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3291]) ).

cnf(c_0_4653,plain,
    ( class_LOrder_Omeet__semilorder(X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3292]) ).

cnf(c_0_4654,plain,
    ( class_Ring__and__Field_Osemiring__1__cancel(X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3293]) ).

cnf(c_0_4655,plain,
    ( class_LOrder_Ojoin__semilorder(X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3294]) ).

cnf(c_0_4656,plain,
    ( class_LOrder_Olorder(X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3295]) ).

cnf(c_0_4657,plain,
    ( class_Orderings_Olinorder(X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3296]) ).

cnf(c_0_4658,plain,
    ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3297]) ).

cnf(c_0_4659,plain,
    ( class_Ring__and__Field_Oordered__semiring__strict(X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3298]) ).

cnf(c_0_4660,plain,
    ( class_Ring__and__Field_Oordered__comm__semiring__strict(X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3299]) ).

cnf(c_0_4661,plain,
    ( class_HOL_Oplus(X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3300]) ).

cnf(c_0_4662,plain,
    ( class_OrderedGroup_Osemigroup__add(X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3301]) ).

cnf(c_0_4663,plain,
    ( class_OrderedGroup_Ocancel__semigroup__add(X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3302]) ).

cnf(c_0_4664,plain,
    ( class_OrderedGroup_Oab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3303]) ).

cnf(c_0_4665,plain,
    ( class_OrderedGroup_Ocomm__monoid__mult(X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3304]) ).

cnf(c_0_4666,plain,
    ( class_OrderedGroup_Ocancel__ab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3305]) ).

cnf(c_0_4667,plain,
    ( class_HOL_Ozero(X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3306]) ).

cnf(c_0_4668,plain,
    ( class_OrderedGroup_Ocomm__monoid__add(X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3307]) ).

cnf(c_0_4669,plain,
    ( class_HOL_Otimes(X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3308]) ).

cnf(c_0_4670,plain,
    ( class_OrderedGroup_Osemigroup__mult(X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3309]) ).

cnf(c_0_4671,plain,
    ( class_Ring__and__Field_Osemiring(X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3310]) ).

cnf(c_0_4672,plain,
    ( class_Ring__and__Field_Osemiring__0(X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3311]) ).

cnf(c_0_4673,plain,
    ( class_Ring__and__Field_Osemiring__0__cancel(X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3312]) ).

cnf(c_0_4674,plain,
    ( class_OrderedGroup_Oab__semigroup__mult(X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3313]) ).

cnf(c_0_4675,plain,
    ( class_Ring__and__Field_Ocomm__semiring(X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3314]) ).

cnf(c_0_4676,plain,
    ( class_Ring__and__Field_Ocomm__semiring__1(X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3315]) ).

cnf(c_0_4677,plain,
    ( class_Ring__and__Field_Ocomm__semiring__1__cancel(X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3316]) ).

cnf(c_0_4678,plain,
    ( class_HOL_Otimes(X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3317]) ).

cnf(c_0_4679,plain,
    ( class_OrderedGroup_Osemigroup__mult(X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3318]) ).

cnf(c_0_4680,plain,
    ( class_Ring__and__Field_Osemiring(X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3319]) ).

cnf(c_0_4681,plain,
    ( class_Ring__and__Field_Osemiring__0(X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3320]) ).

cnf(c_0_4682,plain,
    ( class_OrderedGroup_Ocancel__semigroup__add(X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3321]) ).

cnf(c_0_4683,plain,
    ( class_OrderedGroup_Ocancel__ab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3322]) ).

cnf(c_0_4684,plain,
    ( class_Ring__and__Field_Oaxclass__no__zero__divisors(X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3323]) ).

cnf(c_0_4685,plain,
    ( class_OrderedGroup_Olordered__ab__group__join(X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3324]) ).

cnf(c_0_4686,plain,
    ( class_OrderedGroup_Olordered__ab__group__meet(X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3325]) ).

cnf(c_0_4687,plain,
    ( class_OrderedGroup_Olordered__ab__group__abs(X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3326]) ).

cnf(c_0_4688,plain,
    ( class_Ring__and__Field_Opordered__ring(X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3327]) ).

cnf(c_0_4689,plain,
    ( class_Ring__and__Field_Olordered__ring(X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3328]) ).

cnf(c_0_4690,plain,
    ( class_OrderedGroup_Opordered__ab__group__add(X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3329]) ).

cnf(c_0_4691,plain,
    ( class_Ring__and__Field_Osemiring__0__cancel(X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3330]) ).

cnf(c_0_4692,plain,
    ( class_OrderedGroup_Olordered__ab__group(X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3331]) ).

cnf(c_0_4693,plain,
    ( class_Ring__and__Field_Oaxclass__abs__if(X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3332]) ).

cnf(c_0_4694,plain,
    ( class_Orderings_Oord(X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3333]) ).

cnf(c_0_4695,plain,
    ( class_Orderings_Oorder(X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3334]) ).

cnf(c_0_4696,plain,
    ( class_OrderedGroup_Opordered__ab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3335]) ).

cnf(c_0_4697,plain,
    ( class_Ring__and__Field_Opordered__semiring(X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3336]) ).

cnf(c_0_4698,plain,
    ( class_Ring__and__Field_Opordered__cancel__semiring(X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3337]) ).

cnf(c_0_4699,plain,
    ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3338]) ).

cnf(c_0_4700,plain,
    ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3339]) ).

cnf(c_0_4701,plain,
    ( class_LOrder_Omeet__semilorder(X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3340]) ).

cnf(c_0_4702,plain,
    ( class_HOL_Ominus(X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3341]) ).

cnf(c_0_4703,plain,
    ( class_LOrder_Ojoin__semilorder(X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3342]) ).

cnf(c_0_4704,plain,
    ( class_LOrder_Olorder(X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3343]) ).

cnf(c_0_4705,plain,
    ( class_Orderings_Olinorder(X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3344]) ).

cnf(c_0_4706,plain,
    ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3345]) ).

cnf(c_0_4707,plain,
    ( class_Ring__and__Field_Oordered__semiring__strict(X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3346]) ).

cnf(c_0_4708,plain,
    ( class_HOL_Ozero(X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3347]) ).

cnf(c_0_4709,plain,
    ( class_HOL_Oplus(X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3348]) ).

cnf(c_0_4710,plain,
    ( class_OrderedGroup_Osemigroup__add(X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3349]) ).

cnf(c_0_4711,plain,
    ( class_OrderedGroup_Oab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3350]) ).

cnf(c_0_4712,plain,
    ( class_OrderedGroup_Ocomm__monoid__add(X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3351]) ).

cnf(c_0_4713,plain,
    ( class_OrderedGroup_Oab__group__add(X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3352]) ).

cnf(c_0_4714,plain,
    ( class_Ring__and__Field_Oring(X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3353]) ).

cnf(c_0_4715,plain,
    ( class_Ring__and__Field_Osemiring__1__cancel(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3354]) ).

cnf(c_0_4716,plain,
    ( class_OrderedGroup_Ocomm__monoid__mult(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3355]) ).

cnf(c_0_4717,plain,
    ( class_Ring__and__Field_Ocomm__semiring__1(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3356]) ).

cnf(c_0_4718,plain,
    ( class_Ring__and__Field_Ocomm__semiring__1__cancel(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3357]) ).

cnf(c_0_4719,plain,
    ( class_Ring__and__Field_Oidom(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3358]) ).

cnf(c_0_4720,plain,
    ( class_Ring__and__Field_Oaxclass__no__zero__divisors(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3359]) ).

cnf(c_0_4721,plain,
    ( class_Ring__and__Field_Oordered__semidom(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3360]) ).

cnf(c_0_4722,plain,
    ( class_OrderedGroup_Opordered__ab__group__add(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3361]) ).

cnf(c_0_4723,plain,
    ( class_OrderedGroup_Olordered__ab__group(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3362]) ).

cnf(c_0_4724,plain,
    ( class_OrderedGroup_Olordered__ab__group__join(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3363]) ).

cnf(c_0_4725,plain,
    ( class_OrderedGroup_Olordered__ab__group__meet(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3364]) ).

cnf(c_0_4726,plain,
    ( class_OrderedGroup_Olordered__ab__group__abs(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3365]) ).

cnf(c_0_4727,plain,
    ( class_HOL_Ominus(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3366]) ).

cnf(c_0_4728,plain,
    ( class_Ring__and__Field_Opordered__ring(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3367]) ).

cnf(c_0_4729,plain,
    ( class_Ring__and__Field_Olordered__ring(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3368]) ).

cnf(c_0_4730,plain,
    ( class_Ring__and__Field_Oordered__ring__strict(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3369]) ).

cnf(c_0_4731,plain,
    ( class_Ring__and__Field_Oaxclass__abs__if(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3370]) ).

cnf(c_0_4732,plain,
    ( class_Orderings_Oord(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3371]) ).

cnf(c_0_4733,plain,
    ( class_Orderings_Oorder(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3372]) ).

cnf(c_0_4734,plain,
    ( class_OrderedGroup_Opordered__ab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3373]) ).

cnf(c_0_4735,plain,
    ( class_Ring__and__Field_Opordered__semiring(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3374]) ).

cnf(c_0_4736,plain,
    ( class_Ring__and__Field_Opordered__comm__semiring(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3375]) ).

cnf(c_0_4737,plain,
    ( class_Ring__and__Field_Opordered__cancel__semiring(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3376]) ).

cnf(c_0_4738,plain,
    ( class_OrderedGroup_Oab__group__add(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3377]) ).

cnf(c_0_4739,plain,
    ( class_Ring__and__Field_Opordered__cancel__comm__semiring(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3378]) ).

cnf(c_0_4740,plain,
    ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3379]) ).

cnf(c_0_4741,plain,
    ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3380]) ).

cnf(c_0_4742,plain,
    ( class_LOrder_Omeet__semilorder(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3381]) ).

cnf(c_0_4743,plain,
    ( class_LOrder_Ojoin__semilorder(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3382]) ).

cnf(c_0_4744,plain,
    ( class_LOrder_Olorder(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3383]) ).

cnf(c_0_4745,plain,
    ( class_Orderings_Olinorder(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3384]) ).

cnf(c_0_4746,plain,
    ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3385]) ).

cnf(c_0_4747,plain,
    ( class_Ring__and__Field_Oordered__semiring__strict(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3386]) ).

cnf(c_0_4748,plain,
    ( class_Ring__and__Field_Oordered__comm__semiring__strict(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3387]) ).

cnf(c_0_4749,plain,
    ( class_Ring__and__Field_Oring(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3388]) ).

cnf(c_0_4750,plain,
    ( class_HOL_Oplus(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3389]) ).

cnf(c_0_4751,plain,
    ( class_OrderedGroup_Osemigroup__add(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3390]) ).

cnf(c_0_4752,plain,
    ( class_OrderedGroup_Ocancel__semigroup__add(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3391]) ).

cnf(c_0_4753,plain,
    ( class_OrderedGroup_Oab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3392]) ).

cnf(c_0_4754,plain,
    ( class_OrderedGroup_Ocancel__ab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3393]) ).

cnf(c_0_4755,plain,
    ( class_HOL_Ozero(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3394]) ).

cnf(c_0_4756,plain,
    ( class_OrderedGroup_Ocomm__monoid__add(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3395]) ).

cnf(c_0_4757,plain,
    ( class_HOL_Otimes(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3396]) ).

cnf(c_0_4758,plain,
    ( class_OrderedGroup_Osemigroup__mult(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3397]) ).

cnf(c_0_4759,plain,
    ( class_Ring__and__Field_Osemiring(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3398]) ).

cnf(c_0_4760,plain,
    ( class_Ring__and__Field_Oring__1(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3399]) ).

cnf(c_0_4761,plain,
    ( class_Ring__and__Field_Osemiring__0(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3400]) ).

cnf(c_0_4762,plain,
    ( class_Ring__and__Field_Osemiring__0__cancel(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3401]) ).

cnf(c_0_4763,plain,
    ( class_OrderedGroup_Oab__semigroup__mult(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3402]) ).

cnf(c_0_4764,plain,
    ( class_Ring__and__Field_Ocomm__semiring(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3403]) ).

cnf(c_0_4765,plain,
    ( class_Ring__and__Field_Ocomm__semiring__0(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3404]) ).

cnf(c_0_4766,plain,
    ( class_Ring__and__Field_Ocomm__semiring__0__cancel(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3405]) ).

cnf(c_0_4767,plain,
    ( class_HOL_Oone(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3406]) ).

cnf(c_0_4768,plain,
    ( class_OrderedGroup_Omonoid__mult(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3407]) ).

cnf(c_0_4769,plain,
    ( class_Ring__and__Field_Oaxclass__0__neq__1(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3408]) ).

cnf(c_0_4770,plain,
    ( class_Ring__and__Field_Osemiring__1(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3409]) ).

cnf(c_0_4771,plain,
    ( class_Ring__and__Field_Ocomm__ring(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3410]) ).

cnf(c_0_4772,plain,
    ( class_Ring__and__Field_Ocomm__ring__1(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3411]) ).

cnf(c_0_4773,plain,
    ( class_Ring__and__Field_Ocomm__semiring__1__cancel(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3412]) ).

cnf(c_0_4774,plain,
    ( class_HOL_Ominus(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3413]) ).

cnf(c_0_4775,plain,
    ( class_OrderedGroup_Oab__group__add(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3414]) ).

cnf(c_0_4776,plain,
    ( class_Ring__and__Field_Oordered__semidom(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3415]) ).

cnf(c_0_4777,plain,
    ( class_Ring__and__Field_Oring(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3416]) ).

cnf(c_0_4778,plain,
    ( class_Orderings_Oord(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3417]) ).

cnf(c_0_4779,plain,
    ( class_Orderings_Oorder(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3418]) ).

cnf(c_0_4780,plain,
    ( class_OrderedGroup_Opordered__ab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3419]) ).

cnf(c_0_4781,plain,
    ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3420]) ).

cnf(c_0_4782,plain,
    ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3421]) ).

cnf(c_0_4783,plain,
    ( class_OrderedGroup_Opordered__ab__group__add(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3422]) ).

cnf(c_0_4784,plain,
    ( class_LOrder_Omeet__semilorder(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3423]) ).

cnf(c_0_4785,plain,
    ( class_LOrder_Ojoin__semilorder(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3424]) ).

cnf(c_0_4786,plain,
    ( class_LOrder_Olorder(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3425]) ).

cnf(c_0_4787,plain,
    ( class_OrderedGroup_Olordered__ab__group(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3426]) ).

cnf(c_0_4788,plain,
    ( class_Ring__and__Field_Oring__1(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3427]) ).

cnf(c_0_4789,plain,
    ( class_OrderedGroup_Olordered__ab__group__join(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3428]) ).

cnf(c_0_4790,plain,
    ( class_OrderedGroup_Olordered__ab__group__meet(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3429]) ).

cnf(c_0_4791,plain,
    ( class_OrderedGroup_Olordered__ab__group__abs(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3430]) ).

cnf(c_0_4792,plain,
    ( class_Ring__and__Field_Opordered__semiring(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3431]) ).

cnf(c_0_4793,plain,
    ( class_Ring__and__Field_Opordered__cancel__semiring(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3432]) ).

cnf(c_0_4794,plain,
    ( class_Ring__and__Field_Opordered__ring(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3433]) ).

cnf(c_0_4795,plain,
    ( class_Ring__and__Field_Olordered__ring(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3434]) ).

cnf(c_0_4796,plain,
    ( class_Ring__and__Field_Oaxclass__abs__if(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3435]) ).

cnf(c_0_4797,plain,
    ( class_Orderings_Olinorder(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3436]) ).

cnf(c_0_4798,plain,
    ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3437]) ).

cnf(c_0_4799,plain,
    ( class_Ring__and__Field_Ocomm__ring(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3438]) ).

cnf(c_0_4800,plain,
    ( class_Ring__and__Field_Oordered__semiring__strict(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3439]) ).

cnf(c_0_4801,plain,
    ( class_Ring__and__Field_Oordered__ring__strict(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3440]) ).

cnf(c_0_4802,plain,
    ( class_Ring__and__Field_Opordered__comm__semiring(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3441]) ).

cnf(c_0_4803,plain,
    ( class_Ring__and__Field_Opordered__cancel__comm__semiring(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3442]) ).

cnf(c_0_4804,plain,
    ( class_Ring__and__Field_Oordered__comm__semiring__strict(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3443]) ).

cnf(c_0_4805,plain,
    ( class_Ring__and__Field_Oordered__idom(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3444]) ).

cnf(c_0_4806,plain,
    ( class_HOL_Otimes(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3445]) ).

cnf(c_0_4807,plain,
    ( class_HOL_Ozero(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3446]) ).

cnf(c_0_4808,plain,
    ( class_Ring__and__Field_Oaxclass__no__zero__divisors(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3447]) ).

cnf(c_0_4809,plain,
    ( class_HOL_Oplus(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3448]) ).

cnf(c_0_4810,plain,
    ( class_Ring__and__Field_Ocomm__ring__1(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3449]) ).

cnf(c_0_4811,plain,
    ( class_OrderedGroup_Osemigroup__add(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3450]) ).

cnf(c_0_4812,plain,
    ( class_OrderedGroup_Ocancel__semigroup__add(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3451]) ).

cnf(c_0_4813,plain,
    ( class_OrderedGroup_Oab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3452]) ).

cnf(c_0_4814,plain,
    ( class_OrderedGroup_Ocancel__ab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3453]) ).

cnf(c_0_4815,plain,
    ( class_OrderedGroup_Ocomm__monoid__add(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3454]) ).

cnf(c_0_4816,plain,
    ( class_OrderedGroup_Osemigroup__mult(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3455]) ).

cnf(c_0_4817,plain,
    ( class_Ring__and__Field_Osemiring(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3456]) ).

cnf(c_0_4818,plain,
    ( class_Ring__and__Field_Osemiring__0(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3457]) ).

cnf(c_0_4819,plain,
    ( class_Ring__and__Field_Osemiring__0__cancel(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3458]) ).

cnf(c_0_4820,plain,
    ( class_OrderedGroup_Oab__semigroup__mult(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3459]) ).

cnf(c_0_4821,plain,
    ( class_Ring__and__Field_Oidom(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3460]) ).

cnf(c_0_4822,plain,
    ( class_Ring__and__Field_Ocomm__semiring(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3461]) ).

cnf(c_0_4823,plain,
    ( class_Ring__and__Field_Ocomm__semiring__0(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3462]) ).

cnf(c_0_4824,plain,
    ( class_Ring__and__Field_Ocomm__semiring__0__cancel(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3463]) ).

cnf(c_0_4825,plain,
    ( class_HOL_Oone(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3464]) ).

cnf(c_0_4826,plain,
    ( class_OrderedGroup_Omonoid__mult(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3465]) ).

cnf(c_0_4827,plain,
    ( class_Ring__and__Field_Oaxclass__0__neq__1(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3466]) ).

cnf(c_0_4828,plain,
    ( class_Ring__and__Field_Osemiring__1(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3467]) ).

cnf(c_0_4829,plain,
    ( class_Ring__and__Field_Osemiring__1__cancel(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3468]) ).

cnf(c_0_4830,plain,
    ( class_OrderedGroup_Ocomm__monoid__mult(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3469]) ).

cnf(c_0_4831,plain,
    ( class_Ring__and__Field_Ocomm__semiring__1(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3470]) ).

cnf(c_0_4832,plain,
    ( class_HOL_Oinverse(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3471]) ).

cnf(c_0_4833,plain,
    ( class_Ring__and__Field_Ofield(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3472]) ).

cnf(c_0_4834,plain,
    ( class_OrderedGroup_Osemigroup__add(X1)
    | ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3473]) ).

cnf(c_0_4835,plain,
    ( class_OrderedGroup_Oab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3474]) ).

cnf(c_0_4836,plain,
    ( class_OrderedGroup_Ocomm__monoid__add(X1)
    | ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3475]) ).

cnf(c_0_4837,plain,
    ( class_HOL_Otimes(X1)
    | ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3476]) ).

cnf(c_0_4838,plain,
    ( class_OrderedGroup_Osemigroup__mult(X1)
    | ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3477]) ).

cnf(c_0_4839,plain,
    ( class_Ring__and__Field_Osemiring(X1)
    | ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3478]) ).

cnf(c_0_4840,plain,
    ( class_Ring__and__Field_Osemiring__0(X1)
    | ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3479]) ).

cnf(c_0_4841,plain,
    ( class_Ring__and__Field_Opordered__comm__semiring(X1)
    | ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3480]) ).

cnf(c_0_4842,plain,
    ( class_Ring__and__Field_Opordered__cancel__comm__semiring(X1)
    | ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3481]) ).

cnf(c_0_4843,plain,
    ( class_Ring__and__Field_Opordered__semiring(X1)
    | ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3482]) ).

cnf(c_0_4844,plain,
    ( class_Ring__and__Field_Osemiring__0__cancel(X1)
    | ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3483]) ).

cnf(c_0_4845,plain,
    ( class_Ring__and__Field_Opordered__cancel__semiring(X1)
    | ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3484]) ).

cnf(c_0_4846,plain,
    ( class_Ring__and__Field_Oordered__semiring__strict(X1)
    | ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3485]) ).

cnf(c_0_4847,plain,
    ( class_OrderedGroup_Ocancel__semigroup__add(X1)
    | ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3486]) ).

cnf(c_0_4848,plain,
    ( class_OrderedGroup_Ocancel__ab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3487]) ).

cnf(c_0_4849,plain,
    ( class_Orderings_Oord(X1)
    | ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3488]) ).

cnf(c_0_4850,plain,
    ( class_Orderings_Oorder(X1)
    | ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3489]) ).

cnf(c_0_4851,plain,
    ( class_OrderedGroup_Oab__semigroup__mult(X1)
    | ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3490]) ).

cnf(c_0_4852,plain,
    ( class_OrderedGroup_Opordered__ab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3491]) ).

cnf(c_0_4853,plain,
    ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3492]) ).

cnf(c_0_4854,plain,
    ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
    | ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3493]) ).

cnf(c_0_4855,plain,
    ( class_LOrder_Omeet__semilorder(X1)
    | ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3494]) ).

cnf(c_0_4856,plain,
    ( class_LOrder_Ojoin__semilorder(X1)
    | ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3495]) ).

cnf(c_0_4857,plain,
    ( class_LOrder_Olorder(X1)
    | ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3496]) ).

cnf(c_0_4858,plain,
    ( class_Orderings_Olinorder(X1)
    | ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3497]) ).

cnf(c_0_4859,plain,
    ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3498]) ).

cnf(c_0_4860,plain,
    ( class_HOL_Ozero(X1)
    | ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3499]) ).

cnf(c_0_4861,plain,
    ( class_HOL_Oplus(X1)
    | ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3500]) ).

cnf(c_0_4862,plain,
    ( class_Ring__and__Field_Ocomm__semiring(X1)
    | ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3501]) ).

cnf(c_0_4863,plain,
    ( class_Ring__and__Field_Ocomm__semiring__0(X1)
    | ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3502]) ).

cnf(c_0_4864,plain,
    ( class_OrderedGroup_Opordered__ab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Olordered__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3503]) ).

cnf(c_0_4865,plain,
    ( class_Ring__and__Field_Opordered__semiring(X1)
    | ~ class_Ring__and__Field_Olordered__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3504]) ).

cnf(c_0_4866,plain,
    ( class_Ring__and__Field_Opordered__cancel__semiring(X1)
    | ~ class_Ring__and__Field_Olordered__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3505]) ).

cnf(c_0_4867,plain,
    ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Olordered__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3506]) ).

cnf(c_0_4868,plain,
    ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
    | ~ class_Ring__and__Field_Olordered__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3507]) ).

cnf(c_0_4869,plain,
    ( class_HOL_Ominus(X1)
    | ~ class_Ring__and__Field_Olordered__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3508]) ).

cnf(c_0_4870,plain,
    ( class_OrderedGroup_Olordered__ab__group__join(X1)
    | ~ class_Ring__and__Field_Olordered__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3509]) ).

cnf(c_0_4871,plain,
    ( class_OrderedGroup_Oab__group__add(X1)
    | ~ class_Ring__and__Field_Olordered__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3510]) ).

cnf(c_0_4872,plain,
    ( class_OrderedGroup_Olordered__ab__group__meet(X1)
    | ~ class_Ring__and__Field_Olordered__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3511]) ).

cnf(c_0_4873,plain,
    ( class_LOrder_Omeet__semilorder(X1)
    | ~ class_Ring__and__Field_Olordered__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3512]) ).

cnf(c_0_4874,plain,
    ( class_LOrder_Ojoin__semilorder(X1)
    | ~ class_Ring__and__Field_Olordered__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3513]) ).

cnf(c_0_4875,plain,
    ( class_LOrder_Olorder(X1)
    | ~ class_Ring__and__Field_Olordered__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3514]) ).

cnf(c_0_4876,plain,
    ( class_OrderedGroup_Olordered__ab__group(X1)
    | ~ class_Ring__and__Field_Olordered__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3515]) ).

cnf(c_0_4877,plain,
    ( class_OrderedGroup_Olordered__ab__group__abs(X1)
    | ~ class_Ring__and__Field_Olordered__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3516]) ).

cnf(c_0_4878,plain,
    ( class_HOL_Oplus(X1)
    | ~ class_Ring__and__Field_Olordered__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3517]) ).

cnf(c_0_4879,plain,
    ( class_OrderedGroup_Osemigroup__add(X1)
    | ~ class_Ring__and__Field_Olordered__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3518]) ).

cnf(c_0_4880,plain,
    ( class_OrderedGroup_Ocancel__semigroup__add(X1)
    | ~ class_Ring__and__Field_Olordered__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3519]) ).

cnf(c_0_4881,plain,
    ( class_OrderedGroup_Oab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Olordered__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3520]) ).

cnf(c_0_4882,plain,
    ( class_OrderedGroup_Opordered__ab__group__add(X1)
    | ~ class_Ring__and__Field_Olordered__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3521]) ).

cnf(c_0_4883,plain,
    ( class_OrderedGroup_Ocancel__ab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Olordered__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3522]) ).

cnf(c_0_4884,plain,
    ( class_HOL_Ozero(X1)
    | ~ class_Ring__and__Field_Olordered__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3523]) ).

cnf(c_0_4885,plain,
    ( class_OrderedGroup_Ocomm__monoid__add(X1)
    | ~ class_Ring__and__Field_Olordered__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3524]) ).

cnf(c_0_4886,plain,
    ( class_HOL_Otimes(X1)
    | ~ class_Ring__and__Field_Olordered__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3525]) ).

cnf(c_0_4887,plain,
    ( class_OrderedGroup_Osemigroup__mult(X1)
    | ~ class_Ring__and__Field_Olordered__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3526]) ).

cnf(c_0_4888,plain,
    ( class_Ring__and__Field_Osemiring(X1)
    | ~ class_Ring__and__Field_Olordered__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3527]) ).

cnf(c_0_4889,plain,
    ( class_Ring__and__Field_Osemiring__0(X1)
    | ~ class_Ring__and__Field_Olordered__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3528]) ).

cnf(c_0_4890,plain,
    ( class_Ring__and__Field_Osemiring__0__cancel(X1)
    | ~ class_Ring__and__Field_Olordered__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3529]) ).

cnf(c_0_4891,plain,
    ( class_Orderings_Oord(X1)
    | ~ class_Ring__and__Field_Olordered__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3530]) ).

cnf(c_0_4892,plain,
    ( class_Orderings_Oorder(X1)
    | ~ class_Ring__and__Field_Olordered__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3531]) ).

cnf(c_0_4893,plain,
    ( class_Ring__and__Field_Oring(X1)
    | ~ class_Ring__and__Field_Olordered__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3532]) ).

cnf(c_0_4894,plain,
    ( class_Ring__and__Field_Opordered__ring(X1)
    | ~ class_Ring__and__Field_Olordered__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3533]) ).

cnf(c_0_4895,plain,
    ( class_Ring__and__Field_Osemiring__1__cancel(X1)
    | ~ class_Ring__and__Field_Oidom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3534]) ).

cnf(c_0_4896,plain,
    ( class_OrderedGroup_Ocomm__monoid__mult(X1)
    | ~ class_Ring__and__Field_Oidom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3535]) ).

cnf(c_0_4897,plain,
    ( class_Ring__and__Field_Ocomm__semiring__1(X1)
    | ~ class_Ring__and__Field_Oidom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3536]) ).

cnf(c_0_4898,plain,
    ( class_Ring__and__Field_Ocomm__semiring__1__cancel(X1)
    | ~ class_Ring__and__Field_Oidom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3537]) ).

cnf(c_0_4899,plain,
    ( class_HOL_Ominus(X1)
    | ~ class_Ring__and__Field_Oidom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3538]) ).

cnf(c_0_4900,plain,
    ( class_OrderedGroup_Oab__group__add(X1)
    | ~ class_Ring__and__Field_Oidom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3539]) ).

cnf(c_0_4901,plain,
    ( class_Ring__and__Field_Oaxclass__no__zero__divisors(X1)
    | ~ class_Ring__and__Field_Oidom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3540]) ).

cnf(c_0_4902,plain,
    ( class_Ring__and__Field_Oring(X1)
    | ~ class_Ring__and__Field_Oidom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3541]) ).

cnf(c_0_4903,plain,
    ( class_HOL_Oplus(X1)
    | ~ class_Ring__and__Field_Oidom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3542]) ).

cnf(c_0_4904,plain,
    ( class_OrderedGroup_Osemigroup__add(X1)
    | ~ class_Ring__and__Field_Oidom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3543]) ).

cnf(c_0_4905,plain,
    ( class_OrderedGroup_Ocancel__semigroup__add(X1)
    | ~ class_Ring__and__Field_Oidom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3544]) ).

cnf(c_0_4906,plain,
    ( class_OrderedGroup_Oab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Oidom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3545]) ).

cnf(c_0_4907,plain,
    ( class_OrderedGroup_Ocancel__ab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Oidom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3546]) ).

cnf(c_0_4908,plain,
    ( class_HOL_Ozero(X1)
    | ~ class_Ring__and__Field_Oidom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3547]) ).

cnf(c_0_4909,plain,
    ( class_OrderedGroup_Ocomm__monoid__add(X1)
    | ~ class_Ring__and__Field_Oidom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3548]) ).

cnf(c_0_4910,plain,
    ( class_HOL_Otimes(X1)
    | ~ class_Ring__and__Field_Oidom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3549]) ).

cnf(c_0_4911,plain,
    ( class_OrderedGroup_Osemigroup__mult(X1)
    | ~ class_Ring__and__Field_Oidom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3550]) ).

cnf(c_0_4912,plain,
    ( class_Ring__and__Field_Osemiring(X1)
    | ~ class_Ring__and__Field_Oidom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3551]) ).

cnf(c_0_4913,plain,
    ( class_Ring__and__Field_Oring__1(X1)
    | ~ class_Ring__and__Field_Oidom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3552]) ).

cnf(c_0_4914,plain,
    ( class_Ring__and__Field_Osemiring__0(X1)
    | ~ class_Ring__and__Field_Oidom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3553]) ).

cnf(c_0_4915,plain,
    ( class_Ring__and__Field_Osemiring__0__cancel(X1)
    | ~ class_Ring__and__Field_Oidom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3554]) ).

cnf(c_0_4916,plain,
    ( class_OrderedGroup_Oab__semigroup__mult(X1)
    | ~ class_Ring__and__Field_Oidom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3555]) ).

cnf(c_0_4917,plain,
    ( class_Ring__and__Field_Ocomm__semiring(X1)
    | ~ class_Ring__and__Field_Oidom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3556]) ).

cnf(c_0_4918,plain,
    ( class_Ring__and__Field_Ocomm__semiring__0(X1)
    | ~ class_Ring__and__Field_Oidom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3557]) ).

cnf(c_0_4919,plain,
    ( class_Ring__and__Field_Ocomm__semiring__0__cancel(X1)
    | ~ class_Ring__and__Field_Oidom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3558]) ).

cnf(c_0_4920,plain,
    ( class_HOL_Oone(X1)
    | ~ class_Ring__and__Field_Oidom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3559]) ).

cnf(c_0_4921,plain,
    ( class_OrderedGroup_Omonoid__mult(X1)
    | ~ class_Ring__and__Field_Oidom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3560]) ).

cnf(c_0_4922,plain,
    ( class_Ring__and__Field_Oaxclass__0__neq__1(X1)
    | ~ class_Ring__and__Field_Oidom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3561]) ).

cnf(c_0_4923,plain,
    ( class_Ring__and__Field_Osemiring__1(X1)
    | ~ class_Ring__and__Field_Oidom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3562]) ).

cnf(c_0_4924,plain,
    ( class_Ring__and__Field_Ocomm__ring(X1)
    | ~ class_Ring__and__Field_Oidom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3563]) ).

cnf(c_0_4925,plain,
    ( class_Ring__and__Field_Ocomm__ring__1(X1)
    | ~ class_Ring__and__Field_Oidom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3564]) ).

cnf(c_0_4926,plain,
    ( class_Ring__and__Field_Osemiring__1__cancel(X1)
    | ~ class_Ring__and__Field_Ofield(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3565]) ).

cnf(c_0_4927,plain,
    ( class_OrderedGroup_Ocomm__monoid__mult(X1)
    | ~ class_Ring__and__Field_Ofield(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3566]) ).

cnf(c_0_4928,plain,
    ( class_Ring__and__Field_Ocomm__semiring__1(X1)
    | ~ class_Ring__and__Field_Ofield(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3567]) ).

cnf(c_0_4929,plain,
    ( class_Ring__and__Field_Ocomm__semiring__1__cancel(X1)
    | ~ class_Ring__and__Field_Ofield(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3568]) ).

cnf(c_0_4930,plain,
    ( class_HOL_Ominus(X1)
    | ~ class_Ring__and__Field_Ofield(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3569]) ).

cnf(c_0_4931,plain,
    ( class_OrderedGroup_Oab__group__add(X1)
    | ~ class_Ring__and__Field_Ofield(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3570]) ).

cnf(c_0_4932,plain,
    ( class_Ring__and__Field_Oaxclass__no__zero__divisors(X1)
    | ~ class_Ring__and__Field_Ofield(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3571]) ).

cnf(c_0_4933,plain,
    ( class_Ring__and__Field_Oidom(X1)
    | ~ class_Ring__and__Field_Ofield(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3572]) ).

cnf(c_0_4934,plain,
    ( class_HOL_Oinverse(X1)
    | ~ class_Ring__and__Field_Ofield(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3573]) ).

cnf(c_0_4935,plain,
    ( class_Ring__and__Field_Oring(X1)
    | ~ class_Ring__and__Field_Ofield(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3574]) ).

cnf(c_0_4936,plain,
    ( class_HOL_Oplus(X1)
    | ~ class_Ring__and__Field_Ofield(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3575]) ).

cnf(c_0_4937,plain,
    ( class_OrderedGroup_Osemigroup__add(X1)
    | ~ class_Ring__and__Field_Ofield(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3576]) ).

cnf(c_0_4938,plain,
    ( class_OrderedGroup_Ocancel__semigroup__add(X1)
    | ~ class_Ring__and__Field_Ofield(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3577]) ).

cnf(c_0_4939,plain,
    ( class_OrderedGroup_Oab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Ofield(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3578]) ).

cnf(c_0_4940,plain,
    ( class_OrderedGroup_Ocancel__ab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Ofield(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3579]) ).

cnf(c_0_4941,plain,
    ( class_HOL_Ozero(X1)
    | ~ class_Ring__and__Field_Ofield(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3580]) ).

cnf(c_0_4942,plain,
    ( class_OrderedGroup_Ocomm__monoid__add(X1)
    | ~ class_Ring__and__Field_Ofield(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3581]) ).

cnf(c_0_4943,plain,
    ( class_HOL_Otimes(X1)
    | ~ class_Ring__and__Field_Ofield(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3582]) ).

cnf(c_0_4944,plain,
    ( class_OrderedGroup_Osemigroup__mult(X1)
    | ~ class_Ring__and__Field_Ofield(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3583]) ).

cnf(c_0_4945,plain,
    ( class_Ring__and__Field_Osemiring(X1)
    | ~ class_Ring__and__Field_Ofield(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3584]) ).

cnf(c_0_4946,plain,
    ( class_Ring__and__Field_Oring__1(X1)
    | ~ class_Ring__and__Field_Ofield(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3585]) ).

cnf(c_0_4947,plain,
    ( class_Ring__and__Field_Osemiring__0(X1)
    | ~ class_Ring__and__Field_Ofield(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3586]) ).

cnf(c_0_4948,plain,
    ( class_Ring__and__Field_Osemiring__0__cancel(X1)
    | ~ class_Ring__and__Field_Ofield(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3587]) ).

cnf(c_0_4949,plain,
    ( class_OrderedGroup_Oab__semigroup__mult(X1)
    | ~ class_Ring__and__Field_Ofield(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3588]) ).

cnf(c_0_4950,plain,
    ( class_Ring__and__Field_Ocomm__semiring(X1)
    | ~ class_Ring__and__Field_Ofield(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3589]) ).

cnf(c_0_4951,plain,
    ( class_Ring__and__Field_Ocomm__semiring__0(X1)
    | ~ class_Ring__and__Field_Ofield(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3590]) ).

cnf(c_0_4952,plain,
    ( class_Ring__and__Field_Ocomm__semiring__0__cancel(X1)
    | ~ class_Ring__and__Field_Ofield(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3591]) ).

cnf(c_0_4953,plain,
    ( class_HOL_Oone(X1)
    | ~ class_Ring__and__Field_Ofield(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3592]) ).

cnf(c_0_4954,plain,
    ( class_OrderedGroup_Omonoid__mult(X1)
    | ~ class_Ring__and__Field_Ofield(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3593]) ).

cnf(c_0_4955,plain,
    ( class_Ring__and__Field_Oaxclass__0__neq__1(X1)
    | ~ class_Ring__and__Field_Ofield(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3594]) ).

cnf(c_0_4956,plain,
    ( class_Ring__and__Field_Osemiring__1(X1)
    | ~ class_Ring__and__Field_Ofield(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3595]) ).

cnf(c_0_4957,plain,
    ( class_Ring__and__Field_Ocomm__ring(X1)
    | ~ class_Ring__and__Field_Ofield(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3596]) ).

cnf(c_0_4958,plain,
    ( class_Ring__and__Field_Ocomm__ring__1(X1)
    | ~ class_Ring__and__Field_Ofield(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3597]) ).

cnf(c_0_4959,plain,
    ( class_HOL_Oinverse(X1)
    | ~ class_Ring__and__Field_Odivision__by__zero(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3598]) ).

cnf(c_0_4960,plain,
    ( class_HOL_Ozero(X1)
    | ~ class_Ring__and__Field_Odivision__by__zero(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3599]) ).

cnf(c_0_4961,plain,
    ( class_OrderedGroup_Ocomm__monoid__add(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3600]) ).

cnf(c_0_4962,plain,
    ( class_Ring__and__Field_Osemiring(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3601]) ).

cnf(c_0_4963,plain,
    ( class_Ring__and__Field_Osemiring__0(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3602]) ).

cnf(c_0_4964,plain,
    ( class_Ring__and__Field_Oaxclass__0__neq__1(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3603]) ).

cnf(c_0_4965,plain,
    ( class_Ring__and__Field_Osemiring__1(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3604]) ).

cnf(c_0_4966,plain,
    ( class_OrderedGroup_Oab__semigroup__mult(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3605]) ).

cnf(c_0_4967,plain,
    ( class_OrderedGroup_Ocomm__monoid__mult(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3606]) ).

cnf(c_0_4968,plain,
    ( class_Ring__and__Field_Ocomm__semiring__0__cancel(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3607]) ).

cnf(c_0_4969,plain,
    ( class_Ring__and__Field_Osemiring__0__cancel(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3608]) ).

cnf(c_0_4970,plain,
    ( class_Ring__and__Field_Osemiring__1__cancel(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3609]) ).

cnf(c_0_4971,plain,
    ( class_Ring__and__Field_Ocomm__semiring(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3610]) ).

cnf(c_0_4972,plain,
    ( class_OrderedGroup_Ocancel__semigroup__add(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3611]) ).

cnf(c_0_4973,plain,
    ( class_OrderedGroup_Ocancel__ab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3612]) ).

cnf(c_0_4974,plain,
    ( class_HOL_Otimes(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3613]) ).

cnf(c_0_4975,plain,
    ( class_OrderedGroup_Osemigroup__mult(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3614]) ).

cnf(c_0_4976,plain,
    ( class_HOL_Oone(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3615]) ).

cnf(c_0_4977,plain,
    ( class_OrderedGroup_Omonoid__mult(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3616]) ).

cnf(c_0_4978,plain,
    ( class_HOL_Oplus(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3617]) ).

cnf(c_0_4979,plain,
    ( class_OrderedGroup_Osemigroup__add(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3618]) ).

cnf(c_0_4980,plain,
    ( class_OrderedGroup_Oab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3619]) ).

cnf(c_0_4981,plain,
    ( class_HOL_Ozero(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3620]) ).

cnf(c_0_4982,plain,
    ( class_Ring__and__Field_Ocomm__semiring__0(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3621]) ).

cnf(c_0_4983,plain,
    ( class_Ring__and__Field_Ocomm__semiring__1(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3622]) ).

cnf(c_0_4984,plain,
    ( class_HOL_Otimes(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3623]) ).

cnf(c_0_4985,plain,
    ( class_OrderedGroup_Osemigroup__mult(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3624]) ).

cnf(c_0_4986,plain,
    ( class_Ring__and__Field_Osemiring(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3625]) ).

cnf(c_0_4987,plain,
    ( class_Ring__and__Field_Osemiring__0(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3626]) ).

cnf(c_0_4988,plain,
    ( class_OrderedGroup_Oab__semigroup__mult(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3627]) ).

cnf(c_0_4989,plain,
    ( class_Ring__and__Field_Ocomm__semiring(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3628]) ).

cnf(c_0_4990,plain,
    ( class_Ring__and__Field_Ocomm__semiring__0(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3629]) ).

cnf(c_0_4991,plain,
    ( class_HOL_Oone(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3630]) ).

cnf(c_0_4992,plain,
    ( class_Ring__and__Field_Osemiring__1(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3631]) ).

cnf(c_0_4993,plain,
    ( class_OrderedGroup_Omonoid__mult(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3632]) ).

cnf(c_0_4994,plain,
    ( class_OrderedGroup_Ocomm__monoid__mult(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3633]) ).

cnf(c_0_4995,plain,
    ( class_HOL_Oplus(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3634]) ).

cnf(c_0_4996,plain,
    ( class_OrderedGroup_Osemigroup__add(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3635]) ).

cnf(c_0_4997,plain,
    ( class_OrderedGroup_Oab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3636]) ).

cnf(c_0_4998,plain,
    ( class_OrderedGroup_Ocomm__monoid__add(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3637]) ).

cnf(c_0_4999,plain,
    ( class_HOL_Ozero(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3638]) ).

cnf(c_0_5000,plain,
    ( class_Ring__and__Field_Oaxclass__0__neq__1(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3639]) ).

cnf(c_0_5001,plain,
    ( class_OrderedGroup_Osemigroup__add(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3640]) ).

cnf(c_0_5002,plain,
    ( class_OrderedGroup_Oab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3641]) ).

cnf(c_0_5003,plain,
    ( class_OrderedGroup_Ocomm__monoid__add(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3642]) ).

cnf(c_0_5004,plain,
    ( class_HOL_Otimes(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3643]) ).

cnf(c_0_5005,plain,
    ( class_OrderedGroup_Osemigroup__mult(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3644]) ).

cnf(c_0_5006,plain,
    ( class_Ring__and__Field_Osemiring(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3645]) ).

cnf(c_0_5007,plain,
    ( class_Ring__and__Field_Osemiring__0(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3646]) ).

cnf(c_0_5008,plain,
    ( class_OrderedGroup_Oab__semigroup__mult(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3647]) ).

cnf(c_0_5009,plain,
    ( class_Ring__and__Field_Osemiring__0__cancel(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3648]) ).

cnf(c_0_5010,plain,
    ( class_OrderedGroup_Ocancel__semigroup__add(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3649]) ).

cnf(c_0_5011,plain,
    ( class_OrderedGroup_Ocancel__ab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3650]) ).

cnf(c_0_5012,plain,
    ( class_HOL_Ozero(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3651]) ).

cnf(c_0_5013,plain,
    ( class_HOL_Oplus(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3652]) ).

cnf(c_0_5014,plain,
    ( class_Ring__and__Field_Ocomm__semiring(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3653]) ).

cnf(c_0_5015,plain,
    ( class_Ring__and__Field_Ocomm__semiring__0(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3654]) ).

cnf(c_0_5016,plain,
    ( class_HOL_Ozero(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__0(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3655]) ).

cnf(c_0_5017,plain,
    ( class_OrderedGroup_Ocomm__monoid__add(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__0(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3656]) ).

cnf(c_0_5018,plain,
    ( class_HOL_Otimes(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__0(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3657]) ).

cnf(c_0_5019,plain,
    ( class_OrderedGroup_Osemigroup__mult(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__0(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3658]) ).

cnf(c_0_5020,plain,
    ( class_HOL_Oplus(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__0(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3659]) ).

cnf(c_0_5021,plain,
    ( class_OrderedGroup_Osemigroup__add(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__0(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3660]) ).

cnf(c_0_5022,plain,
    ( class_OrderedGroup_Oab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__0(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3661]) ).

cnf(c_0_5023,plain,
    ( class_Ring__and__Field_Osemiring(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__0(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3662]) ).

cnf(c_0_5024,plain,
    ( class_Ring__and__Field_Osemiring__0(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__0(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3663]) ).

cnf(c_0_5025,plain,
    ( class_OrderedGroup_Oab__semigroup__mult(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__0(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3664]) ).

cnf(c_0_5026,plain,
    ( class_Ring__and__Field_Ocomm__semiring(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__0(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3665]) ).

cnf(c_0_5027,plain,
    ( class_Ring__and__Field_Osemiring(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3666]) ).

cnf(c_0_5028,plain,
    ( class_HOL_Otimes(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3667]) ).

cnf(c_0_5029,plain,
    ( class_OrderedGroup_Osemigroup__mult(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3668]) ).

cnf(c_0_5030,plain,
    ( class_OrderedGroup_Oab__semigroup__mult(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3669]) ).

cnf(c_0_5031,plain,
    ( class_HOL_Oplus(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3670]) ).

cnf(c_0_5032,plain,
    ( class_OrderedGroup_Osemigroup__add(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3671]) ).

cnf(c_0_5033,plain,
    ( class_OrderedGroup_Oab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3672]) ).

cnf(c_0_5034,plain,
    ( class_Ring__and__Field_Osemiring__0(X1)
    | ~ class_Ring__and__Field_Ocomm__ring__1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3673]) ).

cnf(c_0_5035,plain,
    ( class_Ring__and__Field_Osemiring__0__cancel(X1)
    | ~ class_Ring__and__Field_Ocomm__ring__1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3674]) ).

cnf(c_0_5036,plain,
    ( class_OrderedGroup_Oab__semigroup__mult(X1)
    | ~ class_Ring__and__Field_Ocomm__ring__1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3675]) ).

cnf(c_0_5037,plain,
    ( class_Ring__and__Field_Ocomm__semiring(X1)
    | ~ class_Ring__and__Field_Ocomm__ring__1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3676]) ).

cnf(c_0_5038,plain,
    ( class_Ring__and__Field_Ocomm__semiring__0(X1)
    | ~ class_Ring__and__Field_Ocomm__ring__1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3677]) ).

cnf(c_0_5039,plain,
    ( class_Ring__and__Field_Ocomm__semiring__0__cancel(X1)
    | ~ class_Ring__and__Field_Ocomm__ring__1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3678]) ).

cnf(c_0_5040,plain,
    ( class_HOL_Ominus(X1)
    | ~ class_Ring__and__Field_Ocomm__ring__1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3679]) ).

cnf(c_0_5041,plain,
    ( class_Ring__and__Field_Ocomm__semiring__1__cancel(X1)
    | ~ class_Ring__and__Field_Ocomm__ring__1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3680]) ).

cnf(c_0_5042,plain,
    ( class_Ring__and__Field_Osemiring__1__cancel(X1)
    | ~ class_Ring__and__Field_Ocomm__ring__1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3681]) ).

cnf(c_0_5043,plain,
    ( class_Ring__and__Field_Oring__1(X1)
    | ~ class_Ring__and__Field_Ocomm__ring__1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3682]) ).

cnf(c_0_5044,plain,
    ( class_HOL_Oone(X1)
    | ~ class_Ring__and__Field_Ocomm__ring__1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3683]) ).

cnf(c_0_5045,plain,
    ( class_OrderedGroup_Omonoid__mult(X1)
    | ~ class_Ring__and__Field_Ocomm__ring__1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3684]) ).

cnf(c_0_5046,plain,
    ( class_Ring__and__Field_Oaxclass__0__neq__1(X1)
    | ~ class_Ring__and__Field_Ocomm__ring__1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3685]) ).

cnf(c_0_5047,plain,
    ( class_Ring__and__Field_Osemiring__1(X1)
    | ~ class_Ring__and__Field_Ocomm__ring__1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3686]) ).

cnf(c_0_5048,plain,
    ( class_OrderedGroup_Ocomm__monoid__mult(X1)
    | ~ class_Ring__and__Field_Ocomm__ring__1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3687]) ).

cnf(c_0_5049,plain,
    ( class_Ring__and__Field_Ocomm__semiring__1(X1)
    | ~ class_Ring__and__Field_Ocomm__ring__1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3688]) ).

cnf(c_0_5050,plain,
    ( class_OrderedGroup_Oab__group__add(X1)
    | ~ class_Ring__and__Field_Ocomm__ring__1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3689]) ).

cnf(c_0_5051,plain,
    ( class_HOL_Oplus(X1)
    | ~ class_Ring__and__Field_Ocomm__ring__1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3690]) ).

cnf(c_0_5052,plain,
    ( class_OrderedGroup_Osemigroup__add(X1)
    | ~ class_Ring__and__Field_Ocomm__ring__1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3691]) ).

cnf(c_0_5053,plain,
    ( class_OrderedGroup_Ocancel__semigroup__add(X1)
    | ~ class_Ring__and__Field_Ocomm__ring__1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3692]) ).

cnf(c_0_5054,plain,
    ( class_OrderedGroup_Oab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Ocomm__ring__1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3693]) ).

cnf(c_0_5055,plain,
    ( class_OrderedGroup_Ocancel__ab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Ocomm__ring__1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3694]) ).

cnf(c_0_5056,plain,
    ( class_HOL_Ozero(X1)
    | ~ class_Ring__and__Field_Ocomm__ring__1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3695]) ).

cnf(c_0_5057,plain,
    ( class_OrderedGroup_Ocomm__monoid__add(X1)
    | ~ class_Ring__and__Field_Ocomm__ring__1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3696]) ).

cnf(c_0_5058,plain,
    ( class_HOL_Otimes(X1)
    | ~ class_Ring__and__Field_Ocomm__ring__1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3697]) ).

cnf(c_0_5059,plain,
    ( class_OrderedGroup_Osemigroup__mult(X1)
    | ~ class_Ring__and__Field_Ocomm__ring__1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3698]) ).

cnf(c_0_5060,plain,
    ( class_Ring__and__Field_Osemiring(X1)
    | ~ class_Ring__and__Field_Ocomm__ring__1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3699]) ).

cnf(c_0_5061,plain,
    ( class_Ring__and__Field_Oring(X1)
    | ~ class_Ring__and__Field_Ocomm__ring__1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3700]) ).

cnf(c_0_5062,plain,
    ( class_Ring__and__Field_Ocomm__ring(X1)
    | ~ class_Ring__and__Field_Ocomm__ring__1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3701]) ).

cnf(c_0_5063,plain,
    ( class_OrderedGroup_Osemigroup__add(X1)
    | ~ class_Ring__and__Field_Ocomm__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3702]) ).

cnf(c_0_5064,plain,
    ( class_OrderedGroup_Oab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Ocomm__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3703]) ).

cnf(c_0_5065,plain,
    ( class_OrderedGroup_Ocomm__monoid__add(X1)
    | ~ class_Ring__and__Field_Ocomm__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3704]) ).

cnf(c_0_5066,plain,
    ( class_HOL_Otimes(X1)
    | ~ class_Ring__and__Field_Ocomm__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3705]) ).

cnf(c_0_5067,plain,
    ( class_OrderedGroup_Osemigroup__mult(X1)
    | ~ class_Ring__and__Field_Ocomm__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3706]) ).

cnf(c_0_5068,plain,
    ( class_Ring__and__Field_Osemiring(X1)
    | ~ class_Ring__and__Field_Ocomm__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3707]) ).

cnf(c_0_5069,plain,
    ( class_Ring__and__Field_Osemiring__0(X1)
    | ~ class_Ring__and__Field_Ocomm__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3708]) ).

cnf(c_0_5070,plain,
    ( class_OrderedGroup_Oab__semigroup__mult(X1)
    | ~ class_Ring__and__Field_Ocomm__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3709]) ).

cnf(c_0_5071,plain,
    ( class_Ring__and__Field_Ocomm__semiring__0__cancel(X1)
    | ~ class_Ring__and__Field_Ocomm__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3710]) ).

cnf(c_0_5072,plain,
    ( class_Ring__and__Field_Osemiring__0__cancel(X1)
    | ~ class_Ring__and__Field_Ocomm__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3711]) ).

cnf(c_0_5073,plain,
    ( class_Ring__and__Field_Oring(X1)
    | ~ class_Ring__and__Field_Ocomm__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3712]) ).

cnf(c_0_5074,plain,
    ( class_OrderedGroup_Ocancel__semigroup__add(X1)
    | ~ class_Ring__and__Field_Ocomm__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3713]) ).

cnf(c_0_5075,plain,
    ( class_OrderedGroup_Ocancel__ab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Ocomm__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3714]) ).

cnf(c_0_5076,plain,
    ( class_HOL_Ominus(X1)
    | ~ class_Ring__and__Field_Ocomm__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3715]) ).

cnf(c_0_5077,plain,
    ( class_OrderedGroup_Oab__group__add(X1)
    | ~ class_Ring__and__Field_Ocomm__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3716]) ).

cnf(c_0_5078,plain,
    ( class_HOL_Ozero(X1)
    | ~ class_Ring__and__Field_Ocomm__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3717]) ).

cnf(c_0_5079,plain,
    ( class_HOL_Oplus(X1)
    | ~ class_Ring__and__Field_Ocomm__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3718]) ).

cnf(c_0_5080,plain,
    ( class_Ring__and__Field_Ocomm__semiring(X1)
    | ~ class_Ring__and__Field_Ocomm__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3719]) ).

cnf(c_0_5081,plain,
    ( class_Ring__and__Field_Ocomm__semiring__0(X1)
    | ~ class_Ring__and__Field_Ocomm__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3720]) ).

cnf(c_0_5082,plain,
    ( class_HOL_Otimes(X1)
    | ~ class_Ring__and__Field_Oaxclass__no__zero__divisors(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3721]) ).

cnf(c_0_5083,plain,
    ( class_HOL_Ozero(X1)
    | ~ class_Ring__and__Field_Oaxclass__no__zero__divisors(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3722]) ).

cnf(c_0_5084,plain,
    ( class_HOL_Ozero(X1)
    | ~ class_Ring__and__Field_Oaxclass__abs__if(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3723]) ).

cnf(c_0_5085,plain,
    ( class_Orderings_Oord(X1)
    | ~ class_Ring__and__Field_Oaxclass__abs__if(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3724]) ).

cnf(c_0_5086,plain,
    ( class_HOL_Ominus(X1)
    | ~ class_Ring__and__Field_Oaxclass__abs__if(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3725]) ).

cnf(c_0_5087,plain,
    ( class_HOL_Oone(X1)
    | ~ class_Ring__and__Field_Oaxclass__0__neq__1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3726]) ).

cnf(c_0_5088,plain,
    ( class_HOL_Ozero(X1)
    | ~ class_Ring__and__Field_Oaxclass__0__neq__1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3727]) ).

cnf(c_0_5089,plain,
    ( class_OrderedGroup_Oab__semigroup__mult(X1)
    | ~ class_Power_Orecpower(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3728]) ).

cnf(c_0_5090,plain,
    ( class_OrderedGroup_Osemigroup__mult(X1)
    | ~ class_Power_Orecpower(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3729]) ).

cnf(c_0_5091,plain,
    ( class_HOL_Otimes(X1)
    | ~ class_Power_Orecpower(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3730]) ).

cnf(c_0_5092,plain,
    ( class_OrderedGroup_Oab__semigroup__add(X1)
    | ~ class_Power_Orecpower(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3731]) ).

cnf(c_0_5093,plain,
    ( class_OrderedGroup_Osemigroup__add(X1)
    | ~ class_Power_Orecpower(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3732]) ).

cnf(c_0_5094,plain,
    ( class_HOL_Oplus(X1)
    | ~ class_Power_Orecpower(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3733]) ).

cnf(c_0_5095,plain,
    ( class_Ring__and__Field_Oaxclass__0__neq__1(X1)
    | ~ class_Power_Orecpower(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3734]) ).

cnf(c_0_5096,plain,
    ( class_Ring__and__Field_Ocomm__semiring__1__cancel(X1)
    | ~ class_Power_Orecpower(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3735]) ).

cnf(c_0_5097,plain,
    ( class_Ring__and__Field_Ocomm__semiring__0__cancel(X1)
    | ~ class_Power_Orecpower(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3736]) ).

cnf(c_0_5098,plain,
    ( class_Ring__and__Field_Osemiring__1__cancel(X1)
    | ~ class_Power_Orecpower(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3737]) ).

cnf(c_0_5099,plain,
    ( class_Ring__and__Field_Osemiring__0__cancel(X1)
    | ~ class_Power_Orecpower(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3738]) ).

cnf(c_0_5100,plain,
    ( class_OrderedGroup_Ocancel__ab__semigroup__add(X1)
    | ~ class_Power_Orecpower(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3739]) ).

cnf(c_0_5101,plain,
    ( class_HOL_Oone(X1)
    | ~ class_Power_Orecpower(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3740]) ).

cnf(c_0_5102,plain,
    ( class_OrderedGroup_Ocancel__semigroup__add(X1)
    | ~ class_Power_Orecpower(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3741]) ).

cnf(c_0_5103,plain,
    ( class_Ring__and__Field_Ocomm__semiring__1(X1)
    | ~ class_Power_Orecpower(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3742]) ).

cnf(c_0_5104,plain,
    ( class_Ring__and__Field_Osemiring__1(X1)
    | ~ class_Power_Orecpower(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3743]) ).

cnf(c_0_5105,plain,
    ( class_OrderedGroup_Ocomm__monoid__mult(X1)
    | ~ class_Power_Orecpower(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3744]) ).

cnf(c_0_5106,plain,
    ( class_OrderedGroup_Omonoid__mult(X1)
    | ~ class_Power_Orecpower(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3745]) ).

cnf(c_0_5107,plain,
    ( class_Ring__and__Field_Ocomm__semiring__0(X1)
    | ~ class_Power_Orecpower(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3746]) ).

cnf(c_0_5108,plain,
    ( class_Ring__and__Field_Osemiring__0(X1)
    | ~ class_Power_Orecpower(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3747]) ).

cnf(c_0_5109,plain,
    ( class_OrderedGroup_Ocomm__monoid__add(X1)
    | ~ class_Power_Orecpower(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3748]) ).

cnf(c_0_5110,plain,
    ( class_Ring__and__Field_Ocomm__semiring(X1)
    | ~ class_Power_Orecpower(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3749]) ).

cnf(c_0_5111,plain,
    ( class_Ring__and__Field_Osemiring(X1)
    | ~ class_Power_Orecpower(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3750]) ).

cnf(c_0_5112,plain,
    ( class_HOL_Ozero(X1)
    | ~ class_Power_Orecpower(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3751]) ).

cnf(c_0_5113,plain,
    ( class_Nat_Opower(X1)
    | ~ class_Power_Orecpower(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3752]) ).

cnf(c_0_5114,plain,
    ( class_Orderings_Oord(X1)
    | ~ class_Orderings_Oorder(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3753]) ).

cnf(c_0_5115,plain,
    ( class_Orderings_Oorder(X1)
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3754]) ).

cnf(c_0_5116,plain,
    ( class_Orderings_Oord(X1)
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3755]) ).

cnf(c_0_5117,plain,
    ( class_LOrder_Omeet__semilorder(X1)
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3756]) ).

cnf(c_0_5118,plain,
    ( class_LOrder_Ojoin__semilorder(X1)
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3757]) ).

cnf(c_0_5119,plain,
    ( class_LOrder_Olorder(X1)
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3758]) ).

cnf(c_0_5120,plain,
    ( class_HOL_Otimes(X1)
    | ~ class_OrderedGroup_Osemigroup__mult(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3759]) ).

cnf(c_0_5121,plain,
    ( class_HOL_Oplus(X1)
    | ~ class_OrderedGroup_Osemigroup__add(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3760]) ).

cnf(c_0_5122,plain,
    ( class_OrderedGroup_Ocancel__semigroup__add(X1)
    | ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3761]) ).

cnf(c_0_5123,plain,
    ( class_OrderedGroup_Ocancel__ab__semigroup__add(X1)
    | ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3762]) ).

cnf(c_0_5124,plain,
    ( class_HOL_Oplus(X1)
    | ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3763]) ).

cnf(c_0_5125,plain,
    ( class_OrderedGroup_Osemigroup__add(X1)
    | ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3764]) ).

cnf(c_0_5126,plain,
    ( class_OrderedGroup_Oab__semigroup__add(X1)
    | ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3765]) ).

cnf(c_0_5127,plain,
    ( class_Orderings_Oord(X1)
    | ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3766]) ).

cnf(c_0_5128,plain,
    ( class_Orderings_Oorder(X1)
    | ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3767]) ).

cnf(c_0_5129,plain,
    ( class_OrderedGroup_Opordered__ab__semigroup__add(X1)
    | ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3768]) ).

cnf(c_0_5130,plain,
    ( class_HOL_Oplus(X1)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3769]) ).

cnf(c_0_5131,plain,
    ( class_OrderedGroup_Osemigroup__add(X1)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3770]) ).

cnf(c_0_5132,plain,
    ( class_OrderedGroup_Ocancel__semigroup__add(X1)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3771]) ).

cnf(c_0_5133,plain,
    ( class_OrderedGroup_Oab__semigroup__add(X1)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3772]) ).

cnf(c_0_5134,plain,
    ( class_OrderedGroup_Ocancel__ab__semigroup__add(X1)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3773]) ).

cnf(c_0_5135,plain,
    ( class_Orderings_Oord(X1)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3774]) ).

cnf(c_0_5136,plain,
    ( class_Orderings_Oorder(X1)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3775]) ).

cnf(c_0_5137,plain,
    ( class_OrderedGroup_Opordered__ab__semigroup__add(X1)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3776]) ).

cnf(c_0_5138,plain,
    ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3777]) ).

cnf(c_0_5139,plain,
    ( class_HOL_Oplus(X1)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3778]) ).

cnf(c_0_5140,plain,
    ( class_OrderedGroup_Osemigroup__add(X1)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3779]) ).

cnf(c_0_5141,plain,
    ( class_OrderedGroup_Oab__semigroup__add(X1)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3780]) ).

cnf(c_0_5142,plain,
    ( class_Orderings_Oord(X1)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3781]) ).

cnf(c_0_5143,plain,
    ( class_Orderings_Oorder(X1)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3782]) ).

cnf(c_0_5144,plain,
    ( class_OrderedGroup_Opordered__ab__semigroup__add(X1)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3783]) ).

cnf(c_0_5145,plain,
    ( class_HOL_Oplus(X1)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3784]) ).

cnf(c_0_5146,plain,
    ( class_OrderedGroup_Osemigroup__add(X1)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3785]) ).

cnf(c_0_5147,plain,
    ( class_OrderedGroup_Ocancel__semigroup__add(X1)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3786]) ).

cnf(c_0_5148,plain,
    ( class_OrderedGroup_Oab__semigroup__add(X1)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3787]) ).

cnf(c_0_5149,plain,
    ( class_OrderedGroup_Ocancel__ab__semigroup__add(X1)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3788]) ).

cnf(c_0_5150,plain,
    ( class_HOL_Ozero(X1)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3789]) ).

cnf(c_0_5151,plain,
    ( class_OrderedGroup_Ocomm__monoid__add(X1)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3790]) ).

cnf(c_0_5152,plain,
    ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3791]) ).

cnf(c_0_5153,plain,
    ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3792]) ).

cnf(c_0_5154,plain,
    ( class_Orderings_Oord(X1)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3793]) ).

cnf(c_0_5155,plain,
    ( class_Orderings_Oorder(X1)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3794]) ).

cnf(c_0_5156,plain,
    ( class_HOL_Ominus(X1)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3795]) ).

cnf(c_0_5157,plain,
    ( class_OrderedGroup_Oab__group__add(X1)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3796]) ).

cnf(c_0_5158,plain,
    ( class_Orderings_Olinorder(X1)
    | ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3797]) ).

cnf(c_0_5159,plain,
    ( class_HOL_Oplus(X1)
    | ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3798]) ).

cnf(c_0_5160,plain,
    ( class_OrderedGroup_Osemigroup__add(X1)
    | ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3799]) ).

cnf(c_0_5161,plain,
    ( class_OrderedGroup_Ocancel__semigroup__add(X1)
    | ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3800]) ).

cnf(c_0_5162,plain,
    ( class_OrderedGroup_Oab__semigroup__add(X1)
    | ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3801]) ).

cnf(c_0_5163,plain,
    ( class_OrderedGroup_Ocancel__ab__semigroup__add(X1)
    | ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3802]) ).

cnf(c_0_5164,plain,
    ( class_Orderings_Oord(X1)
    | ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3803]) ).

cnf(c_0_5165,plain,
    ( class_Orderings_Oorder(X1)
    | ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3804]) ).

cnf(c_0_5166,plain,
    ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
    | ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3805]) ).

cnf(c_0_5167,plain,
    ( class_LOrder_Omeet__semilorder(X1)
    | ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3806]) ).

cnf(c_0_5168,plain,
    ( class_LOrder_Ojoin__semilorder(X1)
    | ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3807]) ).

cnf(c_0_5169,plain,
    ( class_LOrder_Olorder(X1)
    | ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3808]) ).

cnf(c_0_5170,plain,
    ( class_OrderedGroup_Opordered__ab__semigroup__add(X1)
    | ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3809]) ).

cnf(c_0_5171,plain,
    ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1)
    | ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3810]) ).

cnf(c_0_5172,plain,
    ( class_HOL_Otimes(X1)
    | ~ class_OrderedGroup_Omonoid__mult(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3811]) ).

cnf(c_0_5173,plain,
    ( class_OrderedGroup_Osemigroup__mult(X1)
    | ~ class_OrderedGroup_Omonoid__mult(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3812]) ).

cnf(c_0_5174,plain,
    ( class_HOL_Oone(X1)
    | ~ class_OrderedGroup_Omonoid__mult(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3813]) ).

cnf(c_0_5175,plain,
    ( class_Orderings_Oord(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__meet(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3814]) ).

cnf(c_0_5176,plain,
    ( class_Orderings_Oorder(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__meet(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3815]) ).

cnf(c_0_5177,plain,
    ( class_OrderedGroup_Opordered__ab__semigroup__add(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__meet(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3816]) ).

cnf(c_0_5178,plain,
    ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__meet(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3817]) ).

cnf(c_0_5179,plain,
    ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__meet(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3818]) ).

cnf(c_0_5180,plain,
    ( class_HOL_Ozero(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__meet(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3819]) ).

cnf(c_0_5181,plain,
    ( class_OrderedGroup_Ocomm__monoid__add(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__meet(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3820]) ).

cnf(c_0_5182,plain,
    ( class_HOL_Ominus(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__meet(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3821]) ).

cnf(c_0_5183,plain,
    ( class_LOrder_Ojoin__semilorder(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__meet(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3822]) ).

cnf(c_0_5184,plain,
    ( class_LOrder_Olorder(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__meet(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3823]) ).

cnf(c_0_5185,plain,
    ( class_OrderedGroup_Olordered__ab__group(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__meet(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3824]) ).

cnf(c_0_5186,plain,
    ( class_LOrder_Omeet__semilorder(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__meet(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3825]) ).

cnf(c_0_5187,plain,
    ( class_HOL_Oplus(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__meet(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3826]) ).

cnf(c_0_5188,plain,
    ( class_OrderedGroup_Osemigroup__add(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__meet(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3827]) ).

cnf(c_0_5189,plain,
    ( class_OrderedGroup_Ocancel__semigroup__add(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__meet(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3828]) ).

cnf(c_0_5190,plain,
    ( class_OrderedGroup_Oab__semigroup__add(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__meet(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3829]) ).

cnf(c_0_5191,plain,
    ( class_OrderedGroup_Ocancel__ab__semigroup__add(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__meet(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3830]) ).

cnf(c_0_5192,plain,
    ( class_OrderedGroup_Oab__group__add(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__meet(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3831]) ).

cnf(c_0_5193,plain,
    ( class_OrderedGroup_Opordered__ab__group__add(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__meet(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3832]) ).

cnf(c_0_5194,plain,
    ( class_Orderings_Oord(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__join(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3833]) ).

cnf(c_0_5195,plain,
    ( class_Orderings_Oorder(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__join(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3834]) ).

cnf(c_0_5196,plain,
    ( class_OrderedGroup_Opordered__ab__semigroup__add(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__join(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3835]) ).

cnf(c_0_5197,plain,
    ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__join(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3836]) ).

cnf(c_0_5198,plain,
    ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__join(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3837]) ).

cnf(c_0_5199,plain,
    ( class_HOL_Ozero(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__join(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3838]) ).

cnf(c_0_5200,plain,
    ( class_OrderedGroup_Ocomm__monoid__add(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__join(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3839]) ).

cnf(c_0_5201,plain,
    ( class_HOL_Ominus(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__join(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3840]) ).

cnf(c_0_5202,plain,
    ( class_LOrder_Omeet__semilorder(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__join(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3841]) ).

cnf(c_0_5203,plain,
    ( class_LOrder_Olorder(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__join(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3842]) ).

cnf(c_0_5204,plain,
    ( class_OrderedGroup_Olordered__ab__group(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__join(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3843]) ).

cnf(c_0_5205,plain,
    ( class_LOrder_Ojoin__semilorder(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__join(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3844]) ).

cnf(c_0_5206,plain,
    ( class_HOL_Oplus(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__join(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3845]) ).

cnf(c_0_5207,plain,
    ( class_OrderedGroup_Osemigroup__add(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__join(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3846]) ).

cnf(c_0_5208,plain,
    ( class_OrderedGroup_Ocancel__semigroup__add(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__join(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3847]) ).

cnf(c_0_5209,plain,
    ( class_OrderedGroup_Oab__semigroup__add(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__join(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3848]) ).

cnf(c_0_5210,plain,
    ( class_OrderedGroup_Ocancel__ab__semigroup__add(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__join(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3849]) ).

cnf(c_0_5211,plain,
    ( class_OrderedGroup_Oab__group__add(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__join(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3850]) ).

cnf(c_0_5212,plain,
    ( class_OrderedGroup_Opordered__ab__group__add(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__join(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3851]) ).

cnf(c_0_5213,plain,
    ( class_OrderedGroup_Ocancel__ab__semigroup__add(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__abs(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3852]) ).

cnf(c_0_5214,plain,
    ( class_OrderedGroup_Opordered__ab__semigroup__add(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__abs(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3853]) ).

cnf(c_0_5215,plain,
    ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__abs(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3854]) ).

cnf(c_0_5216,plain,
    ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__abs(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3855]) ).

cnf(c_0_5217,plain,
    ( class_HOL_Ozero(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__abs(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3856]) ).

cnf(c_0_5218,plain,
    ( class_OrderedGroup_Ocomm__monoid__add(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__abs(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3857]) ).

cnf(c_0_5219,plain,
    ( class_HOL_Ominus(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__abs(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3858]) ).

cnf(c_0_5220,plain,
    ( class_OrderedGroup_Oab__group__add(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__abs(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3859]) ).

cnf(c_0_5221,plain,
    ( class_Orderings_Oord(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__abs(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3860]) ).

cnf(c_0_5222,plain,
    ( class_Orderings_Oorder(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__abs(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3861]) ).

cnf(c_0_5223,plain,
    ( class_LOrder_Omeet__semilorder(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__abs(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3862]) ).

cnf(c_0_5224,plain,
    ( class_LOrder_Ojoin__semilorder(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__abs(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3863]) ).

cnf(c_0_5225,plain,
    ( class_LOrder_Olorder(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__abs(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3864]) ).

cnf(c_0_5226,plain,
    ( class_HOL_Oplus(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__abs(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3865]) ).

cnf(c_0_5227,plain,
    ( class_OrderedGroup_Osemigroup__add(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__abs(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3866]) ).

cnf(c_0_5228,plain,
    ( class_OrderedGroup_Ocancel__semigroup__add(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__abs(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3867]) ).

cnf(c_0_5229,plain,
    ( class_OrderedGroup_Oab__semigroup__add(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__abs(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3868]) ).

cnf(c_0_5230,plain,
    ( class_OrderedGroup_Opordered__ab__group__add(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__abs(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3869]) ).

cnf(c_0_5231,plain,
    ( class_OrderedGroup_Olordered__ab__group(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__abs(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3870]) ).

cnf(c_0_5232,plain,
    ( class_Orderings_Oord(X1)
    | ~ class_OrderedGroup_Olordered__ab__group(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3871]) ).

cnf(c_0_5233,plain,
    ( class_Orderings_Oorder(X1)
    | ~ class_OrderedGroup_Olordered__ab__group(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3872]) ).

cnf(c_0_5234,plain,
    ( class_OrderedGroup_Opordered__ab__semigroup__add(X1)
    | ~ class_OrderedGroup_Olordered__ab__group(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3873]) ).

cnf(c_0_5235,plain,
    ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1)
    | ~ class_OrderedGroup_Olordered__ab__group(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3874]) ).

cnf(c_0_5236,plain,
    ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
    | ~ class_OrderedGroup_Olordered__ab__group(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3875]) ).

cnf(c_0_5237,plain,
    ( class_HOL_Ozero(X1)
    | ~ class_OrderedGroup_Olordered__ab__group(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3876]) ).

cnf(c_0_5238,plain,
    ( class_OrderedGroup_Ocomm__monoid__add(X1)
    | ~ class_OrderedGroup_Olordered__ab__group(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3877]) ).

cnf(c_0_5239,plain,
    ( class_HOL_Ominus(X1)
    | ~ class_OrderedGroup_Olordered__ab__group(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3878]) ).

cnf(c_0_5240,plain,
    ( class_LOrder_Omeet__semilorder(X1)
    | ~ class_OrderedGroup_Olordered__ab__group(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3879]) ).

cnf(c_0_5241,plain,
    ( class_LOrder_Ojoin__semilorder(X1)
    | ~ class_OrderedGroup_Olordered__ab__group(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3880]) ).

cnf(c_0_5242,plain,
    ( class_LOrder_Olorder(X1)
    | ~ class_OrderedGroup_Olordered__ab__group(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3881]) ).

cnf(c_0_5243,plain,
    ( class_HOL_Oplus(X1)
    | ~ class_OrderedGroup_Olordered__ab__group(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3882]) ).

cnf(c_0_5244,plain,
    ( class_OrderedGroup_Osemigroup__add(X1)
    | ~ class_OrderedGroup_Olordered__ab__group(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3883]) ).

cnf(c_0_5245,plain,
    ( class_OrderedGroup_Ocancel__semigroup__add(X1)
    | ~ class_OrderedGroup_Olordered__ab__group(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3884]) ).

cnf(c_0_5246,plain,
    ( class_OrderedGroup_Oab__semigroup__add(X1)
    | ~ class_OrderedGroup_Olordered__ab__group(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3885]) ).

cnf(c_0_5247,plain,
    ( class_OrderedGroup_Ocancel__ab__semigroup__add(X1)
    | ~ class_OrderedGroup_Olordered__ab__group(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3886]) ).

cnf(c_0_5248,plain,
    ( class_OrderedGroup_Oab__group__add(X1)
    | ~ class_OrderedGroup_Olordered__ab__group(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3887]) ).

cnf(c_0_5249,plain,
    ( class_OrderedGroup_Opordered__ab__group__add(X1)
    | ~ class_OrderedGroup_Olordered__ab__group(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3888]) ).

cnf(c_0_5250,plain,
    ( class_OrderedGroup_Omonoid__mult(X1)
    | ~ class_OrderedGroup_Ocomm__monoid__mult(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3889]) ).

cnf(c_0_5251,plain,
    ( class_HOL_Otimes(X1)
    | ~ class_OrderedGroup_Ocomm__monoid__mult(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3890]) ).

cnf(c_0_5252,plain,
    ( class_OrderedGroup_Osemigroup__mult(X1)
    | ~ class_OrderedGroup_Ocomm__monoid__mult(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3891]) ).

cnf(c_0_5253,plain,
    ( class_OrderedGroup_Oab__semigroup__mult(X1)
    | ~ class_OrderedGroup_Ocomm__monoid__mult(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3892]) ).

cnf(c_0_5254,plain,
    ( class_HOL_Oone(X1)
    | ~ class_OrderedGroup_Ocomm__monoid__mult(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3893]) ).

cnf(c_0_5255,plain,
    ( class_HOL_Oplus(X1)
    | ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3894]) ).

cnf(c_0_5256,plain,
    ( class_OrderedGroup_Osemigroup__add(X1)
    | ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3895]) ).

cnf(c_0_5257,plain,
    ( class_OrderedGroup_Oab__semigroup__add(X1)
    | ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3896]) ).

cnf(c_0_5258,plain,
    ( class_HOL_Ozero(X1)
    | ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3897]) ).

cnf(c_0_5259,plain,
    ( class_HOL_Oplus(X1)
    | ~ class_OrderedGroup_Ocancel__semigroup__add(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3898]) ).

cnf(c_0_5260,plain,
    ( class_OrderedGroup_Osemigroup__add(X1)
    | ~ class_OrderedGroup_Ocancel__semigroup__add(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3899]) ).

cnf(c_0_5261,plain,
    ( class_OrderedGroup_Ocancel__semigroup__add(X1)
    | ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3900]) ).

cnf(c_0_5262,plain,
    ( class_HOL_Oplus(X1)
    | ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3901]) ).

cnf(c_0_5263,plain,
    ( class_OrderedGroup_Osemigroup__add(X1)
    | ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3902]) ).

cnf(c_0_5264,plain,
    ( class_OrderedGroup_Oab__semigroup__add(X1)
    | ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3903]) ).

cnf(c_0_5265,plain,
    ( class_HOL_Otimes(X1)
    | ~ class_OrderedGroup_Oab__semigroup__mult(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3904]) ).

cnf(c_0_5266,plain,
    ( class_OrderedGroup_Osemigroup__mult(X1)
    | ~ class_OrderedGroup_Oab__semigroup__mult(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3905]) ).

cnf(c_0_5267,plain,
    ( class_HOL_Oplus(X1)
    | ~ class_OrderedGroup_Oab__semigroup__add(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3906]) ).

cnf(c_0_5268,plain,
    ( class_OrderedGroup_Osemigroup__add(X1)
    | ~ class_OrderedGroup_Oab__semigroup__add(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3907]) ).

cnf(c_0_5269,plain,
    ( class_OrderedGroup_Ocancel__semigroup__add(X1)
    | ~ class_OrderedGroup_Oab__group__add(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3908]) ).

cnf(c_0_5270,plain,
    ( class_OrderedGroup_Ocancel__ab__semigroup__add(X1)
    | ~ class_OrderedGroup_Oab__group__add(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3909]) ).

cnf(c_0_5271,plain,
    ( class_HOL_Oplus(X1)
    | ~ class_OrderedGroup_Oab__group__add(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3910]) ).

cnf(c_0_5272,plain,
    ( class_OrderedGroup_Osemigroup__add(X1)
    | ~ class_OrderedGroup_Oab__group__add(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3911]) ).

cnf(c_0_5273,plain,
    ( class_OrderedGroup_Oab__semigroup__add(X1)
    | ~ class_OrderedGroup_Oab__group__add(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3912]) ).

cnf(c_0_5274,plain,
    ( class_HOL_Ozero(X1)
    | ~ class_OrderedGroup_Oab__group__add(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3913]) ).

cnf(c_0_5275,plain,
    ( class_OrderedGroup_Ocomm__monoid__add(X1)
    | ~ class_OrderedGroup_Oab__group__add(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3914]) ).

cnf(c_0_5276,plain,
    ( class_HOL_Ominus(X1)
    | ~ class_OrderedGroup_Oab__group__add(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3915]) ).

cnf(c_0_5277,plain,
    ( class_OrderedGroup_Ocomm__monoid__add(X1)
    | ~ class_Numeral_Onumber__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3916]) ).

cnf(c_0_5278,plain,
    ( class_HOL_Ozero(X1)
    | ~ class_Numeral_Onumber__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3917]) ).

cnf(c_0_5279,plain,
    ( class_Ring__and__Field_Ocomm__semiring(X1)
    | ~ class_Numeral_Onumber__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3918]) ).

cnf(c_0_5280,plain,
    ( class_Ring__and__Field_Osemiring(X1)
    | ~ class_Numeral_Onumber__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3919]) ).

cnf(c_0_5281,plain,
    ( class_OrderedGroup_Oab__semigroup__mult(X1)
    | ~ class_Numeral_Onumber__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3920]) ).

cnf(c_0_5282,plain,
    ( class_OrderedGroup_Osemigroup__mult(X1)
    | ~ class_Numeral_Onumber__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3921]) ).

cnf(c_0_5283,plain,
    ( class_Numeral_Onumber(X1)
    | ~ class_Numeral_Onumber__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3922]) ).

cnf(c_0_5284,plain,
    ( class_HOL_Otimes(X1)
    | ~ class_Numeral_Onumber__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3923]) ).

cnf(c_0_5285,plain,
    ( class_Ring__and__Field_Ocomm__ring__1(X1)
    | ~ class_Numeral_Onumber__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3924]) ).

cnf(c_0_5286,plain,
    ( class_Ring__and__Field_Ocomm__semiring__1__cancel(X1)
    | ~ class_Numeral_Onumber__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3925]) ).

cnf(c_0_5287,plain,
    ( class_Ring__and__Field_Oring__1(X1)
    | ~ class_Numeral_Onumber__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3926]) ).

cnf(c_0_5288,plain,
    ( class_Ring__and__Field_Osemiring__1__cancel(X1)
    | ~ class_Numeral_Onumber__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3927]) ).

cnf(c_0_5289,plain,
    ( class_Ring__and__Field_Ocomm__semiring__1(X1)
    | ~ class_Numeral_Onumber__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3928]) ).

cnf(c_0_5290,plain,
    ( class_Ring__and__Field_Osemiring__1(X1)
    | ~ class_Numeral_Onumber__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3929]) ).

cnf(c_0_5291,plain,
    ( class_OrderedGroup_Ocomm__monoid__mult(X1)
    | ~ class_Numeral_Onumber__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3930]) ).

cnf(c_0_5292,plain,
    ( class_OrderedGroup_Omonoid__mult(X1)
    | ~ class_Numeral_Onumber__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3931]) ).

cnf(c_0_5293,plain,
    ( class_Ring__and__Field_Oaxclass__0__neq__1(X1)
    | ~ class_Numeral_Onumber__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3932]) ).

cnf(c_0_5294,plain,
    ( class_HOL_Oone(X1)
    | ~ class_Numeral_Onumber__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3933]) ).

cnf(c_0_5295,plain,
    ( class_OrderedGroup_Oab__semigroup__add(X1)
    | ~ class_Numeral_Onumber__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3934]) ).

cnf(c_0_5296,plain,
    ( class_Ring__and__Field_Ocomm__ring(X1)
    | ~ class_Numeral_Onumber__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3935]) ).

cnf(c_0_5297,plain,
    ( class_Ring__and__Field_Ocomm__semiring__0__cancel(X1)
    | ~ class_Numeral_Onumber__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3936]) ).

cnf(c_0_5298,plain,
    ( class_Ring__and__Field_Oring(X1)
    | ~ class_Numeral_Onumber__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3937]) ).

cnf(c_0_5299,plain,
    ( class_Ring__and__Field_Osemiring__0__cancel(X1)
    | ~ class_Numeral_Onumber__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3938]) ).

cnf(c_0_5300,plain,
    ( class_OrderedGroup_Oab__group__add(X1)
    | ~ class_Numeral_Onumber__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3939]) ).

cnf(c_0_5301,plain,
    ( class_OrderedGroup_Ocancel__ab__semigroup__add(X1)
    | ~ class_Numeral_Onumber__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3940]) ).

cnf(c_0_5302,plain,
    ( class_OrderedGroup_Ocancel__semigroup__add(X1)
    | ~ class_Numeral_Onumber__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3941]) ).

cnf(c_0_5303,plain,
    ( class_HOL_Ominus(X1)
    | ~ class_Numeral_Onumber__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3942]) ).

cnf(c_0_5304,plain,
    ( class_Ring__and__Field_Ocomm__semiring__0(X1)
    | ~ class_Numeral_Onumber__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3943]) ).

cnf(c_0_5305,plain,
    ( class_Ring__and__Field_Osemiring__0(X1)
    | ~ class_Numeral_Onumber__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3944]) ).

cnf(c_0_5306,plain,
    ( class_OrderedGroup_Osemigroup__add(X1)
    | ~ class_Numeral_Onumber__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3945]) ).

cnf(c_0_5307,plain,
    ( class_HOL_Oplus(X1)
    | ~ class_Numeral_Onumber__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3946]) ).

cnf(c_0_5308,plain,
    ( class_Orderings_Oorder(X1)
    | ~ class_LOrder_Omeet__semilorder(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3947]) ).

cnf(c_0_5309,plain,
    ( class_Orderings_Oord(X1)
    | ~ class_LOrder_Omeet__semilorder(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3948]) ).

cnf(c_0_5310,plain,
    ( class_LOrder_Ojoin__semilorder(X1)
    | ~ class_LOrder_Olorder(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3949]) ).

cnf(c_0_5311,plain,
    ( class_Orderings_Oorder(X1)
    | ~ class_LOrder_Olorder(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3950]) ).

cnf(c_0_5312,plain,
    ( class_Orderings_Oord(X1)
    | ~ class_LOrder_Olorder(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3951]) ).

cnf(c_0_5313,plain,
    ( class_LOrder_Omeet__semilorder(X1)
    | ~ class_LOrder_Olorder(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3952]) ).

cnf(c_0_5314,plain,
    ( class_Orderings_Oorder(X1)
    | ~ class_LOrder_Ojoin__semilorder(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3953]) ).

cnf(c_0_5315,plain,
    ( class_Orderings_Oord(X1)
    | ~ class_LOrder_Ojoin__semilorder(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3954]) ).

cnf(c_0_5316,plain,
    c_Wellfounded__Recursion_Owf(c_Wellfounded__Relations_Oless__than,tc_nat),
    inference(split_conjunct,[status(thm)],[c_0_3955]) ).

cnf(c_0_5317,plain,
    c_Relation_Otrans(c_Wellfounded__Relations_Oless__than,tc_nat),
    inference(split_conjunct,[status(thm)],[c_0_3956]) ).

cnf(c_0_5318,plain,
    class_Nat_Opower(tc_set(X1)),
    inference(split_conjunct,[status(thm)],[c_0_3957]) ).

cnf(c_0_5319,plain,
    class_Orderings_Oorder(tc_set(X1)),
    inference(split_conjunct,[status(thm)],[c_0_3958]) ).

cnf(c_0_5320,plain,
    class_Orderings_Oord(tc_set(X1)),
    inference(split_conjunct,[status(thm)],[c_0_3959]) ).

cnf(c_0_5321,plain,
    class_HOL_Ominus(tc_set(X1)),
    inference(split_conjunct,[status(thm)],[c_0_3960]) ).

cnf(c_0_5322,plain,
    c_0 != c_Suc(X1),
    inference(split_conjunct,[status(thm)],[c_0_3961]) ).

cnf(c_0_5323,plain,
    c_Suc(X1) != c_0,
    inference(split_conjunct,[status(thm)],[c_0_3962]) ).

cnf(c_0_5324,plain,
    class_HOL_Ominus(tc_nat),
    inference(split_conjunct,[status(thm)],[c_0_3963]) ).

cnf(c_0_5325,plain,
    class_Wellfounded__Recursion_Owellorder(tc_nat),
    inference(split_conjunct,[status(thm)],[c_0_3964]) ).

cnf(c_0_5326,plain,
    class_Orderings_Olinorder(tc_nat),
    inference(split_conjunct,[status(thm)],[c_0_3965]) ).

cnf(c_0_5327,plain,
    class_LOrder_Olorder(tc_nat),
    inference(split_conjunct,[status(thm)],[c_0_3966]) ).

cnf(c_0_5328,plain,
    class_LOrder_Ojoin__semilorder(tc_nat),
    inference(split_conjunct,[status(thm)],[c_0_3967]) ).

cnf(c_0_5329,plain,
    class_Parity_Oeven__odd(tc_nat),
    inference(split_conjunct,[status(thm)],[c_0_3968]) ).

cnf(c_0_5330,plain,
    class_Numeral_Onumber(tc_nat),
    inference(split_conjunct,[status(thm)],[c_0_3969]) ).

cnf(c_0_5331,plain,
    class_Power_Orecpower(tc_nat),
    inference(split_conjunct,[status(thm)],[c_0_3970]) ).

cnf(c_0_5332,plain,
    class_Divides_Odiv(tc_nat),
    inference(split_conjunct,[status(thm)],[c_0_3971]) ).

cnf(c_0_5333,plain,
    class_Ring__and__Field_Oordered__semidom(tc_nat),
    inference(split_conjunct,[status(thm)],[c_0_3972]) ).

cnf(c_0_5334,plain,
    class_Ring__and__Field_Oordered__comm__semiring__strict(tc_nat),
    inference(split_conjunct,[status(thm)],[c_0_3973]) ).

cnf(c_0_5335,plain,
    class_Ring__and__Field_Opordered__cancel__comm__semiring(tc_nat),
    inference(split_conjunct,[status(thm)],[c_0_3974]) ).

cnf(c_0_5336,plain,
    class_Ring__and__Field_Opordered__comm__semiring(tc_nat),
    inference(split_conjunct,[status(thm)],[c_0_3975]) ).

cnf(c_0_5337,plain,
    class_LOrder_Omeet__semilorder(tc_nat),
    inference(split_conjunct,[status(thm)],[c_0_3976]) ).

cnf(c_0_5338,plain,
    class_Ring__and__Field_Oordered__semiring__strict(tc_nat),
    inference(split_conjunct,[status(thm)],[c_0_3977]) ).

cnf(c_0_5339,plain,
    class_Ring__and__Field_Opordered__cancel__semiring(tc_nat),
    inference(split_conjunct,[status(thm)],[c_0_3978]) ).

cnf(c_0_5340,plain,
    class_Ring__and__Field_Opordered__semiring(tc_nat),
    inference(split_conjunct,[status(thm)],[c_0_3979]) ).

cnf(c_0_5341,plain,
    class_OrderedGroup_Oordered__cancel__ab__semigroup__add(tc_nat),
    inference(split_conjunct,[status(thm)],[c_0_3980]) ).

cnf(c_0_5342,plain,
    class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat),
    inference(split_conjunct,[status(thm)],[c_0_3981]) ).

cnf(c_0_5343,plain,
    class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat),
    inference(split_conjunct,[status(thm)],[c_0_3982]) ).

cnf(c_0_5344,plain,
    class_OrderedGroup_Opordered__ab__semigroup__add(tc_nat),
    inference(split_conjunct,[status(thm)],[c_0_3983]) ).

cnf(c_0_5345,plain,
    class_Ring__and__Field_Ocomm__semiring__1__cancel(tc_nat),
    inference(split_conjunct,[status(thm)],[c_0_3984]) ).

cnf(c_0_5346,plain,
    class_Ring__and__Field_Ocomm__semiring__0__cancel(tc_nat),
    inference(split_conjunct,[status(thm)],[c_0_3985]) ).

cnf(c_0_5347,plain,
    class_Ring__and__Field_Osemiring__1__cancel(tc_nat),
    inference(split_conjunct,[status(thm)],[c_0_3986]) ).

cnf(c_0_5348,plain,
    class_Orderings_Oorder(tc_nat),
    inference(split_conjunct,[status(thm)],[c_0_3987]) ).

cnf(c_0_5349,plain,
    class_Ring__and__Field_Osemiring__0__cancel(tc_nat),
    inference(split_conjunct,[status(thm)],[c_0_3988]) ).

cnf(c_0_5350,plain,
    class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat),
    inference(split_conjunct,[status(thm)],[c_0_3989]) ).

cnf(c_0_5351,plain,
    class_OrderedGroup_Ocancel__semigroup__add(tc_nat),
    inference(split_conjunct,[status(thm)],[c_0_3990]) ).

cnf(c_0_5352,plain,
    class_Ring__and__Field_Ocomm__semiring__1(tc_nat),
    inference(split_conjunct,[status(thm)],[c_0_3991]) ).

cnf(c_0_5353,plain,
    class_Ring__and__Field_Osemiring__1(tc_nat),
    inference(split_conjunct,[status(thm)],[c_0_3992]) ).

cnf(c_0_5354,plain,
    class_OrderedGroup_Ocomm__monoid__mult(tc_nat),
    inference(split_conjunct,[status(thm)],[c_0_3993]) ).

cnf(c_0_5355,plain,
    class_OrderedGroup_Omonoid__mult(tc_nat),
    inference(split_conjunct,[status(thm)],[c_0_3994]) ).

cnf(c_0_5356,plain,
    class_Ring__and__Field_Ocomm__semiring__0(tc_nat),
    inference(split_conjunct,[status(thm)],[c_0_3995]) ).

cnf(c_0_5357,plain,
    class_Ring__and__Field_Osemiring__0(tc_nat),
    inference(split_conjunct,[status(thm)],[c_0_3996]) ).

cnf(c_0_5358,plain,
    class_OrderedGroup_Ocomm__monoid__add(tc_nat),
    inference(split_conjunct,[status(thm)],[c_0_3997]) ).

cnf(c_0_5359,plain,
    class_Orderings_Oord(tc_nat),
    inference(split_conjunct,[status(thm)],[c_0_3998]) ).

cnf(c_0_5360,plain,
    class_Ring__and__Field_Ocomm__semiring(tc_nat),
    inference(split_conjunct,[status(thm)],[c_0_3999]) ).

cnf(c_0_5361,plain,
    class_Ring__and__Field_Osemiring(tc_nat),
    inference(split_conjunct,[status(thm)],[c_0_4000]) ).

cnf(c_0_5362,plain,
    class_OrderedGroup_Oab__semigroup__mult(tc_nat),
    inference(split_conjunct,[status(thm)],[c_0_4001]) ).

cnf(c_0_5363,plain,
    class_OrderedGroup_Osemigroup__mult(tc_nat),
    inference(split_conjunct,[status(thm)],[c_0_4002]) ).

cnf(c_0_5364,plain,
    class_OrderedGroup_Oab__semigroup__add(tc_nat),
    inference(split_conjunct,[status(thm)],[c_0_4003]) ).

cnf(c_0_5365,plain,
    class_OrderedGroup_Osemigroup__add(tc_nat),
    inference(split_conjunct,[status(thm)],[c_0_4004]) ).

cnf(c_0_5366,plain,
    class_Ring__and__Field_Oaxclass__0__neq__1(tc_nat),
    inference(split_conjunct,[status(thm)],[c_0_4005]) ).

cnf(c_0_5367,plain,
    class_Nat_Opower(tc_nat),
    inference(split_conjunct,[status(thm)],[c_0_4006]) ).

cnf(c_0_5368,plain,
    class_HOL_Otimes(tc_nat),
    inference(split_conjunct,[status(thm)],[c_0_4007]) ).

cnf(c_0_5369,plain,
    class_HOL_Oplus(tc_nat),
    inference(split_conjunct,[status(thm)],[c_0_4008]) ).

cnf(c_0_5370,plain,
    class_HOL_Ozero(tc_nat),
    inference(split_conjunct,[status(thm)],[c_0_4009]) ).

cnf(c_0_5371,plain,
    class_HOL_Oone(tc_nat),
    inference(split_conjunct,[status(thm)],[c_0_4010]) ).

cnf(c_0_5372,plain,
    class_Finite__Set_Ofinite(tc_bool),
    inference(split_conjunct,[status(thm)],[c_0_4011]) ).

cnf(c_0_5373,plain,
    class_Finite__Set_Ofinite(tc_Product__Type_Ounit),
    inference(split_conjunct,[status(thm)],[c_0_4012]) ).

cnf(c_0_5374,plain,
    class_OrderedGroup_Oab__semigroup__mult(tc_IntDef_Oint),
    inference(split_conjunct,[status(thm)],[c_0_4013]) ).

cnf(c_0_5375,plain,
    class_OrderedGroup_Osemigroup__mult(tc_IntDef_Oint),
    inference(split_conjunct,[status(thm)],[c_0_4014]) ).

cnf(c_0_5376,plain,
    class_OrderedGroup_Oab__semigroup__add(tc_IntDef_Oint),
    inference(split_conjunct,[status(thm)],[c_0_4015]) ).

cnf(c_0_5377,plain,
    class_Parity_Oeven__odd(tc_IntDef_Oint),
    inference(split_conjunct,[status(thm)],[c_0_4016]) ).

cnf(c_0_5378,plain,
    class_Power_Orecpower(tc_IntDef_Oint),
    inference(split_conjunct,[status(thm)],[c_0_4017]) ).

cnf(c_0_5379,plain,
    class_Nat_Opower(tc_IntDef_Oint),
    inference(split_conjunct,[status(thm)],[c_0_4018]) ).

cnf(c_0_5380,plain,
    class_Divides_Odiv(tc_IntDef_Oint),
    inference(split_conjunct,[status(thm)],[c_0_4019]) ).

cnf(c_0_5381,plain,
    class_Numeral_Onumber__ring(tc_IntDef_Oint),
    inference(split_conjunct,[status(thm)],[c_0_4020]) ).

cnf(c_0_5382,plain,
    class_OrderedGroup_Osemigroup__add(tc_IntDef_Oint),
    inference(split_conjunct,[status(thm)],[c_0_4021]) ).

cnf(c_0_5383,plain,
    class_Numeral_Onumber(tc_IntDef_Oint),
    inference(split_conjunct,[status(thm)],[c_0_4022]) ).

cnf(c_0_5384,plain,
    class_Ring__and__Field_Oordered__idom(tc_IntDef_Oint),
    inference(split_conjunct,[status(thm)],[c_0_4023]) ).

cnf(c_0_5385,plain,
    class_Ring__and__Field_Oidom(tc_IntDef_Oint),
    inference(split_conjunct,[status(thm)],[c_0_4024]) ).

cnf(c_0_5386,plain,
    class_Ring__and__Field_Oordered__semidom(tc_IntDef_Oint),
    inference(split_conjunct,[status(thm)],[c_0_4025]) ).

cnf(c_0_5387,plain,
    class_Ring__and__Field_Oordered__ring__strict(tc_IntDef_Oint),
    inference(split_conjunct,[status(thm)],[c_0_4026]) ).

cnf(c_0_5388,plain,
    class_Ring__and__Field_Oaxclass__no__zero__divisors(tc_IntDef_Oint),
    inference(split_conjunct,[status(thm)],[c_0_4027]) ).

cnf(c_0_5389,plain,
    class_Ring__and__Field_Olordered__ring(tc_IntDef_Oint),
    inference(split_conjunct,[status(thm)],[c_0_4028]) ).

cnf(c_0_5390,plain,
    class_OrderedGroup_Olordered__ab__group__join(tc_IntDef_Oint),
    inference(split_conjunct,[status(thm)],[c_0_4029]) ).

cnf(c_0_5391,plain,
    class_OrderedGroup_Olordered__ab__group__meet(tc_IntDef_Oint),
    inference(split_conjunct,[status(thm)],[c_0_4030]) ).

cnf(c_0_5392,plain,
    class_OrderedGroup_Olordered__ab__group__abs(tc_IntDef_Oint),
    inference(split_conjunct,[status(thm)],[c_0_4031]) ).

cnf(c_0_5393,plain,
    class_Orderings_Oord(tc_IntDef_Oint),
    inference(split_conjunct,[status(thm)],[c_0_4032]) ).

cnf(c_0_5394,plain,
    class_Ring__and__Field_Opordered__ring(tc_IntDef_Oint),
    inference(split_conjunct,[status(thm)],[c_0_4033]) ).

cnf(c_0_5395,plain,
    class_OrderedGroup_Olordered__ab__group(tc_IntDef_Oint),
    inference(split_conjunct,[status(thm)],[c_0_4034]) ).

cnf(c_0_5396,plain,
    class_OrderedGroup_Opordered__ab__group__add(tc_IntDef_Oint),
    inference(split_conjunct,[status(thm)],[c_0_4035]) ).

cnf(c_0_5397,plain,
    class_Ring__and__Field_Oaxclass__abs__if(tc_IntDef_Oint),
    inference(split_conjunct,[status(thm)],[c_0_4036]) ).

cnf(c_0_5398,plain,
    class_Ring__and__Field_Oordered__comm__semiring__strict(tc_IntDef_Oint),
    inference(split_conjunct,[status(thm)],[c_0_4037]) ).

cnf(c_0_5399,plain,
    class_Ring__and__Field_Opordered__cancel__comm__semiring(tc_IntDef_Oint),
    inference(split_conjunct,[status(thm)],[c_0_4038]) ).

cnf(c_0_5400,plain,
    class_Ring__and__Field_Opordered__comm__semiring(tc_IntDef_Oint),
    inference(split_conjunct,[status(thm)],[c_0_4039]) ).

cnf(c_0_5401,plain,
    class_Ring__and__Field_Oordered__semiring__strict(tc_IntDef_Oint),
    inference(split_conjunct,[status(thm)],[c_0_4040]) ).

cnf(c_0_5402,plain,
    class_Ring__and__Field_Opordered__cancel__semiring(tc_IntDef_Oint),
    inference(split_conjunct,[status(thm)],[c_0_4041]) ).

cnf(c_0_5403,plain,
    class_Ring__and__Field_Opordered__semiring(tc_IntDef_Oint),
    inference(split_conjunct,[status(thm)],[c_0_4042]) ).

cnf(c_0_5404,plain,
    class_HOL_Ozero(tc_IntDef_Oint),
    inference(split_conjunct,[status(thm)],[c_0_4043]) ).

cnf(c_0_5405,plain,
    class_OrderedGroup_Oordered__cancel__ab__semigroup__add(tc_IntDef_Oint),
    inference(split_conjunct,[status(thm)],[c_0_4044]) ).

cnf(c_0_5406,plain,
    class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_IntDef_Oint),
    inference(split_conjunct,[status(thm)],[c_0_4045]) ).

cnf(c_0_5407,plain,
    class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_IntDef_Oint),
    inference(split_conjunct,[status(thm)],[c_0_4046]) ).

cnf(c_0_5408,plain,
    class_OrderedGroup_Opordered__ab__semigroup__add(tc_IntDef_Oint),
    inference(split_conjunct,[status(thm)],[c_0_4047]) ).

cnf(c_0_5409,plain,
    class_Orderings_Olinorder(tc_IntDef_Oint),
    inference(split_conjunct,[status(thm)],[c_0_4048]) ).

cnf(c_0_5410,plain,
    class_LOrder_Olorder(tc_IntDef_Oint),
    inference(split_conjunct,[status(thm)],[c_0_4049]) ).

cnf(c_0_5411,plain,
    class_LOrder_Ojoin__semilorder(tc_IntDef_Oint),
    inference(split_conjunct,[status(thm)],[c_0_4050]) ).

cnf(c_0_5412,plain,
    class_LOrder_Omeet__semilorder(tc_IntDef_Oint),
    inference(split_conjunct,[status(thm)],[c_0_4051]) ).

cnf(c_0_5413,plain,
    class_Orderings_Oorder(tc_IntDef_Oint),
    inference(split_conjunct,[status(thm)],[c_0_4052]) ).

cnf(c_0_5414,plain,
    class_Ring__and__Field_Ocomm__ring__1(tc_IntDef_Oint),
    inference(split_conjunct,[status(thm)],[c_0_4053]) ).

cnf(c_0_5415,plain,
    class_HOL_Otimes(tc_IntDef_Oint),
    inference(split_conjunct,[status(thm)],[c_0_4054]) ).

cnf(c_0_5416,plain,
    class_Ring__and__Field_Ocomm__semiring__1__cancel(tc_IntDef_Oint),
    inference(split_conjunct,[status(thm)],[c_0_4055]) ).

cnf(c_0_5417,plain,
    class_Ring__and__Field_Oring__1(tc_IntDef_Oint),
    inference(split_conjunct,[status(thm)],[c_0_4056]) ).

cnf(c_0_5418,plain,
    class_Ring__and__Field_Osemiring__1__cancel(tc_IntDef_Oint),
    inference(split_conjunct,[status(thm)],[c_0_4057]) ).

cnf(c_0_5419,plain,
    class_Ring__and__Field_Ocomm__semiring__1(tc_IntDef_Oint),
    inference(split_conjunct,[status(thm)],[c_0_4058]) ).

cnf(c_0_5420,plain,
    class_Ring__and__Field_Osemiring__1(tc_IntDef_Oint),
    inference(split_conjunct,[status(thm)],[c_0_4059]) ).

cnf(c_0_5421,plain,
    class_OrderedGroup_Ocomm__monoid__mult(tc_IntDef_Oint),
    inference(split_conjunct,[status(thm)],[c_0_4060]) ).

cnf(c_0_5422,plain,
    class_OrderedGroup_Omonoid__mult(tc_IntDef_Oint),
    inference(split_conjunct,[status(thm)],[c_0_4061]) ).

cnf(c_0_5423,plain,
    class_Ring__and__Field_Oaxclass__0__neq__1(tc_IntDef_Oint),
    inference(split_conjunct,[status(thm)],[c_0_4062]) ).

cnf(c_0_5424,plain,
    class_Ring__and__Field_Ocomm__ring(tc_IntDef_Oint),
    inference(split_conjunct,[status(thm)],[c_0_4063]) ).

cnf(c_0_5425,plain,
    class_Ring__and__Field_Ocomm__semiring__0__cancel(tc_IntDef_Oint),
    inference(split_conjunct,[status(thm)],[c_0_4064]) ).

cnf(c_0_5426,plain,
    class_HOL_Oplus(tc_IntDef_Oint),
    inference(split_conjunct,[status(thm)],[c_0_4065]) ).

cnf(c_0_5427,plain,
    class_Ring__and__Field_Oring(tc_IntDef_Oint),
    inference(split_conjunct,[status(thm)],[c_0_4066]) ).

cnf(c_0_5428,plain,
    class_Ring__and__Field_Osemiring__0__cancel(tc_IntDef_Oint),
    inference(split_conjunct,[status(thm)],[c_0_4067]) ).

cnf(c_0_5429,plain,
    class_OrderedGroup_Oab__group__add(tc_IntDef_Oint),
    inference(split_conjunct,[status(thm)],[c_0_4068]) ).

cnf(c_0_5430,plain,
    class_OrderedGroup_Ocancel__ab__semigroup__add(tc_IntDef_Oint),
    inference(split_conjunct,[status(thm)],[c_0_4069]) ).

cnf(c_0_5431,plain,
    class_OrderedGroup_Ocancel__semigroup__add(tc_IntDef_Oint),
    inference(split_conjunct,[status(thm)],[c_0_4070]) ).

cnf(c_0_5432,plain,
    class_Ring__and__Field_Ocomm__semiring__0(tc_IntDef_Oint),
    inference(split_conjunct,[status(thm)],[c_0_4071]) ).

cnf(c_0_5433,plain,
    class_Ring__and__Field_Osemiring__0(tc_IntDef_Oint),
    inference(split_conjunct,[status(thm)],[c_0_4072]) ).

cnf(c_0_5434,plain,
    class_OrderedGroup_Ocomm__monoid__add(tc_IntDef_Oint),
    inference(split_conjunct,[status(thm)],[c_0_4073]) ).

cnf(c_0_5435,plain,
    class_Ring__and__Field_Ocomm__semiring(tc_IntDef_Oint),
    inference(split_conjunct,[status(thm)],[c_0_4074]) ).

cnf(c_0_5436,plain,
    class_Ring__and__Field_Osemiring(tc_IntDef_Oint),
    inference(split_conjunct,[status(thm)],[c_0_4075]) ).

cnf(c_0_5437,plain,
    class_HOL_Oone(tc_IntDef_Oint),
    inference(split_conjunct,[status(thm)],[c_0_4076]) ).

cnf(c_0_5438,plain,
    class_HOL_Ominus(tc_IntDef_Oint),
    inference(split_conjunct,[status(thm)],[c_0_4077]) ).

cnf(c_0_5439,plain,
    c_UNIV != c_emptyset,
    inference(split_conjunct,[status(thm)],[c_0_4078]) ).

cnf(c_0_5440,plain,
    c_Numeral_Obit_OB1 != c_Numeral_Obit_OB0,
    inference(split_conjunct,[status(thm)],[c_0_4079]) ).

cnf(c_0_5441,plain,
    c_Numeral_Obit_OB0 != c_Numeral_Obit_OB1,
    inference(split_conjunct,[status(thm)],[c_0_4080]) ).

cnf(c_0_5442,plain,
    c_Extraction_Osumbool_ORight != c_Extraction_Osumbool_OLeft,
    inference(split_conjunct,[status(thm)],[c_0_4081]) ).

cnf(c_0_5443,plain,
    c_Extraction_Osumbool_OLeft != c_Extraction_Osumbool_ORight,
    inference(split_conjunct,[status(thm)],[c_0_4082]) ).

cnf(c_0_5444,plain,
    ( c_in(c_Pair(c_Main_Orel__compE__1(X1,X2,X3,X4,X5,X6),c_Main_Orel__compE__2(X1,X2,X3,X4,X5,X6),X6,X4),X2,tc_prod(X6,X4))
    | ~ c_in(X3,c_Relation_Orel__comp(X1,X2,X4,X5,X6),tc_prod(X6,X5)) ),
    c_0_4083,
    [final] ).

cnf(c_0_5445,plain,
    ( c_in(c_Pair(c_Main_Orel__compE__2(X1,X2,X3,X4,X5,X6),c_Main_Orel__compE__3(X1,X2,X3,X4,X5,X6),X4,X5),X1,tc_prod(X4,X5))
    | ~ c_in(X3,c_Relation_Orel__comp(X1,X2,X4,X5,X6),tc_prod(X6,X5)) ),
    c_0_4084,
    [final] ).

cnf(c_0_5446,plain,
    ( c_Pair(c_Main_Orel__compE__1(X2,X3,X1,X4,X5,X6),c_Main_Orel__compE__3(X2,X3,X1,X4,X5,X6),X6,X5) = X1
    | ~ c_in(X1,c_Relation_Orel__comp(X2,X3,X4,X5,X6),tc_prod(X6,X5)) ),
    c_0_4085,
    [final] ).

cnf(c_0_5447,plain,
    ( c_Pair(c_Datatype__Universe_OScons(c_Main_OdprodE__1(X1,X2,X3,X4,X5),c_Main_OdprodE__2(X1,X2,X3,X4,X5),X4,X5),c_Datatype__Universe_OScons(c_Main_OdprodE__3(X1,X2,X3,X4,X5),c_Main_OdprodE__4(X1,X2,X3,X4,X5),X4,X5),tc_set(tc_Datatype__Universe_Onode(X4,X5)),tc_set(tc_Datatype__Universe_Onode(X4,X5))) = X1
    | ~ c_in(X1,c_Datatype__Universe_Odprod(X2,X3,X4,X5),tc_prod(tc_set(tc_Datatype__Universe_Onode(X4,X5)),tc_set(tc_Datatype__Universe_Onode(X4,X5)))) ),
    c_0_4086,
    [final] ).

cnf(c_0_5448,plain,
    ( c_in(c_Pair(c_Main_OdprodE__1(X1,X2,X3,X4,X5),c_Main_OdprodE__3(X1,X2,X3,X4,X5),tc_set(tc_Datatype__Universe_Onode(X4,X5)),tc_set(tc_Datatype__Universe_Onode(X4,X5))),X2,tc_prod(tc_set(tc_Datatype__Universe_Onode(X4,X5)),tc_set(tc_Datatype__Universe_Onode(X4,X5))))
    | ~ c_in(X1,c_Datatype__Universe_Odprod(X2,X3,X4,X5),tc_prod(tc_set(tc_Datatype__Universe_Onode(X4,X5)),tc_set(tc_Datatype__Universe_Onode(X4,X5)))) ),
    c_0_4087,
    [final] ).

cnf(c_0_5449,plain,
    ( c_in(c_Pair(c_Main_OdprodE__2(X1,X2,X3,X4,X5),c_Main_OdprodE__4(X1,X2,X3,X4,X5),tc_set(tc_Datatype__Universe_Onode(X4,X5)),tc_set(tc_Datatype__Universe_Onode(X4,X5))),X3,tc_prod(tc_set(tc_Datatype__Universe_Onode(X4,X5)),tc_set(tc_Datatype__Universe_Onode(X4,X5))))
    | ~ c_in(X1,c_Datatype__Universe_Odprod(X2,X3,X4,X5),tc_prod(tc_set(tc_Datatype__Universe_Onode(X4,X5)),tc_set(tc_Datatype__Universe_Onode(X4,X5)))) ),
    c_0_4088,
    [final] ).

cnf(c_0_5450,plain,
    ( c_in(c_Pair(c_Main_OdsumE__3(X1,X2,X3,X4),c_Main_OdsumE__4(X1,X2,X3,X4),tc_set(tc_Datatype__Universe_Onode(X3,X4)),tc_set(tc_Datatype__Universe_Onode(X3,X4))),X1,tc_prod(tc_set(tc_Datatype__Universe_Onode(X3,X4)),tc_set(tc_Datatype__Universe_Onode(X3,X4))))
    | c_in(c_Pair(c_Main_OdsumE__1(X5,X2,X3,X4),c_Main_OdsumE__2(X5,X2,X3,X4),tc_set(tc_Datatype__Universe_Onode(X3,X4)),tc_set(tc_Datatype__Universe_Onode(X3,X4))),X5,tc_prod(tc_set(tc_Datatype__Universe_Onode(X3,X4)),tc_set(tc_Datatype__Universe_Onode(X3,X4))))
    | ~ c_in(X2,c_Datatype__Universe_Odsum(X5,X1,X3,X4),tc_prod(tc_set(tc_Datatype__Universe_Onode(X3,X4)),tc_set(tc_Datatype__Universe_Onode(X3,X4)))) ),
    c_0_4089,
    [final] ).

cnf(c_0_5451,plain,
    ( c_Pair(c_Datatype__Universe_OIn1(c_Main_OdsumE__3(X2,X1,X3,X4),X3,X4),c_Datatype__Universe_OIn1(c_Main_OdsumE__4(X2,X1,X3,X4),X3,X4),tc_set(tc_Datatype__Universe_Onode(X3,X4)),tc_set(tc_Datatype__Universe_Onode(X3,X4))) = X1
    | c_in(c_Pair(c_Main_OdsumE__1(X5,X1,X3,X4),c_Main_OdsumE__2(X5,X1,X3,X4),tc_set(tc_Datatype__Universe_Onode(X3,X4)),tc_set(tc_Datatype__Universe_Onode(X3,X4))),X5,tc_prod(tc_set(tc_Datatype__Universe_Onode(X3,X4)),tc_set(tc_Datatype__Universe_Onode(X3,X4))))
    | ~ c_in(X1,c_Datatype__Universe_Odsum(X5,X2,X3,X4),tc_prod(tc_set(tc_Datatype__Universe_Onode(X3,X4)),tc_set(tc_Datatype__Universe_Onode(X3,X4)))) ),
    c_0_4090,
    [final] ).

cnf(c_0_5452,plain,
    ( c_Pair(c_Datatype__Universe_OIn0(c_Main_OdsumE__1(X2,X1,X3,X4),X3,X4),c_Datatype__Universe_OIn0(c_Main_OdsumE__2(X2,X1,X3,X4),X3,X4),tc_set(tc_Datatype__Universe_Onode(X3,X4)),tc_set(tc_Datatype__Universe_Onode(X3,X4))) = X1
    | c_in(c_Pair(c_Main_OdsumE__3(X5,X1,X3,X4),c_Main_OdsumE__4(X5,X1,X3,X4),tc_set(tc_Datatype__Universe_Onode(X3,X4)),tc_set(tc_Datatype__Universe_Onode(X3,X4))),X5,tc_prod(tc_set(tc_Datatype__Universe_Onode(X3,X4)),tc_set(tc_Datatype__Universe_Onode(X3,X4))))
    | ~ c_in(X1,c_Datatype__Universe_Odsum(X2,X5,X3,X4),tc_prod(tc_set(tc_Datatype__Universe_Onode(X3,X4)),tc_set(tc_Datatype__Universe_Onode(X3,X4)))) ),
    c_0_4091,
    [final] ).

cnf(c_0_5453,plain,
    ( c_in(c_Pair(c_Main_Olistrel__Cons2__2(X1,X2,X3,X4,X5),X4,tc_List_Olist(X5),tc_List_Olist(X5)),c_List_Olistrel(X1,X5),tc_prod(tc_List_Olist(X5),tc_List_Olist(X5)))
    | ~ c_in(c_Pair(X2,c_List_Olist_OCons(X3,X4,X5),tc_List_Olist(X5),tc_List_Olist(X5)),c_List_Olistrel(X1,X5),tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))) ),
    c_0_4092,
    [final] ).

cnf(c_0_5454,plain,
    ( c_in(c_Pair(X1,c_Main_Olistrel__Cons1__2(X2,X3,X4,X1,X5),tc_List_Olist(X5),tc_List_Olist(X5)),c_List_Olistrel(X2,X5),tc_prod(tc_List_Olist(X5),tc_List_Olist(X5)))
    | ~ c_in(c_Pair(c_List_Olist_OCons(X4,X1,X5),X3,tc_List_Olist(X5),tc_List_Olist(X5)),c_List_Olistrel(X2,X5),tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))) ),
    c_0_4093,
    [final] ).

cnf(c_0_5455,plain,
    ( c_in(c_Pair(c_Datatype__Universe_OScons(X1,X2,X3,X4),c_Datatype__Universe_OScons(X5,X6,X3,X4),tc_set(tc_Datatype__Universe_Onode(X3,X4)),tc_set(tc_Datatype__Universe_Onode(X3,X4))),c_Datatype__Universe_Odprod(X7,X8,X3,X4),tc_prod(tc_set(tc_Datatype__Universe_Onode(X3,X4)),tc_set(tc_Datatype__Universe_Onode(X3,X4))))
    | ~ c_in(c_Pair(X1,X5,tc_set(tc_Datatype__Universe_Onode(X3,X4)),tc_set(tc_Datatype__Universe_Onode(X3,X4))),X7,tc_prod(tc_set(tc_Datatype__Universe_Onode(X3,X4)),tc_set(tc_Datatype__Universe_Onode(X3,X4))))
    | ~ c_in(c_Pair(X2,X6,tc_set(tc_Datatype__Universe_Onode(X3,X4)),tc_set(tc_Datatype__Universe_Onode(X3,X4))),X8,tc_prod(tc_set(tc_Datatype__Universe_Onode(X3,X4)),tc_set(tc_Datatype__Universe_Onode(X3,X4)))) ),
    c_0_4094,
    [final] ).

cnf(c_0_5456,plain,
    ( c_in(c_Pair(c_Main_Olistrel__Cons2__1(X1,X2,X3,X4,X5),X3,X5,X5),X1,tc_prod(X5,X5))
    | ~ c_in(c_Pair(X2,c_List_Olist_OCons(X3,X4,X5),tc_List_Olist(X5),tc_List_Olist(X5)),c_List_Olistrel(X1,X5),tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))) ),
    c_0_4095,
    [final] ).

cnf(c_0_5457,plain,
    ( c_in(c_Pair(X1,c_Main_Olistrel__Cons1__1(X2,X3,X1,X4,X5),X5,X5),X2,tc_prod(X5,X5))
    | ~ c_in(c_Pair(c_List_Olist_OCons(X1,X4,X5),X3,tc_List_Olist(X5),tc_List_Olist(X5)),c_List_Olistrel(X2,X5),tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))) ),
    c_0_4096,
    [final] ).

cnf(c_0_5458,plain,
    ( c_Pair(c_Datatype__Universe_OIn1(c_Main_OdsumE__3(X2,X1,X3,X4),X3,X4),c_Datatype__Universe_OIn1(c_Main_OdsumE__4(X2,X1,X3,X4),X3,X4),tc_set(tc_Datatype__Universe_Onode(X3,X4)),tc_set(tc_Datatype__Universe_Onode(X3,X4))) = X1
    | c_Pair(c_Datatype__Universe_OIn0(c_Main_OdsumE__1(X5,X1,X3,X4),X3,X4),c_Datatype__Universe_OIn0(c_Main_OdsumE__2(X5,X1,X3,X4),X3,X4),tc_set(tc_Datatype__Universe_Onode(X3,X4)),tc_set(tc_Datatype__Universe_Onode(X3,X4))) = X1
    | ~ c_in(X1,c_Datatype__Universe_Odsum(X5,X2,X3,X4),tc_prod(tc_set(tc_Datatype__Universe_Onode(X3,X4)),tc_set(tc_Datatype__Universe_Onode(X3,X4)))) ),
    c_0_4097,
    [final] ).

cnf(c_0_5459,plain,
    ( c_in(c_Pair(c_Main_OImageE__1(X1,X2,X3,X4,X5),X2,X4,X5),X3,tc_prod(X4,X5))
    | ~ c_in(X2,c_Relation_OImage(X3,X1,X4,X5),X5) ),
    c_0_4098,
    [final] ).

cnf(c_0_5460,plain,
    ( c_List_Olist_OCons(c_Main_Olistrel__Cons2__1(X2,X1,X3,X4,X5),c_Main_Olistrel__Cons2__2(X2,X1,X3,X4,X5),X5) = X1
    | ~ c_in(c_Pair(X1,c_List_Olist_OCons(X3,X4,X5),tc_List_Olist(X5),tc_List_Olist(X5)),c_List_Olistrel(X2,X5),tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))) ),
    c_0_4099,
    [final] ).

cnf(c_0_5461,plain,
    ( c_List_Olist_OCons(c_Main_Olistrel__Cons1__1(X2,X1,X3,X4,X5),c_Main_Olistrel__Cons1__2(X2,X1,X3,X4,X5),X5) = X1
    | ~ c_in(c_Pair(c_List_Olist_OCons(X3,X4,X5),X1,tc_List_Olist(X5),tc_List_Olist(X5)),c_List_Olistrel(X2,X5),tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))) ),
    c_0_4100,
    [final] ).

cnf(c_0_5462,plain,
    ( c_Datatype__Universe_OScons(c_Main_OuprodE__1(X2,X3,X1,X4,X5),c_Main_OuprodE__2(X2,X3,X1,X4,X5),X4,X5) = X1
    | ~ c_in(X1,c_Datatype__Universe_Ouprod(X2,X3,X4,X5),tc_set(tc_Datatype__Universe_Onode(X4,X5))) ),
    c_0_4101,
    [final] ).

cnf(c_0_5463,plain,
    ( c_in(c_Pair(X1,X2,X3,X4),c_Relation_Orel__comp(X5,X6,X7,X4,X3),tc_prod(X3,X4))
    | ~ c_in(c_Pair(X1,X8,X3,X7),X6,tc_prod(X3,X7))
    | ~ c_in(c_Pair(X8,X2,X7,X4),X5,tc_prod(X7,X4)) ),
    c_0_4102,
    [final] ).

cnf(c_0_5464,plain,
    ( c_in(c_Pair(c_Datatype__Universe_OIn1(X1,X2,X3),c_Datatype__Universe_OIn1(X4,X2,X3),tc_set(tc_Datatype__Universe_Onode(X2,X3)),tc_set(tc_Datatype__Universe_Onode(X2,X3))),c_Datatype__Universe_Odsum(X5,X6,X2,X3),tc_prod(tc_set(tc_Datatype__Universe_Onode(X2,X3)),tc_set(tc_Datatype__Universe_Onode(X2,X3))))
    | ~ c_in(c_Pair(X1,X4,tc_set(tc_Datatype__Universe_Onode(X2,X3)),tc_set(tc_Datatype__Universe_Onode(X2,X3))),X6,tc_prod(tc_set(tc_Datatype__Universe_Onode(X2,X3)),tc_set(tc_Datatype__Universe_Onode(X2,X3)))) ),
    c_0_4103,
    [final] ).

cnf(c_0_5465,plain,
    ( c_in(c_Pair(c_Datatype__Universe_OIn0(X1,X2,X3),c_Datatype__Universe_OIn0(X4,X2,X3),tc_set(tc_Datatype__Universe_Onode(X2,X3)),tc_set(tc_Datatype__Universe_Onode(X2,X3))),c_Datatype__Universe_Odsum(X5,X6,X2,X3),tc_prod(tc_set(tc_Datatype__Universe_Onode(X2,X3)),tc_set(tc_Datatype__Universe_Onode(X2,X3))))
    | ~ c_in(c_Pair(X1,X4,tc_set(tc_Datatype__Universe_Onode(X2,X3)),tc_set(tc_Datatype__Universe_Onode(X2,X3))),X5,tc_prod(tc_set(tc_Datatype__Universe_Onode(X2,X3)),tc_set(tc_Datatype__Universe_Onode(X2,X3)))) ),
    c_0_4104,
    [final] ).

cnf(c_0_5466,plain,
    ( c_in(c_Main_OuprodE__1(X1,X2,X3,X4,X5),X1,tc_set(tc_Datatype__Universe_Onode(X4,X5)))
    | ~ c_in(X3,c_Datatype__Universe_Ouprod(X1,X2,X4,X5),tc_set(tc_Datatype__Universe_Onode(X4,X5))) ),
    c_0_4105,
    [final] ).

cnf(c_0_5467,plain,
    ( c_in(c_Main_OuprodE__2(X1,X2,X3,X4,X5),X2,tc_set(tc_Datatype__Universe_Onode(X4,X5)))
    | ~ c_in(X3,c_Datatype__Universe_Ouprod(X1,X2,X4,X5),tc_set(tc_Datatype__Universe_Onode(X4,X5))) ),
    c_0_4106,
    [final] ).

cnf(c_0_5468,plain,
    ( c_in(c_Main_OImageE__1(X1,X2,X3,X4,X5),X1,X4)
    | ~ c_in(X2,c_Relation_OImage(X3,X1,X4,X5),X5) ),
    c_0_4107,
    [final] ).

cnf(c_0_5469,plain,
    ( c_in(c_Pair(c_Main_OconverseE__1(X1,X2,X3,X4),c_Main_OconverseE__2(X1,X2,X3,X4),X3,X4),X1,tc_prod(X3,X4))
    | ~ c_in(X2,c_Relation_Oconverse(X1,X3,X4),tc_prod(X4,X3)) ),
    c_0_4108,
    [final] ).

cnf(c_0_5470,plain,
    ( ~ c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Ortrancl(X4,X3),tc_prod(X3,X3))
    | ~ c_Wellfounded__Recursion_Owf(c_insert(c_Pair(X2,X1,X3,X3),X4,tc_prod(X3,X3)),X3) ),
    c_0_4109,
    [final] ).

cnf(c_0_5471,plain,
    ( ~ c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Ortrancl(X4,X3),tc_prod(X3,X3))
    | ~ c_Wellfounded__Recursion_Oacyclic(c_insert(c_Pair(X2,X1,X3,X3),X4,tc_prod(X3,X3)),X3) ),
    c_0_4110,
    [final] ).

cnf(c_0_5472,plain,
    ( c_in(c_Main_OusumE__2(X1,X2,X3,X4),X1,tc_set(tc_Datatype__Universe_Onode(X3,X4)))
    | c_in(c_Main_OusumE__1(X5,X2,X3,X4),X5,tc_set(tc_Datatype__Universe_Onode(X3,X4)))
    | ~ c_in(X2,c_Datatype__Universe_Ousum(X5,X1,X3,X4),tc_set(tc_Datatype__Universe_Onode(X3,X4))) ),
    c_0_4111,
    [final] ).

cnf(c_0_5473,plain,
    ( c_Datatype__Universe_OIn1(c_Main_OusumE__2(X2,X1,X3,X4),X3,X4) = X1
    | c_in(c_Main_OusumE__1(X5,X1,X3,X4),X5,tc_set(tc_Datatype__Universe_Onode(X3,X4)))
    | ~ c_in(X1,c_Datatype__Universe_Ousum(X5,X2,X3,X4),tc_set(tc_Datatype__Universe_Onode(X3,X4))) ),
    c_0_4112,
    [final] ).

cnf(c_0_5474,plain,
    ( c_Datatype__Universe_OIn0(c_Main_OusumE__1(X2,X1,X3,X4),X3,X4) = X1
    | c_in(c_Main_OusumE__2(X5,X1,X3,X4),X5,tc_set(tc_Datatype__Universe_Onode(X3,X4)))
    | ~ c_in(X1,c_Datatype__Universe_Ousum(X2,X5,X3,X4),tc_set(tc_Datatype__Universe_Onode(X3,X4))) ),
    c_0_4113,
    [final] ).

cnf(c_0_5475,plain,
    ( c_Datatype__Universe_OIn1(c_Main_OusumE__2(X2,X1,X3,X4),X3,X4) = X1
    | c_Datatype__Universe_OIn0(c_Main_OusumE__1(X5,X1,X3,X4),X3,X4) = X1
    | ~ c_in(X1,c_Datatype__Universe_Ousum(X5,X2,X3,X4),tc_set(tc_Datatype__Universe_Onode(X3,X4))) ),
    c_0_4114,
    [final] ).

cnf(c_0_5476,plain,
    ( c_Sum__Type_OInr(c_Main_OPlusE__2(X2,X1,X3,X4),X3,X4) = X1
    | c_Sum__Type_OInl(c_Main_OPlusE__1(X5,X1,X4,X3),X4,X3) = X1
    | ~ c_in(X1,c_Sum__Type_OPlus(X5,X2,X4,X3),tc_sum(X4,X3)) ),
    c_0_4115,
    [final] ).

cnf(c_0_5477,plain,
    ( c_Sum__Type_OInr(c_Main_OPlusE__2(X2,X1,X3,X4),X3,X4) = X1
    | c_in(c_Main_OPlusE__1(X5,X1,X4,X3),X5,X4)
    | ~ c_in(X1,c_Sum__Type_OPlus(X5,X2,X4,X3),tc_sum(X4,X3)) ),
    c_0_4116,
    [final] ).

cnf(c_0_5478,plain,
    ( c_Sum__Type_OInl(c_Main_OPlusE__1(X2,X1,X3,X4),X3,X4) = X1
    | c_in(c_Main_OPlusE__2(X5,X1,X4,X3),X5,X4)
    | ~ c_in(X1,c_Sum__Type_OPlus(X2,X5,X3,X4),tc_sum(X3,X4)) ),
    c_0_4117,
    [final] ).

cnf(c_0_5479,plain,
    ( c_in(c_Main_OPlusE__2(X1,X2,X3,X4),X1,X3)
    | c_in(c_Main_OPlusE__1(X5,X2,X4,X3),X5,X4)
    | ~ c_in(X2,c_Sum__Type_OPlus(X5,X1,X4,X3),tc_sum(X4,X3)) ),
    c_0_4118,
    [final] ).

cnf(c_0_5480,plain,
    ( c_Wellfounded__Recursion_Owf(X1,X2)
    | ~ c_Wellfounded__Recursion_Owf(c_insert(c_Pair(X3,X4,X2,X2),X1,tc_prod(X2,X2)),X2) ),
    c_0_4119,
    [final] ).

cnf(c_0_5481,plain,
    ( c_Wellfounded__Recursion_Oacyclic(X1,X2)
    | ~ c_Wellfounded__Recursion_Oacyclic(c_insert(c_Pair(X3,X4,X2,X2),X1,tc_prod(X2,X2)),X2) ),
    c_0_4120,
    [final] ).

cnf(c_0_5482,plain,
    ( c_in(c_Pair(c_Main_ORangeE__1(X1,X2,X3,X4),X1,X4,X3),X2,tc_prod(X4,X3))
    | ~ c_in(X1,c_Relation_ORange(X2,X4,X3),X3) ),
    c_0_4121,
    [final] ).

cnf(c_0_5483,plain,
    ( c_in(c_Pair(X1,c_Main_ODomainE__1(X1,X2,X3,X4),X3,X4),X2,tc_prod(X3,X4))
    | ~ c_in(X1,c_Relation_ODomain(X2,X3,X4),X3) ),
    c_0_4122,
    [final] ).

cnf(c_0_5484,plain,
    ( c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Ortrancl(X4,X3),tc_prod(X3,X3))
    | c_Wellfounded__Recursion_Owf(c_insert(c_Pair(X2,X1,X3,X3),X4,tc_prod(X3,X3)),X3)
    | ~ c_Wellfounded__Recursion_Owf(X4,X3) ),
    c_0_4123,
    [final] ).

cnf(c_0_5485,plain,
    ( c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Ortrancl(X4,X3),tc_prod(X3,X3))
    | c_Wellfounded__Recursion_Oacyclic(c_insert(c_Pair(X2,X1,X3,X3),X4,tc_prod(X3,X3)),X3)
    | ~ c_Wellfounded__Recursion_Oacyclic(X4,X3) ),
    c_0_4124,
    [final] ).

cnf(c_0_5486,plain,
    ( c_in(c_Pair(X1,X2,X3,X4),X5,tc_prod(X3,X4))
    | ~ c_in(X2,c_Relation_OImage(X5,c_insert(X1,c_emptyset,X3),X3,X4),X4) ),
    c_0_4125,
    [final] ).

cnf(c_0_5487,plain,
    ( c_Divides_Oop_Advd(X1,X2,tc_nat)
    | ~ c_Divides_Oop_Advd(X1,c_GCD_Ogcd(c_Pair(X3,X2,tc_nat,tc_nat)),tc_nat) ),
    c_0_4126,
    [final] ).

cnf(c_0_5488,plain,
    ( c_Divides_Oop_Advd(X1,X2,tc_nat)
    | ~ c_Divides_Oop_Advd(X1,c_GCD_Ogcd(c_Pair(X2,X3,tc_nat,tc_nat)),tc_nat) ),
    c_0_4127,
    [final] ).

cnf(c_0_5489,plain,
    ( c_in(X1,c_Relation_OImage(X2,c_insert(X3,c_emptyset,X4),X4,X5),X5)
    | ~ c_in(c_Pair(X3,X1,X4,X5),X2,tc_prod(X4,X5)) ),
    c_0_4128,
    [final] ).

cnf(c_0_5490,plain,
    ( c_in(c_Pair(X1,X2,X3,X4),X5,tc_prod(X3,X4))
    | ~ c_in(c_Pair(X2,X1,X4,X3),c_Relation_Oconverse(X5,X3,X4),tc_prod(X4,X3)) ),
    c_0_4129,
    [final] ).

cnf(c_0_5491,plain,
    ( c_in(c_Pair(X1,X2,X3,X4),c_Relation_Oconverse(X5,X4,X3),tc_prod(X3,X4))
    | ~ c_in(c_Pair(X2,X1,X4,X3),X5,tc_prod(X4,X3)) ),
    c_0_4130,
    [final] ).

cnf(c_0_5492,plain,
    ( c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Ortrancl(X4,X3),tc_prod(X3,X3))
    | ~ c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Otrancl(X4,X3),tc_prod(X3,X3)) ),
    c_0_4131,
    [final] ).

cnf(c_0_5493,plain,
    ( c_in(X1,c_Relation_OImage(X2,X3,X4,X5),X5)
    | ~ c_in(c_Pair(X6,X1,X4,X5),X2,tc_prod(X4,X5))
    | ~ c_in(X6,X3,X4) ),
    c_0_4132,
    [final] ).

cnf(c_0_5494,plain,
    ( c_Pair(c_Main_OconverseE__2(X2,X1,X3,X4),c_Main_OconverseE__1(X2,X1,X3,X4),X4,X3) = X1
    | ~ c_in(X1,c_Relation_Oconverse(X2,X3,X4),tc_prod(X4,X3)) ),
    c_0_4133,
    [final] ).

cnf(c_0_5495,plain,
    ( c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Otrancl(X4,X3),tc_prod(X3,X3))
    | ~ c_in(c_Pair(X1,X2,X3,X3),X4,tc_prod(X3,X3)) ),
    c_0_4134,
    [final] ).

cnf(c_0_5496,plain,
    ( c_in(c_Datatype__Universe_OScons(X1,X2,X3,X4),c_Datatype__Universe_Ouprod(X5,X6,X3,X4),tc_set(tc_Datatype__Universe_Onode(X3,X4)))
    | ~ c_in(X1,X5,tc_set(tc_Datatype__Universe_Onode(X3,X4)))
    | ~ c_in(X2,X6,tc_set(tc_Datatype__Universe_Onode(X3,X4))) ),
    c_0_4135,
    [final] ).

cnf(c_0_5497,plain,
    ( c_Divides_Oop_Advd(X1,c_GCD_Ogcd(c_Pair(X2,X3,tc_nat,tc_nat)),tc_nat)
    | ~ c_Divides_Oop_Advd(X1,X2,tc_nat)
    | ~ c_Divides_Oop_Advd(X1,X3,tc_nat) ),
    c_0_4136,
    [final] ).

cnf(c_0_5498,plain,
    ( c_in(X1,c_Relation_ORange(X2,X3,X4),X4)
    | ~ c_in(c_Pair(X5,X1,X3,X4),X2,tc_prod(X3,X4)) ),
    c_0_4137,
    [final] ).

cnf(c_0_5499,plain,
    ( c_in(X1,c_Relation_ODomain(X2,X3,X4),X3)
    | ~ c_in(c_Pair(X1,X5,X3,X4),X2,tc_prod(X3,X4)) ),
    c_0_4138,
    [final] ).

cnf(c_0_5500,plain,
    ( c_lessequals(c_Union(X1,X2),X3,tc_set(X2))
    | c_lessequals(X4,c_Union(X1,X2),tc_set(X2))
    | ~ c_lessequals(X4,c_Zorn_OUnion__lemma0__1(X3,X4,X1,X2),tc_set(X2)) ),
    c_0_4139,
    [final] ).

cnf(c_0_5501,plain,
    ( c_lessequals(c_Union(X1,X2),X3,tc_set(X2))
    | c_lessequals(X4,c_Union(X1,X2),tc_set(X2))
    | ~ c_lessequals(c_Zorn_OUnion__lemma0__1(X3,X4,X1,X2),X3,tc_set(X2)) ),
    c_0_4140,
    [final] ).

cnf(c_0_5502,plain,
    c_Divides_Oop_Advd(c_GCD_Ogcd(c_Pair(X1,X2,tc_nat,tc_nat)),X2,tc_nat),
    c_0_4141,
    [final] ).

cnf(c_0_5503,plain,
    c_Divides_Oop_Advd(c_GCD_Ogcd(c_Pair(X1,X2,tc_nat,tc_nat)),X1,tc_nat),
    c_0_4142,
    [final] ).

cnf(c_0_5504,plain,
    ( X1 = c_List_Olist_ONil
    | ~ c_in(c_Pair(X1,c_List_Olist_ONil,tc_List_Olist(X2),tc_List_Olist(X2)),c_List_Olistrel(X3,X2),tc_prod(tc_List_Olist(X2),tc_List_Olist(X2))) ),
    c_0_4143,
    [final] ).

cnf(c_0_5505,plain,
    ( X1 = c_List_Olist_ONil
    | ~ c_in(c_Pair(c_List_Olist_ONil,X1,tc_List_Olist(X2),tc_List_Olist(X2)),c_List_Olistrel(X3,X2),tc_prod(tc_List_Olist(X2),tc_List_Olist(X2))) ),
    c_0_4144,
    [final] ).

cnf(c_0_5506,plain,
    ~ c_in(c_Pair(c_List_Olist_ONil,X1,tc_List_Olist(X2),tc_List_Olist(X2)),c_List_Olex(X3,X2),tc_prod(tc_List_Olist(X2),tc_List_Olist(X2))),
    c_0_4145,
    [final] ).

cnf(c_0_5507,plain,
    ~ c_in(c_Pair(X1,c_List_Olist_ONil,tc_List_Olist(X2),tc_List_Olist(X2)),c_List_Olex(X3,X2),tc_prod(tc_List_Olist(X2),tc_List_Olist(X2))),
    c_0_4146,
    [final] ).

cnf(c_0_5508,plain,
    ( c_less(X1,X2,tc_nat)
    | ~ c_in(c_Pair(X1,X2,tc_nat,tc_nat),c_Wellfounded__Relations_Oless__than,tc_prod(tc_nat,tc_nat)) ),
    c_0_4147,
    [final] ).

cnf(c_0_5509,plain,
    ( X1 = X2
    | ~ c_in(c_Pair(X1,X2,X3,X3),c_Relation_OId,tc_prod(X3,X3)) ),
    c_0_4148,
    [final] ).

cnf(c_0_5510,plain,
    ( c_in(c_Datatype__Universe_OIn1(X1,X2,X3),c_Datatype__Universe_Ousum(X4,X5,X2,X3),tc_set(tc_Datatype__Universe_Onode(X2,X3)))
    | ~ c_in(X1,X5,tc_set(tc_Datatype__Universe_Onode(X2,X3))) ),
    c_0_4149,
    [final] ).

cnf(c_0_5511,plain,
    ( c_in(c_Datatype__Universe_OIn0(X1,X2,X3),c_Datatype__Universe_Ousum(X4,X5,X2,X3),tc_set(tc_Datatype__Universe_Onode(X2,X3)))
    | ~ c_in(X1,X4,tc_set(tc_Datatype__Universe_Onode(X2,X3))) ),
    c_0_4150,
    [final] ).

cnf(c_0_5512,plain,
    ( c_in(c_minus(X1,X2,tc_set(X3)),c_Finite__Set_OFinites,tc_set(X3))
    | ~ c_in(c_minus(X1,c_insert(X4,X2,X3),tc_set(X3)),c_Finite__Set_OFinites,tc_set(X3)) ),
    c_0_4151,
    [final] ).

cnf(c_0_5513,plain,
    ( X1 = X2
    | c_Pair(X3,X1,X4,X5) != c_Pair(X6,X2,X4,X5) ),
    c_0_4152,
    [final] ).

cnf(c_0_5514,plain,
    ( X1 = X2
    | c_Pair(X1,X3,X4,X5) != c_Pair(X2,X6,X4,X5) ),
    c_0_4153,
    [final] ).

cnf(c_0_5515,plain,
    ( X1 = X2
    | c_Datatype__Universe_OScons(X3,X1,X4,X5) != c_Datatype__Universe_OScons(X6,X2,X4,X5) ),
    c_0_4154,
    [final] ).

cnf(c_0_5516,plain,
    ( X1 = X2
    | c_Datatype__Universe_OScons(X1,X3,X4,X5) != c_Datatype__Universe_OScons(X2,X6,X4,X5) ),
    c_0_4155,
    [final] ).

cnf(c_0_5517,plain,
    ( c_in(c_Sum__Type_OInr(X1,X2,X3),c_Sum__Type_OPlus(X4,X5,X3,X2),tc_sum(X3,X2))
    | ~ c_in(X1,X5,X2) ),
    c_0_4156,
    [final] ).

cnf(c_0_5518,plain,
    ( c_in(c_Sum__Type_OInl(X1,X2,X3),c_Sum__Type_OPlus(X4,X5,X2,X3),tc_sum(X2,X3))
    | ~ c_in(X1,X4,X2) ),
    c_0_4157,
    [final] ).

cnf(c_0_5519,plain,
    ( c_lessequals(c_Union(X1,X2),X3,tc_set(X2))
    | c_lessequals(X4,c_Union(X1,X2),tc_set(X2))
    | c_in(c_Zorn_OUnion__lemma0__1(X3,X4,X1,X2),X1,tc_set(X2)) ),
    c_0_4158,
    [final] ).

cnf(c_0_5520,plain,
    ( c_in(c_Pair(X1,X1,X2,X2),c_Relation_Odiag(X3,X2),tc_prod(X2,X2))
    | ~ c_in(X1,X3,X2) ),
    c_0_4159,
    [final] ).

cnf(c_0_5521,plain,
    ( c_in(c_minus(X1,c_insert(X2,X3,X4),tc_set(X4)),c_Finite__Set_OFinites,tc_set(X4))
    | ~ c_in(c_minus(X1,X3,tc_set(X4)),c_Finite__Set_OFinites,tc_set(X4)) ),
    c_0_4160,
    [final] ).

cnf(c_0_5522,plain,
    ( c_in(c_Pair(X1,X2,tc_nat,tc_nat),c_Wellfounded__Relations_Oless__than,tc_prod(tc_nat,tc_nat))
    | ~ c_less(X1,X2,tc_nat) ),
    c_0_4161,
    [final] ).

cnf(c_0_5523,plain,
    ( c_Pair(c_Main_OdiagE__1(X2,X1,X3),c_Main_OdiagE__1(X2,X1,X3),X3,X3) = X1
    | ~ c_in(X1,c_Relation_Odiag(X2,X3),tc_prod(X3,X3)) ),
    c_0_4162,
    [final] ).

cnf(c_0_5524,plain,
    c_in(c_Pair(X1,X1,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2)),
    c_0_4163,
    [final] ).

cnf(c_0_5525,plain,
    ( c_Wellfounded__Recursion_Owf(c_Wellfounded__Relations_Olex__prod(X1,X2,X3,X4),tc_prod(X3,X4))
    | ~ c_Wellfounded__Recursion_Owf(X1,X3)
    | ~ c_Wellfounded__Recursion_Owf(X2,X4) ),
    c_0_4164,
    [final] ).

cnf(c_0_5526,plain,
    ( c_Relation_Otrans(c_Wellfounded__Relations_Olex__prod(X1,X2,X3,X4),tc_prod(X3,X4))
    | ~ c_Relation_Otrans(X1,X3)
    | ~ c_Relation_Otrans(X2,X4) ),
    c_0_4165,
    [final] ).

cnf(c_0_5527,plain,
    c_in(c_Pair(X1,X1,X2,X2),c_Relation_OId,tc_prod(X2,X2)),
    c_0_4166,
    [final] ).

cnf(c_0_5528,plain,
    ( X1 = X2
    | c_append(X3,c_List_Olist_OCons(X1,c_List_Olist_ONil,X4),X4) != c_append(X5,c_List_Olist_OCons(X2,c_List_Olist_ONil,X4),X4) ),
    c_0_4167,
    [final] ).

cnf(c_0_5529,plain,
    ( X1 = X2
    | c_append(X1,c_List_Olist_OCons(X3,c_List_Olist_ONil,X4),X4) != c_append(X2,c_List_Olist_OCons(X5,c_List_Olist_ONil,X4),X4) ),
    c_0_4168,
    [final] ).

cnf(c_0_5530,plain,
    c_Datatype__Universe_OScons(X1,X2,X3,X4) != c_Datatype__Universe_ONumb(X5,X3,X4),
    c_0_4169,
    [final] ).

cnf(c_0_5531,plain,
    c_Datatype__Universe_OScons(X1,X2,X3,X4) != c_Datatype__Universe_OLeaf(X5,X3,X4),
    c_0_4170,
    [final] ).

cnf(c_0_5532,plain,
    c_Datatype__Universe_OScons(X1,X2,X3,X4) != c_Datatype__Universe_OAtom(X5,X3,X4),
    c_0_4171,
    [final] ).

cnf(c_0_5533,plain,
    c_Datatype__Universe_ONumb(X1,X2,X3) != c_Datatype__Universe_OScons(X4,X5,X2,X3),
    c_0_4172,
    [final] ).

cnf(c_0_5534,plain,
    c_Datatype__Universe_OLeaf(X1,X2,X3) != c_Datatype__Universe_OScons(X4,X5,X2,X3),
    c_0_4173,
    [final] ).

cnf(c_0_5535,plain,
    c_Datatype__Universe_OAtom(X1,X2,X3) != c_Datatype__Universe_OScons(X4,X5,X2,X3),
    c_0_4174,
    [final] ).

cnf(c_0_5536,plain,
    ( c_in(c_append(X1,X2,X3),c_List_Olists(X4,X3),tc_List_Olist(X3))
    | ~ c_in(X1,c_List_Olists(X4,X3),tc_List_Olist(X3))
    | ~ c_in(X2,c_List_Olists(X4,X3),tc_List_Olist(X3)) ),
    c_0_4175,
    [final] ).

cnf(c_0_5537,plain,
    ( c_in(X1,c_Finite__Set_OFinites,tc_set(tc_prod(X2,X3)))
    | ~ c_in(c_Relation_Oconverse(X1,X2,X3),c_Finite__Set_OFinites,tc_set(tc_prod(X3,X2))) ),
    c_0_4176,
    [final] ).

cnf(c_0_5538,plain,
    c_List_Orev(c_append(c_List_Orev(X1,X2),c_List_Olist_OCons(X3,c_List_Olist_ONil,X2),X2),X2) = c_List_Olist_OCons(X3,X1,X2),
    c_0_4177,
    [final] ).

cnf(c_0_5539,plain,
    ( c_Pair(c_Main_OIdE__1(X1,X2),c_Main_OIdE__1(X1,X2),X2,X2) = X1
    | ~ c_in(X1,c_Relation_OId,tc_prod(X2,X2)) ),
    c_0_4178,
    [final] ).

cnf(c_0_5540,plain,
    ( c_in(c_List_Olist_OCons(X1,X2,X3),c_List_Olists(X4,X3),tc_List_Olist(X3))
    | ~ c_in(X2,c_List_Olists(X4,X3),tc_List_Olist(X3))
    | ~ c_in(X1,X4,X3) ),
    c_0_4179,
    [final] ).

cnf(c_0_5541,plain,
    ( c_in(c_Relation_Oconverse(X1,X2,X3),c_Finite__Set_OFinites,tc_set(tc_prod(X3,X2)))
    | ~ c_in(X1,c_Finite__Set_OFinites,tc_set(tc_prod(X2,X3))) ),
    c_0_4180,
    [final] ).

cnf(c_0_5542,plain,
    ( c_in(X1,c_List_Olists(X2,X3),tc_List_Olist(X3))
    | ~ c_in(c_List_Olist_OCons(X4,X1,X3),c_List_Olists(X2,X3),tc_List_Olist(X3)) ),
    c_0_4181,
    [final] ).

cnf(c_0_5543,plain,
    ( c_in(X1,c_List_Olists(X2,X3),tc_List_Olist(X3))
    | ~ c_in(c_append(X4,X1,X3),c_List_Olists(X2,X3),tc_List_Olist(X3)) ),
    c_0_4182,
    [final] ).

cnf(c_0_5544,plain,
    ( c_in(X1,c_List_Olists(X2,X3),tc_List_Olist(X3))
    | ~ c_in(c_append(X1,X4,X3),c_List_Olists(X2,X3),tc_List_Olist(X3)) ),
    c_0_4183,
    [final] ).

cnf(c_0_5545,plain,
    ( c_insert(X1,c_emptyset,X2) = c_insert(X1,X3,X2)
    | ~ c_lessequals(X3,c_insert(X1,c_emptyset,X2),tc_set(X2)) ),
    c_0_4184,
    [final] ).

cnf(c_0_5546,plain,
    ( c_insert(X1,X2,X3) = c_insert(X1,c_emptyset,X3)
    | ~ c_lessequals(X2,c_insert(X1,c_emptyset,X3),tc_set(X3)) ),
    c_0_4185,
    [final] ).

cnf(c_0_5547,plain,
    ( c_in(X1,X2,X3)
    | c_in(X1,X4,X3)
    | ~ c_in(X1,c_union(X2,X4,X3),X3) ),
    c_0_4186,
    [final] ).

cnf(c_0_5548,plain,
    ( ~ c_in(X1,c_minus(X2,X3,tc_set(X4)),X4)
    | ~ c_in(X1,X3,X4) ),
    c_0_4187,
    [final] ).

cnf(c_0_5549,plain,
    ( c_in(X1,X2,X3)
    | ~ c_in(c_List_Olist_OCons(X1,X4,X3),c_List_Olists(X2,X3),tc_List_Olist(X3)) ),
    c_0_4188,
    [final] ).

cnf(c_0_5550,plain,
    ( c_in(c_union(X1,X2,X3),c_Finite__Set_OFinites,tc_set(X3))
    | ~ c_in(X1,c_Finite__Set_OFinites,tc_set(X3))
    | ~ c_in(X2,c_Finite__Set_OFinites,tc_set(X3)) ),
    c_0_4189,
    [final] ).

cnf(c_0_5551,plain,
    ( c_less(c_0,X1,tc_nat)
    | c_less(c_0,X2,tc_nat)
    | ~ c_less(c_0,c_plus(X1,X2,tc_nat),tc_nat) ),
    c_0_4190,
    [final] ).

cnf(c_0_5552,plain,
    ( c_in(X1,c_List_Olists(X2,X3),tc_List_Olist(X3))
    | ~ c_in(c_Main_Oin__listsI__1(X2,X1,X3),X2,X3) ),
    c_0_4191,
    [final] ).

cnf(c_0_5553,plain,
    ( c_in(X1,c_Inter(X2,X3),X3)
    | ~ c_in(X1,c_Main_OInterI__1(X1,X2,X3),X3) ),
    c_0_4192,
    [final] ).

cnf(c_0_5554,plain,
    ( c_in(X1,c_inter(X2,X3,X4),X4)
    | ~ c_in(X1,X2,X4)
    | ~ c_in(X1,X3,X4) ),
    c_0_4193,
    [final] ).

cnf(c_0_5555,plain,
    ( c_lessequals(X1,c_insert(X2,c_emptyset,X3),tc_set(X3))
    | c_insert(X2,c_emptyset,X3) != c_insert(X4,X1,X3) ),
    c_0_4194,
    [final] ).

cnf(c_0_5556,plain,
    ( c_lessequals(X1,c_insert(X2,c_emptyset,X3),tc_set(X3))
    | c_insert(X4,X1,X3) != c_insert(X2,c_emptyset,X3) ),
    c_0_4195,
    [final] ).

cnf(c_0_5557,plain,
    ( c_in(c_Union(X1,X2),c_Finite__Set_OFinites,tc_set(X2))
    | ~ c_in(c_Main_Ofinite__Union__1(X1,X2),c_Finite__Set_OFinites,tc_set(X2))
    | ~ c_in(X1,c_Finite__Set_OFinites,tc_set(tc_set(X2))) ),
    c_0_4196,
    [final] ).

cnf(c_0_5558,plain,
    ( c_in(c_Main_OdiagE__1(X1,X2,X3),X1,X3)
    | ~ c_in(X2,c_Relation_Odiag(X1,X3),tc_prod(X3,X3)) ),
    c_0_4197,
    [final] ).

cnf(c_0_5559,plain,
    ( c_in(X1,X2,X3)
    | ~ c_in(X1,c_minus(X2,X4,tc_set(X3)),X3) ),
    c_0_4198,
    [final] ).

cnf(c_0_5560,plain,
    ( c_in(X1,c_Finite__Set_OFinites,tc_set(X2))
    | ~ c_in(c_union(X3,X1,X2),c_Finite__Set_OFinites,tc_set(X2)) ),
    c_0_4199,
    [final] ).

cnf(c_0_5561,plain,
    ( c_in(X1,c_Finite__Set_OFinites,tc_set(X2))
    | ~ c_in(c_union(X1,X3,X2),c_Finite__Set_OFinites,tc_set(X2)) ),
    c_0_4200,
    [final] ).

cnf(c_0_5562,plain,
    ( c_in(X1,X2,X3)
    | ~ c_in(X1,c_List_Oset(X4,X3),X3)
    | ~ c_in(X4,c_List_Olists(X2,X3),tc_List_Olist(X3)) ),
    c_0_4201,
    [final] ).

cnf(c_0_5563,plain,
    ( c_lessequals(X1,X2,tc_set(X3))
    | ~ c_in(c_Main_OsubsetI__1(X1,X2,X3),X2,X3) ),
    c_0_4202,
    [final] ).

cnf(c_0_5564,plain,
    ( c_in(X1,c_minus(X2,X3,tc_set(X4)),X4)
    | c_in(X1,X3,X4)
    | ~ c_in(X1,X2,X4) ),
    c_0_4203,
    [final] ).

cnf(c_0_5565,plain,
    ( X1 = X2
    | c_in(X1,X3,X4)
    | ~ c_in(X1,c_insert(X2,X3,X4),X4) ),
    c_0_4204,
    [final] ).

cnf(c_0_5566,plain,
    ( c_in(X1,X2,X3)
    | ~ c_in(X1,c_inter(X2,X4,X3),X3) ),
    c_0_4205,
    [final] ).

cnf(c_0_5567,plain,
    ( c_in(X1,X2,X3)
    | ~ c_in(X1,c_inter(X4,X2,X3),X3) ),
    c_0_4206,
    [final] ).

cnf(c_0_5568,plain,
    ( c_lessequals(X1,c_Zorn_Osucc(X2,X3,X4),tc_set(tc_set(X4)))
    | ~ c_lessequals(X1,X3,tc_set(tc_set(X4))) ),
    c_0_4207,
    [final] ).

cnf(c_0_5569,plain,
    ( c_in(c_Main_OUnionE__1(X1,X2,X3),X2,tc_set(X3))
    | ~ c_in(X1,c_Union(X2,X3),X3) ),
    c_0_4208,
    [final] ).

cnf(c_0_5570,plain,
    ( X1 = c_append(c_List_Orev(X2,X3),c_List_Olist_OCons(X4,c_List_Olist_ONil,X3),X3)
    | c_List_Orev(X1,X3) != c_List_Olist_OCons(X4,X2,X3) ),
    c_0_4209,
    [final] ).

cnf(c_0_5571,plain,
    ( c_in(X1,c_Main_OUnionE__1(X1,X2,X3),X3)
    | ~ c_in(X1,c_Union(X2,X3),X3) ),
    c_0_4210,
    [final] ).

cnf(c_0_5572,plain,
    ( c_in(c_Union(X1,X2),c_Finite__Set_OFinites,tc_set(X2))
    | c_in(c_Main_Ofinite__Union__1(X1,X2),X1,tc_set(X2))
    | ~ c_in(X1,c_Finite__Set_OFinites,tc_set(tc_set(X2))) ),
    c_0_4211,
    [final] ).

cnf(c_0_5573,plain,
    ( c_in(X1,X2,X3)
    | ~ c_in(X1,c_Inter(X4,X3),X3)
    | ~ c_in(X2,X4,tc_set(X3)) ),
    c_0_4212,
    [final] ).

cnf(c_0_5574,plain,
    ( c_lessequals(X1,X2,tc_set(X3))
    | ~ c_lessequals(c_uminus(X2,tc_set(X3)),c_uminus(X1,tc_set(X3)),tc_set(X3)) ),
    c_0_4213,
    [final] ).

cnf(c_0_5575,plain,
    ( c_in(c_Main_Oin__listsI__1(X1,X2,X3),c_List_Oset(X2,X3),X3)
    | c_in(X2,c_List_Olists(X1,X3),tc_List_Olist(X3)) ),
    c_0_4214,
    [final] ).

cnf(c_0_5576,plain,
    ( c_in(X1,c_Union(X2,X3),X3)
    | ~ c_in(X4,X2,tc_set(X3))
    | ~ c_in(X1,X4,X3) ),
    c_0_4215,
    [final] ).

cnf(c_0_5577,plain,
    ( c_in(c_inter(X1,X2,X3),c_Finite__Set_OFinites,tc_set(X3))
    | ~ c_in(X2,c_Finite__Set_OFinites,tc_set(X3)) ),
    c_0_4216,
    [final] ).

cnf(c_0_5578,plain,
    ( c_in(c_inter(X1,X2,X3),c_Finite__Set_OFinites,tc_set(X3))
    | ~ c_in(X1,c_Finite__Set_OFinites,tc_set(X3)) ),
    c_0_4217,
    [final] ).

cnf(c_0_5579,plain,
    ( c_in(c_insert(X1,X2,X3),c_Finite__Set_OFinites,tc_set(X3))
    | ~ c_in(X2,c_Finite__Set_OFinites,tc_set(X3)) ),
    c_0_4218,
    [final] ).

cnf(c_0_5580,plain,
    ( X1 = X2
    | ~ c_in(X1,c_insert(X2,c_emptyset,X3),X3) ),
    c_0_4219,
    [final] ).

cnf(c_0_5581,plain,
    ( c_in(c_Main_OInterI__1(X1,X2,X3),X2,tc_set(X3))
    | c_in(X1,c_Inter(X2,X3),X3) ),
    c_0_4220,
    [final] ).

cnf(c_0_5582,plain,
    ( c_in(X1,c_insert(X2,X3,X4),X4)
    | ~ c_in(X1,X3,X4) ),
    c_0_4221,
    [final] ).

cnf(c_0_5583,plain,
    ( c_in(X1,c_union(X2,X3,X4),X4)
    | ~ c_in(X1,X2,X4) ),
    c_0_4222,
    [final] ).

cnf(c_0_5584,plain,
    ( c_in(X1,c_union(X2,X3,X4),X4)
    | ~ c_in(X1,X3,X4) ),
    c_0_4223,
    [final] ).

cnf(c_0_5585,plain,
    ~ c_less(c_plus(X1,X2,tc_nat),X2,tc_nat),
    c_0_4224,
    [final] ).

cnf(c_0_5586,plain,
    ~ c_less(c_plus(X1,X2,tc_nat),X1,tc_nat),
    c_0_4225,
    [final] ).

cnf(c_0_5587,plain,
    ( c_lessequals(X1,X2,X3)
    | ~ c_lessequals(c_SetInterval_OlessThan(X1,X3),c_SetInterval_OlessThan(X2,X3),tc_set(X3))
    | ~ class_Orderings_Olinorder(X3) ),
    c_0_4226,
    [final] ).

cnf(c_0_5588,plain,
    ( c_lessequals(X1,X2,X3)
    | ~ c_lessequals(c_SetInterval_OgreaterThan(X2,X3),c_SetInterval_OgreaterThan(X1,X3),tc_set(X3))
    | ~ class_Orderings_Olinorder(X3) ),
    c_0_4227,
    [final] ).

cnf(c_0_5589,plain,
    ( c_lessequals(X1,X2,X3)
    | ~ c_lessequals(c_SetInterval_OatMost(X1,X3),c_SetInterval_OatMost(X2,X3),tc_set(X3))
    | ~ class_Orderings_Oorder(X3) ),
    c_0_4228,
    [final] ).

cnf(c_0_5590,plain,
    ( c_lessequals(X1,X2,X3)
    | ~ c_lessequals(c_SetInterval_OatLeast(X2,X3),c_SetInterval_OatLeast(X1,X3),tc_set(X3))
    | ~ class_Orderings_Oorder(X3) ),
    c_0_4229,
    [final] ).

cnf(c_0_5591,plain,
    ( c_in(X1,X2,X3)
    | ~ c_lessequals(X4,X2,tc_set(X3))
    | ~ c_in(X1,X4,X3) ),
    c_0_4230,
    [final] ).

cnf(c_0_5592,plain,
    ( c_less(c_0,c_plus(X1,X2,tc_nat),tc_nat)
    | ~ c_less(c_0,X2,tc_nat) ),
    c_0_4231,
    [final] ).

cnf(c_0_5593,plain,
    ( c_less(c_0,c_plus(X1,X2,tc_nat),tc_nat)
    | ~ c_less(c_0,X1,tc_nat) ),
    c_0_4232,
    [final] ).

cnf(c_0_5594,plain,
    ( c_in(X1,c_Transitive__Closure_Ortrancl(X2,X3),tc_prod(X3,X3))
    | ~ c_in(X1,X2,tc_prod(X3,X3)) ),
    c_0_4233,
    [final] ).

cnf(c_0_5595,plain,
    ( c_lessequals(c_uminus(X1,tc_set(X2)),c_uminus(X3,tc_set(X2)),tc_set(X2))
    | ~ c_lessequals(X3,X1,tc_set(X2)) ),
    c_0_4234,
    [final] ).

cnf(c_0_5596,plain,
    ( ~ c_in(X1,c_uminus(X2,tc_set(X3)),X3)
    | ~ c_in(X1,X2,X3) ),
    c_0_4235,
    [final] ).

cnf(c_0_5597,plain,
    ( c_lessequals(X1,X2,tc_set(X3))
    | c_in(c_Main_OsubsetI__1(X1,X2,X3),X1,X3) ),
    c_0_4236,
    [final] ).

cnf(c_0_5598,plain,
    ( c_in(X1,c_Finite__Set_OFinites,tc_set(X2))
    | ~ c_in(c_Pow(X1,X2),c_Finite__Set_OFinites,tc_set(tc_set(X2))) ),
    c_0_4237,
    [final] ).

cnf(c_0_5599,plain,
    ( c_lessequals(c_SetInterval_OlessThan(X1,X2),c_SetInterval_OlessThan(X3,X2),tc_set(X2))
    | ~ c_lessequals(X1,X3,X2)
    | ~ class_Orderings_Olinorder(X2) ),
    c_0_4238,
    [final] ).

cnf(c_0_5600,plain,
    ( c_lessequals(c_SetInterval_OgreaterThan(X1,X2),c_SetInterval_OgreaterThan(X3,X2),tc_set(X2))
    | ~ c_lessequals(X3,X1,X2)
    | ~ class_Orderings_Olinorder(X2) ),
    c_0_4239,
    [final] ).

cnf(c_0_5601,plain,
    ( c_lessequals(c_SetInterval_OatMost(X1,X2),c_SetInterval_OatMost(X3,X2),tc_set(X2))
    | ~ c_lessequals(X1,X3,X2)
    | ~ class_Orderings_Oorder(X2) ),
    c_0_4240,
    [final] ).

cnf(c_0_5602,plain,
    ( c_lessequals(c_SetInterval_OatLeast(X1,X2),c_SetInterval_OatLeast(X3,X2),tc_set(X2))
    | ~ c_lessequals(X3,X1,X2)
    | ~ class_Orderings_Oorder(X2) ),
    c_0_4241,
    [final] ).

cnf(c_0_5603,plain,
    ( c_Wellfounded__Recursion_Oacyclic(X1,X2)
    | ~ c_Wellfounded__Recursion_Oacyclic(c_Relation_Oconverse(X1,X2,X2),X2) ),
    c_0_4242,
    [final] ).

cnf(c_0_5604,plain,
    ( X1 = X2
    | ~ c_in(X2,X3,X4)
    | ~ c_in(X1,X3,X4)
    | ~ c_Infinite__Set_Oatmost__one(X3,X4) ),
    c_0_4243,
    [final] ).

cnf(c_0_5605,plain,
    ( c_lessequals(X1,X2,tc_set(X3))
    | ~ c_in(X1,c_Pow(X2,X3),tc_set(X3)) ),
    c_0_4244,
    [final] ).

cnf(c_0_5606,plain,
    ( X1 = X2
    | ~ c_lessequals(X1,X2,tc_set(X3))
    | ~ c_lessequals(X2,X1,tc_set(X3)) ),
    c_0_4245,
    [final] ).

cnf(c_0_5607,plain,
    ( ~ c_lessequals(X1,X2,tc_set(X3))
    | ~ c_less(X2,X1,tc_set(X3)) ),
    c_0_4246,
    [final] ).

cnf(c_0_5608,plain,
    ( c_in(c_Pow(X1,X2),c_Finite__Set_OFinites,tc_set(tc_set(X2)))
    | ~ c_in(X1,c_Finite__Set_OFinites,tc_set(X2)) ),
    c_0_4247,
    [final] ).

cnf(c_0_5609,plain,
    ( c_less(X1,X2,X3)
    | ~ c_in(X1,c_SetInterval_OlessThan(X2,X3),X3)
    | ~ class_Orderings_Oord(X3) ),
    c_0_4248,
    [final] ).

cnf(c_0_5610,plain,
    ( c_less(X1,X2,X3)
    | ~ c_in(X2,c_SetInterval_OgreaterThan(X1,X3),X3)
    | ~ class_Orderings_Oord(X3) ),
    c_0_4249,
    [final] ).

cnf(c_0_5611,plain,
    ( c_lessequals(X1,X2,X3)
    | ~ c_in(X1,c_SetInterval_OatMost(X2,X3),X3)
    | ~ class_Orderings_Oord(X3) ),
    c_0_4250,
    [final] ).

cnf(c_0_5612,plain,
    ( c_lessequals(X1,X2,X3)
    | ~ c_in(X2,c_SetInterval_OatLeast(X1,X3),X3)
    | ~ class_Orderings_Oord(X3) ),
    c_0_4251,
    [final] ).

cnf(c_0_5613,plain,
    ( c_in(X1,c_Pow(X2,X3),tc_set(X3))
    | ~ c_lessequals(X1,X2,tc_set(X3)) ),
    c_0_4252,
    [final] ).

cnf(c_0_5614,plain,
    c_lessequals(c_Nat_Osize(c_List_Oremdups(X1,X2),tc_List_Olist(X2)),c_Nat_Osize(X1,tc_List_Olist(X2)),tc_nat),
    c_0_4253,
    [final] ).

cnf(c_0_5615,plain,
    ( c_in(X1,c_SetInterval_OlessThan(X2,X3),X3)
    | ~ c_less(X1,X2,X3)
    | ~ class_Orderings_Oord(X3) ),
    c_0_4254,
    [final] ).

cnf(c_0_5616,plain,
    ( c_in(X1,c_SetInterval_OgreaterThan(X2,X3),X3)
    | ~ c_less(X2,X1,X3)
    | ~ class_Orderings_Oord(X3) ),
    c_0_4255,
    [final] ).

cnf(c_0_5617,plain,
    ( c_in(X1,c_SetInterval_OatMost(X2,X3),X3)
    | ~ c_lessequals(X1,X2,X3)
    | ~ class_Orderings_Oord(X3) ),
    c_0_4256,
    [final] ).

cnf(c_0_5618,plain,
    ( c_in(X1,c_SetInterval_OatLeast(X2,X3),X3)
    | ~ c_lessequals(X2,X1,X3)
    | ~ class_Orderings_Oord(X3) ),
    c_0_4257,
    [final] ).

cnf(c_0_5619,plain,
    ( X1 = X2
    | c_Datatype__Universe_ONumb(X1,X3,X4) != c_Datatype__Universe_ONumb(X2,X3,X4) ),
    c_0_4258,
    [final] ).

cnf(c_0_5620,plain,
    ( X1 = X2
    | c_Datatype__Universe_OLeaf(X1,X3,X4) != c_Datatype__Universe_OLeaf(X2,X3,X4) ),
    c_0_4259,
    [final] ).

cnf(c_0_5621,plain,
    ( X1 = X2
    | c_Sum__Type_OInr(X1,X3,X4) != c_Sum__Type_OInr(X2,X3,X4) ),
    c_0_4260,
    [final] ).

cnf(c_0_5622,plain,
    ( X1 = X2
    | c_Sum__Type_OInl(X1,X3,X4) != c_Sum__Type_OInl(X2,X3,X4) ),
    c_0_4261,
    [final] ).

cnf(c_0_5623,plain,
    ( X1 = X2
    | c_append(X3,X1,X4) != c_append(X3,X2,X4) ),
    c_0_4262,
    [final] ).

cnf(c_0_5624,plain,
    ( X1 = X2
    | c_List_Olist_OCons(X3,X1,X4) != c_List_Olist_OCons(X5,X2,X4) ),
    c_0_4263,
    [final] ).

cnf(c_0_5625,plain,
    ( X1 = X2
    | c_List_Olist_OCons(X1,X3,X4) != c_List_Olist_OCons(X2,X5,X4) ),
    c_0_4264,
    [final] ).

cnf(c_0_5626,plain,
    ( X1 = X2
    | c_append(X1,X3,X4) != c_append(X2,X3,X4) ),
    c_0_4265,
    [final] ).

cnf(c_0_5627,plain,
    ( X1 = X2
    | c_Datatype__Universe_OIn1(X1,X3,X4) != c_Datatype__Universe_OIn1(X2,X3,X4) ),
    c_0_4266,
    [final] ).

cnf(c_0_5628,plain,
    ( X1 = X2
    | c_Datatype__Universe_OIn0(X1,X3,X4) != c_Datatype__Universe_OIn0(X2,X3,X4) ),
    c_0_4267,
    [final] ).

cnf(c_0_5629,plain,
    ( X1 = X2
    | c_Datatype__Universe_OAtom(X1,X3,X4) != c_Datatype__Universe_OAtom(X2,X3,X4) ),
    c_0_4268,
    [final] ).

cnf(c_0_5630,plain,
    ( c_Divides_Oop_Advd(X1,X2,tc_IntDef_Oint)
    | ~ c_Divides_Oop_Advd(c_uminus(X1,tc_IntDef_Oint),X2,tc_IntDef_Oint) ),
    c_0_4269,
    [final] ).

cnf(c_0_5631,plain,
    ( c_Divides_Oop_Advd(X1,X2,tc_IntDef_Oint)
    | ~ c_Divides_Oop_Advd(X1,c_uminus(X2,tc_IntDef_Oint),tc_IntDef_Oint) ),
    c_0_4270,
    [final] ).

cnf(c_0_5632,plain,
    c_Sum__Type_OInr(X1,X2,X3) != c_Sum__Type_OInl(X4,X3,X2),
    c_0_4271,
    [final] ).

cnf(c_0_5633,plain,
    c_Sum__Type_OInl(X1,X2,X3) != c_Sum__Type_OInr(X4,X3,X2),
    c_0_4272,
    [final] ).

cnf(c_0_5634,plain,
    c_Datatype__Universe_ONumb(X1,X2,X3) != c_Datatype__Universe_OLeaf(X4,X2,X3),
    c_0_4273,
    [final] ).

cnf(c_0_5635,plain,
    c_Datatype__Universe_OLeaf(X1,X2,X3) != c_Datatype__Universe_ONumb(X4,X2,X3),
    c_0_4274,
    [final] ).

cnf(c_0_5636,plain,
    c_Datatype__Universe_OIn1(X1,X2,X3) != c_Datatype__Universe_OIn0(X4,X2,X3),
    c_0_4275,
    [final] ).

cnf(c_0_5637,plain,
    c_Datatype__Universe_OIn0(X1,X2,X3) != c_Datatype__Universe_OIn1(X4,X2,X3),
    c_0_4276,
    [final] ).

cnf(c_0_5638,plain,
    ( X1 = X2
    | c_insert(X2,c_emptyset,X3) != c_insert(X1,X4,X3) ),
    c_0_4277,
    [final] ).

cnf(c_0_5639,plain,
    ( X1 = X2
    | c_insert(X1,X3,X4) != c_insert(X2,c_emptyset,X4) ),
    c_0_4278,
    [final] ).

cnf(c_0_5640,plain,
    ( X1 = X2
    | c_insert(X1,c_emptyset,X3) != c_insert(X2,c_emptyset,X3) ),
    c_0_4279,
    [final] ).

cnf(c_0_5641,plain,
    ( c_times(X2,c_Main_Ozmod__eq__0D__dest__1(X2,X1),tc_IntDef_Oint) = X1
    | c_Divides_Oop_Amod(X1,X2,tc_IntDef_Oint) != c_0 ),
    c_0_4280,
    [final] ).

cnf(c_0_5642,plain,
    ( c_times(X2,c_Main_Omod__eq__0D__dest__1(X2,X1),tc_nat) = X1
    | c_Divides_Oop_Amod(X1,X2,tc_nat) != c_0 ),
    c_0_4281,
    [final] ).

cnf(c_0_5643,plain,
    c_in(X1,c_insert(X1,X2,X3),X3),
    c_0_4282,
    [final] ).

cnf(c_0_5644,plain,
    c_in(c_SetInterval_OgreaterThanLessThan(X1,X2,tc_IntDef_Oint),c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)),
    c_0_4283,
    [final] ).

cnf(c_0_5645,plain,
    c_in(c_SetInterval_OgreaterThanLessThan(X1,X2,tc_nat),c_Finite__Set_OFinites,tc_set(tc_nat)),
    c_0_4284,
    [final] ).

cnf(c_0_5646,plain,
    c_in(c_SetInterval_OgreaterThanAtMost(X1,X2,tc_IntDef_Oint),c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)),
    c_0_4285,
    [final] ).

cnf(c_0_5647,plain,
    c_in(c_SetInterval_OgreaterThanAtMost(X1,X2,tc_nat),c_Finite__Set_OFinites,tc_set(tc_nat)),
    c_0_4286,
    [final] ).

cnf(c_0_5648,plain,
    c_in(c_SetInterval_OatLeastLessThan(X1,X2,tc_IntDef_Oint),c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)),
    c_0_4287,
    [final] ).

cnf(c_0_5649,plain,
    c_in(c_SetInterval_OatLeastLessThan(X1,X2,tc_nat),c_Finite__Set_OFinites,tc_set(tc_nat)),
    c_0_4288,
    [final] ).

cnf(c_0_5650,plain,
    c_in(c_SetInterval_OatLeastAtMost(X1,X2,tc_IntDef_Oint),c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)),
    c_0_4289,
    [final] ).

cnf(c_0_5651,plain,
    c_in(c_SetInterval_OatLeastAtMost(X1,X2,tc_nat),c_Finite__Set_OFinites,tc_set(tc_nat)),
    c_0_4290,
    [final] ).

cnf(c_0_5652,plain,
    ( c_Divides_Oop_Advd(c_uminus(X1,tc_IntDef_Oint),X2,tc_IntDef_Oint)
    | ~ c_Divides_Oop_Advd(X1,X2,tc_IntDef_Oint) ),
    c_0_4291,
    [final] ).

cnf(c_0_5653,plain,
    ( c_Divides_Oop_Advd(X1,c_uminus(X2,tc_IntDef_Oint),tc_IntDef_Oint)
    | ~ c_Divides_Oop_Advd(X1,X2,tc_IntDef_Oint) ),
    c_0_4292,
    [final] ).

cnf(c_0_5654,plain,
    ( X1 = X2
    | c_less(X1,X2,tc_set(X3))
    | ~ c_lessequals(X1,X2,tc_set(X3)) ),
    c_0_4293,
    [final] ).

cnf(c_0_5655,plain,
    c_in(X1,c_insert(X1,c_emptyset,X2),X2),
    c_0_4294,
    [final] ).

cnf(c_0_5656,plain,
    c_Divides_Oop_Advd(X1,c_times(X2,X1,tc_IntDef_Oint),tc_IntDef_Oint),
    c_0_4295,
    [final] ).

cnf(c_0_5657,plain,
    c_Divides_Oop_Advd(X1,c_times(X1,X2,tc_IntDef_Oint),tc_IntDef_Oint),
    c_0_4296,
    [final] ).

cnf(c_0_5658,plain,
    c_Divides_Oop_Advd(X1,c_times(X2,X1,tc_nat),tc_nat),
    c_0_4297,
    [final] ).

cnf(c_0_5659,plain,
    c_Divides_Oop_Advd(X1,c_times(X1,X2,tc_nat),tc_nat),
    c_0_4298,
    [final] ).

cnf(c_0_5660,plain,
    ( c_lessequals(X1,X2,tc_set(X3))
    | ~ c_less(X1,X2,tc_set(X3)) ),
    c_0_4299,
    [final] ).

cnf(c_0_5661,plain,
    ( c_less(X1,X2,tc_nat)
    | ~ c_less(c_Suc(X1),c_Suc(X2),tc_nat) ),
    c_0_4300,
    [final] ).

cnf(c_0_5662,plain,
    ( c_lessequals(X1,X2,tc_nat)
    | ~ c_lessequals(c_Suc(X1),c_Suc(X2),tc_nat) ),
    c_0_4301,
    [final] ).

cnf(c_0_5663,plain,
    ( c_less(c_Suc(X1),c_Suc(X2),tc_nat)
    | ~ c_less(X1,X2,tc_nat) ),
    c_0_4302,
    [final] ).

cnf(c_0_5664,plain,
    ( c_lessequals(c_Suc(X1),c_Suc(X2),tc_nat)
    | ~ c_lessequals(X1,X2,tc_nat) ),
    c_0_4303,
    [final] ).

cnf(c_0_5665,plain,
    ( c_in(X1,c_uminus(X2,tc_set(X3)),X3)
    | c_in(X1,X2,X3) ),
    c_0_4304,
    [final] ).

cnf(c_0_5666,plain,
    ( c_Wellfounded__Recursion_Oacyclic(c_Relation_Oconverse(X1,X2,X2),X2)
    | ~ c_Wellfounded__Recursion_Oacyclic(X1,X2) ),
    c_0_4305,
    [final] ).

cnf(c_0_5667,plain,
    ( X1 = c_Datatype_Ooption_OSome(X2,X3)
    | ~ c_in(X2,c_Datatype_Oo2s(X1,X3),X3) ),
    c_0_4306,
    [final] ).

cnf(c_0_5668,plain,
    ~ c_less(c_0,c_Nat_Osize(c_List_Olist_ONil,tc_List_Olist(X1)),tc_nat),
    c_0_4307,
    [final] ).

cnf(c_0_5669,plain,
    c_in(X1,c_Datatype_Oo2s(c_Datatype_Ooption_OSome(X1,X2),X2),X2),
    c_0_4308,
    [final] ).

cnf(c_0_5670,plain,
    ( c_List_Oremdups(X1,X2) = X1
    | c_Nat_Osize(c_List_Oremdups(X1,X2),tc_List_Olist(X2)) != c_Nat_Osize(X1,tc_List_Olist(X2)) ),
    c_0_4309,
    [final] ).

cnf(c_0_5671,plain,
    c_less(c_uminus(c_IntDef_Oint(c_Suc(X1)),tc_IntDef_Oint),c_IntDef_Oint(X2),tc_IntDef_Oint),
    c_0_4310,
    [final] ).

cnf(c_0_5672,plain,
    c_lessequals(c_uminus(c_IntDef_Oint(X1),tc_IntDef_Oint),c_IntDef_Oint(X2),tc_IntDef_Oint),
    c_0_4311,
    [final] ).

cnf(c_0_5673,plain,
    ~ c_less(X1,c_emptyset,tc_set(X2)),
    c_0_4312,
    [final] ).

cnf(c_0_5674,plain,
    ( ~ c_less(X1,X1,X2)
    | ~ class_Orderings_Oorder(X2) ),
    c_0_4313,
    [final] ).

cnf(c_0_5675,plain,
    ( X1 = c_List_Olist_ONil
    | c_less(c_0,c_Nat_Osize(X1,tc_List_Olist(X2)),tc_nat) ),
    c_0_4314,
    [final] ).

cnf(c_0_5676,plain,
    ( c_Nat_Osize(c_List_Oremdups(X1,X2),tc_List_Olist(X2)) = c_Nat_Osize(X1,tc_List_Olist(X2))
    | c_List_Oremdups(X1,X2) != X1 ),
    c_0_4315,
    [final] ).

cnf(c_0_5677,plain,
    ( X1 = c_0
    | ~ c_less(X1,c_Suc(c_0),tc_nat) ),
    c_0_4316,
    [final] ).

cnf(c_0_5678,plain,
    ( X1 = c_List_Olist_ONil
    | c_append(X2,X1,X3) != X2 ),
    c_0_4317,
    [final] ).

cnf(c_0_5679,plain,
    ( X1 = c_List_Olist_ONil
    | c_append(X1,X2,X3) != X2 ),
    c_0_4318,
    [final] ).

cnf(c_0_5680,plain,
    ( X1 = c_List_Olist_ONil
    | c_append(X2,X1,X3) != X2 ),
    c_0_4319,
    [final] ).

cnf(c_0_5681,plain,
    ( X1 = c_List_Olist_ONil
    | c_append(X1,X2,X3) != X2 ),
    c_0_4320,
    [final] ).

cnf(c_0_5682,plain,
    ( X1 = c_emptyset
    | c_union(X2,X1,X3) != c_emptyset ),
    c_0_4321,
    [final] ).

cnf(c_0_5683,plain,
    ( X1 = c_emptyset
    | c_union(X1,X2,X3) != c_emptyset ),
    c_0_4322,
    [final] ).

cnf(c_0_5684,plain,
    ( X1 = c_List_Olist_ONil
    | c_append(X2,X1,X3) != c_List_Olist_ONil ),
    c_0_4323,
    [final] ).

cnf(c_0_5685,plain,
    ( X1 = c_List_Olist_ONil
    | c_append(X1,X2,X3) != c_List_Olist_ONil ),
    c_0_4324,
    [final] ).

cnf(c_0_5686,plain,
    ( X1 = c_List_Olist_ONil
    | c_append(X2,X1,X3) != c_List_Olist_ONil ),
    c_0_4325,
    [final] ).

cnf(c_0_5687,plain,
    ( X1 = c_List_Olist_ONil
    | c_append(X1,X2,X3) != c_List_Olist_ONil ),
    c_0_4326,
    [final] ).

cnf(c_0_5688,plain,
    ( X1 = c_emptyset
    | c_Equiv__Relations_Oquotient(X1,X2,X3) != c_emptyset ),
    c_0_4327,
    [final] ).

cnf(c_0_5689,plain,
    ( X1 = c_emptyset
    | c_Equiv__Relations_Oquotient(X1,X2,X3) != c_emptyset ),
    c_0_4328,
    [final] ).

cnf(c_0_5690,plain,
    c_List_Olist_OCons(X1,X2,X3) != c_List_Olist_ONil,
    c_0_4329,
    [final] ).

cnf(c_0_5691,plain,
    c_List_Olist_OCons(X1,X2,X3) != c_List_Olist_ONil,
    c_0_4330,
    [final] ).

cnf(c_0_5692,plain,
    ~ c_in(c_UNIV,c_Finite__Set_OFinites,tc_set(tc_nat)),
    c_0_4331,
    [final] ).

cnf(c_0_5693,plain,
    c_in(c_List_Olist_ONil,c_List_Olists(X1,X2),tc_List_Olist(X2)),
    c_0_4332,
    [final] ).

cnf(c_0_5694,plain,
    c_in(c_List_Oset(X1,X2),c_Finite__Set_OFinites,tc_set(X2)),
    c_0_4333,
    [final] ).

cnf(c_0_5695,plain,
    ( X1 = c_0
    | c_plus(X2,X1,tc_nat) != c_0 ),
    c_0_4334,
    [final] ).

cnf(c_0_5696,plain,
    ( X1 = c_0
    | c_plus(X1,X2,tc_nat) != c_0 ),
    c_0_4335,
    [final] ).

cnf(c_0_5697,plain,
    ~ c_less(X1,X1,tc_nat),
    c_0_4336,
    [final] ).

cnf(c_0_5698,plain,
    ~ c_in(X1,c_emptyset,X2),
    c_0_4337,
    [final] ).

cnf(c_0_5699,plain,
    ( X1 = c_0
    | ~ c_less(X1,c_1,tc_nat) ),
    c_0_4338,
    [final] ).

cnf(c_0_5700,plain,
    ( X1 = c_0
    | ~ c_lessequals(X1,c_0,tc_nat) ),
    c_0_4339,
    [final] ).

cnf(c_0_5701,plain,
    ( X1 = c_0
    | ~ c_Divides_Oop_Advd(c_0,X1,tc_IntDef_Oint) ),
    c_0_4340,
    [final] ).

cnf(c_0_5702,plain,
    ( X1 = c_0
    | ~ c_Divides_Oop_Advd(c_0,X1,tc_nat) ),
    c_0_4341,
    [final] ).

cnf(c_0_5703,plain,
    ~ c_less(X1,c_0,tc_nat),
    c_0_4342,
    [final] ).

cnf(c_0_5704,plain,
    c_in(c_SetInterval_OlessThan(X1,tc_nat),c_Finite__Set_OFinites,tc_set(tc_nat)),
    c_0_4343,
    [final] ).

cnf(c_0_5705,plain,
    c_in(c_SetInterval_OatMost(X1,tc_nat),c_Finite__Set_OFinites,tc_set(tc_nat)),
    c_0_4344,
    [final] ).

cnf(c_0_5706,plain,
    ~ c_less(c_0,c_0,tc_nat),
    c_0_4345,
    [final] ).

cnf(c_0_5707,plain,
    ( c_Wellfounded__Recursion_Owf(c_List_Olex(X1,X2),tc_List_Olist(X2))
    | ~ c_Wellfounded__Recursion_Owf(X1,X2) ),
    c_0_4346,
    [final] ).

cnf(c_0_5708,plain,
    ( c_Wellfounded__Recursion_Owf(c_List_Olenlex(X1,X2),tc_List_Olist(X2))
    | ~ c_Wellfounded__Recursion_Owf(X1,X2) ),
    c_0_4347,
    [final] ).

cnf(c_0_5709,plain,
    ( X1 = X2
    | c_uminus(X1,tc_set(X3)) != c_uminus(X2,tc_set(X3)) ),
    c_0_4348,
    [final] ).

cnf(c_0_5710,plain,
    ( c_lessequals(X1,X1,X2)
    | ~ class_Orderings_Oorder(X2) ),
    c_0_4349,
    [final] ).

cnf(c_0_5711,plain,
    c_lessequals(X1,X1,tc_set(X2)),
    c_0_4350,
    [final] ).

cnf(c_0_5712,plain,
    c_lessequals(c_emptyset,X1,tc_set(X2)),
    c_0_4351,
    [final] ).

cnf(c_0_5713,plain,
    c_less(X1,c_Suc(X1),tc_nat),
    c_0_4352,
    [final] ).

cnf(c_0_5714,plain,
    c_less(c_0,c_Suc(X1),tc_nat),
    c_0_4353,
    [final] ).

cnf(c_0_5715,plain,
    c_in(c_emptyset,c_Finite__Set_OFinites,tc_set(X1)),
    c_0_4354,
    [final] ).

cnf(c_0_5716,plain,
    c_Divides_Oop_Advd(c_Suc(c_0),X1,tc_nat),
    c_0_4355,
    [final] ).

cnf(c_0_5717,plain,
    c_less(c_0,c_Suc(c_0),tc_nat),
    c_0_4356,
    [final] ).

cnf(c_0_5718,plain,
    c_append(X1,c_List_Olist_ONil,X2) = X1,
    c_0_4357,
    [final] ).

cnf(c_0_5719,plain,
    c_append(c_List_Olist_ONil,X1,X2) = X1,
    c_0_4358,
    [final] ).

cnf(c_0_5720,plain,
    c_append(X1,c_List_Olist_ONil,X2) = X1,
    c_0_4359,
    [final] ).

cnf(c_0_5721,plain,
    c_append(c_List_Olist_ONil,X1,X2) = X1,
    c_0_4360,
    [final] ).

cnf(c_0_5722,plain,
    ( X1 = X2
    | c_SetInterval_OlessThan(X1,X3) != c_SetInterval_OlessThan(X2,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    c_0_4361,
    [final] ).

cnf(c_0_5723,plain,
    ( X1 = X2
    | c_SetInterval_OgreaterThan(X1,X3) != c_SetInterval_OgreaterThan(X2,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    c_0_4362,
    [final] ).

cnf(c_0_5724,plain,
    ( X1 = X2
    | c_SetInterval_OatMost(X1,X3) != c_SetInterval_OatMost(X2,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    c_0_4363,
    [final] ).

cnf(c_0_5725,plain,
    ( X1 = X2
    | c_SetInterval_OatLeast(X1,X3) != c_SetInterval_OatLeast(X2,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    c_0_4364,
    [final] ).

cnf(c_0_5726,plain,
    c_in(X1,c_UNIV,X2),
    c_0_4365,
    [final] ).

cnf(c_0_5727,plain,
    ( X1 = c_0
    | c_less(c_0,X1,tc_nat) ),
    c_0_4366,
    [final] ).

cnf(c_0_5728,plain,
    c_Equiv__Relations_Oquotient(c_emptyset,X1,X2) = c_emptyset,
    c_0_4367,
    [final] ).

cnf(c_0_5729,plain,
    c_Equiv__Relations_Oquotient(c_emptyset,X1,X2) = c_emptyset,
    c_0_4368,
    [final] ).

cnf(c_0_5730,plain,
    c_lessequals(c_0,X1,tc_nat),
    c_0_4369,
    [final] ).

cnf(c_0_5731,plain,
    c_Divides_Oop_Advd(c_1,X1,tc_IntDef_Oint),
    c_0_4370,
    [final] ).

cnf(c_0_5732,plain,
    c_Divides_Oop_Advd(X1,c_0,tc_IntDef_Oint),
    c_0_4371,
    [final] ).

cnf(c_0_5733,plain,
    c_Divides_Oop_Advd(X1,c_0,tc_nat),
    c_0_4372,
    [final] ).

cnf(c_0_5734,plain,
    c_union(c_emptyset,c_emptyset,X1) = c_emptyset,
    c_0_4373,
    [final] ).

cnf(c_0_5735,plain,
    c_append(c_List_Olist_ONil,c_List_Olist_ONil,X1) = c_List_Olist_ONil,
    c_0_4374,
    [final] ).

cnf(c_0_5736,plain,
    c_append(c_List_Olist_ONil,c_List_Olist_ONil,X1) = c_List_Olist_ONil,
    c_0_4375,
    [final] ).

cnf(c_0_5737,plain,
    c_less(c_0,c_1,tc_nat),
    c_0_4376,
    [final] ).

cnf(c_0_5738,plain,
    c_lessequals(c_0,c_0,tc_nat),
    c_0_4377,
    [final] ).

cnf(c_0_5739,plain,
    c_plus(c_0,c_0,tc_nat) = c_0,
    c_0_4378,
    [final] ).

cnf(c_0_5740,plain,
    c_Divides_Oop_Advd(c_0,c_0,tc_IntDef_Oint),
    c_0_4379,
    [final] ).

cnf(c_0_5741,plain,
    c_Divides_Oop_Advd(c_0,c_0,tc_nat),
    c_0_4380,
    [final] ).

cnf(c_0_5742,plain,
    ( X1 = X2
    | c_List_Orev(X1,X3) != c_List_Orev(X2,X3) ),
    c_0_4381,
    [final] ).

cnf(c_0_5743,plain,
    ( X1 = X2
    | c_List_Ochar_OChar(X3,X1) != c_List_Ochar_OChar(X4,X2) ),
    c_0_4382,
    [final] ).

cnf(c_0_5744,plain,
    ( X1 = X2
    | c_List_Ochar_OChar(X1,X3) != c_List_Ochar_OChar(X2,X4) ),
    c_0_4383,
    [final] ).

cnf(c_0_5745,plain,
    ( X1 = X2
    | c_Datatype_Ooption_OSome(X1,X3) != c_Datatype_Ooption_OSome(X2,X3) ),
    c_0_4384,
    [final] ).

cnf(c_0_5746,plain,
    ( class_Finite__Set_Ofinite(tc_sum(X1,X2))
    | ~ class_Finite__Set_Ofinite(X1)
    | ~ class_Finite__Set_Ofinite(X2) ),
    c_0_4385,
    [final] ).

cnf(c_0_5747,plain,
    ( class_Finite__Set_Ofinite(tc_prod(X1,X2))
    | ~ class_Finite__Set_Ofinite(X1)
    | ~ class_Finite__Set_Ofinite(X2) ),
    c_0_4386,
    [final] ).

cnf(c_0_5748,plain,
    ( class_Finite__Set_Ofinite(tc_fun(X1,X2))
    | ~ class_Finite__Set_Ofinite(X1)
    | ~ class_Finite__Set_Ofinite(X2) ),
    c_0_4387,
    [final] ).

cnf(c_0_5749,plain,
    ( c_Datatype_Ooption_OSome(c_Main_Onot__Some__eq__iff1__1(X1,X2),X2) = X1
    | X1 = c_Datatype_Ooption_ONone ),
    c_0_4388,
    [final] ).

cnf(c_0_5750,plain,
    ( c_Datatype_Ooption_OSome(c_Main_Onot__None__eq__iff1__1(X1,X2),X2) = X1
    | X1 = c_Datatype_Ooption_ONone ),
    c_0_4389,
    [final] ).

cnf(c_0_5751,plain,
    c_List_Odistinct(c_List_Oremdups(X1,X2),X2),
    c_0_4390,
    [final] ).

cnf(c_0_5752,plain,
    ( X1 = c_List_Olist_ONil
    | c_Nat_Osize(X1,tc_List_Olist(X2)) != c_0 ),
    c_0_4391,
    [final] ).

cnf(c_0_5753,plain,
    class_Nat_Opower(tc_fun(X1,X2)),
    c_0_4392,
    [final] ).

cnf(c_0_5754,plain,
    ( X1 = c_List_Olist_ONil
    | c_List_Oset(X1,X2) != c_emptyset ),
    c_0_4393,
    [final] ).

cnf(c_0_5755,plain,
    ( X1 = c_List_Olist_ONil
    | c_List_Oset(X1,X2) != c_emptyset ),
    c_0_4394,
    [final] ).

cnf(c_0_5756,plain,
    ( X1 = c_List_Olist_ONil
    | c_List_Orev(X1,X2) != c_List_Olist_ONil ),
    c_0_4395,
    [final] ).

cnf(c_0_5757,plain,
    ( X1 = c_List_Olist_ONil
    | c_List_Orev(X1,X2) != c_List_Olist_ONil ),
    c_0_4396,
    [final] ).

cnf(c_0_5758,plain,
    c_Datatype_Ooption_OSome(X1,X2) != c_Datatype_Ooption_ONone,
    c_0_4397,
    [final] ).

cnf(c_0_5759,plain,
    c_Datatype_Ooption_OSome(X1,X2) != c_Datatype_Ooption_ONone,
    c_0_4398,
    [final] ).

cnf(c_0_5760,plain,
    c_Nat_Osize(c_List_Olist_ONil,tc_List_Olist(X1)) = c_0,
    c_0_4399,
    [final] ).

cnf(c_0_5761,plain,
    ( class_Finite__Set_Ofinite(tc_set(X1))
    | ~ class_Finite__Set_Ofinite(X1) ),
    c_0_4400,
    [final] ).

cnf(c_0_5762,plain,
    ( class_Finite__Set_Ofinite(tc_Datatype_Ooption(X1))
    | ~ class_Finite__Set_Ofinite(X1) ),
    c_0_4401,
    [final] ).

cnf(c_0_5763,plain,
    ( X1 = X2
    | c_Suc(X1) != c_Suc(X2) ),
    c_0_4402,
    [final] ).

cnf(c_0_5764,plain,
    ( X1 = X2
    | c_IntDef_Oint(X1) != c_IntDef_Oint(X2) ),
    c_0_4403,
    [final] ).

cnf(c_0_5765,plain,
    c_Wellfounded__Recursion_Owf(c_emptyset,X1),
    c_0_4404,
    [final] ).

cnf(c_0_5766,plain,
    c_List_Oset(c_List_Olist_ONil,X1) = c_emptyset,
    c_0_4405,
    [final] ).

cnf(c_0_5767,plain,
    c_List_Oset(c_List_Olist_ONil,X1) = c_emptyset,
    c_0_4406,
    [final] ).

cnf(c_0_5768,plain,
    c_List_Orev(c_List_Olist_ONil,X1) = c_List_Olist_ONil,
    c_0_4407,
    [final] ).

cnf(c_0_5769,plain,
    c_List_Orev(c_List_Olist_ONil,X1) = c_List_Olist_ONil,
    c_0_4408,
    [final] ).

cnf(c_0_5770,plain,
    ( class_Orderings_Olinorder(X1)
    | ~ class_Wellfounded__Recursion_Owellorder(X1) ),
    c_0_4409,
    [final] ).

cnf(c_0_5771,plain,
    ( class_LOrder_Olorder(X1)
    | ~ class_Wellfounded__Recursion_Owellorder(X1) ),
    c_0_4410,
    [final] ).

cnf(c_0_5772,plain,
    ( class_LOrder_Ojoin__semilorder(X1)
    | ~ class_Wellfounded__Recursion_Owellorder(X1) ),
    c_0_4411,
    [final] ).

cnf(c_0_5773,plain,
    ( class_LOrder_Omeet__semilorder(X1)
    | ~ class_Wellfounded__Recursion_Owellorder(X1) ),
    c_0_4412,
    [final] ).

cnf(c_0_5774,plain,
    ( class_Orderings_Oorder(X1)
    | ~ class_Wellfounded__Recursion_Owellorder(X1) ),
    c_0_4413,
    [final] ).

cnf(c_0_5775,plain,
    ( class_Orderings_Oord(X1)
    | ~ class_Wellfounded__Recursion_Owellorder(X1) ),
    c_0_4414,
    [final] ).

cnf(c_0_5776,plain,
    ( class_OrderedGroup_Omonoid__mult(X1)
    | ~ class_Ring__and__Field_Osemiring__1__cancel(X1) ),
    c_0_4415,
    [final] ).

cnf(c_0_5777,plain,
    ( class_HOL_Oplus(X1)
    | ~ class_Ring__and__Field_Osemiring__1__cancel(X1) ),
    c_0_4416,
    [final] ).

cnf(c_0_5778,plain,
    ( class_OrderedGroup_Osemigroup__add(X1)
    | ~ class_Ring__and__Field_Osemiring__1__cancel(X1) ),
    c_0_4417,
    [final] ).

cnf(c_0_5779,plain,
    ( class_OrderedGroup_Oab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Osemiring__1__cancel(X1) ),
    c_0_4418,
    [final] ).

cnf(c_0_5780,plain,
    ( class_HOL_Ozero(X1)
    | ~ class_Ring__and__Field_Osemiring__1__cancel(X1) ),
    c_0_4419,
    [final] ).

cnf(c_0_5781,plain,
    ( class_OrderedGroup_Ocomm__monoid__add(X1)
    | ~ class_Ring__and__Field_Osemiring__1__cancel(X1) ),
    c_0_4420,
    [final] ).

cnf(c_0_5782,plain,
    ( class_Ring__and__Field_Osemiring(X1)
    | ~ class_Ring__and__Field_Osemiring__1__cancel(X1) ),
    c_0_4421,
    [final] ).

cnf(c_0_5783,plain,
    ( class_Ring__and__Field_Osemiring__0(X1)
    | ~ class_Ring__and__Field_Osemiring__1__cancel(X1) ),
    c_0_4422,
    [final] ).

cnf(c_0_5784,plain,
    ( class_Ring__and__Field_Osemiring__0__cancel(X1)
    | ~ class_Ring__and__Field_Osemiring__1__cancel(X1) ),
    c_0_4423,
    [final] ).

cnf(c_0_5785,plain,
    ( class_OrderedGroup_Ocancel__semigroup__add(X1)
    | ~ class_Ring__and__Field_Osemiring__1__cancel(X1) ),
    c_0_4424,
    [final] ).

cnf(c_0_5786,plain,
    ( class_OrderedGroup_Ocancel__ab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Osemiring__1__cancel(X1) ),
    c_0_4425,
    [final] ).

cnf(c_0_5787,plain,
    ( class_HOL_Otimes(X1)
    | ~ class_Ring__and__Field_Osemiring__1__cancel(X1) ),
    c_0_4426,
    [final] ).

cnf(c_0_5788,plain,
    ( class_OrderedGroup_Osemigroup__mult(X1)
    | ~ class_Ring__and__Field_Osemiring__1__cancel(X1) ),
    c_0_4427,
    [final] ).

cnf(c_0_5789,plain,
    ( class_HOL_Oone(X1)
    | ~ class_Ring__and__Field_Osemiring__1__cancel(X1) ),
    c_0_4428,
    [final] ).

cnf(c_0_5790,plain,
    ( class_Ring__and__Field_Oaxclass__0__neq__1(X1)
    | ~ class_Ring__and__Field_Osemiring__1__cancel(X1) ),
    c_0_4429,
    [final] ).

cnf(c_0_5791,plain,
    ( class_Ring__and__Field_Osemiring__1(X1)
    | ~ class_Ring__and__Field_Osemiring__1__cancel(X1) ),
    c_0_4430,
    [final] ).

cnf(c_0_5792,plain,
    ( class_OrderedGroup_Osemigroup__add(X1)
    | ~ class_Ring__and__Field_Osemiring__1(X1) ),
    c_0_4431,
    [final] ).

cnf(c_0_5793,plain,
    ( class_OrderedGroup_Oab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Osemiring__1(X1) ),
    c_0_4432,
    [final] ).

cnf(c_0_5794,plain,
    ( class_OrderedGroup_Ocomm__monoid__add(X1)
    | ~ class_Ring__and__Field_Osemiring__1(X1) ),
    c_0_4433,
    [final] ).

cnf(c_0_5795,plain,
    ( class_HOL_Otimes(X1)
    | ~ class_Ring__and__Field_Osemiring__1(X1) ),
    c_0_4434,
    [final] ).

cnf(c_0_5796,plain,
    ( class_OrderedGroup_Osemigroup__mult(X1)
    | ~ class_Ring__and__Field_Osemiring__1(X1) ),
    c_0_4435,
    [final] ).

cnf(c_0_5797,plain,
    ( class_Ring__and__Field_Osemiring(X1)
    | ~ class_Ring__and__Field_Osemiring__1(X1) ),
    c_0_4436,
    [final] ).

cnf(c_0_5798,plain,
    ( class_Ring__and__Field_Osemiring__0(X1)
    | ~ class_Ring__and__Field_Osemiring__1(X1) ),
    c_0_4437,
    [final] ).

cnf(c_0_5799,plain,
    ( class_HOL_Oone(X1)
    | ~ class_Ring__and__Field_Osemiring__1(X1) ),
    c_0_4438,
    [final] ).

cnf(c_0_5800,plain,
    ( class_OrderedGroup_Omonoid__mult(X1)
    | ~ class_Ring__and__Field_Osemiring__1(X1) ),
    c_0_4439,
    [final] ).

cnf(c_0_5801,plain,
    ( class_HOL_Oplus(X1)
    | ~ class_Ring__and__Field_Osemiring__1(X1) ),
    c_0_4440,
    [final] ).

cnf(c_0_5802,plain,
    ( class_HOL_Ozero(X1)
    | ~ class_Ring__and__Field_Osemiring__1(X1) ),
    c_0_4441,
    [final] ).

cnf(c_0_5803,plain,
    ( class_Ring__and__Field_Oaxclass__0__neq__1(X1)
    | ~ class_Ring__and__Field_Osemiring__1(X1) ),
    c_0_4442,
    [final] ).

cnf(c_0_5804,plain,
    ( class_OrderedGroup_Ocancel__ab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Osemiring__0__cancel(X1) ),
    c_0_4443,
    [final] ).

cnf(c_0_5805,plain,
    ( class_HOL_Ozero(X1)
    | ~ class_Ring__and__Field_Osemiring__0__cancel(X1) ),
    c_0_4444,
    [final] ).

cnf(c_0_5806,plain,
    ( class_HOL_Oplus(X1)
    | ~ class_Ring__and__Field_Osemiring__0__cancel(X1) ),
    c_0_4445,
    [final] ).

cnf(c_0_5807,plain,
    ( class_OrderedGroup_Osemigroup__add(X1)
    | ~ class_Ring__and__Field_Osemiring__0__cancel(X1) ),
    c_0_4446,
    [final] ).

cnf(c_0_5808,plain,
    ( class_OrderedGroup_Oab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Osemiring__0__cancel(X1) ),
    c_0_4447,
    [final] ).

cnf(c_0_5809,plain,
    ( class_OrderedGroup_Ocomm__monoid__add(X1)
    | ~ class_Ring__and__Field_Osemiring__0__cancel(X1) ),
    c_0_4448,
    [final] ).

cnf(c_0_5810,plain,
    ( class_HOL_Otimes(X1)
    | ~ class_Ring__and__Field_Osemiring__0__cancel(X1) ),
    c_0_4449,
    [final] ).

cnf(c_0_5811,plain,
    ( class_OrderedGroup_Osemigroup__mult(X1)
    | ~ class_Ring__and__Field_Osemiring__0__cancel(X1) ),
    c_0_4450,
    [final] ).

cnf(c_0_5812,plain,
    ( class_OrderedGroup_Ocancel__semigroup__add(X1)
    | ~ class_Ring__and__Field_Osemiring__0__cancel(X1) ),
    c_0_4451,
    [final] ).

cnf(c_0_5813,plain,
    ( class_Ring__and__Field_Osemiring(X1)
    | ~ class_Ring__and__Field_Osemiring__0__cancel(X1) ),
    c_0_4452,
    [final] ).

cnf(c_0_5814,plain,
    ( class_Ring__and__Field_Osemiring__0(X1)
    | ~ class_Ring__and__Field_Osemiring__0__cancel(X1) ),
    c_0_4453,
    [final] ).

cnf(c_0_5815,plain,
    ( class_HOL_Ozero(X1)
    | ~ class_Ring__and__Field_Osemiring__0(X1) ),
    c_0_4454,
    [final] ).

cnf(c_0_5816,plain,
    ( class_OrderedGroup_Ocomm__monoid__add(X1)
    | ~ class_Ring__and__Field_Osemiring__0(X1) ),
    c_0_4455,
    [final] ).

cnf(c_0_5817,plain,
    ( class_HOL_Otimes(X1)
    | ~ class_Ring__and__Field_Osemiring__0(X1) ),
    c_0_4456,
    [final] ).

cnf(c_0_5818,plain,
    ( class_OrderedGroup_Osemigroup__mult(X1)
    | ~ class_Ring__and__Field_Osemiring__0(X1) ),
    c_0_4457,
    [final] ).

cnf(c_0_5819,plain,
    ( class_HOL_Oplus(X1)
    | ~ class_Ring__and__Field_Osemiring__0(X1) ),
    c_0_4458,
    [final] ).

cnf(c_0_5820,plain,
    ( class_OrderedGroup_Osemigroup__add(X1)
    | ~ class_Ring__and__Field_Osemiring__0(X1) ),
    c_0_4459,
    [final] ).

cnf(c_0_5821,plain,
    ( class_OrderedGroup_Oab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Osemiring__0(X1) ),
    c_0_4460,
    [final] ).

cnf(c_0_5822,plain,
    ( class_Ring__and__Field_Osemiring(X1)
    | ~ class_Ring__and__Field_Osemiring__0(X1) ),
    c_0_4461,
    [final] ).

cnf(c_0_5823,plain,
    ( class_HOL_Otimes(X1)
    | ~ class_Ring__and__Field_Osemiring(X1) ),
    c_0_4462,
    [final] ).

cnf(c_0_5824,plain,
    ( class_OrderedGroup_Osemigroup__mult(X1)
    | ~ class_Ring__and__Field_Osemiring(X1) ),
    c_0_4463,
    [final] ).

cnf(c_0_5825,plain,
    ( class_HOL_Oplus(X1)
    | ~ class_Ring__and__Field_Osemiring(X1) ),
    c_0_4464,
    [final] ).

cnf(c_0_5826,plain,
    ( class_OrderedGroup_Osemigroup__add(X1)
    | ~ class_Ring__and__Field_Osemiring(X1) ),
    c_0_4465,
    [final] ).

cnf(c_0_5827,plain,
    ( class_OrderedGroup_Oab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Osemiring(X1) ),
    c_0_4466,
    [final] ).

cnf(c_0_5828,plain,
    ( class_HOL_Otimes(X1)
    | ~ class_Ring__and__Field_Oring__1(X1) ),
    c_0_4467,
    [final] ).

cnf(c_0_5829,plain,
    ( class_OrderedGroup_Osemigroup__mult(X1)
    | ~ class_Ring__and__Field_Oring__1(X1) ),
    c_0_4468,
    [final] ).

cnf(c_0_5830,plain,
    ( class_Ring__and__Field_Osemiring(X1)
    | ~ class_Ring__and__Field_Oring__1(X1) ),
    c_0_4469,
    [final] ).

cnf(c_0_5831,plain,
    ( class_Ring__and__Field_Osemiring__0(X1)
    | ~ class_Ring__and__Field_Oring__1(X1) ),
    c_0_4470,
    [final] ).

cnf(c_0_5832,plain,
    ( class_OrderedGroup_Ocancel__semigroup__add(X1)
    | ~ class_Ring__and__Field_Oring__1(X1) ),
    c_0_4471,
    [final] ).

cnf(c_0_5833,plain,
    ( class_OrderedGroup_Ocancel__ab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Oring__1(X1) ),
    c_0_4472,
    [final] ).

cnf(c_0_5834,plain,
    ( class_Ring__and__Field_Osemiring__0__cancel(X1)
    | ~ class_Ring__and__Field_Oring__1(X1) ),
    c_0_4473,
    [final] ).

cnf(c_0_5835,plain,
    ( class_HOL_Ominus(X1)
    | ~ class_Ring__and__Field_Oring__1(X1) ),
    c_0_4474,
    [final] ).

cnf(c_0_5836,plain,
    ( class_Ring__and__Field_Osemiring__1__cancel(X1)
    | ~ class_Ring__and__Field_Oring__1(X1) ),
    c_0_4475,
    [final] ).

cnf(c_0_5837,plain,
    ( class_HOL_Oone(X1)
    | ~ class_Ring__and__Field_Oring__1(X1) ),
    c_0_4476,
    [final] ).

cnf(c_0_5838,plain,
    ( class_OrderedGroup_Omonoid__mult(X1)
    | ~ class_Ring__and__Field_Oring__1(X1) ),
    c_0_4477,
    [final] ).

cnf(c_0_5839,plain,
    ( class_Ring__and__Field_Oaxclass__0__neq__1(X1)
    | ~ class_Ring__and__Field_Oring__1(X1) ),
    c_0_4478,
    [final] ).

cnf(c_0_5840,plain,
    ( class_Ring__and__Field_Osemiring__1(X1)
    | ~ class_Ring__and__Field_Oring__1(X1) ),
    c_0_4479,
    [final] ).

cnf(c_0_5841,plain,
    ( class_HOL_Ozero(X1)
    | ~ class_Ring__and__Field_Oring__1(X1) ),
    c_0_4480,
    [final] ).

cnf(c_0_5842,plain,
    ( class_HOL_Oplus(X1)
    | ~ class_Ring__and__Field_Oring__1(X1) ),
    c_0_4481,
    [final] ).

cnf(c_0_5843,plain,
    ( class_OrderedGroup_Osemigroup__add(X1)
    | ~ class_Ring__and__Field_Oring__1(X1) ),
    c_0_4482,
    [final] ).

cnf(c_0_5844,plain,
    ( class_OrderedGroup_Oab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Oring__1(X1) ),
    c_0_4483,
    [final] ).

cnf(c_0_5845,plain,
    ( class_OrderedGroup_Ocomm__monoid__add(X1)
    | ~ class_Ring__and__Field_Oring__1(X1) ),
    c_0_4484,
    [final] ).

cnf(c_0_5846,plain,
    ( class_OrderedGroup_Oab__group__add(X1)
    | ~ class_Ring__and__Field_Oring__1(X1) ),
    c_0_4485,
    [final] ).

cnf(c_0_5847,plain,
    ( class_Ring__and__Field_Oring(X1)
    | ~ class_Ring__and__Field_Oring__1(X1) ),
    c_0_4486,
    [final] ).

cnf(c_0_5848,plain,
    ( class_HOL_Ozero(X1)
    | ~ class_Ring__and__Field_Oring(X1) ),
    c_0_4487,
    [final] ).

cnf(c_0_5849,plain,
    ( class_OrderedGroup_Ocomm__monoid__add(X1)
    | ~ class_Ring__and__Field_Oring(X1) ),
    c_0_4488,
    [final] ).

cnf(c_0_5850,plain,
    ( class_HOL_Ominus(X1)
    | ~ class_Ring__and__Field_Oring(X1) ),
    c_0_4489,
    [final] ).

cnf(c_0_5851,plain,
    ( class_OrderedGroup_Oab__group__add(X1)
    | ~ class_Ring__and__Field_Oring(X1) ),
    c_0_4490,
    [final] ).

cnf(c_0_5852,plain,
    ( class_HOL_Otimes(X1)
    | ~ class_Ring__and__Field_Oring(X1) ),
    c_0_4491,
    [final] ).

cnf(c_0_5853,plain,
    ( class_OrderedGroup_Osemigroup__mult(X1)
    | ~ class_Ring__and__Field_Oring(X1) ),
    c_0_4492,
    [final] ).

cnf(c_0_5854,plain,
    ( class_HOL_Oplus(X1)
    | ~ class_Ring__and__Field_Oring(X1) ),
    c_0_4493,
    [final] ).

cnf(c_0_5855,plain,
    ( class_OrderedGroup_Osemigroup__add(X1)
    | ~ class_Ring__and__Field_Oring(X1) ),
    c_0_4494,
    [final] ).

cnf(c_0_5856,plain,
    ( class_Ring__and__Field_Osemiring__0(X1)
    | ~ class_Ring__and__Field_Oring(X1) ),
    c_0_4495,
    [final] ).

cnf(c_0_5857,plain,
    ( class_Ring__and__Field_Osemiring__0__cancel(X1)
    | ~ class_Ring__and__Field_Oring(X1) ),
    c_0_4496,
    [final] ).

cnf(c_0_5858,plain,
    ( class_OrderedGroup_Ocancel__semigroup__add(X1)
    | ~ class_Ring__and__Field_Oring(X1) ),
    c_0_4497,
    [final] ).

cnf(c_0_5859,plain,
    ( class_OrderedGroup_Ocancel__ab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Oring(X1) ),
    c_0_4498,
    [final] ).

cnf(c_0_5860,plain,
    ( class_OrderedGroup_Oab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Oring(X1) ),
    c_0_4499,
    [final] ).

cnf(c_0_5861,plain,
    ( class_Ring__and__Field_Osemiring(X1)
    | ~ class_Ring__and__Field_Oring(X1) ),
    c_0_4500,
    [final] ).

cnf(c_0_5862,plain,
    ( class_OrderedGroup_Opordered__ab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Opordered__semiring(X1) ),
    c_0_4501,
    [final] ).

cnf(c_0_5863,plain,
    ( class_HOL_Ozero(X1)
    | ~ class_Ring__and__Field_Opordered__semiring(X1) ),
    c_0_4502,
    [final] ).

cnf(c_0_5864,plain,
    ( class_HOL_Oplus(X1)
    | ~ class_Ring__and__Field_Opordered__semiring(X1) ),
    c_0_4503,
    [final] ).

cnf(c_0_5865,plain,
    ( class_OrderedGroup_Osemigroup__add(X1)
    | ~ class_Ring__and__Field_Opordered__semiring(X1) ),
    c_0_4504,
    [final] ).

cnf(c_0_5866,plain,
    ( class_OrderedGroup_Oab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Opordered__semiring(X1) ),
    c_0_4505,
    [final] ).

cnf(c_0_5867,plain,
    ( class_OrderedGroup_Ocomm__monoid__add(X1)
    | ~ class_Ring__and__Field_Opordered__semiring(X1) ),
    c_0_4506,
    [final] ).

cnf(c_0_5868,plain,
    ( class_HOL_Otimes(X1)
    | ~ class_Ring__and__Field_Opordered__semiring(X1) ),
    c_0_4507,
    [final] ).

cnf(c_0_5869,plain,
    ( class_OrderedGroup_Osemigroup__mult(X1)
    | ~ class_Ring__and__Field_Opordered__semiring(X1) ),
    c_0_4508,
    [final] ).

cnf(c_0_5870,plain,
    ( class_Orderings_Oord(X1)
    | ~ class_Ring__and__Field_Opordered__semiring(X1) ),
    c_0_4509,
    [final] ).

cnf(c_0_5871,plain,
    ( class_Orderings_Oorder(X1)
    | ~ class_Ring__and__Field_Opordered__semiring(X1) ),
    c_0_4510,
    [final] ).

cnf(c_0_5872,plain,
    ( class_Ring__and__Field_Osemiring(X1)
    | ~ class_Ring__and__Field_Opordered__semiring(X1) ),
    c_0_4511,
    [final] ).

cnf(c_0_5873,plain,
    ( class_Ring__and__Field_Osemiring__0(X1)
    | ~ class_Ring__and__Field_Opordered__semiring(X1) ),
    c_0_4512,
    [final] ).

cnf(c_0_5874,plain,
    ( class_HOL_Otimes(X1)
    | ~ class_Ring__and__Field_Opordered__ring(X1) ),
    c_0_4513,
    [final] ).

cnf(c_0_5875,plain,
    ( class_OrderedGroup_Osemigroup__mult(X1)
    | ~ class_Ring__and__Field_Opordered__ring(X1) ),
    c_0_4514,
    [final] ).

cnf(c_0_5876,plain,
    ( class_Ring__and__Field_Osemiring(X1)
    | ~ class_Ring__and__Field_Opordered__ring(X1) ),
    c_0_4515,
    [final] ).

cnf(c_0_5877,plain,
    ( class_Ring__and__Field_Osemiring__0(X1)
    | ~ class_Ring__and__Field_Opordered__ring(X1) ),
    c_0_4516,
    [final] ).

cnf(c_0_5878,plain,
    ( class_OrderedGroup_Ocancel__semigroup__add(X1)
    | ~ class_Ring__and__Field_Opordered__ring(X1) ),
    c_0_4517,
    [final] ).

cnf(c_0_5879,plain,
    ( class_OrderedGroup_Ocancel__ab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Opordered__ring(X1) ),
    c_0_4518,
    [final] ).

cnf(c_0_5880,plain,
    ( class_Ring__and__Field_Osemiring__0__cancel(X1)
    | ~ class_Ring__and__Field_Opordered__ring(X1) ),
    c_0_4519,
    [final] ).

cnf(c_0_5881,plain,
    ( class_Ring__and__Field_Opordered__cancel__semiring(X1)
    | ~ class_Ring__and__Field_Opordered__ring(X1) ),
    c_0_4520,
    [final] ).

cnf(c_0_5882,plain,
    ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Opordered__ring(X1) ),
    c_0_4521,
    [final] ).

cnf(c_0_5883,plain,
    ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
    | ~ class_Ring__and__Field_Opordered__ring(X1) ),
    c_0_4522,
    [final] ).

cnf(c_0_5884,plain,
    ( class_HOL_Ominus(X1)
    | ~ class_Ring__and__Field_Opordered__ring(X1) ),
    c_0_4523,
    [final] ).

cnf(c_0_5885,plain,
    ( class_OrderedGroup_Opordered__ab__group__add(X1)
    | ~ class_Ring__and__Field_Opordered__ring(X1) ),
    c_0_4524,
    [final] ).

cnf(c_0_5886,plain,
    ( class_Orderings_Oord(X1)
    | ~ class_Ring__and__Field_Opordered__ring(X1) ),
    c_0_4525,
    [final] ).

cnf(c_0_5887,plain,
    ( class_Orderings_Oorder(X1)
    | ~ class_Ring__and__Field_Opordered__ring(X1) ),
    c_0_4526,
    [final] ).

cnf(c_0_5888,plain,
    ( class_OrderedGroup_Opordered__ab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Opordered__ring(X1) ),
    c_0_4527,
    [final] ).

cnf(c_0_5889,plain,
    ( class_Ring__and__Field_Opordered__semiring(X1)
    | ~ class_Ring__and__Field_Opordered__ring(X1) ),
    c_0_4528,
    [final] ).

cnf(c_0_5890,plain,
    ( class_HOL_Ozero(X1)
    | ~ class_Ring__and__Field_Opordered__ring(X1) ),
    c_0_4529,
    [final] ).

cnf(c_0_5891,plain,
    ( class_HOL_Oplus(X1)
    | ~ class_Ring__and__Field_Opordered__ring(X1) ),
    c_0_4530,
    [final] ).

cnf(c_0_5892,plain,
    ( class_OrderedGroup_Osemigroup__add(X1)
    | ~ class_Ring__and__Field_Opordered__ring(X1) ),
    c_0_4531,
    [final] ).

cnf(c_0_5893,plain,
    ( class_OrderedGroup_Oab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Opordered__ring(X1) ),
    c_0_4532,
    [final] ).

cnf(c_0_5894,plain,
    ( class_OrderedGroup_Ocomm__monoid__add(X1)
    | ~ class_Ring__and__Field_Opordered__ring(X1) ),
    c_0_4533,
    [final] ).

cnf(c_0_5895,plain,
    ( class_OrderedGroup_Oab__group__add(X1)
    | ~ class_Ring__and__Field_Opordered__ring(X1) ),
    c_0_4534,
    [final] ).

cnf(c_0_5896,plain,
    ( class_Ring__and__Field_Oring(X1)
    | ~ class_Ring__and__Field_Opordered__ring(X1) ),
    c_0_4535,
    [final] ).

cnf(c_0_5897,plain,
    ( class_OrderedGroup_Osemigroup__add(X1)
    | ~ class_Ring__and__Field_Opordered__comm__semiring(X1) ),
    c_0_4536,
    [final] ).

cnf(c_0_5898,plain,
    ( class_OrderedGroup_Oab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Opordered__comm__semiring(X1) ),
    c_0_4537,
    [final] ).

cnf(c_0_5899,plain,
    ( class_OrderedGroup_Ocomm__monoid__add(X1)
    | ~ class_Ring__and__Field_Opordered__comm__semiring(X1) ),
    c_0_4538,
    [final] ).

cnf(c_0_5900,plain,
    ( class_HOL_Otimes(X1)
    | ~ class_Ring__and__Field_Opordered__comm__semiring(X1) ),
    c_0_4539,
    [final] ).

cnf(c_0_5901,plain,
    ( class_OrderedGroup_Osemigroup__mult(X1)
    | ~ class_Ring__and__Field_Opordered__comm__semiring(X1) ),
    c_0_4540,
    [final] ).

cnf(c_0_5902,plain,
    ( class_Ring__and__Field_Osemiring(X1)
    | ~ class_Ring__and__Field_Opordered__comm__semiring(X1) ),
    c_0_4541,
    [final] ).

cnf(c_0_5903,plain,
    ( class_Ring__and__Field_Osemiring__0(X1)
    | ~ class_Ring__and__Field_Opordered__comm__semiring(X1) ),
    c_0_4542,
    [final] ).

cnf(c_0_5904,plain,
    ( class_OrderedGroup_Oab__semigroup__mult(X1)
    | ~ class_Ring__and__Field_Opordered__comm__semiring(X1) ),
    c_0_4543,
    [final] ).

cnf(c_0_5905,plain,
    ( class_Ring__and__Field_Opordered__semiring(X1)
    | ~ class_Ring__and__Field_Opordered__comm__semiring(X1) ),
    c_0_4544,
    [final] ).

cnf(c_0_5906,plain,
    ( class_Orderings_Oord(X1)
    | ~ class_Ring__and__Field_Opordered__comm__semiring(X1) ),
    c_0_4545,
    [final] ).

cnf(c_0_5907,plain,
    ( class_Orderings_Oorder(X1)
    | ~ class_Ring__and__Field_Opordered__comm__semiring(X1) ),
    c_0_4546,
    [final] ).

cnf(c_0_5908,plain,
    ( class_OrderedGroup_Opordered__ab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Opordered__comm__semiring(X1) ),
    c_0_4547,
    [final] ).

cnf(c_0_5909,plain,
    ( class_HOL_Ozero(X1)
    | ~ class_Ring__and__Field_Opordered__comm__semiring(X1) ),
    c_0_4548,
    [final] ).

cnf(c_0_5910,plain,
    ( class_HOL_Oplus(X1)
    | ~ class_Ring__and__Field_Opordered__comm__semiring(X1) ),
    c_0_4549,
    [final] ).

cnf(c_0_5911,plain,
    ( class_Ring__and__Field_Ocomm__semiring(X1)
    | ~ class_Ring__and__Field_Opordered__comm__semiring(X1) ),
    c_0_4550,
    [final] ).

cnf(c_0_5912,plain,
    ( class_Ring__and__Field_Ocomm__semiring__0(X1)
    | ~ class_Ring__and__Field_Opordered__comm__semiring(X1) ),
    c_0_4551,
    [final] ).

cnf(c_0_5913,plain,
    ( class_Ring__and__Field_Osemiring__0(X1)
    | ~ class_Ring__and__Field_Opordered__comm__ring(X1) ),
    c_0_4552,
    [final] ).

cnf(c_0_5914,plain,
    ( class_Ring__and__Field_Osemiring__0__cancel(X1)
    | ~ class_Ring__and__Field_Opordered__comm__ring(X1) ),
    c_0_4553,
    [final] ).

cnf(c_0_5915,plain,
    ( class_OrderedGroup_Oab__semigroup__mult(X1)
    | ~ class_Ring__and__Field_Opordered__comm__ring(X1) ),
    c_0_4554,
    [final] ).

cnf(c_0_5916,plain,
    ( class_Ring__and__Field_Ocomm__semiring(X1)
    | ~ class_Ring__and__Field_Opordered__comm__ring(X1) ),
    c_0_4555,
    [final] ).

cnf(c_0_5917,plain,
    ( class_Ring__and__Field_Ocomm__semiring__0(X1)
    | ~ class_Ring__and__Field_Opordered__comm__ring(X1) ),
    c_0_4556,
    [final] ).

cnf(c_0_5918,plain,
    ( class_Ring__and__Field_Ocomm__semiring__0__cancel(X1)
    | ~ class_Ring__and__Field_Opordered__comm__ring(X1) ),
    c_0_4557,
    [final] ).

cnf(c_0_5919,plain,
    ( class_HOL_Ominus(X1)
    | ~ class_Ring__and__Field_Opordered__comm__ring(X1) ),
    c_0_4558,
    [final] ).

cnf(c_0_5920,plain,
    ( class_Orderings_Oord(X1)
    | ~ class_Ring__and__Field_Opordered__comm__ring(X1) ),
    c_0_4559,
    [final] ).

cnf(c_0_5921,plain,
    ( class_Orderings_Oorder(X1)
    | ~ class_Ring__and__Field_Opordered__comm__ring(X1) ),
    c_0_4560,
    [final] ).

cnf(c_0_5922,plain,
    ( class_OrderedGroup_Opordered__ab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Opordered__comm__ring(X1) ),
    c_0_4561,
    [final] ).

cnf(c_0_5923,plain,
    ( class_Ring__and__Field_Opordered__semiring(X1)
    | ~ class_Ring__and__Field_Opordered__comm__ring(X1) ),
    c_0_4562,
    [final] ).

cnf(c_0_5924,plain,
    ( class_Ring__and__Field_Opordered__comm__semiring(X1)
    | ~ class_Ring__and__Field_Opordered__comm__ring(X1) ),
    c_0_4563,
    [final] ).

cnf(c_0_5925,plain,
    ( class_OrderedGroup_Oab__group__add(X1)
    | ~ class_Ring__and__Field_Opordered__comm__ring(X1) ),
    c_0_4564,
    [final] ).

cnf(c_0_5926,plain,
    ( class_HOL_Oplus(X1)
    | ~ class_Ring__and__Field_Opordered__comm__ring(X1) ),
    c_0_4565,
    [final] ).

cnf(c_0_5927,plain,
    ( class_OrderedGroup_Osemigroup__add(X1)
    | ~ class_Ring__and__Field_Opordered__comm__ring(X1) ),
    c_0_4566,
    [final] ).

cnf(c_0_5928,plain,
    ( class_OrderedGroup_Ocancel__semigroup__add(X1)
    | ~ class_Ring__and__Field_Opordered__comm__ring(X1) ),
    c_0_4567,
    [final] ).

cnf(c_0_5929,plain,
    ( class_OrderedGroup_Oab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Opordered__comm__ring(X1) ),
    c_0_4568,
    [final] ).

cnf(c_0_5930,plain,
    ( class_OrderedGroup_Ocancel__ab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Opordered__comm__ring(X1) ),
    c_0_4569,
    [final] ).

cnf(c_0_5931,plain,
    ( class_HOL_Ozero(X1)
    | ~ class_Ring__and__Field_Opordered__comm__ring(X1) ),
    c_0_4570,
    [final] ).

cnf(c_0_5932,plain,
    ( class_OrderedGroup_Ocomm__monoid__add(X1)
    | ~ class_Ring__and__Field_Opordered__comm__ring(X1) ),
    c_0_4571,
    [final] ).

cnf(c_0_5933,plain,
    ( class_HOL_Otimes(X1)
    | ~ class_Ring__and__Field_Opordered__comm__ring(X1) ),
    c_0_4572,
    [final] ).

cnf(c_0_5934,plain,
    ( class_OrderedGroup_Osemigroup__mult(X1)
    | ~ class_Ring__and__Field_Opordered__comm__ring(X1) ),
    c_0_4573,
    [final] ).

cnf(c_0_5935,plain,
    ( class_Ring__and__Field_Osemiring(X1)
    | ~ class_Ring__and__Field_Opordered__comm__ring(X1) ),
    c_0_4574,
    [final] ).

cnf(c_0_5936,plain,
    ( class_Ring__and__Field_Oring(X1)
    | ~ class_Ring__and__Field_Opordered__comm__ring(X1) ),
    c_0_4575,
    [final] ).

cnf(c_0_5937,plain,
    ( class_Ring__and__Field_Ocomm__ring(X1)
    | ~ class_Ring__and__Field_Opordered__comm__ring(X1) ),
    c_0_4576,
    [final] ).

cnf(c_0_5938,plain,
    ( class_OrderedGroup_Osemigroup__add(X1)
    | ~ class_Ring__and__Field_Opordered__cancel__semiring(X1) ),
    c_0_4577,
    [final] ).

cnf(c_0_5939,plain,
    ( class_OrderedGroup_Oab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Opordered__cancel__semiring(X1) ),
    c_0_4578,
    [final] ).

cnf(c_0_5940,plain,
    ( class_OrderedGroup_Opordered__ab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Opordered__cancel__semiring(X1) ),
    c_0_4579,
    [final] ).

cnf(c_0_5941,plain,
    ( class_HOL_Ozero(X1)
    | ~ class_Ring__and__Field_Opordered__cancel__semiring(X1) ),
    c_0_4580,
    [final] ).

cnf(c_0_5942,plain,
    ( class_OrderedGroup_Ocomm__monoid__add(X1)
    | ~ class_Ring__and__Field_Opordered__cancel__semiring(X1) ),
    c_0_4581,
    [final] ).

cnf(c_0_5943,plain,
    ( class_HOL_Otimes(X1)
    | ~ class_Ring__and__Field_Opordered__cancel__semiring(X1) ),
    c_0_4582,
    [final] ).

cnf(c_0_5944,plain,
    ( class_OrderedGroup_Osemigroup__mult(X1)
    | ~ class_Ring__and__Field_Opordered__cancel__semiring(X1) ),
    c_0_4583,
    [final] ).

cnf(c_0_5945,plain,
    ( class_Ring__and__Field_Osemiring(X1)
    | ~ class_Ring__and__Field_Opordered__cancel__semiring(X1) ),
    c_0_4584,
    [final] ).

cnf(c_0_5946,plain,
    ( class_Ring__and__Field_Osemiring__0__cancel(X1)
    | ~ class_Ring__and__Field_Opordered__cancel__semiring(X1) ),
    c_0_4585,
    [final] ).

cnf(c_0_5947,plain,
    ( class_OrderedGroup_Ocancel__semigroup__add(X1)
    | ~ class_Ring__and__Field_Opordered__cancel__semiring(X1) ),
    c_0_4586,
    [final] ).

cnf(c_0_5948,plain,
    ( class_OrderedGroup_Ocancel__ab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Opordered__cancel__semiring(X1) ),
    c_0_4587,
    [final] ).

cnf(c_0_5949,plain,
    ( class_Orderings_Oord(X1)
    | ~ class_Ring__and__Field_Opordered__cancel__semiring(X1) ),
    c_0_4588,
    [final] ).

cnf(c_0_5950,plain,
    ( class_Orderings_Oorder(X1)
    | ~ class_Ring__and__Field_Opordered__cancel__semiring(X1) ),
    c_0_4589,
    [final] ).

cnf(c_0_5951,plain,
    ( class_HOL_Oplus(X1)
    | ~ class_Ring__and__Field_Opordered__cancel__semiring(X1) ),
    c_0_4590,
    [final] ).

cnf(c_0_5952,plain,
    ( class_Ring__and__Field_Osemiring__0(X1)
    | ~ class_Ring__and__Field_Opordered__cancel__semiring(X1) ),
    c_0_4591,
    [final] ).

cnf(c_0_5953,plain,
    ( class_Ring__and__Field_Opordered__semiring(X1)
    | ~ class_Ring__and__Field_Opordered__cancel__semiring(X1) ),
    c_0_4592,
    [final] ).

cnf(c_0_5954,plain,
    ( class_HOL_Ozero(X1)
    | ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X1) ),
    c_0_4593,
    [final] ).

cnf(c_0_5955,plain,
    ( class_OrderedGroup_Ocomm__monoid__add(X1)
    | ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X1) ),
    c_0_4594,
    [final] ).

cnf(c_0_5956,plain,
    ( class_HOL_Otimes(X1)
    | ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X1) ),
    c_0_4595,
    [final] ).

cnf(c_0_5957,plain,
    ( class_OrderedGroup_Osemigroup__mult(X1)
    | ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X1) ),
    c_0_4596,
    [final] ).

cnf(c_0_5958,plain,
    ( class_Ring__and__Field_Osemiring(X1)
    | ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X1) ),
    c_0_4597,
    [final] ).

cnf(c_0_5959,plain,
    ( class_Ring__and__Field_Osemiring__0(X1)
    | ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X1) ),
    c_0_4598,
    [final] ).

cnf(c_0_5960,plain,
    ( class_OrderedGroup_Oab__semigroup__mult(X1)
    | ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X1) ),
    c_0_4599,
    [final] ).

cnf(c_0_5961,plain,
    ( class_Ring__and__Field_Osemiring__0__cancel(X1)
    | ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X1) ),
    c_0_4600,
    [final] ).

cnf(c_0_5962,plain,
    ( class_Ring__and__Field_Ocomm__semiring(X1)
    | ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X1) ),
    c_0_4601,
    [final] ).

cnf(c_0_5963,plain,
    ( class_Ring__and__Field_Opordered__cancel__semiring(X1)
    | ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X1) ),
    c_0_4602,
    [final] ).

cnf(c_0_5964,plain,
    ( class_Ring__and__Field_Opordered__semiring(X1)
    | ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X1) ),
    c_0_4603,
    [final] ).

cnf(c_0_5965,plain,
    ( class_OrderedGroup_Ocancel__semigroup__add(X1)
    | ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X1) ),
    c_0_4604,
    [final] ).

cnf(c_0_5966,plain,
    ( class_OrderedGroup_Ocancel__ab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X1) ),
    c_0_4605,
    [final] ).

cnf(c_0_5967,plain,
    ( class_Orderings_Oord(X1)
    | ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X1) ),
    c_0_4606,
    [final] ).

cnf(c_0_5968,plain,
    ( class_Orderings_Oorder(X1)
    | ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X1) ),
    c_0_4607,
    [final] ).

cnf(c_0_5969,plain,
    ( class_HOL_Oplus(X1)
    | ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X1) ),
    c_0_4608,
    [final] ).

cnf(c_0_5970,plain,
    ( class_OrderedGroup_Osemigroup__add(X1)
    | ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X1) ),
    c_0_4609,
    [final] ).

cnf(c_0_5971,plain,
    ( class_OrderedGroup_Oab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X1) ),
    c_0_4610,
    [final] ).

cnf(c_0_5972,plain,
    ( class_OrderedGroup_Opordered__ab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X1) ),
    c_0_4611,
    [final] ).

cnf(c_0_5973,plain,
    ( class_Ring__and__Field_Ocomm__semiring__0(X1)
    | ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X1) ),
    c_0_4612,
    [final] ).

cnf(c_0_5974,plain,
    ( class_Ring__and__Field_Opordered__comm__semiring(X1)
    | ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X1) ),
    c_0_4613,
    [final] ).

cnf(c_0_5975,plain,
    ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
    c_0_4614,
    [final] ).

cnf(c_0_5976,plain,
    ( class_HOL_Ozero(X1)
    | ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
    c_0_4615,
    [final] ).

cnf(c_0_5977,plain,
    ( class_HOL_Oplus(X1)
    | ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
    c_0_4616,
    [final] ).

cnf(c_0_5978,plain,
    ( class_OrderedGroup_Osemigroup__add(X1)
    | ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
    c_0_4617,
    [final] ).

cnf(c_0_5979,plain,
    ( class_OrderedGroup_Oab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
    c_0_4618,
    [final] ).

cnf(c_0_5980,plain,
    ( class_OrderedGroup_Ocomm__monoid__add(X1)
    | ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
    c_0_4619,
    [final] ).

cnf(c_0_5981,plain,
    ( class_HOL_Otimes(X1)
    | ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
    c_0_4620,
    [final] ).

cnf(c_0_5982,plain,
    ( class_Ring__and__Field_Opordered__semiring(X1)
    | ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
    c_0_4621,
    [final] ).

cnf(c_0_5983,plain,
    ( class_Ring__and__Field_Opordered__cancel__semiring(X1)
    | ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
    c_0_4622,
    [final] ).

cnf(c_0_5984,plain,
    ( class_Ring__and__Field_Osemiring__0__cancel(X1)
    | ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
    c_0_4623,
    [final] ).

cnf(c_0_5985,plain,
    ( class_OrderedGroup_Ocancel__semigroup__add(X1)
    | ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
    c_0_4624,
    [final] ).

cnf(c_0_5986,plain,
    ( class_OrderedGroup_Osemigroup__mult(X1)
    | ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
    c_0_4625,
    [final] ).

cnf(c_0_5987,plain,
    ( class_OrderedGroup_Ocancel__ab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
    c_0_4626,
    [final] ).

cnf(c_0_5988,plain,
    ( class_Orderings_Oord(X1)
    | ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
    c_0_4627,
    [final] ).

cnf(c_0_5989,plain,
    ( class_Orderings_Oorder(X1)
    | ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
    c_0_4628,
    [final] ).

cnf(c_0_5990,plain,
    ( class_OrderedGroup_Opordered__ab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
    c_0_4629,
    [final] ).

cnf(c_0_5991,plain,
    ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
    c_0_4630,
    [final] ).

cnf(c_0_5992,plain,
    ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
    | ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
    c_0_4631,
    [final] ).

cnf(c_0_5993,plain,
    ( class_LOrder_Omeet__semilorder(X1)
    | ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
    c_0_4632,
    [final] ).

cnf(c_0_5994,plain,
    ( class_LOrder_Ojoin__semilorder(X1)
    | ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
    c_0_4633,
    [final] ).

cnf(c_0_5995,plain,
    ( class_LOrder_Olorder(X1)
    | ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
    c_0_4634,
    [final] ).

cnf(c_0_5996,plain,
    ( class_Orderings_Olinorder(X1)
    | ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
    c_0_4635,
    [final] ).

cnf(c_0_5997,plain,
    ( class_Ring__and__Field_Osemiring(X1)
    | ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
    c_0_4636,
    [final] ).

cnf(c_0_5998,plain,
    ( class_Ring__and__Field_Osemiring__0(X1)
    | ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
    c_0_4637,
    [final] ).

cnf(c_0_5999,plain,
    ( class_Ring__and__Field_Ocomm__semiring__0(X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    c_0_4638,
    [final] ).

cnf(c_0_6000,plain,
    ( class_Ring__and__Field_Ocomm__semiring__0__cancel(X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    c_0_4639,
    [final] ).

cnf(c_0_6001,plain,
    ( class_HOL_Oone(X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    c_0_4640,
    [final] ).

cnf(c_0_6002,plain,
    ( class_OrderedGroup_Omonoid__mult(X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    c_0_4641,
    [final] ).

cnf(c_0_6003,plain,
    ( class_Ring__and__Field_Oaxclass__0__neq__1(X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    c_0_4642,
    [final] ).

cnf(c_0_6004,plain,
    ( class_Ring__and__Field_Osemiring__1(X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    c_0_4643,
    [final] ).

cnf(c_0_6005,plain,
    ( class_Orderings_Oord(X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    c_0_4644,
    [final] ).

cnf(c_0_6006,plain,
    ( class_Orderings_Oorder(X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    c_0_4645,
    [final] ).

cnf(c_0_6007,plain,
    ( class_OrderedGroup_Opordered__ab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    c_0_4646,
    [final] ).

cnf(c_0_6008,plain,
    ( class_Ring__and__Field_Opordered__semiring(X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    c_0_4647,
    [final] ).

cnf(c_0_6009,plain,
    ( class_Ring__and__Field_Opordered__comm__semiring(X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    c_0_4648,
    [final] ).

cnf(c_0_6010,plain,
    ( class_Ring__and__Field_Opordered__cancel__semiring(X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    c_0_4649,
    [final] ).

cnf(c_0_6011,plain,
    ( class_Ring__and__Field_Opordered__cancel__comm__semiring(X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    c_0_4650,
    [final] ).

cnf(c_0_6012,plain,
    ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    c_0_4651,
    [final] ).

cnf(c_0_6013,plain,
    ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    c_0_4652,
    [final] ).

cnf(c_0_6014,plain,
    ( class_LOrder_Omeet__semilorder(X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    c_0_4653,
    [final] ).

cnf(c_0_6015,plain,
    ( class_Ring__and__Field_Osemiring__1__cancel(X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    c_0_4654,
    [final] ).

cnf(c_0_6016,plain,
    ( class_LOrder_Ojoin__semilorder(X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    c_0_4655,
    [final] ).

cnf(c_0_6017,plain,
    ( class_LOrder_Olorder(X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    c_0_4656,
    [final] ).

cnf(c_0_6018,plain,
    ( class_Orderings_Olinorder(X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    c_0_4657,
    [final] ).

cnf(c_0_6019,plain,
    ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    c_0_4658,
    [final] ).

cnf(c_0_6020,plain,
    ( class_Ring__and__Field_Oordered__semiring__strict(X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    c_0_4659,
    [final] ).

cnf(c_0_6021,plain,
    ( class_Ring__and__Field_Oordered__comm__semiring__strict(X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    c_0_4660,
    [final] ).

cnf(c_0_6022,plain,
    ( class_HOL_Oplus(X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    c_0_4661,
    [final] ).

cnf(c_0_6023,plain,
    ( class_OrderedGroup_Osemigroup__add(X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    c_0_4662,
    [final] ).

cnf(c_0_6024,plain,
    ( class_OrderedGroup_Ocancel__semigroup__add(X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    c_0_4663,
    [final] ).

cnf(c_0_6025,plain,
    ( class_OrderedGroup_Oab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    c_0_4664,
    [final] ).

cnf(c_0_6026,plain,
    ( class_OrderedGroup_Ocomm__monoid__mult(X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    c_0_4665,
    [final] ).

cnf(c_0_6027,plain,
    ( class_OrderedGroup_Ocancel__ab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    c_0_4666,
    [final] ).

cnf(c_0_6028,plain,
    ( class_HOL_Ozero(X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    c_0_4667,
    [final] ).

cnf(c_0_6029,plain,
    ( class_OrderedGroup_Ocomm__monoid__add(X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    c_0_4668,
    [final] ).

cnf(c_0_6030,plain,
    ( class_HOL_Otimes(X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    c_0_4669,
    [final] ).

cnf(c_0_6031,plain,
    ( class_OrderedGroup_Osemigroup__mult(X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    c_0_4670,
    [final] ).

cnf(c_0_6032,plain,
    ( class_Ring__and__Field_Osemiring(X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    c_0_4671,
    [final] ).

cnf(c_0_6033,plain,
    ( class_Ring__and__Field_Osemiring__0(X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    c_0_4672,
    [final] ).

cnf(c_0_6034,plain,
    ( class_Ring__and__Field_Osemiring__0__cancel(X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    c_0_4673,
    [final] ).

cnf(c_0_6035,plain,
    ( class_OrderedGroup_Oab__semigroup__mult(X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    c_0_4674,
    [final] ).

cnf(c_0_6036,plain,
    ( class_Ring__and__Field_Ocomm__semiring(X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    c_0_4675,
    [final] ).

cnf(c_0_6037,plain,
    ( class_Ring__and__Field_Ocomm__semiring__1(X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    c_0_4676,
    [final] ).

cnf(c_0_6038,plain,
    ( class_Ring__and__Field_Ocomm__semiring__1__cancel(X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    c_0_4677,
    [final] ).

cnf(c_0_6039,plain,
    ( class_HOL_Otimes(X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    c_0_4678,
    [final] ).

cnf(c_0_6040,plain,
    ( class_OrderedGroup_Osemigroup__mult(X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    c_0_4679,
    [final] ).

cnf(c_0_6041,plain,
    ( class_Ring__and__Field_Osemiring(X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    c_0_4680,
    [final] ).

cnf(c_0_6042,plain,
    ( class_Ring__and__Field_Osemiring__0(X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    c_0_4681,
    [final] ).

cnf(c_0_6043,plain,
    ( class_OrderedGroup_Ocancel__semigroup__add(X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    c_0_4682,
    [final] ).

cnf(c_0_6044,plain,
    ( class_OrderedGroup_Ocancel__ab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    c_0_4683,
    [final] ).

cnf(c_0_6045,plain,
    ( class_Ring__and__Field_Oaxclass__no__zero__divisors(X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    c_0_4684,
    [final] ).

cnf(c_0_6046,plain,
    ( class_OrderedGroup_Olordered__ab__group__join(X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    c_0_4685,
    [final] ).

cnf(c_0_6047,plain,
    ( class_OrderedGroup_Olordered__ab__group__meet(X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    c_0_4686,
    [final] ).

cnf(c_0_6048,plain,
    ( class_OrderedGroup_Olordered__ab__group__abs(X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    c_0_4687,
    [final] ).

cnf(c_0_6049,plain,
    ( class_Ring__and__Field_Opordered__ring(X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    c_0_4688,
    [final] ).

cnf(c_0_6050,plain,
    ( class_Ring__and__Field_Olordered__ring(X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    c_0_4689,
    [final] ).

cnf(c_0_6051,plain,
    ( class_OrderedGroup_Opordered__ab__group__add(X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    c_0_4690,
    [final] ).

cnf(c_0_6052,plain,
    ( class_Ring__and__Field_Osemiring__0__cancel(X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    c_0_4691,
    [final] ).

cnf(c_0_6053,plain,
    ( class_OrderedGroup_Olordered__ab__group(X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    c_0_4692,
    [final] ).

cnf(c_0_6054,plain,
    ( class_Ring__and__Field_Oaxclass__abs__if(X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    c_0_4693,
    [final] ).

cnf(c_0_6055,plain,
    ( class_Orderings_Oord(X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    c_0_4694,
    [final] ).

cnf(c_0_6056,plain,
    ( class_Orderings_Oorder(X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    c_0_4695,
    [final] ).

cnf(c_0_6057,plain,
    ( class_OrderedGroup_Opordered__ab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    c_0_4696,
    [final] ).

cnf(c_0_6058,plain,
    ( class_Ring__and__Field_Opordered__semiring(X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    c_0_4697,
    [final] ).

cnf(c_0_6059,plain,
    ( class_Ring__and__Field_Opordered__cancel__semiring(X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    c_0_4698,
    [final] ).

cnf(c_0_6060,plain,
    ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    c_0_4699,
    [final] ).

cnf(c_0_6061,plain,
    ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    c_0_4700,
    [final] ).

cnf(c_0_6062,plain,
    ( class_LOrder_Omeet__semilorder(X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    c_0_4701,
    [final] ).

cnf(c_0_6063,plain,
    ( class_HOL_Ominus(X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    c_0_4702,
    [final] ).

cnf(c_0_6064,plain,
    ( class_LOrder_Ojoin__semilorder(X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    c_0_4703,
    [final] ).

cnf(c_0_6065,plain,
    ( class_LOrder_Olorder(X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    c_0_4704,
    [final] ).

cnf(c_0_6066,plain,
    ( class_Orderings_Olinorder(X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    c_0_4705,
    [final] ).

cnf(c_0_6067,plain,
    ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    c_0_4706,
    [final] ).

cnf(c_0_6068,plain,
    ( class_Ring__and__Field_Oordered__semiring__strict(X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    c_0_4707,
    [final] ).

cnf(c_0_6069,plain,
    ( class_HOL_Ozero(X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    c_0_4708,
    [final] ).

cnf(c_0_6070,plain,
    ( class_HOL_Oplus(X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    c_0_4709,
    [final] ).

cnf(c_0_6071,plain,
    ( class_OrderedGroup_Osemigroup__add(X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    c_0_4710,
    [final] ).

cnf(c_0_6072,plain,
    ( class_OrderedGroup_Oab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    c_0_4711,
    [final] ).

cnf(c_0_6073,plain,
    ( class_OrderedGroup_Ocomm__monoid__add(X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    c_0_4712,
    [final] ).

cnf(c_0_6074,plain,
    ( class_OrderedGroup_Oab__group__add(X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    c_0_4713,
    [final] ).

cnf(c_0_6075,plain,
    ( class_Ring__and__Field_Oring(X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    c_0_4714,
    [final] ).

cnf(c_0_6076,plain,
    ( class_Ring__and__Field_Osemiring__1__cancel(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    c_0_4715,
    [final] ).

cnf(c_0_6077,plain,
    ( class_OrderedGroup_Ocomm__monoid__mult(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    c_0_4716,
    [final] ).

cnf(c_0_6078,plain,
    ( class_Ring__and__Field_Ocomm__semiring__1(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    c_0_4717,
    [final] ).

cnf(c_0_6079,plain,
    ( class_Ring__and__Field_Ocomm__semiring__1__cancel(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    c_0_4718,
    [final] ).

cnf(c_0_6080,plain,
    ( class_Ring__and__Field_Oidom(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    c_0_4719,
    [final] ).

cnf(c_0_6081,plain,
    ( class_Ring__and__Field_Oaxclass__no__zero__divisors(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    c_0_4720,
    [final] ).

cnf(c_0_6082,plain,
    ( class_Ring__and__Field_Oordered__semidom(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    c_0_4721,
    [final] ).

cnf(c_0_6083,plain,
    ( class_OrderedGroup_Opordered__ab__group__add(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    c_0_4722,
    [final] ).

cnf(c_0_6084,plain,
    ( class_OrderedGroup_Olordered__ab__group(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    c_0_4723,
    [final] ).

cnf(c_0_6085,plain,
    ( class_OrderedGroup_Olordered__ab__group__join(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    c_0_4724,
    [final] ).

cnf(c_0_6086,plain,
    ( class_OrderedGroup_Olordered__ab__group__meet(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    c_0_4725,
    [final] ).

cnf(c_0_6087,plain,
    ( class_OrderedGroup_Olordered__ab__group__abs(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    c_0_4726,
    [final] ).

cnf(c_0_6088,plain,
    ( class_HOL_Ominus(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    c_0_4727,
    [final] ).

cnf(c_0_6089,plain,
    ( class_Ring__and__Field_Opordered__ring(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    c_0_4728,
    [final] ).

cnf(c_0_6090,plain,
    ( class_Ring__and__Field_Olordered__ring(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    c_0_4729,
    [final] ).

cnf(c_0_6091,plain,
    ( class_Ring__and__Field_Oordered__ring__strict(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    c_0_4730,
    [final] ).

cnf(c_0_6092,plain,
    ( class_Ring__and__Field_Oaxclass__abs__if(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    c_0_4731,
    [final] ).

cnf(c_0_6093,plain,
    ( class_Orderings_Oord(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    c_0_4732,
    [final] ).

cnf(c_0_6094,plain,
    ( class_Orderings_Oorder(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    c_0_4733,
    [final] ).

cnf(c_0_6095,plain,
    ( class_OrderedGroup_Opordered__ab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    c_0_4734,
    [final] ).

cnf(c_0_6096,plain,
    ( class_Ring__and__Field_Opordered__semiring(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    c_0_4735,
    [final] ).

cnf(c_0_6097,plain,
    ( class_Ring__and__Field_Opordered__comm__semiring(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    c_0_4736,
    [final] ).

cnf(c_0_6098,plain,
    ( class_Ring__and__Field_Opordered__cancel__semiring(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    c_0_4737,
    [final] ).

cnf(c_0_6099,plain,
    ( class_OrderedGroup_Oab__group__add(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    c_0_4738,
    [final] ).

cnf(c_0_6100,plain,
    ( class_Ring__and__Field_Opordered__cancel__comm__semiring(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    c_0_4739,
    [final] ).

cnf(c_0_6101,plain,
    ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    c_0_4740,
    [final] ).

cnf(c_0_6102,plain,
    ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    c_0_4741,
    [final] ).

cnf(c_0_6103,plain,
    ( class_LOrder_Omeet__semilorder(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    c_0_4742,
    [final] ).

cnf(c_0_6104,plain,
    ( class_LOrder_Ojoin__semilorder(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    c_0_4743,
    [final] ).

cnf(c_0_6105,plain,
    ( class_LOrder_Olorder(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    c_0_4744,
    [final] ).

cnf(c_0_6106,plain,
    ( class_Orderings_Olinorder(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    c_0_4745,
    [final] ).

cnf(c_0_6107,plain,
    ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    c_0_4746,
    [final] ).

cnf(c_0_6108,plain,
    ( class_Ring__and__Field_Oordered__semiring__strict(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    c_0_4747,
    [final] ).

cnf(c_0_6109,plain,
    ( class_Ring__and__Field_Oordered__comm__semiring__strict(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    c_0_4748,
    [final] ).

cnf(c_0_6110,plain,
    ( class_Ring__and__Field_Oring(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    c_0_4749,
    [final] ).

cnf(c_0_6111,plain,
    ( class_HOL_Oplus(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    c_0_4750,
    [final] ).

cnf(c_0_6112,plain,
    ( class_OrderedGroup_Osemigroup__add(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    c_0_4751,
    [final] ).

cnf(c_0_6113,plain,
    ( class_OrderedGroup_Ocancel__semigroup__add(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    c_0_4752,
    [final] ).

cnf(c_0_6114,plain,
    ( class_OrderedGroup_Oab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    c_0_4753,
    [final] ).

cnf(c_0_6115,plain,
    ( class_OrderedGroup_Ocancel__ab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    c_0_4754,
    [final] ).

cnf(c_0_6116,plain,
    ( class_HOL_Ozero(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    c_0_4755,
    [final] ).

cnf(c_0_6117,plain,
    ( class_OrderedGroup_Ocomm__monoid__add(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    c_0_4756,
    [final] ).

cnf(c_0_6118,plain,
    ( class_HOL_Otimes(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    c_0_4757,
    [final] ).

cnf(c_0_6119,plain,
    ( class_OrderedGroup_Osemigroup__mult(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    c_0_4758,
    [final] ).

cnf(c_0_6120,plain,
    ( class_Ring__and__Field_Osemiring(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    c_0_4759,
    [final] ).

cnf(c_0_6121,plain,
    ( class_Ring__and__Field_Oring__1(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    c_0_4760,
    [final] ).

cnf(c_0_6122,plain,
    ( class_Ring__and__Field_Osemiring__0(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    c_0_4761,
    [final] ).

cnf(c_0_6123,plain,
    ( class_Ring__and__Field_Osemiring__0__cancel(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    c_0_4762,
    [final] ).

cnf(c_0_6124,plain,
    ( class_OrderedGroup_Oab__semigroup__mult(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    c_0_4763,
    [final] ).

cnf(c_0_6125,plain,
    ( class_Ring__and__Field_Ocomm__semiring(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    c_0_4764,
    [final] ).

cnf(c_0_6126,plain,
    ( class_Ring__and__Field_Ocomm__semiring__0(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    c_0_4765,
    [final] ).

cnf(c_0_6127,plain,
    ( class_Ring__and__Field_Ocomm__semiring__0__cancel(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    c_0_4766,
    [final] ).

cnf(c_0_6128,plain,
    ( class_HOL_Oone(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    c_0_4767,
    [final] ).

cnf(c_0_6129,plain,
    ( class_OrderedGroup_Omonoid__mult(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    c_0_4768,
    [final] ).

cnf(c_0_6130,plain,
    ( class_Ring__and__Field_Oaxclass__0__neq__1(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    c_0_4769,
    [final] ).

cnf(c_0_6131,plain,
    ( class_Ring__and__Field_Osemiring__1(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    c_0_4770,
    [final] ).

cnf(c_0_6132,plain,
    ( class_Ring__and__Field_Ocomm__ring(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    c_0_4771,
    [final] ).

cnf(c_0_6133,plain,
    ( class_Ring__and__Field_Ocomm__ring__1(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    c_0_4772,
    [final] ).

cnf(c_0_6134,plain,
    ( class_Ring__and__Field_Ocomm__semiring__1__cancel(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    c_0_4773,
    [final] ).

cnf(c_0_6135,plain,
    ( class_HOL_Ominus(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    c_0_4774,
    [final] ).

cnf(c_0_6136,plain,
    ( class_OrderedGroup_Oab__group__add(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    c_0_4775,
    [final] ).

cnf(c_0_6137,plain,
    ( class_Ring__and__Field_Oordered__semidom(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    c_0_4776,
    [final] ).

cnf(c_0_6138,plain,
    ( class_Ring__and__Field_Oring(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    c_0_4777,
    [final] ).

cnf(c_0_6139,plain,
    ( class_Orderings_Oord(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    c_0_4778,
    [final] ).

cnf(c_0_6140,plain,
    ( class_Orderings_Oorder(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    c_0_4779,
    [final] ).

cnf(c_0_6141,plain,
    ( class_OrderedGroup_Opordered__ab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    c_0_4780,
    [final] ).

cnf(c_0_6142,plain,
    ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    c_0_4781,
    [final] ).

cnf(c_0_6143,plain,
    ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    c_0_4782,
    [final] ).

cnf(c_0_6144,plain,
    ( class_OrderedGroup_Opordered__ab__group__add(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    c_0_4783,
    [final] ).

cnf(c_0_6145,plain,
    ( class_LOrder_Omeet__semilorder(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    c_0_4784,
    [final] ).

cnf(c_0_6146,plain,
    ( class_LOrder_Ojoin__semilorder(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    c_0_4785,
    [final] ).

cnf(c_0_6147,plain,
    ( class_LOrder_Olorder(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    c_0_4786,
    [final] ).

cnf(c_0_6148,plain,
    ( class_OrderedGroup_Olordered__ab__group(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    c_0_4787,
    [final] ).

cnf(c_0_6149,plain,
    ( class_Ring__and__Field_Oring__1(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    c_0_4788,
    [final] ).

cnf(c_0_6150,plain,
    ( class_OrderedGroup_Olordered__ab__group__join(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    c_0_4789,
    [final] ).

cnf(c_0_6151,plain,
    ( class_OrderedGroup_Olordered__ab__group__meet(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    c_0_4790,
    [final] ).

cnf(c_0_6152,plain,
    ( class_OrderedGroup_Olordered__ab__group__abs(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    c_0_4791,
    [final] ).

cnf(c_0_6153,plain,
    ( class_Ring__and__Field_Opordered__semiring(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    c_0_4792,
    [final] ).

cnf(c_0_6154,plain,
    ( class_Ring__and__Field_Opordered__cancel__semiring(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    c_0_4793,
    [final] ).

cnf(c_0_6155,plain,
    ( class_Ring__and__Field_Opordered__ring(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    c_0_4794,
    [final] ).

cnf(c_0_6156,plain,
    ( class_Ring__and__Field_Olordered__ring(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    c_0_4795,
    [final] ).

cnf(c_0_6157,plain,
    ( class_Ring__and__Field_Oaxclass__abs__if(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    c_0_4796,
    [final] ).

cnf(c_0_6158,plain,
    ( class_Orderings_Olinorder(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    c_0_4797,
    [final] ).

cnf(c_0_6159,plain,
    ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    c_0_4798,
    [final] ).

cnf(c_0_6160,plain,
    ( class_Ring__and__Field_Ocomm__ring(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    c_0_4799,
    [final] ).

cnf(c_0_6161,plain,
    ( class_Ring__and__Field_Oordered__semiring__strict(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    c_0_4800,
    [final] ).

cnf(c_0_6162,plain,
    ( class_Ring__and__Field_Oordered__ring__strict(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    c_0_4801,
    [final] ).

cnf(c_0_6163,plain,
    ( class_Ring__and__Field_Opordered__comm__semiring(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    c_0_4802,
    [final] ).

cnf(c_0_6164,plain,
    ( class_Ring__and__Field_Opordered__cancel__comm__semiring(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    c_0_4803,
    [final] ).

cnf(c_0_6165,plain,
    ( class_Ring__and__Field_Oordered__comm__semiring__strict(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    c_0_4804,
    [final] ).

cnf(c_0_6166,plain,
    ( class_Ring__and__Field_Oordered__idom(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    c_0_4805,
    [final] ).

cnf(c_0_6167,plain,
    ( class_HOL_Otimes(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    c_0_4806,
    [final] ).

cnf(c_0_6168,plain,
    ( class_HOL_Ozero(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    c_0_4807,
    [final] ).

cnf(c_0_6169,plain,
    ( class_Ring__and__Field_Oaxclass__no__zero__divisors(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    c_0_4808,
    [final] ).

cnf(c_0_6170,plain,
    ( class_HOL_Oplus(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    c_0_4809,
    [final] ).

cnf(c_0_6171,plain,
    ( class_Ring__and__Field_Ocomm__ring__1(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    c_0_4810,
    [final] ).

cnf(c_0_6172,plain,
    ( class_OrderedGroup_Osemigroup__add(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    c_0_4811,
    [final] ).

cnf(c_0_6173,plain,
    ( class_OrderedGroup_Ocancel__semigroup__add(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    c_0_4812,
    [final] ).

cnf(c_0_6174,plain,
    ( class_OrderedGroup_Oab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    c_0_4813,
    [final] ).

cnf(c_0_6175,plain,
    ( class_OrderedGroup_Ocancel__ab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    c_0_4814,
    [final] ).

cnf(c_0_6176,plain,
    ( class_OrderedGroup_Ocomm__monoid__add(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    c_0_4815,
    [final] ).

cnf(c_0_6177,plain,
    ( class_OrderedGroup_Osemigroup__mult(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    c_0_4816,
    [final] ).

cnf(c_0_6178,plain,
    ( class_Ring__and__Field_Osemiring(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    c_0_4817,
    [final] ).

cnf(c_0_6179,plain,
    ( class_Ring__and__Field_Osemiring__0(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    c_0_4818,
    [final] ).

cnf(c_0_6180,plain,
    ( class_Ring__and__Field_Osemiring__0__cancel(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    c_0_4819,
    [final] ).

cnf(c_0_6181,plain,
    ( class_OrderedGroup_Oab__semigroup__mult(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    c_0_4820,
    [final] ).

cnf(c_0_6182,plain,
    ( class_Ring__and__Field_Oidom(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    c_0_4821,
    [final] ).

cnf(c_0_6183,plain,
    ( class_Ring__and__Field_Ocomm__semiring(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    c_0_4822,
    [final] ).

cnf(c_0_6184,plain,
    ( class_Ring__and__Field_Ocomm__semiring__0(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    c_0_4823,
    [final] ).

cnf(c_0_6185,plain,
    ( class_Ring__and__Field_Ocomm__semiring__0__cancel(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    c_0_4824,
    [final] ).

cnf(c_0_6186,plain,
    ( class_HOL_Oone(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    c_0_4825,
    [final] ).

cnf(c_0_6187,plain,
    ( class_OrderedGroup_Omonoid__mult(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    c_0_4826,
    [final] ).

cnf(c_0_6188,plain,
    ( class_Ring__and__Field_Oaxclass__0__neq__1(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    c_0_4827,
    [final] ).

cnf(c_0_6189,plain,
    ( class_Ring__and__Field_Osemiring__1(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    c_0_4828,
    [final] ).

cnf(c_0_6190,plain,
    ( class_Ring__and__Field_Osemiring__1__cancel(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    c_0_4829,
    [final] ).

cnf(c_0_6191,plain,
    ( class_OrderedGroup_Ocomm__monoid__mult(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    c_0_4830,
    [final] ).

cnf(c_0_6192,plain,
    ( class_Ring__and__Field_Ocomm__semiring__1(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    c_0_4831,
    [final] ).

cnf(c_0_6193,plain,
    ( class_HOL_Oinverse(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    c_0_4832,
    [final] ).

cnf(c_0_6194,plain,
    ( class_Ring__and__Field_Ofield(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    c_0_4833,
    [final] ).

cnf(c_0_6195,plain,
    ( class_OrderedGroup_Osemigroup__add(X1)
    | ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X1) ),
    c_0_4834,
    [final] ).

cnf(c_0_6196,plain,
    ( class_OrderedGroup_Oab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X1) ),
    c_0_4835,
    [final] ).

cnf(c_0_6197,plain,
    ( class_OrderedGroup_Ocomm__monoid__add(X1)
    | ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X1) ),
    c_0_4836,
    [final] ).

cnf(c_0_6198,plain,
    ( class_HOL_Otimes(X1)
    | ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X1) ),
    c_0_4837,
    [final] ).

cnf(c_0_6199,plain,
    ( class_OrderedGroup_Osemigroup__mult(X1)
    | ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X1) ),
    c_0_4838,
    [final] ).

cnf(c_0_6200,plain,
    ( class_Ring__and__Field_Osemiring(X1)
    | ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X1) ),
    c_0_4839,
    [final] ).

cnf(c_0_6201,plain,
    ( class_Ring__and__Field_Osemiring__0(X1)
    | ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X1) ),
    c_0_4840,
    [final] ).

cnf(c_0_6202,plain,
    ( class_Ring__and__Field_Opordered__comm__semiring(X1)
    | ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X1) ),
    c_0_4841,
    [final] ).

cnf(c_0_6203,plain,
    ( class_Ring__and__Field_Opordered__cancel__comm__semiring(X1)
    | ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X1) ),
    c_0_4842,
    [final] ).

cnf(c_0_6204,plain,
    ( class_Ring__and__Field_Opordered__semiring(X1)
    | ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X1) ),
    c_0_4843,
    [final] ).

cnf(c_0_6205,plain,
    ( class_Ring__and__Field_Osemiring__0__cancel(X1)
    | ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X1) ),
    c_0_4844,
    [final] ).

cnf(c_0_6206,plain,
    ( class_Ring__and__Field_Opordered__cancel__semiring(X1)
    | ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X1) ),
    c_0_4845,
    [final] ).

cnf(c_0_6207,plain,
    ( class_Ring__and__Field_Oordered__semiring__strict(X1)
    | ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X1) ),
    c_0_4846,
    [final] ).

cnf(c_0_6208,plain,
    ( class_OrderedGroup_Ocancel__semigroup__add(X1)
    | ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X1) ),
    c_0_4847,
    [final] ).

cnf(c_0_6209,plain,
    ( class_OrderedGroup_Ocancel__ab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X1) ),
    c_0_4848,
    [final] ).

cnf(c_0_6210,plain,
    ( class_Orderings_Oord(X1)
    | ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X1) ),
    c_0_4849,
    [final] ).

cnf(c_0_6211,plain,
    ( class_Orderings_Oorder(X1)
    | ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X1) ),
    c_0_4850,
    [final] ).

cnf(c_0_6212,plain,
    ( class_OrderedGroup_Oab__semigroup__mult(X1)
    | ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X1) ),
    c_0_4851,
    [final] ).

cnf(c_0_6213,plain,
    ( class_OrderedGroup_Opordered__ab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X1) ),
    c_0_4852,
    [final] ).

cnf(c_0_6214,plain,
    ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X1) ),
    c_0_4853,
    [final] ).

cnf(c_0_6215,plain,
    ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
    | ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X1) ),
    c_0_4854,
    [final] ).

cnf(c_0_6216,plain,
    ( class_LOrder_Omeet__semilorder(X1)
    | ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X1) ),
    c_0_4855,
    [final] ).

cnf(c_0_6217,plain,
    ( class_LOrder_Ojoin__semilorder(X1)
    | ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X1) ),
    c_0_4856,
    [final] ).

cnf(c_0_6218,plain,
    ( class_LOrder_Olorder(X1)
    | ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X1) ),
    c_0_4857,
    [final] ).

cnf(c_0_6219,plain,
    ( class_Orderings_Olinorder(X1)
    | ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X1) ),
    c_0_4858,
    [final] ).

cnf(c_0_6220,plain,
    ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X1) ),
    c_0_4859,
    [final] ).

cnf(c_0_6221,plain,
    ( class_HOL_Ozero(X1)
    | ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X1) ),
    c_0_4860,
    [final] ).

cnf(c_0_6222,plain,
    ( class_HOL_Oplus(X1)
    | ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X1) ),
    c_0_4861,
    [final] ).

cnf(c_0_6223,plain,
    ( class_Ring__and__Field_Ocomm__semiring(X1)
    | ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X1) ),
    c_0_4862,
    [final] ).

cnf(c_0_6224,plain,
    ( class_Ring__and__Field_Ocomm__semiring__0(X1)
    | ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X1) ),
    c_0_4863,
    [final] ).

cnf(c_0_6225,plain,
    ( class_OrderedGroup_Opordered__ab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Olordered__ring(X1) ),
    c_0_4864,
    [final] ).

cnf(c_0_6226,plain,
    ( class_Ring__and__Field_Opordered__semiring(X1)
    | ~ class_Ring__and__Field_Olordered__ring(X1) ),
    c_0_4865,
    [final] ).

cnf(c_0_6227,plain,
    ( class_Ring__and__Field_Opordered__cancel__semiring(X1)
    | ~ class_Ring__and__Field_Olordered__ring(X1) ),
    c_0_4866,
    [final] ).

cnf(c_0_6228,plain,
    ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Olordered__ring(X1) ),
    c_0_4867,
    [final] ).

cnf(c_0_6229,plain,
    ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
    | ~ class_Ring__and__Field_Olordered__ring(X1) ),
    c_0_4868,
    [final] ).

cnf(c_0_6230,plain,
    ( class_HOL_Ominus(X1)
    | ~ class_Ring__and__Field_Olordered__ring(X1) ),
    c_0_4869,
    [final] ).

cnf(c_0_6231,plain,
    ( class_OrderedGroup_Olordered__ab__group__join(X1)
    | ~ class_Ring__and__Field_Olordered__ring(X1) ),
    c_0_4870,
    [final] ).

cnf(c_0_6232,plain,
    ( class_OrderedGroup_Oab__group__add(X1)
    | ~ class_Ring__and__Field_Olordered__ring(X1) ),
    c_0_4871,
    [final] ).

cnf(c_0_6233,plain,
    ( class_OrderedGroup_Olordered__ab__group__meet(X1)
    | ~ class_Ring__and__Field_Olordered__ring(X1) ),
    c_0_4872,
    [final] ).

cnf(c_0_6234,plain,
    ( class_LOrder_Omeet__semilorder(X1)
    | ~ class_Ring__and__Field_Olordered__ring(X1) ),
    c_0_4873,
    [final] ).

cnf(c_0_6235,plain,
    ( class_LOrder_Ojoin__semilorder(X1)
    | ~ class_Ring__and__Field_Olordered__ring(X1) ),
    c_0_4874,
    [final] ).

cnf(c_0_6236,plain,
    ( class_LOrder_Olorder(X1)
    | ~ class_Ring__and__Field_Olordered__ring(X1) ),
    c_0_4875,
    [final] ).

cnf(c_0_6237,plain,
    ( class_OrderedGroup_Olordered__ab__group(X1)
    | ~ class_Ring__and__Field_Olordered__ring(X1) ),
    c_0_4876,
    [final] ).

cnf(c_0_6238,plain,
    ( class_OrderedGroup_Olordered__ab__group__abs(X1)
    | ~ class_Ring__and__Field_Olordered__ring(X1) ),
    c_0_4877,
    [final] ).

cnf(c_0_6239,plain,
    ( class_HOL_Oplus(X1)
    | ~ class_Ring__and__Field_Olordered__ring(X1) ),
    c_0_4878,
    [final] ).

cnf(c_0_6240,plain,
    ( class_OrderedGroup_Osemigroup__add(X1)
    | ~ class_Ring__and__Field_Olordered__ring(X1) ),
    c_0_4879,
    [final] ).

cnf(c_0_6241,plain,
    ( class_OrderedGroup_Ocancel__semigroup__add(X1)
    | ~ class_Ring__and__Field_Olordered__ring(X1) ),
    c_0_4880,
    [final] ).

cnf(c_0_6242,plain,
    ( class_OrderedGroup_Oab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Olordered__ring(X1) ),
    c_0_4881,
    [final] ).

cnf(c_0_6243,plain,
    ( class_OrderedGroup_Opordered__ab__group__add(X1)
    | ~ class_Ring__and__Field_Olordered__ring(X1) ),
    c_0_4882,
    [final] ).

cnf(c_0_6244,plain,
    ( class_OrderedGroup_Ocancel__ab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Olordered__ring(X1) ),
    c_0_4883,
    [final] ).

cnf(c_0_6245,plain,
    ( class_HOL_Ozero(X1)
    | ~ class_Ring__and__Field_Olordered__ring(X1) ),
    c_0_4884,
    [final] ).

cnf(c_0_6246,plain,
    ( class_OrderedGroup_Ocomm__monoid__add(X1)
    | ~ class_Ring__and__Field_Olordered__ring(X1) ),
    c_0_4885,
    [final] ).

cnf(c_0_6247,plain,
    ( class_HOL_Otimes(X1)
    | ~ class_Ring__and__Field_Olordered__ring(X1) ),
    c_0_4886,
    [final] ).

cnf(c_0_6248,plain,
    ( class_OrderedGroup_Osemigroup__mult(X1)
    | ~ class_Ring__and__Field_Olordered__ring(X1) ),
    c_0_4887,
    [final] ).

cnf(c_0_6249,plain,
    ( class_Ring__and__Field_Osemiring(X1)
    | ~ class_Ring__and__Field_Olordered__ring(X1) ),
    c_0_4888,
    [final] ).

cnf(c_0_6250,plain,
    ( class_Ring__and__Field_Osemiring__0(X1)
    | ~ class_Ring__and__Field_Olordered__ring(X1) ),
    c_0_4889,
    [final] ).

cnf(c_0_6251,plain,
    ( class_Ring__and__Field_Osemiring__0__cancel(X1)
    | ~ class_Ring__and__Field_Olordered__ring(X1) ),
    c_0_4890,
    [final] ).

cnf(c_0_6252,plain,
    ( class_Orderings_Oord(X1)
    | ~ class_Ring__and__Field_Olordered__ring(X1) ),
    c_0_4891,
    [final] ).

cnf(c_0_6253,plain,
    ( class_Orderings_Oorder(X1)
    | ~ class_Ring__and__Field_Olordered__ring(X1) ),
    c_0_4892,
    [final] ).

cnf(c_0_6254,plain,
    ( class_Ring__and__Field_Oring(X1)
    | ~ class_Ring__and__Field_Olordered__ring(X1) ),
    c_0_4893,
    [final] ).

cnf(c_0_6255,plain,
    ( class_Ring__and__Field_Opordered__ring(X1)
    | ~ class_Ring__and__Field_Olordered__ring(X1) ),
    c_0_4894,
    [final] ).

cnf(c_0_6256,plain,
    ( class_Ring__and__Field_Osemiring__1__cancel(X1)
    | ~ class_Ring__and__Field_Oidom(X1) ),
    c_0_4895,
    [final] ).

cnf(c_0_6257,plain,
    ( class_OrderedGroup_Ocomm__monoid__mult(X1)
    | ~ class_Ring__and__Field_Oidom(X1) ),
    c_0_4896,
    [final] ).

cnf(c_0_6258,plain,
    ( class_Ring__and__Field_Ocomm__semiring__1(X1)
    | ~ class_Ring__and__Field_Oidom(X1) ),
    c_0_4897,
    [final] ).

cnf(c_0_6259,plain,
    ( class_Ring__and__Field_Ocomm__semiring__1__cancel(X1)
    | ~ class_Ring__and__Field_Oidom(X1) ),
    c_0_4898,
    [final] ).

cnf(c_0_6260,plain,
    ( class_HOL_Ominus(X1)
    | ~ class_Ring__and__Field_Oidom(X1) ),
    c_0_4899,
    [final] ).

cnf(c_0_6261,plain,
    ( class_OrderedGroup_Oab__group__add(X1)
    | ~ class_Ring__and__Field_Oidom(X1) ),
    c_0_4900,
    [final] ).

cnf(c_0_6262,plain,
    ( class_Ring__and__Field_Oaxclass__no__zero__divisors(X1)
    | ~ class_Ring__and__Field_Oidom(X1) ),
    c_0_4901,
    [final] ).

cnf(c_0_6263,plain,
    ( class_Ring__and__Field_Oring(X1)
    | ~ class_Ring__and__Field_Oidom(X1) ),
    c_0_4902,
    [final] ).

cnf(c_0_6264,plain,
    ( class_HOL_Oplus(X1)
    | ~ class_Ring__and__Field_Oidom(X1) ),
    c_0_4903,
    [final] ).

cnf(c_0_6265,plain,
    ( class_OrderedGroup_Osemigroup__add(X1)
    | ~ class_Ring__and__Field_Oidom(X1) ),
    c_0_4904,
    [final] ).

cnf(c_0_6266,plain,
    ( class_OrderedGroup_Ocancel__semigroup__add(X1)
    | ~ class_Ring__and__Field_Oidom(X1) ),
    c_0_4905,
    [final] ).

cnf(c_0_6267,plain,
    ( class_OrderedGroup_Oab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Oidom(X1) ),
    c_0_4906,
    [final] ).

cnf(c_0_6268,plain,
    ( class_OrderedGroup_Ocancel__ab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Oidom(X1) ),
    c_0_4907,
    [final] ).

cnf(c_0_6269,plain,
    ( class_HOL_Ozero(X1)
    | ~ class_Ring__and__Field_Oidom(X1) ),
    c_0_4908,
    [final] ).

cnf(c_0_6270,plain,
    ( class_OrderedGroup_Ocomm__monoid__add(X1)
    | ~ class_Ring__and__Field_Oidom(X1) ),
    c_0_4909,
    [final] ).

cnf(c_0_6271,plain,
    ( class_HOL_Otimes(X1)
    | ~ class_Ring__and__Field_Oidom(X1) ),
    c_0_4910,
    [final] ).

cnf(c_0_6272,plain,
    ( class_OrderedGroup_Osemigroup__mult(X1)
    | ~ class_Ring__and__Field_Oidom(X1) ),
    c_0_4911,
    [final] ).

cnf(c_0_6273,plain,
    ( class_Ring__and__Field_Osemiring(X1)
    | ~ class_Ring__and__Field_Oidom(X1) ),
    c_0_4912,
    [final] ).

cnf(c_0_6274,plain,
    ( class_Ring__and__Field_Oring__1(X1)
    | ~ class_Ring__and__Field_Oidom(X1) ),
    c_0_4913,
    [final] ).

cnf(c_0_6275,plain,
    ( class_Ring__and__Field_Osemiring__0(X1)
    | ~ class_Ring__and__Field_Oidom(X1) ),
    c_0_4914,
    [final] ).

cnf(c_0_6276,plain,
    ( class_Ring__and__Field_Osemiring__0__cancel(X1)
    | ~ class_Ring__and__Field_Oidom(X1) ),
    c_0_4915,
    [final] ).

cnf(c_0_6277,plain,
    ( class_OrderedGroup_Oab__semigroup__mult(X1)
    | ~ class_Ring__and__Field_Oidom(X1) ),
    c_0_4916,
    [final] ).

cnf(c_0_6278,plain,
    ( class_Ring__and__Field_Ocomm__semiring(X1)
    | ~ class_Ring__and__Field_Oidom(X1) ),
    c_0_4917,
    [final] ).

cnf(c_0_6279,plain,
    ( class_Ring__and__Field_Ocomm__semiring__0(X1)
    | ~ class_Ring__and__Field_Oidom(X1) ),
    c_0_4918,
    [final] ).

cnf(c_0_6280,plain,
    ( class_Ring__and__Field_Ocomm__semiring__0__cancel(X1)
    | ~ class_Ring__and__Field_Oidom(X1) ),
    c_0_4919,
    [final] ).

cnf(c_0_6281,plain,
    ( class_HOL_Oone(X1)
    | ~ class_Ring__and__Field_Oidom(X1) ),
    c_0_4920,
    [final] ).

cnf(c_0_6282,plain,
    ( class_OrderedGroup_Omonoid__mult(X1)
    | ~ class_Ring__and__Field_Oidom(X1) ),
    c_0_4921,
    [final] ).

cnf(c_0_6283,plain,
    ( class_Ring__and__Field_Oaxclass__0__neq__1(X1)
    | ~ class_Ring__and__Field_Oidom(X1) ),
    c_0_4922,
    [final] ).

cnf(c_0_6284,plain,
    ( class_Ring__and__Field_Osemiring__1(X1)
    | ~ class_Ring__and__Field_Oidom(X1) ),
    c_0_4923,
    [final] ).

cnf(c_0_6285,plain,
    ( class_Ring__and__Field_Ocomm__ring(X1)
    | ~ class_Ring__and__Field_Oidom(X1) ),
    c_0_4924,
    [final] ).

cnf(c_0_6286,plain,
    ( class_Ring__and__Field_Ocomm__ring__1(X1)
    | ~ class_Ring__and__Field_Oidom(X1) ),
    c_0_4925,
    [final] ).

cnf(c_0_6287,plain,
    ( class_Ring__and__Field_Osemiring__1__cancel(X1)
    | ~ class_Ring__and__Field_Ofield(X1) ),
    c_0_4926,
    [final] ).

cnf(c_0_6288,plain,
    ( class_OrderedGroup_Ocomm__monoid__mult(X1)
    | ~ class_Ring__and__Field_Ofield(X1) ),
    c_0_4927,
    [final] ).

cnf(c_0_6289,plain,
    ( class_Ring__and__Field_Ocomm__semiring__1(X1)
    | ~ class_Ring__and__Field_Ofield(X1) ),
    c_0_4928,
    [final] ).

cnf(c_0_6290,plain,
    ( class_Ring__and__Field_Ocomm__semiring__1__cancel(X1)
    | ~ class_Ring__and__Field_Ofield(X1) ),
    c_0_4929,
    [final] ).

cnf(c_0_6291,plain,
    ( class_HOL_Ominus(X1)
    | ~ class_Ring__and__Field_Ofield(X1) ),
    c_0_4930,
    [final] ).

cnf(c_0_6292,plain,
    ( class_OrderedGroup_Oab__group__add(X1)
    | ~ class_Ring__and__Field_Ofield(X1) ),
    c_0_4931,
    [final] ).

cnf(c_0_6293,plain,
    ( class_Ring__and__Field_Oaxclass__no__zero__divisors(X1)
    | ~ class_Ring__and__Field_Ofield(X1) ),
    c_0_4932,
    [final] ).

cnf(c_0_6294,plain,
    ( class_Ring__and__Field_Oidom(X1)
    | ~ class_Ring__and__Field_Ofield(X1) ),
    c_0_4933,
    [final] ).

cnf(c_0_6295,plain,
    ( class_HOL_Oinverse(X1)
    | ~ class_Ring__and__Field_Ofield(X1) ),
    c_0_4934,
    [final] ).

cnf(c_0_6296,plain,
    ( class_Ring__and__Field_Oring(X1)
    | ~ class_Ring__and__Field_Ofield(X1) ),
    c_0_4935,
    [final] ).

cnf(c_0_6297,plain,
    ( class_HOL_Oplus(X1)
    | ~ class_Ring__and__Field_Ofield(X1) ),
    c_0_4936,
    [final] ).

cnf(c_0_6298,plain,
    ( class_OrderedGroup_Osemigroup__add(X1)
    | ~ class_Ring__and__Field_Ofield(X1) ),
    c_0_4937,
    [final] ).

cnf(c_0_6299,plain,
    ( class_OrderedGroup_Ocancel__semigroup__add(X1)
    | ~ class_Ring__and__Field_Ofield(X1) ),
    c_0_4938,
    [final] ).

cnf(c_0_6300,plain,
    ( class_OrderedGroup_Oab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Ofield(X1) ),
    c_0_4939,
    [final] ).

cnf(c_0_6301,plain,
    ( class_OrderedGroup_Ocancel__ab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Ofield(X1) ),
    c_0_4940,
    [final] ).

cnf(c_0_6302,plain,
    ( class_HOL_Ozero(X1)
    | ~ class_Ring__and__Field_Ofield(X1) ),
    c_0_4941,
    [final] ).

cnf(c_0_6303,plain,
    ( class_OrderedGroup_Ocomm__monoid__add(X1)
    | ~ class_Ring__and__Field_Ofield(X1) ),
    c_0_4942,
    [final] ).

cnf(c_0_6304,plain,
    ( class_HOL_Otimes(X1)
    | ~ class_Ring__and__Field_Ofield(X1) ),
    c_0_4943,
    [final] ).

cnf(c_0_6305,plain,
    ( class_OrderedGroup_Osemigroup__mult(X1)
    | ~ class_Ring__and__Field_Ofield(X1) ),
    c_0_4944,
    [final] ).

cnf(c_0_6306,plain,
    ( class_Ring__and__Field_Osemiring(X1)
    | ~ class_Ring__and__Field_Ofield(X1) ),
    c_0_4945,
    [final] ).

cnf(c_0_6307,plain,
    ( class_Ring__and__Field_Oring__1(X1)
    | ~ class_Ring__and__Field_Ofield(X1) ),
    c_0_4946,
    [final] ).

cnf(c_0_6308,plain,
    ( class_Ring__and__Field_Osemiring__0(X1)
    | ~ class_Ring__and__Field_Ofield(X1) ),
    c_0_4947,
    [final] ).

cnf(c_0_6309,plain,
    ( class_Ring__and__Field_Osemiring__0__cancel(X1)
    | ~ class_Ring__and__Field_Ofield(X1) ),
    c_0_4948,
    [final] ).

cnf(c_0_6310,plain,
    ( class_OrderedGroup_Oab__semigroup__mult(X1)
    | ~ class_Ring__and__Field_Ofield(X1) ),
    c_0_4949,
    [final] ).

cnf(c_0_6311,plain,
    ( class_Ring__and__Field_Ocomm__semiring(X1)
    | ~ class_Ring__and__Field_Ofield(X1) ),
    c_0_4950,
    [final] ).

cnf(c_0_6312,plain,
    ( class_Ring__and__Field_Ocomm__semiring__0(X1)
    | ~ class_Ring__and__Field_Ofield(X1) ),
    c_0_4951,
    [final] ).

cnf(c_0_6313,plain,
    ( class_Ring__and__Field_Ocomm__semiring__0__cancel(X1)
    | ~ class_Ring__and__Field_Ofield(X1) ),
    c_0_4952,
    [final] ).

cnf(c_0_6314,plain,
    ( class_HOL_Oone(X1)
    | ~ class_Ring__and__Field_Ofield(X1) ),
    c_0_4953,
    [final] ).

cnf(c_0_6315,plain,
    ( class_OrderedGroup_Omonoid__mult(X1)
    | ~ class_Ring__and__Field_Ofield(X1) ),
    c_0_4954,
    [final] ).

cnf(c_0_6316,plain,
    ( class_Ring__and__Field_Oaxclass__0__neq__1(X1)
    | ~ class_Ring__and__Field_Ofield(X1) ),
    c_0_4955,
    [final] ).

cnf(c_0_6317,plain,
    ( class_Ring__and__Field_Osemiring__1(X1)
    | ~ class_Ring__and__Field_Ofield(X1) ),
    c_0_4956,
    [final] ).

cnf(c_0_6318,plain,
    ( class_Ring__and__Field_Ocomm__ring(X1)
    | ~ class_Ring__and__Field_Ofield(X1) ),
    c_0_4957,
    [final] ).

cnf(c_0_6319,plain,
    ( class_Ring__and__Field_Ocomm__ring__1(X1)
    | ~ class_Ring__and__Field_Ofield(X1) ),
    c_0_4958,
    [final] ).

cnf(c_0_6320,plain,
    ( class_HOL_Oinverse(X1)
    | ~ class_Ring__and__Field_Odivision__by__zero(X1) ),
    c_0_4959,
    [final] ).

cnf(c_0_6321,plain,
    ( class_HOL_Ozero(X1)
    | ~ class_Ring__and__Field_Odivision__by__zero(X1) ),
    c_0_4960,
    [final] ).

cnf(c_0_6322,plain,
    ( class_OrderedGroup_Ocomm__monoid__add(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X1) ),
    c_0_4961,
    [final] ).

cnf(c_0_6323,plain,
    ( class_Ring__and__Field_Osemiring(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X1) ),
    c_0_4962,
    [final] ).

cnf(c_0_6324,plain,
    ( class_Ring__and__Field_Osemiring__0(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X1) ),
    c_0_4963,
    [final] ).

cnf(c_0_6325,plain,
    ( class_Ring__and__Field_Oaxclass__0__neq__1(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X1) ),
    c_0_4964,
    [final] ).

cnf(c_0_6326,plain,
    ( class_Ring__and__Field_Osemiring__1(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X1) ),
    c_0_4965,
    [final] ).

cnf(c_0_6327,plain,
    ( class_OrderedGroup_Oab__semigroup__mult(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X1) ),
    c_0_4966,
    [final] ).

cnf(c_0_6328,plain,
    ( class_OrderedGroup_Ocomm__monoid__mult(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X1) ),
    c_0_4967,
    [final] ).

cnf(c_0_6329,plain,
    ( class_Ring__and__Field_Ocomm__semiring__0__cancel(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X1) ),
    c_0_4968,
    [final] ).

cnf(c_0_6330,plain,
    ( class_Ring__and__Field_Osemiring__0__cancel(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X1) ),
    c_0_4969,
    [final] ).

cnf(c_0_6331,plain,
    ( class_Ring__and__Field_Osemiring__1__cancel(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X1) ),
    c_0_4970,
    [final] ).

cnf(c_0_6332,plain,
    ( class_Ring__and__Field_Ocomm__semiring(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X1) ),
    c_0_4971,
    [final] ).

cnf(c_0_6333,plain,
    ( class_OrderedGroup_Ocancel__semigroup__add(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X1) ),
    c_0_4972,
    [final] ).

cnf(c_0_6334,plain,
    ( class_OrderedGroup_Ocancel__ab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X1) ),
    c_0_4973,
    [final] ).

cnf(c_0_6335,plain,
    ( class_HOL_Otimes(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X1) ),
    c_0_4974,
    [final] ).

cnf(c_0_6336,plain,
    ( class_OrderedGroup_Osemigroup__mult(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X1) ),
    c_0_4975,
    [final] ).

cnf(c_0_6337,plain,
    ( class_HOL_Oone(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X1) ),
    c_0_4976,
    [final] ).

cnf(c_0_6338,plain,
    ( class_OrderedGroup_Omonoid__mult(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X1) ),
    c_0_4977,
    [final] ).

cnf(c_0_6339,plain,
    ( class_HOL_Oplus(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X1) ),
    c_0_4978,
    [final] ).

cnf(c_0_6340,plain,
    ( class_OrderedGroup_Osemigroup__add(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X1) ),
    c_0_4979,
    [final] ).

cnf(c_0_6341,plain,
    ( class_OrderedGroup_Oab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X1) ),
    c_0_4980,
    [final] ).

cnf(c_0_6342,plain,
    ( class_HOL_Ozero(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X1) ),
    c_0_4981,
    [final] ).

cnf(c_0_6343,plain,
    ( class_Ring__and__Field_Ocomm__semiring__0(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X1) ),
    c_0_4982,
    [final] ).

cnf(c_0_6344,plain,
    ( class_Ring__and__Field_Ocomm__semiring__1(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X1) ),
    c_0_4983,
    [final] ).

cnf(c_0_6345,plain,
    ( class_HOL_Otimes(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    c_0_4984,
    [final] ).

cnf(c_0_6346,plain,
    ( class_OrderedGroup_Osemigroup__mult(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    c_0_4985,
    [final] ).

cnf(c_0_6347,plain,
    ( class_Ring__and__Field_Osemiring(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    c_0_4986,
    [final] ).

cnf(c_0_6348,plain,
    ( class_Ring__and__Field_Osemiring__0(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    c_0_4987,
    [final] ).

cnf(c_0_6349,plain,
    ( class_OrderedGroup_Oab__semigroup__mult(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    c_0_4988,
    [final] ).

cnf(c_0_6350,plain,
    ( class_Ring__and__Field_Ocomm__semiring(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    c_0_4989,
    [final] ).

cnf(c_0_6351,plain,
    ( class_Ring__and__Field_Ocomm__semiring__0(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    c_0_4990,
    [final] ).

cnf(c_0_6352,plain,
    ( class_HOL_Oone(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    c_0_4991,
    [final] ).

cnf(c_0_6353,plain,
    ( class_Ring__and__Field_Osemiring__1(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    c_0_4992,
    [final] ).

cnf(c_0_6354,plain,
    ( class_OrderedGroup_Omonoid__mult(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    c_0_4993,
    [final] ).

cnf(c_0_6355,plain,
    ( class_OrderedGroup_Ocomm__monoid__mult(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    c_0_4994,
    [final] ).

cnf(c_0_6356,plain,
    ( class_HOL_Oplus(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    c_0_4995,
    [final] ).

cnf(c_0_6357,plain,
    ( class_OrderedGroup_Osemigroup__add(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    c_0_4996,
    [final] ).

cnf(c_0_6358,plain,
    ( class_OrderedGroup_Oab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    c_0_4997,
    [final] ).

cnf(c_0_6359,plain,
    ( class_OrderedGroup_Ocomm__monoid__add(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    c_0_4998,
    [final] ).

cnf(c_0_6360,plain,
    ( class_HOL_Ozero(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    c_0_4999,
    [final] ).

cnf(c_0_6361,plain,
    ( class_Ring__and__Field_Oaxclass__0__neq__1(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    c_0_5000,
    [final] ).

cnf(c_0_6362,plain,
    ( class_OrderedGroup_Osemigroup__add(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X1) ),
    c_0_5001,
    [final] ).

cnf(c_0_6363,plain,
    ( class_OrderedGroup_Oab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X1) ),
    c_0_5002,
    [final] ).

cnf(c_0_6364,plain,
    ( class_OrderedGroup_Ocomm__monoid__add(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X1) ),
    c_0_5003,
    [final] ).

cnf(c_0_6365,plain,
    ( class_HOL_Otimes(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X1) ),
    c_0_5004,
    [final] ).

cnf(c_0_6366,plain,
    ( class_OrderedGroup_Osemigroup__mult(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X1) ),
    c_0_5005,
    [final] ).

cnf(c_0_6367,plain,
    ( class_Ring__and__Field_Osemiring(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X1) ),
    c_0_5006,
    [final] ).

cnf(c_0_6368,plain,
    ( class_Ring__and__Field_Osemiring__0(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X1) ),
    c_0_5007,
    [final] ).

cnf(c_0_6369,plain,
    ( class_OrderedGroup_Oab__semigroup__mult(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X1) ),
    c_0_5008,
    [final] ).

cnf(c_0_6370,plain,
    ( class_Ring__and__Field_Osemiring__0__cancel(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X1) ),
    c_0_5009,
    [final] ).

cnf(c_0_6371,plain,
    ( class_OrderedGroup_Ocancel__semigroup__add(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X1) ),
    c_0_5010,
    [final] ).

cnf(c_0_6372,plain,
    ( class_OrderedGroup_Ocancel__ab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X1) ),
    c_0_5011,
    [final] ).

cnf(c_0_6373,plain,
    ( class_HOL_Ozero(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X1) ),
    c_0_5012,
    [final] ).

cnf(c_0_6374,plain,
    ( class_HOL_Oplus(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X1) ),
    c_0_5013,
    [final] ).

cnf(c_0_6375,plain,
    ( class_Ring__and__Field_Ocomm__semiring(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X1) ),
    c_0_5014,
    [final] ).

cnf(c_0_6376,plain,
    ( class_Ring__and__Field_Ocomm__semiring__0(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X1) ),
    c_0_5015,
    [final] ).

cnf(c_0_6377,plain,
    ( class_HOL_Ozero(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__0(X1) ),
    c_0_5016,
    [final] ).

cnf(c_0_6378,plain,
    ( class_OrderedGroup_Ocomm__monoid__add(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__0(X1) ),
    c_0_5017,
    [final] ).

cnf(c_0_6379,plain,
    ( class_HOL_Otimes(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__0(X1) ),
    c_0_5018,
    [final] ).

cnf(c_0_6380,plain,
    ( class_OrderedGroup_Osemigroup__mult(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__0(X1) ),
    c_0_5019,
    [final] ).

cnf(c_0_6381,plain,
    ( class_HOL_Oplus(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__0(X1) ),
    c_0_5020,
    [final] ).

cnf(c_0_6382,plain,
    ( class_OrderedGroup_Osemigroup__add(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__0(X1) ),
    c_0_5021,
    [final] ).

cnf(c_0_6383,plain,
    ( class_OrderedGroup_Oab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__0(X1) ),
    c_0_5022,
    [final] ).

cnf(c_0_6384,plain,
    ( class_Ring__and__Field_Osemiring(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__0(X1) ),
    c_0_5023,
    [final] ).

cnf(c_0_6385,plain,
    ( class_Ring__and__Field_Osemiring__0(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__0(X1) ),
    c_0_5024,
    [final] ).

cnf(c_0_6386,plain,
    ( class_OrderedGroup_Oab__semigroup__mult(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__0(X1) ),
    c_0_5025,
    [final] ).

cnf(c_0_6387,plain,
    ( class_Ring__and__Field_Ocomm__semiring(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__0(X1) ),
    c_0_5026,
    [final] ).

cnf(c_0_6388,plain,
    ( class_Ring__and__Field_Osemiring(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring(X1) ),
    c_0_5027,
    [final] ).

cnf(c_0_6389,plain,
    ( class_HOL_Otimes(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring(X1) ),
    c_0_5028,
    [final] ).

cnf(c_0_6390,plain,
    ( class_OrderedGroup_Osemigroup__mult(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring(X1) ),
    c_0_5029,
    [final] ).

cnf(c_0_6391,plain,
    ( class_OrderedGroup_Oab__semigroup__mult(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring(X1) ),
    c_0_5030,
    [final] ).

cnf(c_0_6392,plain,
    ( class_HOL_Oplus(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring(X1) ),
    c_0_5031,
    [final] ).

cnf(c_0_6393,plain,
    ( class_OrderedGroup_Osemigroup__add(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring(X1) ),
    c_0_5032,
    [final] ).

cnf(c_0_6394,plain,
    ( class_OrderedGroup_Oab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring(X1) ),
    c_0_5033,
    [final] ).

cnf(c_0_6395,plain,
    ( class_Ring__and__Field_Osemiring__0(X1)
    | ~ class_Ring__and__Field_Ocomm__ring__1(X1) ),
    c_0_5034,
    [final] ).

cnf(c_0_6396,plain,
    ( class_Ring__and__Field_Osemiring__0__cancel(X1)
    | ~ class_Ring__and__Field_Ocomm__ring__1(X1) ),
    c_0_5035,
    [final] ).

cnf(c_0_6397,plain,
    ( class_OrderedGroup_Oab__semigroup__mult(X1)
    | ~ class_Ring__and__Field_Ocomm__ring__1(X1) ),
    c_0_5036,
    [final] ).

cnf(c_0_6398,plain,
    ( class_Ring__and__Field_Ocomm__semiring(X1)
    | ~ class_Ring__and__Field_Ocomm__ring__1(X1) ),
    c_0_5037,
    [final] ).

cnf(c_0_6399,plain,
    ( class_Ring__and__Field_Ocomm__semiring__0(X1)
    | ~ class_Ring__and__Field_Ocomm__ring__1(X1) ),
    c_0_5038,
    [final] ).

cnf(c_0_6400,plain,
    ( class_Ring__and__Field_Ocomm__semiring__0__cancel(X1)
    | ~ class_Ring__and__Field_Ocomm__ring__1(X1) ),
    c_0_5039,
    [final] ).

cnf(c_0_6401,plain,
    ( class_HOL_Ominus(X1)
    | ~ class_Ring__and__Field_Ocomm__ring__1(X1) ),
    c_0_5040,
    [final] ).

cnf(c_0_6402,plain,
    ( class_Ring__and__Field_Ocomm__semiring__1__cancel(X1)
    | ~ class_Ring__and__Field_Ocomm__ring__1(X1) ),
    c_0_5041,
    [final] ).

cnf(c_0_6403,plain,
    ( class_Ring__and__Field_Osemiring__1__cancel(X1)
    | ~ class_Ring__and__Field_Ocomm__ring__1(X1) ),
    c_0_5042,
    [final] ).

cnf(c_0_6404,plain,
    ( class_Ring__and__Field_Oring__1(X1)
    | ~ class_Ring__and__Field_Ocomm__ring__1(X1) ),
    c_0_5043,
    [final] ).

cnf(c_0_6405,plain,
    ( class_HOL_Oone(X1)
    | ~ class_Ring__and__Field_Ocomm__ring__1(X1) ),
    c_0_5044,
    [final] ).

cnf(c_0_6406,plain,
    ( class_OrderedGroup_Omonoid__mult(X1)
    | ~ class_Ring__and__Field_Ocomm__ring__1(X1) ),
    c_0_5045,
    [final] ).

cnf(c_0_6407,plain,
    ( class_Ring__and__Field_Oaxclass__0__neq__1(X1)
    | ~ class_Ring__and__Field_Ocomm__ring__1(X1) ),
    c_0_5046,
    [final] ).

cnf(c_0_6408,plain,
    ( class_Ring__and__Field_Osemiring__1(X1)
    | ~ class_Ring__and__Field_Ocomm__ring__1(X1) ),
    c_0_5047,
    [final] ).

cnf(c_0_6409,plain,
    ( class_OrderedGroup_Ocomm__monoid__mult(X1)
    | ~ class_Ring__and__Field_Ocomm__ring__1(X1) ),
    c_0_5048,
    [final] ).

cnf(c_0_6410,plain,
    ( class_Ring__and__Field_Ocomm__semiring__1(X1)
    | ~ class_Ring__and__Field_Ocomm__ring__1(X1) ),
    c_0_5049,
    [final] ).

cnf(c_0_6411,plain,
    ( class_OrderedGroup_Oab__group__add(X1)
    | ~ class_Ring__and__Field_Ocomm__ring__1(X1) ),
    c_0_5050,
    [final] ).

cnf(c_0_6412,plain,
    ( class_HOL_Oplus(X1)
    | ~ class_Ring__and__Field_Ocomm__ring__1(X1) ),
    c_0_5051,
    [final] ).

cnf(c_0_6413,plain,
    ( class_OrderedGroup_Osemigroup__add(X1)
    | ~ class_Ring__and__Field_Ocomm__ring__1(X1) ),
    c_0_5052,
    [final] ).

cnf(c_0_6414,plain,
    ( class_OrderedGroup_Ocancel__semigroup__add(X1)
    | ~ class_Ring__and__Field_Ocomm__ring__1(X1) ),
    c_0_5053,
    [final] ).

cnf(c_0_6415,plain,
    ( class_OrderedGroup_Oab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Ocomm__ring__1(X1) ),
    c_0_5054,
    [final] ).

cnf(c_0_6416,plain,
    ( class_OrderedGroup_Ocancel__ab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Ocomm__ring__1(X1) ),
    c_0_5055,
    [final] ).

cnf(c_0_6417,plain,
    ( class_HOL_Ozero(X1)
    | ~ class_Ring__and__Field_Ocomm__ring__1(X1) ),
    c_0_5056,
    [final] ).

cnf(c_0_6418,plain,
    ( class_OrderedGroup_Ocomm__monoid__add(X1)
    | ~ class_Ring__and__Field_Ocomm__ring__1(X1) ),
    c_0_5057,
    [final] ).

cnf(c_0_6419,plain,
    ( class_HOL_Otimes(X1)
    | ~ class_Ring__and__Field_Ocomm__ring__1(X1) ),
    c_0_5058,
    [final] ).

cnf(c_0_6420,plain,
    ( class_OrderedGroup_Osemigroup__mult(X1)
    | ~ class_Ring__and__Field_Ocomm__ring__1(X1) ),
    c_0_5059,
    [final] ).

cnf(c_0_6421,plain,
    ( class_Ring__and__Field_Osemiring(X1)
    | ~ class_Ring__and__Field_Ocomm__ring__1(X1) ),
    c_0_5060,
    [final] ).

cnf(c_0_6422,plain,
    ( class_Ring__and__Field_Oring(X1)
    | ~ class_Ring__and__Field_Ocomm__ring__1(X1) ),
    c_0_5061,
    [final] ).

cnf(c_0_6423,plain,
    ( class_Ring__and__Field_Ocomm__ring(X1)
    | ~ class_Ring__and__Field_Ocomm__ring__1(X1) ),
    c_0_5062,
    [final] ).

cnf(c_0_6424,plain,
    ( class_OrderedGroup_Osemigroup__add(X1)
    | ~ class_Ring__and__Field_Ocomm__ring(X1) ),
    c_0_5063,
    [final] ).

cnf(c_0_6425,plain,
    ( class_OrderedGroup_Oab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Ocomm__ring(X1) ),
    c_0_5064,
    [final] ).

cnf(c_0_6426,plain,
    ( class_OrderedGroup_Ocomm__monoid__add(X1)
    | ~ class_Ring__and__Field_Ocomm__ring(X1) ),
    c_0_5065,
    [final] ).

cnf(c_0_6427,plain,
    ( class_HOL_Otimes(X1)
    | ~ class_Ring__and__Field_Ocomm__ring(X1) ),
    c_0_5066,
    [final] ).

cnf(c_0_6428,plain,
    ( class_OrderedGroup_Osemigroup__mult(X1)
    | ~ class_Ring__and__Field_Ocomm__ring(X1) ),
    c_0_5067,
    [final] ).

cnf(c_0_6429,plain,
    ( class_Ring__and__Field_Osemiring(X1)
    | ~ class_Ring__and__Field_Ocomm__ring(X1) ),
    c_0_5068,
    [final] ).

cnf(c_0_6430,plain,
    ( class_Ring__and__Field_Osemiring__0(X1)
    | ~ class_Ring__and__Field_Ocomm__ring(X1) ),
    c_0_5069,
    [final] ).

cnf(c_0_6431,plain,
    ( class_OrderedGroup_Oab__semigroup__mult(X1)
    | ~ class_Ring__and__Field_Ocomm__ring(X1) ),
    c_0_5070,
    [final] ).

cnf(c_0_6432,plain,
    ( class_Ring__and__Field_Ocomm__semiring__0__cancel(X1)
    | ~ class_Ring__and__Field_Ocomm__ring(X1) ),
    c_0_5071,
    [final] ).

cnf(c_0_6433,plain,
    ( class_Ring__and__Field_Osemiring__0__cancel(X1)
    | ~ class_Ring__and__Field_Ocomm__ring(X1) ),
    c_0_5072,
    [final] ).

cnf(c_0_6434,plain,
    ( class_Ring__and__Field_Oring(X1)
    | ~ class_Ring__and__Field_Ocomm__ring(X1) ),
    c_0_5073,
    [final] ).

cnf(c_0_6435,plain,
    ( class_OrderedGroup_Ocancel__semigroup__add(X1)
    | ~ class_Ring__and__Field_Ocomm__ring(X1) ),
    c_0_5074,
    [final] ).

cnf(c_0_6436,plain,
    ( class_OrderedGroup_Ocancel__ab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Ocomm__ring(X1) ),
    c_0_5075,
    [final] ).

cnf(c_0_6437,plain,
    ( class_HOL_Ominus(X1)
    | ~ class_Ring__and__Field_Ocomm__ring(X1) ),
    c_0_5076,
    [final] ).

cnf(c_0_6438,plain,
    ( class_OrderedGroup_Oab__group__add(X1)
    | ~ class_Ring__and__Field_Ocomm__ring(X1) ),
    c_0_5077,
    [final] ).

cnf(c_0_6439,plain,
    ( class_HOL_Ozero(X1)
    | ~ class_Ring__and__Field_Ocomm__ring(X1) ),
    c_0_5078,
    [final] ).

cnf(c_0_6440,plain,
    ( class_HOL_Oplus(X1)
    | ~ class_Ring__and__Field_Ocomm__ring(X1) ),
    c_0_5079,
    [final] ).

cnf(c_0_6441,plain,
    ( class_Ring__and__Field_Ocomm__semiring(X1)
    | ~ class_Ring__and__Field_Ocomm__ring(X1) ),
    c_0_5080,
    [final] ).

cnf(c_0_6442,plain,
    ( class_Ring__and__Field_Ocomm__semiring__0(X1)
    | ~ class_Ring__and__Field_Ocomm__ring(X1) ),
    c_0_5081,
    [final] ).

cnf(c_0_6443,plain,
    ( class_HOL_Otimes(X1)
    | ~ class_Ring__and__Field_Oaxclass__no__zero__divisors(X1) ),
    c_0_5082,
    [final] ).

cnf(c_0_6444,plain,
    ( class_HOL_Ozero(X1)
    | ~ class_Ring__and__Field_Oaxclass__no__zero__divisors(X1) ),
    c_0_5083,
    [final] ).

cnf(c_0_6445,plain,
    ( class_HOL_Ozero(X1)
    | ~ class_Ring__and__Field_Oaxclass__abs__if(X1) ),
    c_0_5084,
    [final] ).

cnf(c_0_6446,plain,
    ( class_Orderings_Oord(X1)
    | ~ class_Ring__and__Field_Oaxclass__abs__if(X1) ),
    c_0_5085,
    [final] ).

cnf(c_0_6447,plain,
    ( class_HOL_Ominus(X1)
    | ~ class_Ring__and__Field_Oaxclass__abs__if(X1) ),
    c_0_5086,
    [final] ).

cnf(c_0_6448,plain,
    ( class_HOL_Oone(X1)
    | ~ class_Ring__and__Field_Oaxclass__0__neq__1(X1) ),
    c_0_5087,
    [final] ).

cnf(c_0_6449,plain,
    ( class_HOL_Ozero(X1)
    | ~ class_Ring__and__Field_Oaxclass__0__neq__1(X1) ),
    c_0_5088,
    [final] ).

cnf(c_0_6450,plain,
    ( class_OrderedGroup_Oab__semigroup__mult(X1)
    | ~ class_Power_Orecpower(X1) ),
    c_0_5089,
    [final] ).

cnf(c_0_6451,plain,
    ( class_OrderedGroup_Osemigroup__mult(X1)
    | ~ class_Power_Orecpower(X1) ),
    c_0_5090,
    [final] ).

cnf(c_0_6452,plain,
    ( class_HOL_Otimes(X1)
    | ~ class_Power_Orecpower(X1) ),
    c_0_5091,
    [final] ).

cnf(c_0_6453,plain,
    ( class_OrderedGroup_Oab__semigroup__add(X1)
    | ~ class_Power_Orecpower(X1) ),
    c_0_5092,
    [final] ).

cnf(c_0_6454,plain,
    ( class_OrderedGroup_Osemigroup__add(X1)
    | ~ class_Power_Orecpower(X1) ),
    c_0_5093,
    [final] ).

cnf(c_0_6455,plain,
    ( class_HOL_Oplus(X1)
    | ~ class_Power_Orecpower(X1) ),
    c_0_5094,
    [final] ).

cnf(c_0_6456,plain,
    ( class_Ring__and__Field_Oaxclass__0__neq__1(X1)
    | ~ class_Power_Orecpower(X1) ),
    c_0_5095,
    [final] ).

cnf(c_0_6457,plain,
    ( class_Ring__and__Field_Ocomm__semiring__1__cancel(X1)
    | ~ class_Power_Orecpower(X1) ),
    c_0_5096,
    [final] ).

cnf(c_0_6458,plain,
    ( class_Ring__and__Field_Ocomm__semiring__0__cancel(X1)
    | ~ class_Power_Orecpower(X1) ),
    c_0_5097,
    [final] ).

cnf(c_0_6459,plain,
    ( class_Ring__and__Field_Osemiring__1__cancel(X1)
    | ~ class_Power_Orecpower(X1) ),
    c_0_5098,
    [final] ).

cnf(c_0_6460,plain,
    ( class_Ring__and__Field_Osemiring__0__cancel(X1)
    | ~ class_Power_Orecpower(X1) ),
    c_0_5099,
    [final] ).

cnf(c_0_6461,plain,
    ( class_OrderedGroup_Ocancel__ab__semigroup__add(X1)
    | ~ class_Power_Orecpower(X1) ),
    c_0_5100,
    [final] ).

cnf(c_0_6462,plain,
    ( class_HOL_Oone(X1)
    | ~ class_Power_Orecpower(X1) ),
    c_0_5101,
    [final] ).

cnf(c_0_6463,plain,
    ( class_OrderedGroup_Ocancel__semigroup__add(X1)
    | ~ class_Power_Orecpower(X1) ),
    c_0_5102,
    [final] ).

cnf(c_0_6464,plain,
    ( class_Ring__and__Field_Ocomm__semiring__1(X1)
    | ~ class_Power_Orecpower(X1) ),
    c_0_5103,
    [final] ).

cnf(c_0_6465,plain,
    ( class_Ring__and__Field_Osemiring__1(X1)
    | ~ class_Power_Orecpower(X1) ),
    c_0_5104,
    [final] ).

cnf(c_0_6466,plain,
    ( class_OrderedGroup_Ocomm__monoid__mult(X1)
    | ~ class_Power_Orecpower(X1) ),
    c_0_5105,
    [final] ).

cnf(c_0_6467,plain,
    ( class_OrderedGroup_Omonoid__mult(X1)
    | ~ class_Power_Orecpower(X1) ),
    c_0_5106,
    [final] ).

cnf(c_0_6468,plain,
    ( class_Ring__and__Field_Ocomm__semiring__0(X1)
    | ~ class_Power_Orecpower(X1) ),
    c_0_5107,
    [final] ).

cnf(c_0_6469,plain,
    ( class_Ring__and__Field_Osemiring__0(X1)
    | ~ class_Power_Orecpower(X1) ),
    c_0_5108,
    [final] ).

cnf(c_0_6470,plain,
    ( class_OrderedGroup_Ocomm__monoid__add(X1)
    | ~ class_Power_Orecpower(X1) ),
    c_0_5109,
    [final] ).

cnf(c_0_6471,plain,
    ( class_Ring__and__Field_Ocomm__semiring(X1)
    | ~ class_Power_Orecpower(X1) ),
    c_0_5110,
    [final] ).

cnf(c_0_6472,plain,
    ( class_Ring__and__Field_Osemiring(X1)
    | ~ class_Power_Orecpower(X1) ),
    c_0_5111,
    [final] ).

cnf(c_0_6473,plain,
    ( class_HOL_Ozero(X1)
    | ~ class_Power_Orecpower(X1) ),
    c_0_5112,
    [final] ).

cnf(c_0_6474,plain,
    ( class_Nat_Opower(X1)
    | ~ class_Power_Orecpower(X1) ),
    c_0_5113,
    [final] ).

cnf(c_0_6475,plain,
    ( class_Orderings_Oord(X1)
    | ~ class_Orderings_Oorder(X1) ),
    c_0_5114,
    [final] ).

cnf(c_0_6476,plain,
    ( class_Orderings_Oorder(X1)
    | ~ class_Orderings_Olinorder(X1) ),
    c_0_5115,
    [final] ).

cnf(c_0_6477,plain,
    ( class_Orderings_Oord(X1)
    | ~ class_Orderings_Olinorder(X1) ),
    c_0_5116,
    [final] ).

cnf(c_0_6478,plain,
    ( class_LOrder_Omeet__semilorder(X1)
    | ~ class_Orderings_Olinorder(X1) ),
    c_0_5117,
    [final] ).

cnf(c_0_6479,plain,
    ( class_LOrder_Ojoin__semilorder(X1)
    | ~ class_Orderings_Olinorder(X1) ),
    c_0_5118,
    [final] ).

cnf(c_0_6480,plain,
    ( class_LOrder_Olorder(X1)
    | ~ class_Orderings_Olinorder(X1) ),
    c_0_5119,
    [final] ).

cnf(c_0_6481,plain,
    ( class_HOL_Otimes(X1)
    | ~ class_OrderedGroup_Osemigroup__mult(X1) ),
    c_0_5120,
    [final] ).

cnf(c_0_6482,plain,
    ( class_HOL_Oplus(X1)
    | ~ class_OrderedGroup_Osemigroup__add(X1) ),
    c_0_5121,
    [final] ).

cnf(c_0_6483,plain,
    ( class_OrderedGroup_Ocancel__semigroup__add(X1)
    | ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1) ),
    c_0_5122,
    [final] ).

cnf(c_0_6484,plain,
    ( class_OrderedGroup_Ocancel__ab__semigroup__add(X1)
    | ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1) ),
    c_0_5123,
    [final] ).

cnf(c_0_6485,plain,
    ( class_HOL_Oplus(X1)
    | ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1) ),
    c_0_5124,
    [final] ).

cnf(c_0_6486,plain,
    ( class_OrderedGroup_Osemigroup__add(X1)
    | ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1) ),
    c_0_5125,
    [final] ).

cnf(c_0_6487,plain,
    ( class_OrderedGroup_Oab__semigroup__add(X1)
    | ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1) ),
    c_0_5126,
    [final] ).

cnf(c_0_6488,plain,
    ( class_Orderings_Oord(X1)
    | ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1) ),
    c_0_5127,
    [final] ).

cnf(c_0_6489,plain,
    ( class_Orderings_Oorder(X1)
    | ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1) ),
    c_0_5128,
    [final] ).

cnf(c_0_6490,plain,
    ( class_OrderedGroup_Opordered__ab__semigroup__add(X1)
    | ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1) ),
    c_0_5129,
    [final] ).

cnf(c_0_6491,plain,
    ( class_HOL_Oplus(X1)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
    c_0_5130,
    [final] ).

cnf(c_0_6492,plain,
    ( class_OrderedGroup_Osemigroup__add(X1)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
    c_0_5131,
    [final] ).

cnf(c_0_6493,plain,
    ( class_OrderedGroup_Ocancel__semigroup__add(X1)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
    c_0_5132,
    [final] ).

cnf(c_0_6494,plain,
    ( class_OrderedGroup_Oab__semigroup__add(X1)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
    c_0_5133,
    [final] ).

cnf(c_0_6495,plain,
    ( class_OrderedGroup_Ocancel__ab__semigroup__add(X1)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
    c_0_5134,
    [final] ).

cnf(c_0_6496,plain,
    ( class_Orderings_Oord(X1)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
    c_0_5135,
    [final] ).

cnf(c_0_6497,plain,
    ( class_Orderings_Oorder(X1)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
    c_0_5136,
    [final] ).

cnf(c_0_6498,plain,
    ( class_OrderedGroup_Opordered__ab__semigroup__add(X1)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
    c_0_5137,
    [final] ).

cnf(c_0_6499,plain,
    ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
    c_0_5138,
    [final] ).

cnf(c_0_6500,plain,
    ( class_HOL_Oplus(X1)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add(X1) ),
    c_0_5139,
    [final] ).

cnf(c_0_6501,plain,
    ( class_OrderedGroup_Osemigroup__add(X1)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add(X1) ),
    c_0_5140,
    [final] ).

cnf(c_0_6502,plain,
    ( class_OrderedGroup_Oab__semigroup__add(X1)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add(X1) ),
    c_0_5141,
    [final] ).

cnf(c_0_6503,plain,
    ( class_Orderings_Oord(X1)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add(X1) ),
    c_0_5142,
    [final] ).

cnf(c_0_6504,plain,
    ( class_Orderings_Oorder(X1)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add(X1) ),
    c_0_5143,
    [final] ).

cnf(c_0_6505,plain,
    ( class_OrderedGroup_Opordered__ab__semigroup__add(X1)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X1) ),
    c_0_5144,
    [final] ).

cnf(c_0_6506,plain,
    ( class_HOL_Oplus(X1)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X1) ),
    c_0_5145,
    [final] ).

cnf(c_0_6507,plain,
    ( class_OrderedGroup_Osemigroup__add(X1)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X1) ),
    c_0_5146,
    [final] ).

cnf(c_0_6508,plain,
    ( class_OrderedGroup_Ocancel__semigroup__add(X1)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X1) ),
    c_0_5147,
    [final] ).

cnf(c_0_6509,plain,
    ( class_OrderedGroup_Oab__semigroup__add(X1)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X1) ),
    c_0_5148,
    [final] ).

cnf(c_0_6510,plain,
    ( class_OrderedGroup_Ocancel__ab__semigroup__add(X1)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X1) ),
    c_0_5149,
    [final] ).

cnf(c_0_6511,plain,
    ( class_HOL_Ozero(X1)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X1) ),
    c_0_5150,
    [final] ).

cnf(c_0_6512,plain,
    ( class_OrderedGroup_Ocomm__monoid__add(X1)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X1) ),
    c_0_5151,
    [final] ).

cnf(c_0_6513,plain,
    ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X1) ),
    c_0_5152,
    [final] ).

cnf(c_0_6514,plain,
    ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X1) ),
    c_0_5153,
    [final] ).

cnf(c_0_6515,plain,
    ( class_Orderings_Oord(X1)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X1) ),
    c_0_5154,
    [final] ).

cnf(c_0_6516,plain,
    ( class_Orderings_Oorder(X1)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X1) ),
    c_0_5155,
    [final] ).

cnf(c_0_6517,plain,
    ( class_HOL_Ominus(X1)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X1) ),
    c_0_5156,
    [final] ).

cnf(c_0_6518,plain,
    ( class_OrderedGroup_Oab__group__add(X1)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X1) ),
    c_0_5157,
    [final] ).

cnf(c_0_6519,plain,
    ( class_Orderings_Olinorder(X1)
    | ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X1) ),
    c_0_5158,
    [final] ).

cnf(c_0_6520,plain,
    ( class_HOL_Oplus(X1)
    | ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X1) ),
    c_0_5159,
    [final] ).

cnf(c_0_6521,plain,
    ( class_OrderedGroup_Osemigroup__add(X1)
    | ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X1) ),
    c_0_5160,
    [final] ).

cnf(c_0_6522,plain,
    ( class_OrderedGroup_Ocancel__semigroup__add(X1)
    | ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X1) ),
    c_0_5161,
    [final] ).

cnf(c_0_6523,plain,
    ( class_OrderedGroup_Oab__semigroup__add(X1)
    | ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X1) ),
    c_0_5162,
    [final] ).

cnf(c_0_6524,plain,
    ( class_OrderedGroup_Ocancel__ab__semigroup__add(X1)
    | ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X1) ),
    c_0_5163,
    [final] ).

cnf(c_0_6525,plain,
    ( class_Orderings_Oord(X1)
    | ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X1) ),
    c_0_5164,
    [final] ).

cnf(c_0_6526,plain,
    ( class_Orderings_Oorder(X1)
    | ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X1) ),
    c_0_5165,
    [final] ).

cnf(c_0_6527,plain,
    ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
    | ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X1) ),
    c_0_5166,
    [final] ).

cnf(c_0_6528,plain,
    ( class_LOrder_Omeet__semilorder(X1)
    | ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X1) ),
    c_0_5167,
    [final] ).

cnf(c_0_6529,plain,
    ( class_LOrder_Ojoin__semilorder(X1)
    | ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X1) ),
    c_0_5168,
    [final] ).

cnf(c_0_6530,plain,
    ( class_LOrder_Olorder(X1)
    | ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X1) ),
    c_0_5169,
    [final] ).

cnf(c_0_6531,plain,
    ( class_OrderedGroup_Opordered__ab__semigroup__add(X1)
    | ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X1) ),
    c_0_5170,
    [final] ).

cnf(c_0_6532,plain,
    ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1)
    | ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X1) ),
    c_0_5171,
    [final] ).

cnf(c_0_6533,plain,
    ( class_HOL_Otimes(X1)
    | ~ class_OrderedGroup_Omonoid__mult(X1) ),
    c_0_5172,
    [final] ).

cnf(c_0_6534,plain,
    ( class_OrderedGroup_Osemigroup__mult(X1)
    | ~ class_OrderedGroup_Omonoid__mult(X1) ),
    c_0_5173,
    [final] ).

cnf(c_0_6535,plain,
    ( class_HOL_Oone(X1)
    | ~ class_OrderedGroup_Omonoid__mult(X1) ),
    c_0_5174,
    [final] ).

cnf(c_0_6536,plain,
    ( class_Orderings_Oord(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__meet(X1) ),
    c_0_5175,
    [final] ).

cnf(c_0_6537,plain,
    ( class_Orderings_Oorder(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__meet(X1) ),
    c_0_5176,
    [final] ).

cnf(c_0_6538,plain,
    ( class_OrderedGroup_Opordered__ab__semigroup__add(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__meet(X1) ),
    c_0_5177,
    [final] ).

cnf(c_0_6539,plain,
    ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__meet(X1) ),
    c_0_5178,
    [final] ).

cnf(c_0_6540,plain,
    ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__meet(X1) ),
    c_0_5179,
    [final] ).

cnf(c_0_6541,plain,
    ( class_HOL_Ozero(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__meet(X1) ),
    c_0_5180,
    [final] ).

cnf(c_0_6542,plain,
    ( class_OrderedGroup_Ocomm__monoid__add(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__meet(X1) ),
    c_0_5181,
    [final] ).

cnf(c_0_6543,plain,
    ( class_HOL_Ominus(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__meet(X1) ),
    c_0_5182,
    [final] ).

cnf(c_0_6544,plain,
    ( class_LOrder_Ojoin__semilorder(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__meet(X1) ),
    c_0_5183,
    [final] ).

cnf(c_0_6545,plain,
    ( class_LOrder_Olorder(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__meet(X1) ),
    c_0_5184,
    [final] ).

cnf(c_0_6546,plain,
    ( class_OrderedGroup_Olordered__ab__group(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__meet(X1) ),
    c_0_5185,
    [final] ).

cnf(c_0_6547,plain,
    ( class_LOrder_Omeet__semilorder(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__meet(X1) ),
    c_0_5186,
    [final] ).

cnf(c_0_6548,plain,
    ( class_HOL_Oplus(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__meet(X1) ),
    c_0_5187,
    [final] ).

cnf(c_0_6549,plain,
    ( class_OrderedGroup_Osemigroup__add(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__meet(X1) ),
    c_0_5188,
    [final] ).

cnf(c_0_6550,plain,
    ( class_OrderedGroup_Ocancel__semigroup__add(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__meet(X1) ),
    c_0_5189,
    [final] ).

cnf(c_0_6551,plain,
    ( class_OrderedGroup_Oab__semigroup__add(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__meet(X1) ),
    c_0_5190,
    [final] ).

cnf(c_0_6552,plain,
    ( class_OrderedGroup_Ocancel__ab__semigroup__add(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__meet(X1) ),
    c_0_5191,
    [final] ).

cnf(c_0_6553,plain,
    ( class_OrderedGroup_Oab__group__add(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__meet(X1) ),
    c_0_5192,
    [final] ).

cnf(c_0_6554,plain,
    ( class_OrderedGroup_Opordered__ab__group__add(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__meet(X1) ),
    c_0_5193,
    [final] ).

cnf(c_0_6555,plain,
    ( class_Orderings_Oord(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__join(X1) ),
    c_0_5194,
    [final] ).

cnf(c_0_6556,plain,
    ( class_Orderings_Oorder(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__join(X1) ),
    c_0_5195,
    [final] ).

cnf(c_0_6557,plain,
    ( class_OrderedGroup_Opordered__ab__semigroup__add(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__join(X1) ),
    c_0_5196,
    [final] ).

cnf(c_0_6558,plain,
    ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__join(X1) ),
    c_0_5197,
    [final] ).

cnf(c_0_6559,plain,
    ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__join(X1) ),
    c_0_5198,
    [final] ).

cnf(c_0_6560,plain,
    ( class_HOL_Ozero(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__join(X1) ),
    c_0_5199,
    [final] ).

cnf(c_0_6561,plain,
    ( class_OrderedGroup_Ocomm__monoid__add(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__join(X1) ),
    c_0_5200,
    [final] ).

cnf(c_0_6562,plain,
    ( class_HOL_Ominus(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__join(X1) ),
    c_0_5201,
    [final] ).

cnf(c_0_6563,plain,
    ( class_LOrder_Omeet__semilorder(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__join(X1) ),
    c_0_5202,
    [final] ).

cnf(c_0_6564,plain,
    ( class_LOrder_Olorder(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__join(X1) ),
    c_0_5203,
    [final] ).

cnf(c_0_6565,plain,
    ( class_OrderedGroup_Olordered__ab__group(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__join(X1) ),
    c_0_5204,
    [final] ).

cnf(c_0_6566,plain,
    ( class_LOrder_Ojoin__semilorder(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__join(X1) ),
    c_0_5205,
    [final] ).

cnf(c_0_6567,plain,
    ( class_HOL_Oplus(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__join(X1) ),
    c_0_5206,
    [final] ).

cnf(c_0_6568,plain,
    ( class_OrderedGroup_Osemigroup__add(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__join(X1) ),
    c_0_5207,
    [final] ).

cnf(c_0_6569,plain,
    ( class_OrderedGroup_Ocancel__semigroup__add(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__join(X1) ),
    c_0_5208,
    [final] ).

cnf(c_0_6570,plain,
    ( class_OrderedGroup_Oab__semigroup__add(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__join(X1) ),
    c_0_5209,
    [final] ).

cnf(c_0_6571,plain,
    ( class_OrderedGroup_Ocancel__ab__semigroup__add(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__join(X1) ),
    c_0_5210,
    [final] ).

cnf(c_0_6572,plain,
    ( class_OrderedGroup_Oab__group__add(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__join(X1) ),
    c_0_5211,
    [final] ).

cnf(c_0_6573,plain,
    ( class_OrderedGroup_Opordered__ab__group__add(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__join(X1) ),
    c_0_5212,
    [final] ).

cnf(c_0_6574,plain,
    ( class_OrderedGroup_Ocancel__ab__semigroup__add(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__abs(X1) ),
    c_0_5213,
    [final] ).

cnf(c_0_6575,plain,
    ( class_OrderedGroup_Opordered__ab__semigroup__add(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__abs(X1) ),
    c_0_5214,
    [final] ).

cnf(c_0_6576,plain,
    ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__abs(X1) ),
    c_0_5215,
    [final] ).

cnf(c_0_6577,plain,
    ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__abs(X1) ),
    c_0_5216,
    [final] ).

cnf(c_0_6578,plain,
    ( class_HOL_Ozero(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__abs(X1) ),
    c_0_5217,
    [final] ).

cnf(c_0_6579,plain,
    ( class_OrderedGroup_Ocomm__monoid__add(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__abs(X1) ),
    c_0_5218,
    [final] ).

cnf(c_0_6580,plain,
    ( class_HOL_Ominus(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__abs(X1) ),
    c_0_5219,
    [final] ).

cnf(c_0_6581,plain,
    ( class_OrderedGroup_Oab__group__add(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__abs(X1) ),
    c_0_5220,
    [final] ).

cnf(c_0_6582,plain,
    ( class_Orderings_Oord(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__abs(X1) ),
    c_0_5221,
    [final] ).

cnf(c_0_6583,plain,
    ( class_Orderings_Oorder(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__abs(X1) ),
    c_0_5222,
    [final] ).

cnf(c_0_6584,plain,
    ( class_LOrder_Omeet__semilorder(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__abs(X1) ),
    c_0_5223,
    [final] ).

cnf(c_0_6585,plain,
    ( class_LOrder_Ojoin__semilorder(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__abs(X1) ),
    c_0_5224,
    [final] ).

cnf(c_0_6586,plain,
    ( class_LOrder_Olorder(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__abs(X1) ),
    c_0_5225,
    [final] ).

cnf(c_0_6587,plain,
    ( class_HOL_Oplus(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__abs(X1) ),
    c_0_5226,
    [final] ).

cnf(c_0_6588,plain,
    ( class_OrderedGroup_Osemigroup__add(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__abs(X1) ),
    c_0_5227,
    [final] ).

cnf(c_0_6589,plain,
    ( class_OrderedGroup_Ocancel__semigroup__add(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__abs(X1) ),
    c_0_5228,
    [final] ).

cnf(c_0_6590,plain,
    ( class_OrderedGroup_Oab__semigroup__add(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__abs(X1) ),
    c_0_5229,
    [final] ).

cnf(c_0_6591,plain,
    ( class_OrderedGroup_Opordered__ab__group__add(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__abs(X1) ),
    c_0_5230,
    [final] ).

cnf(c_0_6592,plain,
    ( class_OrderedGroup_Olordered__ab__group(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__abs(X1) ),
    c_0_5231,
    [final] ).

cnf(c_0_6593,plain,
    ( class_Orderings_Oord(X1)
    | ~ class_OrderedGroup_Olordered__ab__group(X1) ),
    c_0_5232,
    [final] ).

cnf(c_0_6594,plain,
    ( class_Orderings_Oorder(X1)
    | ~ class_OrderedGroup_Olordered__ab__group(X1) ),
    c_0_5233,
    [final] ).

cnf(c_0_6595,plain,
    ( class_OrderedGroup_Opordered__ab__semigroup__add(X1)
    | ~ class_OrderedGroup_Olordered__ab__group(X1) ),
    c_0_5234,
    [final] ).

cnf(c_0_6596,plain,
    ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1)
    | ~ class_OrderedGroup_Olordered__ab__group(X1) ),
    c_0_5235,
    [final] ).

cnf(c_0_6597,plain,
    ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
    | ~ class_OrderedGroup_Olordered__ab__group(X1) ),
    c_0_5236,
    [final] ).

cnf(c_0_6598,plain,
    ( class_HOL_Ozero(X1)
    | ~ class_OrderedGroup_Olordered__ab__group(X1) ),
    c_0_5237,
    [final] ).

cnf(c_0_6599,plain,
    ( class_OrderedGroup_Ocomm__monoid__add(X1)
    | ~ class_OrderedGroup_Olordered__ab__group(X1) ),
    c_0_5238,
    [final] ).

cnf(c_0_6600,plain,
    ( class_HOL_Ominus(X1)
    | ~ class_OrderedGroup_Olordered__ab__group(X1) ),
    c_0_5239,
    [final] ).

cnf(c_0_6601,plain,
    ( class_LOrder_Omeet__semilorder(X1)
    | ~ class_OrderedGroup_Olordered__ab__group(X1) ),
    c_0_5240,
    [final] ).

cnf(c_0_6602,plain,
    ( class_LOrder_Ojoin__semilorder(X1)
    | ~ class_OrderedGroup_Olordered__ab__group(X1) ),
    c_0_5241,
    [final] ).

cnf(c_0_6603,plain,
    ( class_LOrder_Olorder(X1)
    | ~ class_OrderedGroup_Olordered__ab__group(X1) ),
    c_0_5242,
    [final] ).

cnf(c_0_6604,plain,
    ( class_HOL_Oplus(X1)
    | ~ class_OrderedGroup_Olordered__ab__group(X1) ),
    c_0_5243,
    [final] ).

cnf(c_0_6605,plain,
    ( class_OrderedGroup_Osemigroup__add(X1)
    | ~ class_OrderedGroup_Olordered__ab__group(X1) ),
    c_0_5244,
    [final] ).

cnf(c_0_6606,plain,
    ( class_OrderedGroup_Ocancel__semigroup__add(X1)
    | ~ class_OrderedGroup_Olordered__ab__group(X1) ),
    c_0_5245,
    [final] ).

cnf(c_0_6607,plain,
    ( class_OrderedGroup_Oab__semigroup__add(X1)
    | ~ class_OrderedGroup_Olordered__ab__group(X1) ),
    c_0_5246,
    [final] ).

cnf(c_0_6608,plain,
    ( class_OrderedGroup_Ocancel__ab__semigroup__add(X1)
    | ~ class_OrderedGroup_Olordered__ab__group(X1) ),
    c_0_5247,
    [final] ).

cnf(c_0_6609,plain,
    ( class_OrderedGroup_Oab__group__add(X1)
    | ~ class_OrderedGroup_Olordered__ab__group(X1) ),
    c_0_5248,
    [final] ).

cnf(c_0_6610,plain,
    ( class_OrderedGroup_Opordered__ab__group__add(X1)
    | ~ class_OrderedGroup_Olordered__ab__group(X1) ),
    c_0_5249,
    [final] ).

cnf(c_0_6611,plain,
    ( class_OrderedGroup_Omonoid__mult(X1)
    | ~ class_OrderedGroup_Ocomm__monoid__mult(X1) ),
    c_0_5250,
    [final] ).

cnf(c_0_6612,plain,
    ( class_HOL_Otimes(X1)
    | ~ class_OrderedGroup_Ocomm__monoid__mult(X1) ),
    c_0_5251,
    [final] ).

cnf(c_0_6613,plain,
    ( class_OrderedGroup_Osemigroup__mult(X1)
    | ~ class_OrderedGroup_Ocomm__monoid__mult(X1) ),
    c_0_5252,
    [final] ).

cnf(c_0_6614,plain,
    ( class_OrderedGroup_Oab__semigroup__mult(X1)
    | ~ class_OrderedGroup_Ocomm__monoid__mult(X1) ),
    c_0_5253,
    [final] ).

cnf(c_0_6615,plain,
    ( class_HOL_Oone(X1)
    | ~ class_OrderedGroup_Ocomm__monoid__mult(X1) ),
    c_0_5254,
    [final] ).

cnf(c_0_6616,plain,
    ( class_HOL_Oplus(X1)
    | ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
    c_0_5255,
    [final] ).

cnf(c_0_6617,plain,
    ( class_OrderedGroup_Osemigroup__add(X1)
    | ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
    c_0_5256,
    [final] ).

cnf(c_0_6618,plain,
    ( class_OrderedGroup_Oab__semigroup__add(X1)
    | ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
    c_0_5257,
    [final] ).

cnf(c_0_6619,plain,
    ( class_HOL_Ozero(X1)
    | ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
    c_0_5258,
    [final] ).

cnf(c_0_6620,plain,
    ( class_HOL_Oplus(X1)
    | ~ class_OrderedGroup_Ocancel__semigroup__add(X1) ),
    c_0_5259,
    [final] ).

cnf(c_0_6621,plain,
    ( class_OrderedGroup_Osemigroup__add(X1)
    | ~ class_OrderedGroup_Ocancel__semigroup__add(X1) ),
    c_0_5260,
    [final] ).

cnf(c_0_6622,plain,
    ( class_OrderedGroup_Ocancel__semigroup__add(X1)
    | ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X1) ),
    c_0_5261,
    [final] ).

cnf(c_0_6623,plain,
    ( class_HOL_Oplus(X1)
    | ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X1) ),
    c_0_5262,
    [final] ).

cnf(c_0_6624,plain,
    ( class_OrderedGroup_Osemigroup__add(X1)
    | ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X1) ),
    c_0_5263,
    [final] ).

cnf(c_0_6625,plain,
    ( class_OrderedGroup_Oab__semigroup__add(X1)
    | ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X1) ),
    c_0_5264,
    [final] ).

cnf(c_0_6626,plain,
    ( class_HOL_Otimes(X1)
    | ~ class_OrderedGroup_Oab__semigroup__mult(X1) ),
    c_0_5265,
    [final] ).

cnf(c_0_6627,plain,
    ( class_OrderedGroup_Osemigroup__mult(X1)
    | ~ class_OrderedGroup_Oab__semigroup__mult(X1) ),
    c_0_5266,
    [final] ).

cnf(c_0_6628,plain,
    ( class_HOL_Oplus(X1)
    | ~ class_OrderedGroup_Oab__semigroup__add(X1) ),
    c_0_5267,
    [final] ).

cnf(c_0_6629,plain,
    ( class_OrderedGroup_Osemigroup__add(X1)
    | ~ class_OrderedGroup_Oab__semigroup__add(X1) ),
    c_0_5268,
    [final] ).

cnf(c_0_6630,plain,
    ( class_OrderedGroup_Ocancel__semigroup__add(X1)
    | ~ class_OrderedGroup_Oab__group__add(X1) ),
    c_0_5269,
    [final] ).

cnf(c_0_6631,plain,
    ( class_OrderedGroup_Ocancel__ab__semigroup__add(X1)
    | ~ class_OrderedGroup_Oab__group__add(X1) ),
    c_0_5270,
    [final] ).

cnf(c_0_6632,plain,
    ( class_HOL_Oplus(X1)
    | ~ class_OrderedGroup_Oab__group__add(X1) ),
    c_0_5271,
    [final] ).

cnf(c_0_6633,plain,
    ( class_OrderedGroup_Osemigroup__add(X1)
    | ~ class_OrderedGroup_Oab__group__add(X1) ),
    c_0_5272,
    [final] ).

cnf(c_0_6634,plain,
    ( class_OrderedGroup_Oab__semigroup__add(X1)
    | ~ class_OrderedGroup_Oab__group__add(X1) ),
    c_0_5273,
    [final] ).

cnf(c_0_6635,plain,
    ( class_HOL_Ozero(X1)
    | ~ class_OrderedGroup_Oab__group__add(X1) ),
    c_0_5274,
    [final] ).

cnf(c_0_6636,plain,
    ( class_OrderedGroup_Ocomm__monoid__add(X1)
    | ~ class_OrderedGroup_Oab__group__add(X1) ),
    c_0_5275,
    [final] ).

cnf(c_0_6637,plain,
    ( class_HOL_Ominus(X1)
    | ~ class_OrderedGroup_Oab__group__add(X1) ),
    c_0_5276,
    [final] ).

cnf(c_0_6638,plain,
    ( class_OrderedGroup_Ocomm__monoid__add(X1)
    | ~ class_Numeral_Onumber__ring(X1) ),
    c_0_5277,
    [final] ).

cnf(c_0_6639,plain,
    ( class_HOL_Ozero(X1)
    | ~ class_Numeral_Onumber__ring(X1) ),
    c_0_5278,
    [final] ).

cnf(c_0_6640,plain,
    ( class_Ring__and__Field_Ocomm__semiring(X1)
    | ~ class_Numeral_Onumber__ring(X1) ),
    c_0_5279,
    [final] ).

cnf(c_0_6641,plain,
    ( class_Ring__and__Field_Osemiring(X1)
    | ~ class_Numeral_Onumber__ring(X1) ),
    c_0_5280,
    [final] ).

cnf(c_0_6642,plain,
    ( class_OrderedGroup_Oab__semigroup__mult(X1)
    | ~ class_Numeral_Onumber__ring(X1) ),
    c_0_5281,
    [final] ).

cnf(c_0_6643,plain,
    ( class_OrderedGroup_Osemigroup__mult(X1)
    | ~ class_Numeral_Onumber__ring(X1) ),
    c_0_5282,
    [final] ).

cnf(c_0_6644,plain,
    ( class_Numeral_Onumber(X1)
    | ~ class_Numeral_Onumber__ring(X1) ),
    c_0_5283,
    [final] ).

cnf(c_0_6645,plain,
    ( class_HOL_Otimes(X1)
    | ~ class_Numeral_Onumber__ring(X1) ),
    c_0_5284,
    [final] ).

cnf(c_0_6646,plain,
    ( class_Ring__and__Field_Ocomm__ring__1(X1)
    | ~ class_Numeral_Onumber__ring(X1) ),
    c_0_5285,
    [final] ).

cnf(c_0_6647,plain,
    ( class_Ring__and__Field_Ocomm__semiring__1__cancel(X1)
    | ~ class_Numeral_Onumber__ring(X1) ),
    c_0_5286,
    [final] ).

cnf(c_0_6648,plain,
    ( class_Ring__and__Field_Oring__1(X1)
    | ~ class_Numeral_Onumber__ring(X1) ),
    c_0_5287,
    [final] ).

cnf(c_0_6649,plain,
    ( class_Ring__and__Field_Osemiring__1__cancel(X1)
    | ~ class_Numeral_Onumber__ring(X1) ),
    c_0_5288,
    [final] ).

cnf(c_0_6650,plain,
    ( class_Ring__and__Field_Ocomm__semiring__1(X1)
    | ~ class_Numeral_Onumber__ring(X1) ),
    c_0_5289,
    [final] ).

cnf(c_0_6651,plain,
    ( class_Ring__and__Field_Osemiring__1(X1)
    | ~ class_Numeral_Onumber__ring(X1) ),
    c_0_5290,
    [final] ).

cnf(c_0_6652,plain,
    ( class_OrderedGroup_Ocomm__monoid__mult(X1)
    | ~ class_Numeral_Onumber__ring(X1) ),
    c_0_5291,
    [final] ).

cnf(c_0_6653,plain,
    ( class_OrderedGroup_Omonoid__mult(X1)
    | ~ class_Numeral_Onumber__ring(X1) ),
    c_0_5292,
    [final] ).

cnf(c_0_6654,plain,
    ( class_Ring__and__Field_Oaxclass__0__neq__1(X1)
    | ~ class_Numeral_Onumber__ring(X1) ),
    c_0_5293,
    [final] ).

cnf(c_0_6655,plain,
    ( class_HOL_Oone(X1)
    | ~ class_Numeral_Onumber__ring(X1) ),
    c_0_5294,
    [final] ).

cnf(c_0_6656,plain,
    ( class_OrderedGroup_Oab__semigroup__add(X1)
    | ~ class_Numeral_Onumber__ring(X1) ),
    c_0_5295,
    [final] ).

cnf(c_0_6657,plain,
    ( class_Ring__and__Field_Ocomm__ring(X1)
    | ~ class_Numeral_Onumber__ring(X1) ),
    c_0_5296,
    [final] ).

cnf(c_0_6658,plain,
    ( class_Ring__and__Field_Ocomm__semiring__0__cancel(X1)
    | ~ class_Numeral_Onumber__ring(X1) ),
    c_0_5297,
    [final] ).

cnf(c_0_6659,plain,
    ( class_Ring__and__Field_Oring(X1)
    | ~ class_Numeral_Onumber__ring(X1) ),
    c_0_5298,
    [final] ).

cnf(c_0_6660,plain,
    ( class_Ring__and__Field_Osemiring__0__cancel(X1)
    | ~ class_Numeral_Onumber__ring(X1) ),
    c_0_5299,
    [final] ).

cnf(c_0_6661,plain,
    ( class_OrderedGroup_Oab__group__add(X1)
    | ~ class_Numeral_Onumber__ring(X1) ),
    c_0_5300,
    [final] ).

cnf(c_0_6662,plain,
    ( class_OrderedGroup_Ocancel__ab__semigroup__add(X1)
    | ~ class_Numeral_Onumber__ring(X1) ),
    c_0_5301,
    [final] ).

cnf(c_0_6663,plain,
    ( class_OrderedGroup_Ocancel__semigroup__add(X1)
    | ~ class_Numeral_Onumber__ring(X1) ),
    c_0_5302,
    [final] ).

cnf(c_0_6664,plain,
    ( class_HOL_Ominus(X1)
    | ~ class_Numeral_Onumber__ring(X1) ),
    c_0_5303,
    [final] ).

cnf(c_0_6665,plain,
    ( class_Ring__and__Field_Ocomm__semiring__0(X1)
    | ~ class_Numeral_Onumber__ring(X1) ),
    c_0_5304,
    [final] ).

cnf(c_0_6666,plain,
    ( class_Ring__and__Field_Osemiring__0(X1)
    | ~ class_Numeral_Onumber__ring(X1) ),
    c_0_5305,
    [final] ).

cnf(c_0_6667,plain,
    ( class_OrderedGroup_Osemigroup__add(X1)
    | ~ class_Numeral_Onumber__ring(X1) ),
    c_0_5306,
    [final] ).

cnf(c_0_6668,plain,
    ( class_HOL_Oplus(X1)
    | ~ class_Numeral_Onumber__ring(X1) ),
    c_0_5307,
    [final] ).

cnf(c_0_6669,plain,
    ( class_Orderings_Oorder(X1)
    | ~ class_LOrder_Omeet__semilorder(X1) ),
    c_0_5308,
    [final] ).

cnf(c_0_6670,plain,
    ( class_Orderings_Oord(X1)
    | ~ class_LOrder_Omeet__semilorder(X1) ),
    c_0_5309,
    [final] ).

cnf(c_0_6671,plain,
    ( class_LOrder_Ojoin__semilorder(X1)
    | ~ class_LOrder_Olorder(X1) ),
    c_0_5310,
    [final] ).

cnf(c_0_6672,plain,
    ( class_Orderings_Oorder(X1)
    | ~ class_LOrder_Olorder(X1) ),
    c_0_5311,
    [final] ).

cnf(c_0_6673,plain,
    ( class_Orderings_Oord(X1)
    | ~ class_LOrder_Olorder(X1) ),
    c_0_5312,
    [final] ).

cnf(c_0_6674,plain,
    ( class_LOrder_Omeet__semilorder(X1)
    | ~ class_LOrder_Olorder(X1) ),
    c_0_5313,
    [final] ).

cnf(c_0_6675,plain,
    ( class_Orderings_Oorder(X1)
    | ~ class_LOrder_Ojoin__semilorder(X1) ),
    c_0_5314,
    [final] ).

cnf(c_0_6676,plain,
    ( class_Orderings_Oord(X1)
    | ~ class_LOrder_Ojoin__semilorder(X1) ),
    c_0_5315,
    [final] ).

cnf(c_0_6677,plain,
    c_Wellfounded__Recursion_Owf(c_Wellfounded__Relations_Oless__than,tc_nat),
    c_0_5316,
    [final] ).

cnf(c_0_6678,plain,
    c_Relation_Otrans(c_Wellfounded__Relations_Oless__than,tc_nat),
    c_0_5317,
    [final] ).

cnf(c_0_6679,plain,
    class_Nat_Opower(tc_set(X1)),
    c_0_5318,
    [final] ).

cnf(c_0_6680,plain,
    class_Orderings_Oorder(tc_set(X1)),
    c_0_5319,
    [final] ).

cnf(c_0_6681,plain,
    class_Orderings_Oord(tc_set(X1)),
    c_0_5320,
    [final] ).

cnf(c_0_6682,plain,
    class_HOL_Ominus(tc_set(X1)),
    c_0_5321,
    [final] ).

cnf(c_0_6683,plain,
    c_Suc(X1) != c_0,
    c_0_5322,
    [final] ).

cnf(c_0_6684,plain,
    c_Suc(X1) != c_0,
    c_0_5323,
    [final] ).

cnf(c_0_6685,plain,
    class_HOL_Ominus(tc_nat),
    c_0_5324,
    [final] ).

cnf(c_0_6686,plain,
    class_Wellfounded__Recursion_Owellorder(tc_nat),
    c_0_5325,
    [final] ).

cnf(c_0_6687,plain,
    class_Orderings_Olinorder(tc_nat),
    c_0_5326,
    [final] ).

cnf(c_0_6688,plain,
    class_LOrder_Olorder(tc_nat),
    c_0_5327,
    [final] ).

cnf(c_0_6689,plain,
    class_LOrder_Ojoin__semilorder(tc_nat),
    c_0_5328,
    [final] ).

cnf(c_0_6690,plain,
    class_Parity_Oeven__odd(tc_nat),
    c_0_5329,
    [final] ).

cnf(c_0_6691,plain,
    class_Numeral_Onumber(tc_nat),
    c_0_5330,
    [final] ).

cnf(c_0_6692,plain,
    class_Power_Orecpower(tc_nat),
    c_0_5331,
    [final] ).

cnf(c_0_6693,plain,
    class_Divides_Odiv(tc_nat),
    c_0_5332,
    [final] ).

cnf(c_0_6694,plain,
    class_Ring__and__Field_Oordered__semidom(tc_nat),
    c_0_5333,
    [final] ).

cnf(c_0_6695,plain,
    class_Ring__and__Field_Oordered__comm__semiring__strict(tc_nat),
    c_0_5334,
    [final] ).

cnf(c_0_6696,plain,
    class_Ring__and__Field_Opordered__cancel__comm__semiring(tc_nat),
    c_0_5335,
    [final] ).

cnf(c_0_6697,plain,
    class_Ring__and__Field_Opordered__comm__semiring(tc_nat),
    c_0_5336,
    [final] ).

cnf(c_0_6698,plain,
    class_LOrder_Omeet__semilorder(tc_nat),
    c_0_5337,
    [final] ).

cnf(c_0_6699,plain,
    class_Ring__and__Field_Oordered__semiring__strict(tc_nat),
    c_0_5338,
    [final] ).

cnf(c_0_6700,plain,
    class_Ring__and__Field_Opordered__cancel__semiring(tc_nat),
    c_0_5339,
    [final] ).

cnf(c_0_6701,plain,
    class_Ring__and__Field_Opordered__semiring(tc_nat),
    c_0_5340,
    [final] ).

cnf(c_0_6702,plain,
    class_OrderedGroup_Oordered__cancel__ab__semigroup__add(tc_nat),
    c_0_5341,
    [final] ).

cnf(c_0_6703,plain,
    class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat),
    c_0_5342,
    [final] ).

cnf(c_0_6704,plain,
    class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat),
    c_0_5343,
    [final] ).

cnf(c_0_6705,plain,
    class_OrderedGroup_Opordered__ab__semigroup__add(tc_nat),
    c_0_5344,
    [final] ).

cnf(c_0_6706,plain,
    class_Ring__and__Field_Ocomm__semiring__1__cancel(tc_nat),
    c_0_5345,
    [final] ).

cnf(c_0_6707,plain,
    class_Ring__and__Field_Ocomm__semiring__0__cancel(tc_nat),
    c_0_5346,
    [final] ).

cnf(c_0_6708,plain,
    class_Ring__and__Field_Osemiring__1__cancel(tc_nat),
    c_0_5347,
    [final] ).

cnf(c_0_6709,plain,
    class_Orderings_Oorder(tc_nat),
    c_0_5348,
    [final] ).

cnf(c_0_6710,plain,
    class_Ring__and__Field_Osemiring__0__cancel(tc_nat),
    c_0_5349,
    [final] ).

cnf(c_0_6711,plain,
    class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat),
    c_0_5350,
    [final] ).

cnf(c_0_6712,plain,
    class_OrderedGroup_Ocancel__semigroup__add(tc_nat),
    c_0_5351,
    [final] ).

cnf(c_0_6713,plain,
    class_Ring__and__Field_Ocomm__semiring__1(tc_nat),
    c_0_5352,
    [final] ).

cnf(c_0_6714,plain,
    class_Ring__and__Field_Osemiring__1(tc_nat),
    c_0_5353,
    [final] ).

cnf(c_0_6715,plain,
    class_OrderedGroup_Ocomm__monoid__mult(tc_nat),
    c_0_5354,
    [final] ).

cnf(c_0_6716,plain,
    class_OrderedGroup_Omonoid__mult(tc_nat),
    c_0_5355,
    [final] ).

cnf(c_0_6717,plain,
    class_Ring__and__Field_Ocomm__semiring__0(tc_nat),
    c_0_5356,
    [final] ).

cnf(c_0_6718,plain,
    class_Ring__and__Field_Osemiring__0(tc_nat),
    c_0_5357,
    [final] ).

cnf(c_0_6719,plain,
    class_OrderedGroup_Ocomm__monoid__add(tc_nat),
    c_0_5358,
    [final] ).

cnf(c_0_6720,plain,
    class_Orderings_Oord(tc_nat),
    c_0_5359,
    [final] ).

cnf(c_0_6721,plain,
    class_Ring__and__Field_Ocomm__semiring(tc_nat),
    c_0_5360,
    [final] ).

cnf(c_0_6722,plain,
    class_Ring__and__Field_Osemiring(tc_nat),
    c_0_5361,
    [final] ).

cnf(c_0_6723,plain,
    class_OrderedGroup_Oab__semigroup__mult(tc_nat),
    c_0_5362,
    [final] ).

cnf(c_0_6724,plain,
    class_OrderedGroup_Osemigroup__mult(tc_nat),
    c_0_5363,
    [final] ).

cnf(c_0_6725,plain,
    class_OrderedGroup_Oab__semigroup__add(tc_nat),
    c_0_5364,
    [final] ).

cnf(c_0_6726,plain,
    class_OrderedGroup_Osemigroup__add(tc_nat),
    c_0_5365,
    [final] ).

cnf(c_0_6727,plain,
    class_Ring__and__Field_Oaxclass__0__neq__1(tc_nat),
    c_0_5366,
    [final] ).

cnf(c_0_6728,plain,
    class_Nat_Opower(tc_nat),
    c_0_5367,
    [final] ).

cnf(c_0_6729,plain,
    class_HOL_Otimes(tc_nat),
    c_0_5368,
    [final] ).

cnf(c_0_6730,plain,
    class_HOL_Oplus(tc_nat),
    c_0_5369,
    [final] ).

cnf(c_0_6731,plain,
    class_HOL_Ozero(tc_nat),
    c_0_5370,
    [final] ).

cnf(c_0_6732,plain,
    class_HOL_Oone(tc_nat),
    c_0_5371,
    [final] ).

cnf(c_0_6733,plain,
    class_Finite__Set_Ofinite(tc_bool),
    c_0_5372,
    [final] ).

cnf(c_0_6734,plain,
    class_Finite__Set_Ofinite(tc_Product__Type_Ounit),
    c_0_5373,
    [final] ).

cnf(c_0_6735,plain,
    class_OrderedGroup_Oab__semigroup__mult(tc_IntDef_Oint),
    c_0_5374,
    [final] ).

cnf(c_0_6736,plain,
    class_OrderedGroup_Osemigroup__mult(tc_IntDef_Oint),
    c_0_5375,
    [final] ).

cnf(c_0_6737,plain,
    class_OrderedGroup_Oab__semigroup__add(tc_IntDef_Oint),
    c_0_5376,
    [final] ).

cnf(c_0_6738,plain,
    class_Parity_Oeven__odd(tc_IntDef_Oint),
    c_0_5377,
    [final] ).

cnf(c_0_6739,plain,
    class_Power_Orecpower(tc_IntDef_Oint),
    c_0_5378,
    [final] ).

cnf(c_0_6740,plain,
    class_Nat_Opower(tc_IntDef_Oint),
    c_0_5379,
    [final] ).

cnf(c_0_6741,plain,
    class_Divides_Odiv(tc_IntDef_Oint),
    c_0_5380,
    [final] ).

cnf(c_0_6742,plain,
    class_Numeral_Onumber__ring(tc_IntDef_Oint),
    c_0_5381,
    [final] ).

cnf(c_0_6743,plain,
    class_OrderedGroup_Osemigroup__add(tc_IntDef_Oint),
    c_0_5382,
    [final] ).

cnf(c_0_6744,plain,
    class_Numeral_Onumber(tc_IntDef_Oint),
    c_0_5383,
    [final] ).

cnf(c_0_6745,plain,
    class_Ring__and__Field_Oordered__idom(tc_IntDef_Oint),
    c_0_5384,
    [final] ).

cnf(c_0_6746,plain,
    class_Ring__and__Field_Oidom(tc_IntDef_Oint),
    c_0_5385,
    [final] ).

cnf(c_0_6747,plain,
    class_Ring__and__Field_Oordered__semidom(tc_IntDef_Oint),
    c_0_5386,
    [final] ).

cnf(c_0_6748,plain,
    class_Ring__and__Field_Oordered__ring__strict(tc_IntDef_Oint),
    c_0_5387,
    [final] ).

cnf(c_0_6749,plain,
    class_Ring__and__Field_Oaxclass__no__zero__divisors(tc_IntDef_Oint),
    c_0_5388,
    [final] ).

cnf(c_0_6750,plain,
    class_Ring__and__Field_Olordered__ring(tc_IntDef_Oint),
    c_0_5389,
    [final] ).

cnf(c_0_6751,plain,
    class_OrderedGroup_Olordered__ab__group__join(tc_IntDef_Oint),
    c_0_5390,
    [final] ).

cnf(c_0_6752,plain,
    class_OrderedGroup_Olordered__ab__group__meet(tc_IntDef_Oint),
    c_0_5391,
    [final] ).

cnf(c_0_6753,plain,
    class_OrderedGroup_Olordered__ab__group__abs(tc_IntDef_Oint),
    c_0_5392,
    [final] ).

cnf(c_0_6754,plain,
    class_Orderings_Oord(tc_IntDef_Oint),
    c_0_5393,
    [final] ).

cnf(c_0_6755,plain,
    class_Ring__and__Field_Opordered__ring(tc_IntDef_Oint),
    c_0_5394,
    [final] ).

cnf(c_0_6756,plain,
    class_OrderedGroup_Olordered__ab__group(tc_IntDef_Oint),
    c_0_5395,
    [final] ).

cnf(c_0_6757,plain,
    class_OrderedGroup_Opordered__ab__group__add(tc_IntDef_Oint),
    c_0_5396,
    [final] ).

cnf(c_0_6758,plain,
    class_Ring__and__Field_Oaxclass__abs__if(tc_IntDef_Oint),
    c_0_5397,
    [final] ).

cnf(c_0_6759,plain,
    class_Ring__and__Field_Oordered__comm__semiring__strict(tc_IntDef_Oint),
    c_0_5398,
    [final] ).

cnf(c_0_6760,plain,
    class_Ring__and__Field_Opordered__cancel__comm__semiring(tc_IntDef_Oint),
    c_0_5399,
    [final] ).

cnf(c_0_6761,plain,
    class_Ring__and__Field_Opordered__comm__semiring(tc_IntDef_Oint),
    c_0_5400,
    [final] ).

cnf(c_0_6762,plain,
    class_Ring__and__Field_Oordered__semiring__strict(tc_IntDef_Oint),
    c_0_5401,
    [final] ).

cnf(c_0_6763,plain,
    class_Ring__and__Field_Opordered__cancel__semiring(tc_IntDef_Oint),
    c_0_5402,
    [final] ).

cnf(c_0_6764,plain,
    class_Ring__and__Field_Opordered__semiring(tc_IntDef_Oint),
    c_0_5403,
    [final] ).

cnf(c_0_6765,plain,
    class_HOL_Ozero(tc_IntDef_Oint),
    c_0_5404,
    [final] ).

cnf(c_0_6766,plain,
    class_OrderedGroup_Oordered__cancel__ab__semigroup__add(tc_IntDef_Oint),
    c_0_5405,
    [final] ).

cnf(c_0_6767,plain,
    class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_IntDef_Oint),
    c_0_5406,
    [final] ).

cnf(c_0_6768,plain,
    class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_IntDef_Oint),
    c_0_5407,
    [final] ).

cnf(c_0_6769,plain,
    class_OrderedGroup_Opordered__ab__semigroup__add(tc_IntDef_Oint),
    c_0_5408,
    [final] ).

cnf(c_0_6770,plain,
    class_Orderings_Olinorder(tc_IntDef_Oint),
    c_0_5409,
    [final] ).

cnf(c_0_6771,plain,
    class_LOrder_Olorder(tc_IntDef_Oint),
    c_0_5410,
    [final] ).

cnf(c_0_6772,plain,
    class_LOrder_Ojoin__semilorder(tc_IntDef_Oint),
    c_0_5411,
    [final] ).

cnf(c_0_6773,plain,
    class_LOrder_Omeet__semilorder(tc_IntDef_Oint),
    c_0_5412,
    [final] ).

cnf(c_0_6774,plain,
    class_Orderings_Oorder(tc_IntDef_Oint),
    c_0_5413,
    [final] ).

cnf(c_0_6775,plain,
    class_Ring__and__Field_Ocomm__ring__1(tc_IntDef_Oint),
    c_0_5414,
    [final] ).

cnf(c_0_6776,plain,
    class_HOL_Otimes(tc_IntDef_Oint),
    c_0_5415,
    [final] ).

cnf(c_0_6777,plain,
    class_Ring__and__Field_Ocomm__semiring__1__cancel(tc_IntDef_Oint),
    c_0_5416,
    [final] ).

cnf(c_0_6778,plain,
    class_Ring__and__Field_Oring__1(tc_IntDef_Oint),
    c_0_5417,
    [final] ).

cnf(c_0_6779,plain,
    class_Ring__and__Field_Osemiring__1__cancel(tc_IntDef_Oint),
    c_0_5418,
    [final] ).

cnf(c_0_6780,plain,
    class_Ring__and__Field_Ocomm__semiring__1(tc_IntDef_Oint),
    c_0_5419,
    [final] ).

cnf(c_0_6781,plain,
    class_Ring__and__Field_Osemiring__1(tc_IntDef_Oint),
    c_0_5420,
    [final] ).

cnf(c_0_6782,plain,
    class_OrderedGroup_Ocomm__monoid__mult(tc_IntDef_Oint),
    c_0_5421,
    [final] ).

cnf(c_0_6783,plain,
    class_OrderedGroup_Omonoid__mult(tc_IntDef_Oint),
    c_0_5422,
    [final] ).

cnf(c_0_6784,plain,
    class_Ring__and__Field_Oaxclass__0__neq__1(tc_IntDef_Oint),
    c_0_5423,
    [final] ).

cnf(c_0_6785,plain,
    class_Ring__and__Field_Ocomm__ring(tc_IntDef_Oint),
    c_0_5424,
    [final] ).

cnf(c_0_6786,plain,
    class_Ring__and__Field_Ocomm__semiring__0__cancel(tc_IntDef_Oint),
    c_0_5425,
    [final] ).

cnf(c_0_6787,plain,
    class_HOL_Oplus(tc_IntDef_Oint),
    c_0_5426,
    [final] ).

cnf(c_0_6788,plain,
    class_Ring__and__Field_Oring(tc_IntDef_Oint),
    c_0_5427,
    [final] ).

cnf(c_0_6789,plain,
    class_Ring__and__Field_Osemiring__0__cancel(tc_IntDef_Oint),
    c_0_5428,
    [final] ).

cnf(c_0_6790,plain,
    class_OrderedGroup_Oab__group__add(tc_IntDef_Oint),
    c_0_5429,
    [final] ).

cnf(c_0_6791,plain,
    class_OrderedGroup_Ocancel__ab__semigroup__add(tc_IntDef_Oint),
    c_0_5430,
    [final] ).

cnf(c_0_6792,plain,
    class_OrderedGroup_Ocancel__semigroup__add(tc_IntDef_Oint),
    c_0_5431,
    [final] ).

cnf(c_0_6793,plain,
    class_Ring__and__Field_Ocomm__semiring__0(tc_IntDef_Oint),
    c_0_5432,
    [final] ).

cnf(c_0_6794,plain,
    class_Ring__and__Field_Osemiring__0(tc_IntDef_Oint),
    c_0_5433,
    [final] ).

cnf(c_0_6795,plain,
    class_OrderedGroup_Ocomm__monoid__add(tc_IntDef_Oint),
    c_0_5434,
    [final] ).

cnf(c_0_6796,plain,
    class_Ring__and__Field_Ocomm__semiring(tc_IntDef_Oint),
    c_0_5435,
    [final] ).

cnf(c_0_6797,plain,
    class_Ring__and__Field_Osemiring(tc_IntDef_Oint),
    c_0_5436,
    [final] ).

cnf(c_0_6798,plain,
    class_HOL_Oone(tc_IntDef_Oint),
    c_0_5437,
    [final] ).

cnf(c_0_6799,plain,
    class_HOL_Ominus(tc_IntDef_Oint),
    c_0_5438,
    [final] ).

cnf(c_0_6800,plain,
    c_UNIV != c_emptyset,
    c_0_5439,
    [final] ).

cnf(c_0_6801,plain,
    c_Numeral_Obit_OB1 != c_Numeral_Obit_OB0,
    c_0_5440,
    [final] ).

cnf(c_0_6802,plain,
    c_Numeral_Obit_OB1 != c_Numeral_Obit_OB0,
    c_0_5441,
    [final] ).

cnf(c_0_6803,plain,
    c_Extraction_Osumbool_ORight != c_Extraction_Osumbool_OLeft,
    c_0_5442,
    [final] ).

cnf(c_0_6804,plain,
    c_Extraction_Osumbool_ORight != c_Extraction_Osumbool_OLeft,
    c_0_5443,
    [final] ).

% End CNF derivation
% Generating one_way clauses for all literals in the CNF.
cnf(c_0_5444_0,axiom,
    ( c_in(c_Pair(c_Main_Orel__compE__1(X1,X2,X3,X4,X5,X6),c_Main_Orel__compE__2(X1,X2,X3,X4,X5,X6),X6,X4),X2,tc_prod(X6,X4))
    | ~ c_in(X3,c_Relation_Orel__comp(X1,X2,X4,X5,X6),tc_prod(X6,X5)) ),
    inference(literals_permutation,[status(thm)],[c_0_5444]) ).

cnf(c_0_5444_1,axiom,
    ( ~ c_in(X3,c_Relation_Orel__comp(X1,X2,X4,X5,X6),tc_prod(X6,X5))
    | c_in(c_Pair(c_Main_Orel__compE__1(X1,X2,X3,X4,X5,X6),c_Main_Orel__compE__2(X1,X2,X3,X4,X5,X6),X6,X4),X2,tc_prod(X6,X4)) ),
    inference(literals_permutation,[status(thm)],[c_0_5444]) ).

cnf(c_0_5445_0,axiom,
    ( c_in(c_Pair(c_Main_Orel__compE__2(X1,X2,X3,X4,X5,X6),c_Main_Orel__compE__3(X1,X2,X3,X4,X5,X6),X4,X5),X1,tc_prod(X4,X5))
    | ~ c_in(X3,c_Relation_Orel__comp(X1,X2,X4,X5,X6),tc_prod(X6,X5)) ),
    inference(literals_permutation,[status(thm)],[c_0_5445]) ).

cnf(c_0_5445_1,axiom,
    ( ~ c_in(X3,c_Relation_Orel__comp(X1,X2,X4,X5,X6),tc_prod(X6,X5))
    | c_in(c_Pair(c_Main_Orel__compE__2(X1,X2,X3,X4,X5,X6),c_Main_Orel__compE__3(X1,X2,X3,X4,X5,X6),X4,X5),X1,tc_prod(X4,X5)) ),
    inference(literals_permutation,[status(thm)],[c_0_5445]) ).

cnf(c_0_5446_0,axiom,
    ( c_Pair(c_Main_Orel__compE__1(X2,X3,X1,X4,X5,X6),c_Main_Orel__compE__3(X2,X3,X1,X4,X5,X6),X6,X5) = X1
    | ~ c_in(X1,c_Relation_Orel__comp(X2,X3,X4,X5,X6),tc_prod(X6,X5)) ),
    inference(literals_permutation,[status(thm)],[c_0_5446]) ).

cnf(c_0_5446_1,axiom,
    ( ~ c_in(X1,c_Relation_Orel__comp(X2,X3,X4,X5,X6),tc_prod(X6,X5))
    | c_Pair(c_Main_Orel__compE__1(X2,X3,X1,X4,X5,X6),c_Main_Orel__compE__3(X2,X3,X1,X4,X5,X6),X6,X5) = X1 ),
    inference(literals_permutation,[status(thm)],[c_0_5446]) ).

cnf(c_0_5447_0,axiom,
    ( c_Pair(c_Datatype__Universe_OScons(c_Main_OdprodE__1(X1,X2,X3,X4,X5),c_Main_OdprodE__2(X1,X2,X3,X4,X5),X4,X5),c_Datatype__Universe_OScons(c_Main_OdprodE__3(X1,X2,X3,X4,X5),c_Main_OdprodE__4(X1,X2,X3,X4,X5),X4,X5),tc_set(tc_Datatype__Universe_Onode(X4,X5)),tc_set(tc_Datatype__Universe_Onode(X4,X5))) = X1
    | ~ c_in(X1,c_Datatype__Universe_Odprod(X2,X3,X4,X5),tc_prod(tc_set(tc_Datatype__Universe_Onode(X4,X5)),tc_set(tc_Datatype__Universe_Onode(X4,X5)))) ),
    inference(literals_permutation,[status(thm)],[c_0_5447]) ).

cnf(c_0_5447_1,axiom,
    ( ~ c_in(X1,c_Datatype__Universe_Odprod(X2,X3,X4,X5),tc_prod(tc_set(tc_Datatype__Universe_Onode(X4,X5)),tc_set(tc_Datatype__Universe_Onode(X4,X5))))
    | c_Pair(c_Datatype__Universe_OScons(c_Main_OdprodE__1(X1,X2,X3,X4,X5),c_Main_OdprodE__2(X1,X2,X3,X4,X5),X4,X5),c_Datatype__Universe_OScons(c_Main_OdprodE__3(X1,X2,X3,X4,X5),c_Main_OdprodE__4(X1,X2,X3,X4,X5),X4,X5),tc_set(tc_Datatype__Universe_Onode(X4,X5)),tc_set(tc_Datatype__Universe_Onode(X4,X5))) = X1 ),
    inference(literals_permutation,[status(thm)],[c_0_5447]) ).

cnf(c_0_5448_0,axiom,
    ( c_in(c_Pair(c_Main_OdprodE__1(X1,X2,X3,X4,X5),c_Main_OdprodE__3(X1,X2,X3,X4,X5),tc_set(tc_Datatype__Universe_Onode(X4,X5)),tc_set(tc_Datatype__Universe_Onode(X4,X5))),X2,tc_prod(tc_set(tc_Datatype__Universe_Onode(X4,X5)),tc_set(tc_Datatype__Universe_Onode(X4,X5))))
    | ~ c_in(X1,c_Datatype__Universe_Odprod(X2,X3,X4,X5),tc_prod(tc_set(tc_Datatype__Universe_Onode(X4,X5)),tc_set(tc_Datatype__Universe_Onode(X4,X5)))) ),
    inference(literals_permutation,[status(thm)],[c_0_5448]) ).

cnf(c_0_5448_1,axiom,
    ( ~ c_in(X1,c_Datatype__Universe_Odprod(X2,X3,X4,X5),tc_prod(tc_set(tc_Datatype__Universe_Onode(X4,X5)),tc_set(tc_Datatype__Universe_Onode(X4,X5))))
    | c_in(c_Pair(c_Main_OdprodE__1(X1,X2,X3,X4,X5),c_Main_OdprodE__3(X1,X2,X3,X4,X5),tc_set(tc_Datatype__Universe_Onode(X4,X5)),tc_set(tc_Datatype__Universe_Onode(X4,X5))),X2,tc_prod(tc_set(tc_Datatype__Universe_Onode(X4,X5)),tc_set(tc_Datatype__Universe_Onode(X4,X5)))) ),
    inference(literals_permutation,[status(thm)],[c_0_5448]) ).

cnf(c_0_5449_0,axiom,
    ( c_in(c_Pair(c_Main_OdprodE__2(X1,X2,X3,X4,X5),c_Main_OdprodE__4(X1,X2,X3,X4,X5),tc_set(tc_Datatype__Universe_Onode(X4,X5)),tc_set(tc_Datatype__Universe_Onode(X4,X5))),X3,tc_prod(tc_set(tc_Datatype__Universe_Onode(X4,X5)),tc_set(tc_Datatype__Universe_Onode(X4,X5))))
    | ~ c_in(X1,c_Datatype__Universe_Odprod(X2,X3,X4,X5),tc_prod(tc_set(tc_Datatype__Universe_Onode(X4,X5)),tc_set(tc_Datatype__Universe_Onode(X4,X5)))) ),
    inference(literals_permutation,[status(thm)],[c_0_5449]) ).

cnf(c_0_5449_1,axiom,
    ( ~ c_in(X1,c_Datatype__Universe_Odprod(X2,X3,X4,X5),tc_prod(tc_set(tc_Datatype__Universe_Onode(X4,X5)),tc_set(tc_Datatype__Universe_Onode(X4,X5))))
    | c_in(c_Pair(c_Main_OdprodE__2(X1,X2,X3,X4,X5),c_Main_OdprodE__4(X1,X2,X3,X4,X5),tc_set(tc_Datatype__Universe_Onode(X4,X5)),tc_set(tc_Datatype__Universe_Onode(X4,X5))),X3,tc_prod(tc_set(tc_Datatype__Universe_Onode(X4,X5)),tc_set(tc_Datatype__Universe_Onode(X4,X5)))) ),
    inference(literals_permutation,[status(thm)],[c_0_5449]) ).

cnf(c_0_5450_0,axiom,
    ( c_in(c_Pair(c_Main_OdsumE__3(X1,X2,X3,X4),c_Main_OdsumE__4(X1,X2,X3,X4),tc_set(tc_Datatype__Universe_Onode(X3,X4)),tc_set(tc_Datatype__Universe_Onode(X3,X4))),X1,tc_prod(tc_set(tc_Datatype__Universe_Onode(X3,X4)),tc_set(tc_Datatype__Universe_Onode(X3,X4))))
    | c_in(c_Pair(c_Main_OdsumE__1(X5,X2,X3,X4),c_Main_OdsumE__2(X5,X2,X3,X4),tc_set(tc_Datatype__Universe_Onode(X3,X4)),tc_set(tc_Datatype__Universe_Onode(X3,X4))),X5,tc_prod(tc_set(tc_Datatype__Universe_Onode(X3,X4)),tc_set(tc_Datatype__Universe_Onode(X3,X4))))
    | ~ c_in(X2,c_Datatype__Universe_Odsum(X5,X1,X3,X4),tc_prod(tc_set(tc_Datatype__Universe_Onode(X3,X4)),tc_set(tc_Datatype__Universe_Onode(X3,X4)))) ),
    inference(literals_permutation,[status(thm)],[c_0_5450]) ).

cnf(c_0_5450_1,axiom,
    ( c_in(c_Pair(c_Main_OdsumE__1(X5,X2,X3,X4),c_Main_OdsumE__2(X5,X2,X3,X4),tc_set(tc_Datatype__Universe_Onode(X3,X4)),tc_set(tc_Datatype__Universe_Onode(X3,X4))),X5,tc_prod(tc_set(tc_Datatype__Universe_Onode(X3,X4)),tc_set(tc_Datatype__Universe_Onode(X3,X4))))
    | c_in(c_Pair(c_Main_OdsumE__3(X1,X2,X3,X4),c_Main_OdsumE__4(X1,X2,X3,X4),tc_set(tc_Datatype__Universe_Onode(X3,X4)),tc_set(tc_Datatype__Universe_Onode(X3,X4))),X1,tc_prod(tc_set(tc_Datatype__Universe_Onode(X3,X4)),tc_set(tc_Datatype__Universe_Onode(X3,X4))))
    | ~ c_in(X2,c_Datatype__Universe_Odsum(X5,X1,X3,X4),tc_prod(tc_set(tc_Datatype__Universe_Onode(X3,X4)),tc_set(tc_Datatype__Universe_Onode(X3,X4)))) ),
    inference(literals_permutation,[status(thm)],[c_0_5450]) ).

cnf(c_0_5450_2,axiom,
    ( ~ c_in(X2,c_Datatype__Universe_Odsum(X5,X1,X3,X4),tc_prod(tc_set(tc_Datatype__Universe_Onode(X3,X4)),tc_set(tc_Datatype__Universe_Onode(X3,X4))))
    | c_in(c_Pair(c_Main_OdsumE__1(X5,X2,X3,X4),c_Main_OdsumE__2(X5,X2,X3,X4),tc_set(tc_Datatype__Universe_Onode(X3,X4)),tc_set(tc_Datatype__Universe_Onode(X3,X4))),X5,tc_prod(tc_set(tc_Datatype__Universe_Onode(X3,X4)),tc_set(tc_Datatype__Universe_Onode(X3,X4))))
    | c_in(c_Pair(c_Main_OdsumE__3(X1,X2,X3,X4),c_Main_OdsumE__4(X1,X2,X3,X4),tc_set(tc_Datatype__Universe_Onode(X3,X4)),tc_set(tc_Datatype__Universe_Onode(X3,X4))),X1,tc_prod(tc_set(tc_Datatype__Universe_Onode(X3,X4)),tc_set(tc_Datatype__Universe_Onode(X3,X4)))) ),
    inference(literals_permutation,[status(thm)],[c_0_5450]) ).

cnf(c_0_5451_0,axiom,
    ( c_Pair(c_Datatype__Universe_OIn1(c_Main_OdsumE__3(X2,X1,X3,X4),X3,X4),c_Datatype__Universe_OIn1(c_Main_OdsumE__4(X2,X1,X3,X4),X3,X4),tc_set(tc_Datatype__Universe_Onode(X3,X4)),tc_set(tc_Datatype__Universe_Onode(X3,X4))) = X1
    | c_in(c_Pair(c_Main_OdsumE__1(X5,X1,X3,X4),c_Main_OdsumE__2(X5,X1,X3,X4),tc_set(tc_Datatype__Universe_Onode(X3,X4)),tc_set(tc_Datatype__Universe_Onode(X3,X4))),X5,tc_prod(tc_set(tc_Datatype__Universe_Onode(X3,X4)),tc_set(tc_Datatype__Universe_Onode(X3,X4))))
    | ~ c_in(X1,c_Datatype__Universe_Odsum(X5,X2,X3,X4),tc_prod(tc_set(tc_Datatype__Universe_Onode(X3,X4)),tc_set(tc_Datatype__Universe_Onode(X3,X4)))) ),
    inference(literals_permutation,[status(thm)],[c_0_5451]) ).

cnf(c_0_5451_1,axiom,
    ( c_in(c_Pair(c_Main_OdsumE__1(X5,X1,X3,X4),c_Main_OdsumE__2(X5,X1,X3,X4),tc_set(tc_Datatype__Universe_Onode(X3,X4)),tc_set(tc_Datatype__Universe_Onode(X3,X4))),X5,tc_prod(tc_set(tc_Datatype__Universe_Onode(X3,X4)),tc_set(tc_Datatype__Universe_Onode(X3,X4))))
    | c_Pair(c_Datatype__Universe_OIn1(c_Main_OdsumE__3(X2,X1,X3,X4),X3,X4),c_Datatype__Universe_OIn1(c_Main_OdsumE__4(X2,X1,X3,X4),X3,X4),tc_set(tc_Datatype__Universe_Onode(X3,X4)),tc_set(tc_Datatype__Universe_Onode(X3,X4))) = X1
    | ~ c_in(X1,c_Datatype__Universe_Odsum(X5,X2,X3,X4),tc_prod(tc_set(tc_Datatype__Universe_Onode(X3,X4)),tc_set(tc_Datatype__Universe_Onode(X3,X4)))) ),
    inference(literals_permutation,[status(thm)],[c_0_5451]) ).

cnf(c_0_5451_2,axiom,
    ( ~ c_in(X1,c_Datatype__Universe_Odsum(X5,X2,X3,X4),tc_prod(tc_set(tc_Datatype__Universe_Onode(X3,X4)),tc_set(tc_Datatype__Universe_Onode(X3,X4))))
    | c_in(c_Pair(c_Main_OdsumE__1(X5,X1,X3,X4),c_Main_OdsumE__2(X5,X1,X3,X4),tc_set(tc_Datatype__Universe_Onode(X3,X4)),tc_set(tc_Datatype__Universe_Onode(X3,X4))),X5,tc_prod(tc_set(tc_Datatype__Universe_Onode(X3,X4)),tc_set(tc_Datatype__Universe_Onode(X3,X4))))
    | c_Pair(c_Datatype__Universe_OIn1(c_Main_OdsumE__3(X2,X1,X3,X4),X3,X4),c_Datatype__Universe_OIn1(c_Main_OdsumE__4(X2,X1,X3,X4),X3,X4),tc_set(tc_Datatype__Universe_Onode(X3,X4)),tc_set(tc_Datatype__Universe_Onode(X3,X4))) = X1 ),
    inference(literals_permutation,[status(thm)],[c_0_5451]) ).

cnf(c_0_5452_0,axiom,
    ( c_Pair(c_Datatype__Universe_OIn0(c_Main_OdsumE__1(X2,X1,X3,X4),X3,X4),c_Datatype__Universe_OIn0(c_Main_OdsumE__2(X2,X1,X3,X4),X3,X4),tc_set(tc_Datatype__Universe_Onode(X3,X4)),tc_set(tc_Datatype__Universe_Onode(X3,X4))) = X1
    | c_in(c_Pair(c_Main_OdsumE__3(X5,X1,X3,X4),c_Main_OdsumE__4(X5,X1,X3,X4),tc_set(tc_Datatype__Universe_Onode(X3,X4)),tc_set(tc_Datatype__Universe_Onode(X3,X4))),X5,tc_prod(tc_set(tc_Datatype__Universe_Onode(X3,X4)),tc_set(tc_Datatype__Universe_Onode(X3,X4))))
    | ~ c_in(X1,c_Datatype__Universe_Odsum(X2,X5,X3,X4),tc_prod(tc_set(tc_Datatype__Universe_Onode(X3,X4)),tc_set(tc_Datatype__Universe_Onode(X3,X4)))) ),
    inference(literals_permutation,[status(thm)],[c_0_5452]) ).

cnf(c_0_5452_1,axiom,
    ( c_in(c_Pair(c_Main_OdsumE__3(X5,X1,X3,X4),c_Main_OdsumE__4(X5,X1,X3,X4),tc_set(tc_Datatype__Universe_Onode(X3,X4)),tc_set(tc_Datatype__Universe_Onode(X3,X4))),X5,tc_prod(tc_set(tc_Datatype__Universe_Onode(X3,X4)),tc_set(tc_Datatype__Universe_Onode(X3,X4))))
    | c_Pair(c_Datatype__Universe_OIn0(c_Main_OdsumE__1(X2,X1,X3,X4),X3,X4),c_Datatype__Universe_OIn0(c_Main_OdsumE__2(X2,X1,X3,X4),X3,X4),tc_set(tc_Datatype__Universe_Onode(X3,X4)),tc_set(tc_Datatype__Universe_Onode(X3,X4))) = X1
    | ~ c_in(X1,c_Datatype__Universe_Odsum(X2,X5,X3,X4),tc_prod(tc_set(tc_Datatype__Universe_Onode(X3,X4)),tc_set(tc_Datatype__Universe_Onode(X3,X4)))) ),
    inference(literals_permutation,[status(thm)],[c_0_5452]) ).

cnf(c_0_5452_2,axiom,
    ( ~ c_in(X1,c_Datatype__Universe_Odsum(X2,X5,X3,X4),tc_prod(tc_set(tc_Datatype__Universe_Onode(X3,X4)),tc_set(tc_Datatype__Universe_Onode(X3,X4))))
    | c_in(c_Pair(c_Main_OdsumE__3(X5,X1,X3,X4),c_Main_OdsumE__4(X5,X1,X3,X4),tc_set(tc_Datatype__Universe_Onode(X3,X4)),tc_set(tc_Datatype__Universe_Onode(X3,X4))),X5,tc_prod(tc_set(tc_Datatype__Universe_Onode(X3,X4)),tc_set(tc_Datatype__Universe_Onode(X3,X4))))
    | c_Pair(c_Datatype__Universe_OIn0(c_Main_OdsumE__1(X2,X1,X3,X4),X3,X4),c_Datatype__Universe_OIn0(c_Main_OdsumE__2(X2,X1,X3,X4),X3,X4),tc_set(tc_Datatype__Universe_Onode(X3,X4)),tc_set(tc_Datatype__Universe_Onode(X3,X4))) = X1 ),
    inference(literals_permutation,[status(thm)],[c_0_5452]) ).

cnf(c_0_5453_0,axiom,
    ( c_in(c_Pair(c_Main_Olistrel__Cons2__2(X1,X2,X3,X4,X5),X4,tc_List_Olist(X5),tc_List_Olist(X5)),c_List_Olistrel(X1,X5),tc_prod(tc_List_Olist(X5),tc_List_Olist(X5)))
    | ~ c_in(c_Pair(X2,c_List_Olist_OCons(X3,X4,X5),tc_List_Olist(X5),tc_List_Olist(X5)),c_List_Olistrel(X1,X5),tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))) ),
    inference(literals_permutation,[status(thm)],[c_0_5453]) ).

cnf(c_0_5453_1,axiom,
    ( ~ c_in(c_Pair(X2,c_List_Olist_OCons(X3,X4,X5),tc_List_Olist(X5),tc_List_Olist(X5)),c_List_Olistrel(X1,X5),tc_prod(tc_List_Olist(X5),tc_List_Olist(X5)))
    | c_in(c_Pair(c_Main_Olistrel__Cons2__2(X1,X2,X3,X4,X5),X4,tc_List_Olist(X5),tc_List_Olist(X5)),c_List_Olistrel(X1,X5),tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))) ),
    inference(literals_permutation,[status(thm)],[c_0_5453]) ).

cnf(c_0_5454_0,axiom,
    ( c_in(c_Pair(X1,c_Main_Olistrel__Cons1__2(X2,X3,X4,X1,X5),tc_List_Olist(X5),tc_List_Olist(X5)),c_List_Olistrel(X2,X5),tc_prod(tc_List_Olist(X5),tc_List_Olist(X5)))
    | ~ c_in(c_Pair(c_List_Olist_OCons(X4,X1,X5),X3,tc_List_Olist(X5),tc_List_Olist(X5)),c_List_Olistrel(X2,X5),tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))) ),
    inference(literals_permutation,[status(thm)],[c_0_5454]) ).

cnf(c_0_5454_1,axiom,
    ( ~ c_in(c_Pair(c_List_Olist_OCons(X4,X1,X5),X3,tc_List_Olist(X5),tc_List_Olist(X5)),c_List_Olistrel(X2,X5),tc_prod(tc_List_Olist(X5),tc_List_Olist(X5)))
    | c_in(c_Pair(X1,c_Main_Olistrel__Cons1__2(X2,X3,X4,X1,X5),tc_List_Olist(X5),tc_List_Olist(X5)),c_List_Olistrel(X2,X5),tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))) ),
    inference(literals_permutation,[status(thm)],[c_0_5454]) ).

cnf(c_0_5455_0,axiom,
    ( c_in(c_Pair(c_Datatype__Universe_OScons(X1,X2,X3,X4),c_Datatype__Universe_OScons(X5,X6,X3,X4),tc_set(tc_Datatype__Universe_Onode(X3,X4)),tc_set(tc_Datatype__Universe_Onode(X3,X4))),c_Datatype__Universe_Odprod(X7,X8,X3,X4),tc_prod(tc_set(tc_Datatype__Universe_Onode(X3,X4)),tc_set(tc_Datatype__Universe_Onode(X3,X4))))
    | ~ c_in(c_Pair(X1,X5,tc_set(tc_Datatype__Universe_Onode(X3,X4)),tc_set(tc_Datatype__Universe_Onode(X3,X4))),X7,tc_prod(tc_set(tc_Datatype__Universe_Onode(X3,X4)),tc_set(tc_Datatype__Universe_Onode(X3,X4))))
    | ~ c_in(c_Pair(X2,X6,tc_set(tc_Datatype__Universe_Onode(X3,X4)),tc_set(tc_Datatype__Universe_Onode(X3,X4))),X8,tc_prod(tc_set(tc_Datatype__Universe_Onode(X3,X4)),tc_set(tc_Datatype__Universe_Onode(X3,X4)))) ),
    inference(literals_permutation,[status(thm)],[c_0_5455]) ).

cnf(c_0_5455_1,axiom,
    ( ~ c_in(c_Pair(X1,X5,tc_set(tc_Datatype__Universe_Onode(X3,X4)),tc_set(tc_Datatype__Universe_Onode(X3,X4))),X7,tc_prod(tc_set(tc_Datatype__Universe_Onode(X3,X4)),tc_set(tc_Datatype__Universe_Onode(X3,X4))))
    | c_in(c_Pair(c_Datatype__Universe_OScons(X1,X2,X3,X4),c_Datatype__Universe_OScons(X5,X6,X3,X4),tc_set(tc_Datatype__Universe_Onode(X3,X4)),tc_set(tc_Datatype__Universe_Onode(X3,X4))),c_Datatype__Universe_Odprod(X7,X8,X3,X4),tc_prod(tc_set(tc_Datatype__Universe_Onode(X3,X4)),tc_set(tc_Datatype__Universe_Onode(X3,X4))))
    | ~ c_in(c_Pair(X2,X6,tc_set(tc_Datatype__Universe_Onode(X3,X4)),tc_set(tc_Datatype__Universe_Onode(X3,X4))),X8,tc_prod(tc_set(tc_Datatype__Universe_Onode(X3,X4)),tc_set(tc_Datatype__Universe_Onode(X3,X4)))) ),
    inference(literals_permutation,[status(thm)],[c_0_5455]) ).

cnf(c_0_5455_2,axiom,
    ( ~ c_in(c_Pair(X2,X6,tc_set(tc_Datatype__Universe_Onode(X3,X4)),tc_set(tc_Datatype__Universe_Onode(X3,X4))),X8,tc_prod(tc_set(tc_Datatype__Universe_Onode(X3,X4)),tc_set(tc_Datatype__Universe_Onode(X3,X4))))
    | ~ c_in(c_Pair(X1,X5,tc_set(tc_Datatype__Universe_Onode(X3,X4)),tc_set(tc_Datatype__Universe_Onode(X3,X4))),X7,tc_prod(tc_set(tc_Datatype__Universe_Onode(X3,X4)),tc_set(tc_Datatype__Universe_Onode(X3,X4))))
    | c_in(c_Pair(c_Datatype__Universe_OScons(X1,X2,X3,X4),c_Datatype__Universe_OScons(X5,X6,X3,X4),tc_set(tc_Datatype__Universe_Onode(X3,X4)),tc_set(tc_Datatype__Universe_Onode(X3,X4))),c_Datatype__Universe_Odprod(X7,X8,X3,X4),tc_prod(tc_set(tc_Datatype__Universe_Onode(X3,X4)),tc_set(tc_Datatype__Universe_Onode(X3,X4)))) ),
    inference(literals_permutation,[status(thm)],[c_0_5455]) ).

cnf(c_0_5456_0,axiom,
    ( c_in(c_Pair(c_Main_Olistrel__Cons2__1(X1,X2,X3,X4,X5),X3,X5,X5),X1,tc_prod(X5,X5))
    | ~ c_in(c_Pair(X2,c_List_Olist_OCons(X3,X4,X5),tc_List_Olist(X5),tc_List_Olist(X5)),c_List_Olistrel(X1,X5),tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))) ),
    inference(literals_permutation,[status(thm)],[c_0_5456]) ).

cnf(c_0_5456_1,axiom,
    ( ~ c_in(c_Pair(X2,c_List_Olist_OCons(X3,X4,X5),tc_List_Olist(X5),tc_List_Olist(X5)),c_List_Olistrel(X1,X5),tc_prod(tc_List_Olist(X5),tc_List_Olist(X5)))
    | c_in(c_Pair(c_Main_Olistrel__Cons2__1(X1,X2,X3,X4,X5),X3,X5,X5),X1,tc_prod(X5,X5)) ),
    inference(literals_permutation,[status(thm)],[c_0_5456]) ).

cnf(c_0_5457_0,axiom,
    ( c_in(c_Pair(X1,c_Main_Olistrel__Cons1__1(X2,X3,X1,X4,X5),X5,X5),X2,tc_prod(X5,X5))
    | ~ c_in(c_Pair(c_List_Olist_OCons(X1,X4,X5),X3,tc_List_Olist(X5),tc_List_Olist(X5)),c_List_Olistrel(X2,X5),tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))) ),
    inference(literals_permutation,[status(thm)],[c_0_5457]) ).

cnf(c_0_5457_1,axiom,
    ( ~ c_in(c_Pair(c_List_Olist_OCons(X1,X4,X5),X3,tc_List_Olist(X5),tc_List_Olist(X5)),c_List_Olistrel(X2,X5),tc_prod(tc_List_Olist(X5),tc_List_Olist(X5)))
    | c_in(c_Pair(X1,c_Main_Olistrel__Cons1__1(X2,X3,X1,X4,X5),X5,X5),X2,tc_prod(X5,X5)) ),
    inference(literals_permutation,[status(thm)],[c_0_5457]) ).

cnf(c_0_5458_0,axiom,
    ( c_Pair(c_Datatype__Universe_OIn1(c_Main_OdsumE__3(X2,X1,X3,X4),X3,X4),c_Datatype__Universe_OIn1(c_Main_OdsumE__4(X2,X1,X3,X4),X3,X4),tc_set(tc_Datatype__Universe_Onode(X3,X4)),tc_set(tc_Datatype__Universe_Onode(X3,X4))) = X1
    | c_Pair(c_Datatype__Universe_OIn0(c_Main_OdsumE__1(X5,X1,X3,X4),X3,X4),c_Datatype__Universe_OIn0(c_Main_OdsumE__2(X5,X1,X3,X4),X3,X4),tc_set(tc_Datatype__Universe_Onode(X3,X4)),tc_set(tc_Datatype__Universe_Onode(X3,X4))) = X1
    | ~ c_in(X1,c_Datatype__Universe_Odsum(X5,X2,X3,X4),tc_prod(tc_set(tc_Datatype__Universe_Onode(X3,X4)),tc_set(tc_Datatype__Universe_Onode(X3,X4)))) ),
    inference(literals_permutation,[status(thm)],[c_0_5458]) ).

cnf(c_0_5458_1,axiom,
    ( c_Pair(c_Datatype__Universe_OIn0(c_Main_OdsumE__1(X5,X1,X3,X4),X3,X4),c_Datatype__Universe_OIn0(c_Main_OdsumE__2(X5,X1,X3,X4),X3,X4),tc_set(tc_Datatype__Universe_Onode(X3,X4)),tc_set(tc_Datatype__Universe_Onode(X3,X4))) = X1
    | c_Pair(c_Datatype__Universe_OIn1(c_Main_OdsumE__3(X2,X1,X3,X4),X3,X4),c_Datatype__Universe_OIn1(c_Main_OdsumE__4(X2,X1,X3,X4),X3,X4),tc_set(tc_Datatype__Universe_Onode(X3,X4)),tc_set(tc_Datatype__Universe_Onode(X3,X4))) = X1
    | ~ c_in(X1,c_Datatype__Universe_Odsum(X5,X2,X3,X4),tc_prod(tc_set(tc_Datatype__Universe_Onode(X3,X4)),tc_set(tc_Datatype__Universe_Onode(X3,X4)))) ),
    inference(literals_permutation,[status(thm)],[c_0_5458]) ).

cnf(c_0_5458_2,axiom,
    ( ~ c_in(X1,c_Datatype__Universe_Odsum(X5,X2,X3,X4),tc_prod(tc_set(tc_Datatype__Universe_Onode(X3,X4)),tc_set(tc_Datatype__Universe_Onode(X3,X4))))
    | c_Pair(c_Datatype__Universe_OIn0(c_Main_OdsumE__1(X5,X1,X3,X4),X3,X4),c_Datatype__Universe_OIn0(c_Main_OdsumE__2(X5,X1,X3,X4),X3,X4),tc_set(tc_Datatype__Universe_Onode(X3,X4)),tc_set(tc_Datatype__Universe_Onode(X3,X4))) = X1
    | c_Pair(c_Datatype__Universe_OIn1(c_Main_OdsumE__3(X2,X1,X3,X4),X3,X4),c_Datatype__Universe_OIn1(c_Main_OdsumE__4(X2,X1,X3,X4),X3,X4),tc_set(tc_Datatype__Universe_Onode(X3,X4)),tc_set(tc_Datatype__Universe_Onode(X3,X4))) = X1 ),
    inference(literals_permutation,[status(thm)],[c_0_5458]) ).

cnf(c_0_5459_0,axiom,
    ( c_in(c_Pair(c_Main_OImageE__1(X1,X2,X3,X4,X5),X2,X4,X5),X3,tc_prod(X4,X5))
    | ~ c_in(X2,c_Relation_OImage(X3,X1,X4,X5),X5) ),
    inference(literals_permutation,[status(thm)],[c_0_5459]) ).

cnf(c_0_5459_1,axiom,
    ( ~ c_in(X2,c_Relation_OImage(X3,X1,X4,X5),X5)
    | c_in(c_Pair(c_Main_OImageE__1(X1,X2,X3,X4,X5),X2,X4,X5),X3,tc_prod(X4,X5)) ),
    inference(literals_permutation,[status(thm)],[c_0_5459]) ).

cnf(c_0_5460_0,axiom,
    ( c_List_Olist_OCons(c_Main_Olistrel__Cons2__1(X2,X1,X3,X4,X5),c_Main_Olistrel__Cons2__2(X2,X1,X3,X4,X5),X5) = X1
    | ~ c_in(c_Pair(X1,c_List_Olist_OCons(X3,X4,X5),tc_List_Olist(X5),tc_List_Olist(X5)),c_List_Olistrel(X2,X5),tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))) ),
    inference(literals_permutation,[status(thm)],[c_0_5460]) ).

cnf(c_0_5460_1,axiom,
    ( ~ c_in(c_Pair(X1,c_List_Olist_OCons(X3,X4,X5),tc_List_Olist(X5),tc_List_Olist(X5)),c_List_Olistrel(X2,X5),tc_prod(tc_List_Olist(X5),tc_List_Olist(X5)))
    | c_List_Olist_OCons(c_Main_Olistrel__Cons2__1(X2,X1,X3,X4,X5),c_Main_Olistrel__Cons2__2(X2,X1,X3,X4,X5),X5) = X1 ),
    inference(literals_permutation,[status(thm)],[c_0_5460]) ).

cnf(c_0_5461_0,axiom,
    ( c_List_Olist_OCons(c_Main_Olistrel__Cons1__1(X2,X1,X3,X4,X5),c_Main_Olistrel__Cons1__2(X2,X1,X3,X4,X5),X5) = X1
    | ~ c_in(c_Pair(c_List_Olist_OCons(X3,X4,X5),X1,tc_List_Olist(X5),tc_List_Olist(X5)),c_List_Olistrel(X2,X5),tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))) ),
    inference(literals_permutation,[status(thm)],[c_0_5461]) ).

cnf(c_0_5461_1,axiom,
    ( ~ c_in(c_Pair(c_List_Olist_OCons(X3,X4,X5),X1,tc_List_Olist(X5),tc_List_Olist(X5)),c_List_Olistrel(X2,X5),tc_prod(tc_List_Olist(X5),tc_List_Olist(X5)))
    | c_List_Olist_OCons(c_Main_Olistrel__Cons1__1(X2,X1,X3,X4,X5),c_Main_Olistrel__Cons1__2(X2,X1,X3,X4,X5),X5) = X1 ),
    inference(literals_permutation,[status(thm)],[c_0_5461]) ).

cnf(c_0_5462_0,axiom,
    ( c_Datatype__Universe_OScons(c_Main_OuprodE__1(X2,X3,X1,X4,X5),c_Main_OuprodE__2(X2,X3,X1,X4,X5),X4,X5) = X1
    | ~ c_in(X1,c_Datatype__Universe_Ouprod(X2,X3,X4,X5),tc_set(tc_Datatype__Universe_Onode(X4,X5))) ),
    inference(literals_permutation,[status(thm)],[c_0_5462]) ).

cnf(c_0_5462_1,axiom,
    ( ~ c_in(X1,c_Datatype__Universe_Ouprod(X2,X3,X4,X5),tc_set(tc_Datatype__Universe_Onode(X4,X5)))
    | c_Datatype__Universe_OScons(c_Main_OuprodE__1(X2,X3,X1,X4,X5),c_Main_OuprodE__2(X2,X3,X1,X4,X5),X4,X5) = X1 ),
    inference(literals_permutation,[status(thm)],[c_0_5462]) ).

cnf(c_0_5463_0,axiom,
    ( c_in(c_Pair(X1,X2,X3,X4),c_Relation_Orel__comp(X5,X6,X7,X4,X3),tc_prod(X3,X4))
    | ~ c_in(c_Pair(X1,X8,X3,X7),X6,tc_prod(X3,X7))
    | ~ c_in(c_Pair(X8,X2,X7,X4),X5,tc_prod(X7,X4)) ),
    inference(literals_permutation,[status(thm)],[c_0_5463]) ).

cnf(c_0_5463_1,axiom,
    ( ~ c_in(c_Pair(X1,X8,X3,X7),X6,tc_prod(X3,X7))
    | c_in(c_Pair(X1,X2,X3,X4),c_Relation_Orel__comp(X5,X6,X7,X4,X3),tc_prod(X3,X4))
    | ~ c_in(c_Pair(X8,X2,X7,X4),X5,tc_prod(X7,X4)) ),
    inference(literals_permutation,[status(thm)],[c_0_5463]) ).

cnf(c_0_5463_2,axiom,
    ( ~ c_in(c_Pair(X8,X2,X7,X4),X5,tc_prod(X7,X4))
    | ~ c_in(c_Pair(X1,X8,X3,X7),X6,tc_prod(X3,X7))
    | c_in(c_Pair(X1,X2,X3,X4),c_Relation_Orel__comp(X5,X6,X7,X4,X3),tc_prod(X3,X4)) ),
    inference(literals_permutation,[status(thm)],[c_0_5463]) ).

cnf(c_0_5464_0,axiom,
    ( c_in(c_Pair(c_Datatype__Universe_OIn1(X1,X2,X3),c_Datatype__Universe_OIn1(X4,X2,X3),tc_set(tc_Datatype__Universe_Onode(X2,X3)),tc_set(tc_Datatype__Universe_Onode(X2,X3))),c_Datatype__Universe_Odsum(X5,X6,X2,X3),tc_prod(tc_set(tc_Datatype__Universe_Onode(X2,X3)),tc_set(tc_Datatype__Universe_Onode(X2,X3))))
    | ~ c_in(c_Pair(X1,X4,tc_set(tc_Datatype__Universe_Onode(X2,X3)),tc_set(tc_Datatype__Universe_Onode(X2,X3))),X6,tc_prod(tc_set(tc_Datatype__Universe_Onode(X2,X3)),tc_set(tc_Datatype__Universe_Onode(X2,X3)))) ),
    inference(literals_permutation,[status(thm)],[c_0_5464]) ).

cnf(c_0_5464_1,axiom,
    ( ~ c_in(c_Pair(X1,X4,tc_set(tc_Datatype__Universe_Onode(X2,X3)),tc_set(tc_Datatype__Universe_Onode(X2,X3))),X6,tc_prod(tc_set(tc_Datatype__Universe_Onode(X2,X3)),tc_set(tc_Datatype__Universe_Onode(X2,X3))))
    | c_in(c_Pair(c_Datatype__Universe_OIn1(X1,X2,X3),c_Datatype__Universe_OIn1(X4,X2,X3),tc_set(tc_Datatype__Universe_Onode(X2,X3)),tc_set(tc_Datatype__Universe_Onode(X2,X3))),c_Datatype__Universe_Odsum(X5,X6,X2,X3),tc_prod(tc_set(tc_Datatype__Universe_Onode(X2,X3)),tc_set(tc_Datatype__Universe_Onode(X2,X3)))) ),
    inference(literals_permutation,[status(thm)],[c_0_5464]) ).

cnf(c_0_5465_0,axiom,
    ( c_in(c_Pair(c_Datatype__Universe_OIn0(X1,X2,X3),c_Datatype__Universe_OIn0(X4,X2,X3),tc_set(tc_Datatype__Universe_Onode(X2,X3)),tc_set(tc_Datatype__Universe_Onode(X2,X3))),c_Datatype__Universe_Odsum(X5,X6,X2,X3),tc_prod(tc_set(tc_Datatype__Universe_Onode(X2,X3)),tc_set(tc_Datatype__Universe_Onode(X2,X3))))
    | ~ c_in(c_Pair(X1,X4,tc_set(tc_Datatype__Universe_Onode(X2,X3)),tc_set(tc_Datatype__Universe_Onode(X2,X3))),X5,tc_prod(tc_set(tc_Datatype__Universe_Onode(X2,X3)),tc_set(tc_Datatype__Universe_Onode(X2,X3)))) ),
    inference(literals_permutation,[status(thm)],[c_0_5465]) ).

cnf(c_0_5465_1,axiom,
    ( ~ c_in(c_Pair(X1,X4,tc_set(tc_Datatype__Universe_Onode(X2,X3)),tc_set(tc_Datatype__Universe_Onode(X2,X3))),X5,tc_prod(tc_set(tc_Datatype__Universe_Onode(X2,X3)),tc_set(tc_Datatype__Universe_Onode(X2,X3))))
    | c_in(c_Pair(c_Datatype__Universe_OIn0(X1,X2,X3),c_Datatype__Universe_OIn0(X4,X2,X3),tc_set(tc_Datatype__Universe_Onode(X2,X3)),tc_set(tc_Datatype__Universe_Onode(X2,X3))),c_Datatype__Universe_Odsum(X5,X6,X2,X3),tc_prod(tc_set(tc_Datatype__Universe_Onode(X2,X3)),tc_set(tc_Datatype__Universe_Onode(X2,X3)))) ),
    inference(literals_permutation,[status(thm)],[c_0_5465]) ).

cnf(c_0_5466_0,axiom,
    ( c_in(c_Main_OuprodE__1(X1,X2,X3,X4,X5),X1,tc_set(tc_Datatype__Universe_Onode(X4,X5)))
    | ~ c_in(X3,c_Datatype__Universe_Ouprod(X1,X2,X4,X5),tc_set(tc_Datatype__Universe_Onode(X4,X5))) ),
    inference(literals_permutation,[status(thm)],[c_0_5466]) ).

cnf(c_0_5466_1,axiom,
    ( ~ c_in(X3,c_Datatype__Universe_Ouprod(X1,X2,X4,X5),tc_set(tc_Datatype__Universe_Onode(X4,X5)))
    | c_in(c_Main_OuprodE__1(X1,X2,X3,X4,X5),X1,tc_set(tc_Datatype__Universe_Onode(X4,X5))) ),
    inference(literals_permutation,[status(thm)],[c_0_5466]) ).

cnf(c_0_5467_0,axiom,
    ( c_in(c_Main_OuprodE__2(X1,X2,X3,X4,X5),X2,tc_set(tc_Datatype__Universe_Onode(X4,X5)))
    | ~ c_in(X3,c_Datatype__Universe_Ouprod(X1,X2,X4,X5),tc_set(tc_Datatype__Universe_Onode(X4,X5))) ),
    inference(literals_permutation,[status(thm)],[c_0_5467]) ).

cnf(c_0_5467_1,axiom,
    ( ~ c_in(X3,c_Datatype__Universe_Ouprod(X1,X2,X4,X5),tc_set(tc_Datatype__Universe_Onode(X4,X5)))
    | c_in(c_Main_OuprodE__2(X1,X2,X3,X4,X5),X2,tc_set(tc_Datatype__Universe_Onode(X4,X5))) ),
    inference(literals_permutation,[status(thm)],[c_0_5467]) ).

cnf(c_0_5468_0,axiom,
    ( c_in(c_Main_OImageE__1(X1,X2,X3,X4,X5),X1,X4)
    | ~ c_in(X2,c_Relation_OImage(X3,X1,X4,X5),X5) ),
    inference(literals_permutation,[status(thm)],[c_0_5468]) ).

cnf(c_0_5468_1,axiom,
    ( ~ c_in(X2,c_Relation_OImage(X3,X1,X4,X5),X5)
    | c_in(c_Main_OImageE__1(X1,X2,X3,X4,X5),X1,X4) ),
    inference(literals_permutation,[status(thm)],[c_0_5468]) ).

cnf(c_0_5469_0,axiom,
    ( c_in(c_Pair(c_Main_OconverseE__1(X1,X2,X3,X4),c_Main_OconverseE__2(X1,X2,X3,X4),X3,X4),X1,tc_prod(X3,X4))
    | ~ c_in(X2,c_Relation_Oconverse(X1,X3,X4),tc_prod(X4,X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_5469]) ).

cnf(c_0_5469_1,axiom,
    ( ~ c_in(X2,c_Relation_Oconverse(X1,X3,X4),tc_prod(X4,X3))
    | c_in(c_Pair(c_Main_OconverseE__1(X1,X2,X3,X4),c_Main_OconverseE__2(X1,X2,X3,X4),X3,X4),X1,tc_prod(X3,X4)) ),
    inference(literals_permutation,[status(thm)],[c_0_5469]) ).

cnf(c_0_5470_0,axiom,
    ( ~ c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Ortrancl(X4,X3),tc_prod(X3,X3))
    | ~ c_Wellfounded__Recursion_Owf(c_insert(c_Pair(X2,X1,X3,X3),X4,tc_prod(X3,X3)),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5470]) ).

cnf(c_0_5470_1,axiom,
    ( ~ c_Wellfounded__Recursion_Owf(c_insert(c_Pair(X2,X1,X3,X3),X4,tc_prod(X3,X3)),X3)
    | ~ c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Ortrancl(X4,X3),tc_prod(X3,X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_5470]) ).

cnf(c_0_5471_0,axiom,
    ( ~ c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Ortrancl(X4,X3),tc_prod(X3,X3))
    | ~ c_Wellfounded__Recursion_Oacyclic(c_insert(c_Pair(X2,X1,X3,X3),X4,tc_prod(X3,X3)),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5471]) ).

cnf(c_0_5471_1,axiom,
    ( ~ c_Wellfounded__Recursion_Oacyclic(c_insert(c_Pair(X2,X1,X3,X3),X4,tc_prod(X3,X3)),X3)
    | ~ c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Ortrancl(X4,X3),tc_prod(X3,X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_5471]) ).

cnf(c_0_5472_0,axiom,
    ( c_in(c_Main_OusumE__2(X1,X2,X3,X4),X1,tc_set(tc_Datatype__Universe_Onode(X3,X4)))
    | c_in(c_Main_OusumE__1(X5,X2,X3,X4),X5,tc_set(tc_Datatype__Universe_Onode(X3,X4)))
    | ~ c_in(X2,c_Datatype__Universe_Ousum(X5,X1,X3,X4),tc_set(tc_Datatype__Universe_Onode(X3,X4))) ),
    inference(literals_permutation,[status(thm)],[c_0_5472]) ).

cnf(c_0_5472_1,axiom,
    ( c_in(c_Main_OusumE__1(X5,X2,X3,X4),X5,tc_set(tc_Datatype__Universe_Onode(X3,X4)))
    | c_in(c_Main_OusumE__2(X1,X2,X3,X4),X1,tc_set(tc_Datatype__Universe_Onode(X3,X4)))
    | ~ c_in(X2,c_Datatype__Universe_Ousum(X5,X1,X3,X4),tc_set(tc_Datatype__Universe_Onode(X3,X4))) ),
    inference(literals_permutation,[status(thm)],[c_0_5472]) ).

cnf(c_0_5472_2,axiom,
    ( ~ c_in(X2,c_Datatype__Universe_Ousum(X5,X1,X3,X4),tc_set(tc_Datatype__Universe_Onode(X3,X4)))
    | c_in(c_Main_OusumE__1(X5,X2,X3,X4),X5,tc_set(tc_Datatype__Universe_Onode(X3,X4)))
    | c_in(c_Main_OusumE__2(X1,X2,X3,X4),X1,tc_set(tc_Datatype__Universe_Onode(X3,X4))) ),
    inference(literals_permutation,[status(thm)],[c_0_5472]) ).

cnf(c_0_5473_0,axiom,
    ( c_Datatype__Universe_OIn1(c_Main_OusumE__2(X2,X1,X3,X4),X3,X4) = X1
    | c_in(c_Main_OusumE__1(X5,X1,X3,X4),X5,tc_set(tc_Datatype__Universe_Onode(X3,X4)))
    | ~ c_in(X1,c_Datatype__Universe_Ousum(X5,X2,X3,X4),tc_set(tc_Datatype__Universe_Onode(X3,X4))) ),
    inference(literals_permutation,[status(thm)],[c_0_5473]) ).

cnf(c_0_5473_1,axiom,
    ( c_in(c_Main_OusumE__1(X5,X1,X3,X4),X5,tc_set(tc_Datatype__Universe_Onode(X3,X4)))
    | c_Datatype__Universe_OIn1(c_Main_OusumE__2(X2,X1,X3,X4),X3,X4) = X1
    | ~ c_in(X1,c_Datatype__Universe_Ousum(X5,X2,X3,X4),tc_set(tc_Datatype__Universe_Onode(X3,X4))) ),
    inference(literals_permutation,[status(thm)],[c_0_5473]) ).

cnf(c_0_5473_2,axiom,
    ( ~ c_in(X1,c_Datatype__Universe_Ousum(X5,X2,X3,X4),tc_set(tc_Datatype__Universe_Onode(X3,X4)))
    | c_in(c_Main_OusumE__1(X5,X1,X3,X4),X5,tc_set(tc_Datatype__Universe_Onode(X3,X4)))
    | c_Datatype__Universe_OIn1(c_Main_OusumE__2(X2,X1,X3,X4),X3,X4) = X1 ),
    inference(literals_permutation,[status(thm)],[c_0_5473]) ).

cnf(c_0_5474_0,axiom,
    ( c_Datatype__Universe_OIn0(c_Main_OusumE__1(X2,X1,X3,X4),X3,X4) = X1
    | c_in(c_Main_OusumE__2(X5,X1,X3,X4),X5,tc_set(tc_Datatype__Universe_Onode(X3,X4)))
    | ~ c_in(X1,c_Datatype__Universe_Ousum(X2,X5,X3,X4),tc_set(tc_Datatype__Universe_Onode(X3,X4))) ),
    inference(literals_permutation,[status(thm)],[c_0_5474]) ).

cnf(c_0_5474_1,axiom,
    ( c_in(c_Main_OusumE__2(X5,X1,X3,X4),X5,tc_set(tc_Datatype__Universe_Onode(X3,X4)))
    | c_Datatype__Universe_OIn0(c_Main_OusumE__1(X2,X1,X3,X4),X3,X4) = X1
    | ~ c_in(X1,c_Datatype__Universe_Ousum(X2,X5,X3,X4),tc_set(tc_Datatype__Universe_Onode(X3,X4))) ),
    inference(literals_permutation,[status(thm)],[c_0_5474]) ).

cnf(c_0_5474_2,axiom,
    ( ~ c_in(X1,c_Datatype__Universe_Ousum(X2,X5,X3,X4),tc_set(tc_Datatype__Universe_Onode(X3,X4)))
    | c_in(c_Main_OusumE__2(X5,X1,X3,X4),X5,tc_set(tc_Datatype__Universe_Onode(X3,X4)))
    | c_Datatype__Universe_OIn0(c_Main_OusumE__1(X2,X1,X3,X4),X3,X4) = X1 ),
    inference(literals_permutation,[status(thm)],[c_0_5474]) ).

cnf(c_0_5475_0,axiom,
    ( c_Datatype__Universe_OIn1(c_Main_OusumE__2(X2,X1,X3,X4),X3,X4) = X1
    | c_Datatype__Universe_OIn0(c_Main_OusumE__1(X5,X1,X3,X4),X3,X4) = X1
    | ~ c_in(X1,c_Datatype__Universe_Ousum(X5,X2,X3,X4),tc_set(tc_Datatype__Universe_Onode(X3,X4))) ),
    inference(literals_permutation,[status(thm)],[c_0_5475]) ).

cnf(c_0_5475_1,axiom,
    ( c_Datatype__Universe_OIn0(c_Main_OusumE__1(X5,X1,X3,X4),X3,X4) = X1
    | c_Datatype__Universe_OIn1(c_Main_OusumE__2(X2,X1,X3,X4),X3,X4) = X1
    | ~ c_in(X1,c_Datatype__Universe_Ousum(X5,X2,X3,X4),tc_set(tc_Datatype__Universe_Onode(X3,X4))) ),
    inference(literals_permutation,[status(thm)],[c_0_5475]) ).

cnf(c_0_5475_2,axiom,
    ( ~ c_in(X1,c_Datatype__Universe_Ousum(X5,X2,X3,X4),tc_set(tc_Datatype__Universe_Onode(X3,X4)))
    | c_Datatype__Universe_OIn0(c_Main_OusumE__1(X5,X1,X3,X4),X3,X4) = X1
    | c_Datatype__Universe_OIn1(c_Main_OusumE__2(X2,X1,X3,X4),X3,X4) = X1 ),
    inference(literals_permutation,[status(thm)],[c_0_5475]) ).

cnf(c_0_5476_0,axiom,
    ( c_Sum__Type_OInr(c_Main_OPlusE__2(X2,X1,X3,X4),X3,X4) = X1
    | c_Sum__Type_OInl(c_Main_OPlusE__1(X5,X1,X4,X3),X4,X3) = X1
    | ~ c_in(X1,c_Sum__Type_OPlus(X5,X2,X4,X3),tc_sum(X4,X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_5476]) ).

cnf(c_0_5476_1,axiom,
    ( c_Sum__Type_OInl(c_Main_OPlusE__1(X5,X1,X4,X3),X4,X3) = X1
    | c_Sum__Type_OInr(c_Main_OPlusE__2(X2,X1,X3,X4),X3,X4) = X1
    | ~ c_in(X1,c_Sum__Type_OPlus(X5,X2,X4,X3),tc_sum(X4,X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_5476]) ).

cnf(c_0_5476_2,axiom,
    ( ~ c_in(X1,c_Sum__Type_OPlus(X5,X2,X4,X3),tc_sum(X4,X3))
    | c_Sum__Type_OInl(c_Main_OPlusE__1(X5,X1,X4,X3),X4,X3) = X1
    | c_Sum__Type_OInr(c_Main_OPlusE__2(X2,X1,X3,X4),X3,X4) = X1 ),
    inference(literals_permutation,[status(thm)],[c_0_5476]) ).

cnf(c_0_5477_0,axiom,
    ( c_Sum__Type_OInr(c_Main_OPlusE__2(X2,X1,X3,X4),X3,X4) = X1
    | c_in(c_Main_OPlusE__1(X5,X1,X4,X3),X5,X4)
    | ~ c_in(X1,c_Sum__Type_OPlus(X5,X2,X4,X3),tc_sum(X4,X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_5477]) ).

cnf(c_0_5477_1,axiom,
    ( c_in(c_Main_OPlusE__1(X5,X1,X4,X3),X5,X4)
    | c_Sum__Type_OInr(c_Main_OPlusE__2(X2,X1,X3,X4),X3,X4) = X1
    | ~ c_in(X1,c_Sum__Type_OPlus(X5,X2,X4,X3),tc_sum(X4,X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_5477]) ).

cnf(c_0_5477_2,axiom,
    ( ~ c_in(X1,c_Sum__Type_OPlus(X5,X2,X4,X3),tc_sum(X4,X3))
    | c_in(c_Main_OPlusE__1(X5,X1,X4,X3),X5,X4)
    | c_Sum__Type_OInr(c_Main_OPlusE__2(X2,X1,X3,X4),X3,X4) = X1 ),
    inference(literals_permutation,[status(thm)],[c_0_5477]) ).

cnf(c_0_5478_0,axiom,
    ( c_Sum__Type_OInl(c_Main_OPlusE__1(X2,X1,X3,X4),X3,X4) = X1
    | c_in(c_Main_OPlusE__2(X5,X1,X4,X3),X5,X4)
    | ~ c_in(X1,c_Sum__Type_OPlus(X2,X5,X3,X4),tc_sum(X3,X4)) ),
    inference(literals_permutation,[status(thm)],[c_0_5478]) ).

cnf(c_0_5478_1,axiom,
    ( c_in(c_Main_OPlusE__2(X5,X1,X4,X3),X5,X4)
    | c_Sum__Type_OInl(c_Main_OPlusE__1(X2,X1,X3,X4),X3,X4) = X1
    | ~ c_in(X1,c_Sum__Type_OPlus(X2,X5,X3,X4),tc_sum(X3,X4)) ),
    inference(literals_permutation,[status(thm)],[c_0_5478]) ).

cnf(c_0_5478_2,axiom,
    ( ~ c_in(X1,c_Sum__Type_OPlus(X2,X5,X3,X4),tc_sum(X3,X4))
    | c_in(c_Main_OPlusE__2(X5,X1,X4,X3),X5,X4)
    | c_Sum__Type_OInl(c_Main_OPlusE__1(X2,X1,X3,X4),X3,X4) = X1 ),
    inference(literals_permutation,[status(thm)],[c_0_5478]) ).

cnf(c_0_5479_0,axiom,
    ( c_in(c_Main_OPlusE__2(X1,X2,X3,X4),X1,X3)
    | c_in(c_Main_OPlusE__1(X5,X2,X4,X3),X5,X4)
    | ~ c_in(X2,c_Sum__Type_OPlus(X5,X1,X4,X3),tc_sum(X4,X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_5479]) ).

cnf(c_0_5479_1,axiom,
    ( c_in(c_Main_OPlusE__1(X5,X2,X4,X3),X5,X4)
    | c_in(c_Main_OPlusE__2(X1,X2,X3,X4),X1,X3)
    | ~ c_in(X2,c_Sum__Type_OPlus(X5,X1,X4,X3),tc_sum(X4,X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_5479]) ).

cnf(c_0_5479_2,axiom,
    ( ~ c_in(X2,c_Sum__Type_OPlus(X5,X1,X4,X3),tc_sum(X4,X3))
    | c_in(c_Main_OPlusE__1(X5,X2,X4,X3),X5,X4)
    | c_in(c_Main_OPlusE__2(X1,X2,X3,X4),X1,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5479]) ).

cnf(c_0_5480_0,axiom,
    ( c_Wellfounded__Recursion_Owf(X1,X2)
    | ~ c_Wellfounded__Recursion_Owf(c_insert(c_Pair(X3,X4,X2,X2),X1,tc_prod(X2,X2)),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5480]) ).

cnf(c_0_5480_1,axiom,
    ( ~ c_Wellfounded__Recursion_Owf(c_insert(c_Pair(X3,X4,X2,X2),X1,tc_prod(X2,X2)),X2)
    | c_Wellfounded__Recursion_Owf(X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5480]) ).

cnf(c_0_5481_0,axiom,
    ( c_Wellfounded__Recursion_Oacyclic(X1,X2)
    | ~ c_Wellfounded__Recursion_Oacyclic(c_insert(c_Pair(X3,X4,X2,X2),X1,tc_prod(X2,X2)),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5481]) ).

cnf(c_0_5481_1,axiom,
    ( ~ c_Wellfounded__Recursion_Oacyclic(c_insert(c_Pair(X3,X4,X2,X2),X1,tc_prod(X2,X2)),X2)
    | c_Wellfounded__Recursion_Oacyclic(X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5481]) ).

cnf(c_0_5482_0,axiom,
    ( c_in(c_Pair(c_Main_ORangeE__1(X1,X2,X3,X4),X1,X4,X3),X2,tc_prod(X4,X3))
    | ~ c_in(X1,c_Relation_ORange(X2,X4,X3),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5482]) ).

cnf(c_0_5482_1,axiom,
    ( ~ c_in(X1,c_Relation_ORange(X2,X4,X3),X3)
    | c_in(c_Pair(c_Main_ORangeE__1(X1,X2,X3,X4),X1,X4,X3),X2,tc_prod(X4,X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_5482]) ).

cnf(c_0_5483_0,axiom,
    ( c_in(c_Pair(X1,c_Main_ODomainE__1(X1,X2,X3,X4),X3,X4),X2,tc_prod(X3,X4))
    | ~ c_in(X1,c_Relation_ODomain(X2,X3,X4),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5483]) ).

cnf(c_0_5483_1,axiom,
    ( ~ c_in(X1,c_Relation_ODomain(X2,X3,X4),X3)
    | c_in(c_Pair(X1,c_Main_ODomainE__1(X1,X2,X3,X4),X3,X4),X2,tc_prod(X3,X4)) ),
    inference(literals_permutation,[status(thm)],[c_0_5483]) ).

cnf(c_0_5484_0,axiom,
    ( c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Ortrancl(X4,X3),tc_prod(X3,X3))
    | c_Wellfounded__Recursion_Owf(c_insert(c_Pair(X2,X1,X3,X3),X4,tc_prod(X3,X3)),X3)
    | ~ c_Wellfounded__Recursion_Owf(X4,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5484]) ).

cnf(c_0_5484_1,axiom,
    ( c_Wellfounded__Recursion_Owf(c_insert(c_Pair(X2,X1,X3,X3),X4,tc_prod(X3,X3)),X3)
    | c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Ortrancl(X4,X3),tc_prod(X3,X3))
    | ~ c_Wellfounded__Recursion_Owf(X4,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5484]) ).

cnf(c_0_5484_2,axiom,
    ( ~ c_Wellfounded__Recursion_Owf(X4,X3)
    | c_Wellfounded__Recursion_Owf(c_insert(c_Pair(X2,X1,X3,X3),X4,tc_prod(X3,X3)),X3)
    | c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Ortrancl(X4,X3),tc_prod(X3,X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_5484]) ).

cnf(c_0_5485_0,axiom,
    ( c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Ortrancl(X4,X3),tc_prod(X3,X3))
    | c_Wellfounded__Recursion_Oacyclic(c_insert(c_Pair(X2,X1,X3,X3),X4,tc_prod(X3,X3)),X3)
    | ~ c_Wellfounded__Recursion_Oacyclic(X4,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5485]) ).

cnf(c_0_5485_1,axiom,
    ( c_Wellfounded__Recursion_Oacyclic(c_insert(c_Pair(X2,X1,X3,X3),X4,tc_prod(X3,X3)),X3)
    | c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Ortrancl(X4,X3),tc_prod(X3,X3))
    | ~ c_Wellfounded__Recursion_Oacyclic(X4,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5485]) ).

cnf(c_0_5485_2,axiom,
    ( ~ c_Wellfounded__Recursion_Oacyclic(X4,X3)
    | c_Wellfounded__Recursion_Oacyclic(c_insert(c_Pair(X2,X1,X3,X3),X4,tc_prod(X3,X3)),X3)
    | c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Ortrancl(X4,X3),tc_prod(X3,X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_5485]) ).

cnf(c_0_5486_0,axiom,
    ( c_in(c_Pair(X1,X2,X3,X4),X5,tc_prod(X3,X4))
    | ~ c_in(X2,c_Relation_OImage(X5,c_insert(X1,c_emptyset,X3),X3,X4),X4) ),
    inference(literals_permutation,[status(thm)],[c_0_5486]) ).

cnf(c_0_5486_1,axiom,
    ( ~ c_in(X2,c_Relation_OImage(X5,c_insert(X1,c_emptyset,X3),X3,X4),X4)
    | c_in(c_Pair(X1,X2,X3,X4),X5,tc_prod(X3,X4)) ),
    inference(literals_permutation,[status(thm)],[c_0_5486]) ).

cnf(c_0_5487_0,axiom,
    ( c_Divides_Oop_Advd(X1,X2,tc_nat)
    | ~ c_Divides_Oop_Advd(X1,c_GCD_Ogcd(c_Pair(X3,X2,tc_nat,tc_nat)),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_5487]) ).

cnf(c_0_5487_1,axiom,
    ( ~ c_Divides_Oop_Advd(X1,c_GCD_Ogcd(c_Pair(X3,X2,tc_nat,tc_nat)),tc_nat)
    | c_Divides_Oop_Advd(X1,X2,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_5487]) ).

cnf(c_0_5488_0,axiom,
    ( c_Divides_Oop_Advd(X1,X2,tc_nat)
    | ~ c_Divides_Oop_Advd(X1,c_GCD_Ogcd(c_Pair(X2,X3,tc_nat,tc_nat)),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_5488]) ).

cnf(c_0_5488_1,axiom,
    ( ~ c_Divides_Oop_Advd(X1,c_GCD_Ogcd(c_Pair(X2,X3,tc_nat,tc_nat)),tc_nat)
    | c_Divides_Oop_Advd(X1,X2,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_5488]) ).

cnf(c_0_5489_0,axiom,
    ( c_in(X1,c_Relation_OImage(X2,c_insert(X3,c_emptyset,X4),X4,X5),X5)
    | ~ c_in(c_Pair(X3,X1,X4,X5),X2,tc_prod(X4,X5)) ),
    inference(literals_permutation,[status(thm)],[c_0_5489]) ).

cnf(c_0_5489_1,axiom,
    ( ~ c_in(c_Pair(X3,X1,X4,X5),X2,tc_prod(X4,X5))
    | c_in(X1,c_Relation_OImage(X2,c_insert(X3,c_emptyset,X4),X4,X5),X5) ),
    inference(literals_permutation,[status(thm)],[c_0_5489]) ).

cnf(c_0_5490_0,axiom,
    ( c_in(c_Pair(X1,X2,X3,X4),X5,tc_prod(X3,X4))
    | ~ c_in(c_Pair(X2,X1,X4,X3),c_Relation_Oconverse(X5,X3,X4),tc_prod(X4,X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_5490]) ).

cnf(c_0_5490_1,axiom,
    ( ~ c_in(c_Pair(X2,X1,X4,X3),c_Relation_Oconverse(X5,X3,X4),tc_prod(X4,X3))
    | c_in(c_Pair(X1,X2,X3,X4),X5,tc_prod(X3,X4)) ),
    inference(literals_permutation,[status(thm)],[c_0_5490]) ).

cnf(c_0_5491_0,axiom,
    ( c_in(c_Pair(X1,X2,X3,X4),c_Relation_Oconverse(X5,X4,X3),tc_prod(X3,X4))
    | ~ c_in(c_Pair(X2,X1,X4,X3),X5,tc_prod(X4,X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_5491]) ).

cnf(c_0_5491_1,axiom,
    ( ~ c_in(c_Pair(X2,X1,X4,X3),X5,tc_prod(X4,X3))
    | c_in(c_Pair(X1,X2,X3,X4),c_Relation_Oconverse(X5,X4,X3),tc_prod(X3,X4)) ),
    inference(literals_permutation,[status(thm)],[c_0_5491]) ).

cnf(c_0_5492_0,axiom,
    ( c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Ortrancl(X4,X3),tc_prod(X3,X3))
    | ~ c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Otrancl(X4,X3),tc_prod(X3,X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_5492]) ).

cnf(c_0_5492_1,axiom,
    ( ~ c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Otrancl(X4,X3),tc_prod(X3,X3))
    | c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Ortrancl(X4,X3),tc_prod(X3,X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_5492]) ).

cnf(c_0_5493_0,axiom,
    ( c_in(X1,c_Relation_OImage(X2,X3,X4,X5),X5)
    | ~ c_in(c_Pair(X6,X1,X4,X5),X2,tc_prod(X4,X5))
    | ~ c_in(X6,X3,X4) ),
    inference(literals_permutation,[status(thm)],[c_0_5493]) ).

cnf(c_0_5493_1,axiom,
    ( ~ c_in(c_Pair(X6,X1,X4,X5),X2,tc_prod(X4,X5))
    | c_in(X1,c_Relation_OImage(X2,X3,X4,X5),X5)
    | ~ c_in(X6,X3,X4) ),
    inference(literals_permutation,[status(thm)],[c_0_5493]) ).

cnf(c_0_5493_2,axiom,
    ( ~ c_in(X6,X3,X4)
    | ~ c_in(c_Pair(X6,X1,X4,X5),X2,tc_prod(X4,X5))
    | c_in(X1,c_Relation_OImage(X2,X3,X4,X5),X5) ),
    inference(literals_permutation,[status(thm)],[c_0_5493]) ).

cnf(c_0_5494_0,axiom,
    ( c_Pair(c_Main_OconverseE__2(X2,X1,X3,X4),c_Main_OconverseE__1(X2,X1,X3,X4),X4,X3) = X1
    | ~ c_in(X1,c_Relation_Oconverse(X2,X3,X4),tc_prod(X4,X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_5494]) ).

cnf(c_0_5494_1,axiom,
    ( ~ c_in(X1,c_Relation_Oconverse(X2,X3,X4),tc_prod(X4,X3))
    | c_Pair(c_Main_OconverseE__2(X2,X1,X3,X4),c_Main_OconverseE__1(X2,X1,X3,X4),X4,X3) = X1 ),
    inference(literals_permutation,[status(thm)],[c_0_5494]) ).

cnf(c_0_5495_0,axiom,
    ( c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Otrancl(X4,X3),tc_prod(X3,X3))
    | ~ c_in(c_Pair(X1,X2,X3,X3),X4,tc_prod(X3,X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_5495]) ).

cnf(c_0_5495_1,axiom,
    ( ~ c_in(c_Pair(X1,X2,X3,X3),X4,tc_prod(X3,X3))
    | c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Otrancl(X4,X3),tc_prod(X3,X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_5495]) ).

cnf(c_0_5496_0,axiom,
    ( c_in(c_Datatype__Universe_OScons(X1,X2,X3,X4),c_Datatype__Universe_Ouprod(X5,X6,X3,X4),tc_set(tc_Datatype__Universe_Onode(X3,X4)))
    | ~ c_in(X1,X5,tc_set(tc_Datatype__Universe_Onode(X3,X4)))
    | ~ c_in(X2,X6,tc_set(tc_Datatype__Universe_Onode(X3,X4))) ),
    inference(literals_permutation,[status(thm)],[c_0_5496]) ).

cnf(c_0_5496_1,axiom,
    ( ~ c_in(X1,X5,tc_set(tc_Datatype__Universe_Onode(X3,X4)))
    | c_in(c_Datatype__Universe_OScons(X1,X2,X3,X4),c_Datatype__Universe_Ouprod(X5,X6,X3,X4),tc_set(tc_Datatype__Universe_Onode(X3,X4)))
    | ~ c_in(X2,X6,tc_set(tc_Datatype__Universe_Onode(X3,X4))) ),
    inference(literals_permutation,[status(thm)],[c_0_5496]) ).

cnf(c_0_5496_2,axiom,
    ( ~ c_in(X2,X6,tc_set(tc_Datatype__Universe_Onode(X3,X4)))
    | ~ c_in(X1,X5,tc_set(tc_Datatype__Universe_Onode(X3,X4)))
    | c_in(c_Datatype__Universe_OScons(X1,X2,X3,X4),c_Datatype__Universe_Ouprod(X5,X6,X3,X4),tc_set(tc_Datatype__Universe_Onode(X3,X4))) ),
    inference(literals_permutation,[status(thm)],[c_0_5496]) ).

cnf(c_0_5497_0,axiom,
    ( c_Divides_Oop_Advd(X1,c_GCD_Ogcd(c_Pair(X2,X3,tc_nat,tc_nat)),tc_nat)
    | ~ c_Divides_Oop_Advd(X1,X2,tc_nat)
    | ~ c_Divides_Oop_Advd(X1,X3,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_5497]) ).

cnf(c_0_5497_1,axiom,
    ( ~ c_Divides_Oop_Advd(X1,X2,tc_nat)
    | c_Divides_Oop_Advd(X1,c_GCD_Ogcd(c_Pair(X2,X3,tc_nat,tc_nat)),tc_nat)
    | ~ c_Divides_Oop_Advd(X1,X3,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_5497]) ).

cnf(c_0_5497_2,axiom,
    ( ~ c_Divides_Oop_Advd(X1,X3,tc_nat)
    | ~ c_Divides_Oop_Advd(X1,X2,tc_nat)
    | c_Divides_Oop_Advd(X1,c_GCD_Ogcd(c_Pair(X2,X3,tc_nat,tc_nat)),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_5497]) ).

cnf(c_0_5498_0,axiom,
    ( c_in(X1,c_Relation_ORange(X2,X3,X4),X4)
    | ~ c_in(c_Pair(X5,X1,X3,X4),X2,tc_prod(X3,X4)) ),
    inference(literals_permutation,[status(thm)],[c_0_5498]) ).

cnf(c_0_5498_1,axiom,
    ( ~ c_in(c_Pair(X5,X1,X3,X4),X2,tc_prod(X3,X4))
    | c_in(X1,c_Relation_ORange(X2,X3,X4),X4) ),
    inference(literals_permutation,[status(thm)],[c_0_5498]) ).

cnf(c_0_5499_0,axiom,
    ( c_in(X1,c_Relation_ODomain(X2,X3,X4),X3)
    | ~ c_in(c_Pair(X1,X5,X3,X4),X2,tc_prod(X3,X4)) ),
    inference(literals_permutation,[status(thm)],[c_0_5499]) ).

cnf(c_0_5499_1,axiom,
    ( ~ c_in(c_Pair(X1,X5,X3,X4),X2,tc_prod(X3,X4))
    | c_in(X1,c_Relation_ODomain(X2,X3,X4),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5499]) ).

cnf(c_0_5500_0,axiom,
    ( c_lessequals(c_Union(X1,X2),X3,tc_set(X2))
    | c_lessequals(X4,c_Union(X1,X2),tc_set(X2))
    | ~ c_lessequals(X4,c_Zorn_OUnion__lemma0__1(X3,X4,X1,X2),tc_set(X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_5500]) ).

cnf(c_0_5500_1,axiom,
    ( c_lessequals(X4,c_Union(X1,X2),tc_set(X2))
    | c_lessequals(c_Union(X1,X2),X3,tc_set(X2))
    | ~ c_lessequals(X4,c_Zorn_OUnion__lemma0__1(X3,X4,X1,X2),tc_set(X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_5500]) ).

cnf(c_0_5500_2,axiom,
    ( ~ c_lessequals(X4,c_Zorn_OUnion__lemma0__1(X3,X4,X1,X2),tc_set(X2))
    | c_lessequals(X4,c_Union(X1,X2),tc_set(X2))
    | c_lessequals(c_Union(X1,X2),X3,tc_set(X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_5500]) ).

cnf(c_0_5501_0,axiom,
    ( c_lessequals(c_Union(X1,X2),X3,tc_set(X2))
    | c_lessequals(X4,c_Union(X1,X2),tc_set(X2))
    | ~ c_lessequals(c_Zorn_OUnion__lemma0__1(X3,X4,X1,X2),X3,tc_set(X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_5501]) ).

cnf(c_0_5501_1,axiom,
    ( c_lessequals(X4,c_Union(X1,X2),tc_set(X2))
    | c_lessequals(c_Union(X1,X2),X3,tc_set(X2))
    | ~ c_lessequals(c_Zorn_OUnion__lemma0__1(X3,X4,X1,X2),X3,tc_set(X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_5501]) ).

cnf(c_0_5501_2,axiom,
    ( ~ c_lessequals(c_Zorn_OUnion__lemma0__1(X3,X4,X1,X2),X3,tc_set(X2))
    | c_lessequals(X4,c_Union(X1,X2),tc_set(X2))
    | c_lessequals(c_Union(X1,X2),X3,tc_set(X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_5501]) ).

cnf(c_0_5504_0,axiom,
    ( X1 = c_List_Olist_ONil
    | ~ c_in(c_Pair(X1,c_List_Olist_ONil,tc_List_Olist(X2),tc_List_Olist(X2)),c_List_Olistrel(X3,X2),tc_prod(tc_List_Olist(X2),tc_List_Olist(X2))) ),
    inference(literals_permutation,[status(thm)],[c_0_5504]) ).

cnf(c_0_5504_1,axiom,
    ( ~ c_in(c_Pair(X1,c_List_Olist_ONil,tc_List_Olist(X2),tc_List_Olist(X2)),c_List_Olistrel(X3,X2),tc_prod(tc_List_Olist(X2),tc_List_Olist(X2)))
    | X1 = c_List_Olist_ONil ),
    inference(literals_permutation,[status(thm)],[c_0_5504]) ).

cnf(c_0_5505_0,axiom,
    ( X1 = c_List_Olist_ONil
    | ~ c_in(c_Pair(c_List_Olist_ONil,X1,tc_List_Olist(X2),tc_List_Olist(X2)),c_List_Olistrel(X3,X2),tc_prod(tc_List_Olist(X2),tc_List_Olist(X2))) ),
    inference(literals_permutation,[status(thm)],[c_0_5505]) ).

cnf(c_0_5505_1,axiom,
    ( ~ c_in(c_Pair(c_List_Olist_ONil,X1,tc_List_Olist(X2),tc_List_Olist(X2)),c_List_Olistrel(X3,X2),tc_prod(tc_List_Olist(X2),tc_List_Olist(X2)))
    | X1 = c_List_Olist_ONil ),
    inference(literals_permutation,[status(thm)],[c_0_5505]) ).

cnf(c_0_5508_0,axiom,
    ( c_less(X1,X2,tc_nat)
    | ~ c_in(c_Pair(X1,X2,tc_nat,tc_nat),c_Wellfounded__Relations_Oless__than,tc_prod(tc_nat,tc_nat)) ),
    inference(literals_permutation,[status(thm)],[c_0_5508]) ).

cnf(c_0_5508_1,axiom,
    ( ~ c_in(c_Pair(X1,X2,tc_nat,tc_nat),c_Wellfounded__Relations_Oless__than,tc_prod(tc_nat,tc_nat))
    | c_less(X1,X2,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_5508]) ).

cnf(c_0_5509_0,axiom,
    ( X1 = X2
    | ~ c_in(c_Pair(X1,X2,X3,X3),c_Relation_OId,tc_prod(X3,X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_5509]) ).

cnf(c_0_5509_1,axiom,
    ( ~ c_in(c_Pair(X1,X2,X3,X3),c_Relation_OId,tc_prod(X3,X3))
    | X1 = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_5509]) ).

cnf(c_0_5510_0,axiom,
    ( c_in(c_Datatype__Universe_OIn1(X1,X2,X3),c_Datatype__Universe_Ousum(X4,X5,X2,X3),tc_set(tc_Datatype__Universe_Onode(X2,X3)))
    | ~ c_in(X1,X5,tc_set(tc_Datatype__Universe_Onode(X2,X3))) ),
    inference(literals_permutation,[status(thm)],[c_0_5510]) ).

cnf(c_0_5510_1,axiom,
    ( ~ c_in(X1,X5,tc_set(tc_Datatype__Universe_Onode(X2,X3)))
    | c_in(c_Datatype__Universe_OIn1(X1,X2,X3),c_Datatype__Universe_Ousum(X4,X5,X2,X3),tc_set(tc_Datatype__Universe_Onode(X2,X3))) ),
    inference(literals_permutation,[status(thm)],[c_0_5510]) ).

cnf(c_0_5511_0,axiom,
    ( c_in(c_Datatype__Universe_OIn0(X1,X2,X3),c_Datatype__Universe_Ousum(X4,X5,X2,X3),tc_set(tc_Datatype__Universe_Onode(X2,X3)))
    | ~ c_in(X1,X4,tc_set(tc_Datatype__Universe_Onode(X2,X3))) ),
    inference(literals_permutation,[status(thm)],[c_0_5511]) ).

cnf(c_0_5511_1,axiom,
    ( ~ c_in(X1,X4,tc_set(tc_Datatype__Universe_Onode(X2,X3)))
    | c_in(c_Datatype__Universe_OIn0(X1,X2,X3),c_Datatype__Universe_Ousum(X4,X5,X2,X3),tc_set(tc_Datatype__Universe_Onode(X2,X3))) ),
    inference(literals_permutation,[status(thm)],[c_0_5511]) ).

cnf(c_0_5512_0,axiom,
    ( c_in(c_minus(X1,X2,tc_set(X3)),c_Finite__Set_OFinites,tc_set(X3))
    | ~ c_in(c_minus(X1,c_insert(X4,X2,X3),tc_set(X3)),c_Finite__Set_OFinites,tc_set(X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_5512]) ).

cnf(c_0_5512_1,axiom,
    ( ~ c_in(c_minus(X1,c_insert(X4,X2,X3),tc_set(X3)),c_Finite__Set_OFinites,tc_set(X3))
    | c_in(c_minus(X1,X2,tc_set(X3)),c_Finite__Set_OFinites,tc_set(X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_5512]) ).

cnf(c_0_5513_0,axiom,
    ( X1 = X2
    | c_Pair(X3,X1,X4,X5) != c_Pair(X6,X2,X4,X5) ),
    inference(literals_permutation,[status(thm)],[c_0_5513]) ).

cnf(c_0_5513_1,axiom,
    ( c_Pair(X3,X1,X4,X5) != c_Pair(X6,X2,X4,X5)
    | X1 = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_5513]) ).

cnf(c_0_5514_0,axiom,
    ( X1 = X2
    | c_Pair(X1,X3,X4,X5) != c_Pair(X2,X6,X4,X5) ),
    inference(literals_permutation,[status(thm)],[c_0_5514]) ).

cnf(c_0_5514_1,axiom,
    ( c_Pair(X1,X3,X4,X5) != c_Pair(X2,X6,X4,X5)
    | X1 = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_5514]) ).

cnf(c_0_5515_0,axiom,
    ( X1 = X2
    | c_Datatype__Universe_OScons(X3,X1,X4,X5) != c_Datatype__Universe_OScons(X6,X2,X4,X5) ),
    inference(literals_permutation,[status(thm)],[c_0_5515]) ).

cnf(c_0_5515_1,axiom,
    ( c_Datatype__Universe_OScons(X3,X1,X4,X5) != c_Datatype__Universe_OScons(X6,X2,X4,X5)
    | X1 = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_5515]) ).

cnf(c_0_5516_0,axiom,
    ( X1 = X2
    | c_Datatype__Universe_OScons(X1,X3,X4,X5) != c_Datatype__Universe_OScons(X2,X6,X4,X5) ),
    inference(literals_permutation,[status(thm)],[c_0_5516]) ).

cnf(c_0_5516_1,axiom,
    ( c_Datatype__Universe_OScons(X1,X3,X4,X5) != c_Datatype__Universe_OScons(X2,X6,X4,X5)
    | X1 = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_5516]) ).

cnf(c_0_5517_0,axiom,
    ( c_in(c_Sum__Type_OInr(X1,X2,X3),c_Sum__Type_OPlus(X4,X5,X3,X2),tc_sum(X3,X2))
    | ~ c_in(X1,X5,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5517]) ).

cnf(c_0_5517_1,axiom,
    ( ~ c_in(X1,X5,X2)
    | c_in(c_Sum__Type_OInr(X1,X2,X3),c_Sum__Type_OPlus(X4,X5,X3,X2),tc_sum(X3,X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_5517]) ).

cnf(c_0_5518_0,axiom,
    ( c_in(c_Sum__Type_OInl(X1,X2,X3),c_Sum__Type_OPlus(X4,X5,X2,X3),tc_sum(X2,X3))
    | ~ c_in(X1,X4,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5518]) ).

cnf(c_0_5518_1,axiom,
    ( ~ c_in(X1,X4,X2)
    | c_in(c_Sum__Type_OInl(X1,X2,X3),c_Sum__Type_OPlus(X4,X5,X2,X3),tc_sum(X2,X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_5518]) ).

cnf(c_0_5519_0,axiom,
    ( c_lessequals(c_Union(X1,X2),X3,tc_set(X2))
    | c_lessequals(X4,c_Union(X1,X2),tc_set(X2))
    | c_in(c_Zorn_OUnion__lemma0__1(X3,X4,X1,X2),X1,tc_set(X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_5519]) ).

cnf(c_0_5519_1,axiom,
    ( c_lessequals(X4,c_Union(X1,X2),tc_set(X2))
    | c_lessequals(c_Union(X1,X2),X3,tc_set(X2))
    | c_in(c_Zorn_OUnion__lemma0__1(X3,X4,X1,X2),X1,tc_set(X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_5519]) ).

cnf(c_0_5519_2,axiom,
    ( c_in(c_Zorn_OUnion__lemma0__1(X3,X4,X1,X2),X1,tc_set(X2))
    | c_lessequals(X4,c_Union(X1,X2),tc_set(X2))
    | c_lessequals(c_Union(X1,X2),X3,tc_set(X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_5519]) ).

cnf(c_0_5520_0,axiom,
    ( c_in(c_Pair(X1,X1,X2,X2),c_Relation_Odiag(X3,X2),tc_prod(X2,X2))
    | ~ c_in(X1,X3,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5520]) ).

cnf(c_0_5520_1,axiom,
    ( ~ c_in(X1,X3,X2)
    | c_in(c_Pair(X1,X1,X2,X2),c_Relation_Odiag(X3,X2),tc_prod(X2,X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_5520]) ).

cnf(c_0_5521_0,axiom,
    ( c_in(c_minus(X1,c_insert(X2,X3,X4),tc_set(X4)),c_Finite__Set_OFinites,tc_set(X4))
    | ~ c_in(c_minus(X1,X3,tc_set(X4)),c_Finite__Set_OFinites,tc_set(X4)) ),
    inference(literals_permutation,[status(thm)],[c_0_5521]) ).

cnf(c_0_5521_1,axiom,
    ( ~ c_in(c_minus(X1,X3,tc_set(X4)),c_Finite__Set_OFinites,tc_set(X4))
    | c_in(c_minus(X1,c_insert(X2,X3,X4),tc_set(X4)),c_Finite__Set_OFinites,tc_set(X4)) ),
    inference(literals_permutation,[status(thm)],[c_0_5521]) ).

cnf(c_0_5522_0,axiom,
    ( c_in(c_Pair(X1,X2,tc_nat,tc_nat),c_Wellfounded__Relations_Oless__than,tc_prod(tc_nat,tc_nat))
    | ~ c_less(X1,X2,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_5522]) ).

cnf(c_0_5522_1,axiom,
    ( ~ c_less(X1,X2,tc_nat)
    | c_in(c_Pair(X1,X2,tc_nat,tc_nat),c_Wellfounded__Relations_Oless__than,tc_prod(tc_nat,tc_nat)) ),
    inference(literals_permutation,[status(thm)],[c_0_5522]) ).

cnf(c_0_5523_0,axiom,
    ( c_Pair(c_Main_OdiagE__1(X2,X1,X3),c_Main_OdiagE__1(X2,X1,X3),X3,X3) = X1
    | ~ c_in(X1,c_Relation_Odiag(X2,X3),tc_prod(X3,X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_5523]) ).

cnf(c_0_5523_1,axiom,
    ( ~ c_in(X1,c_Relation_Odiag(X2,X3),tc_prod(X3,X3))
    | c_Pair(c_Main_OdiagE__1(X2,X1,X3),c_Main_OdiagE__1(X2,X1,X3),X3,X3) = X1 ),
    inference(literals_permutation,[status(thm)],[c_0_5523]) ).

cnf(c_0_5525_0,axiom,
    ( c_Wellfounded__Recursion_Owf(c_Wellfounded__Relations_Olex__prod(X1,X2,X3,X4),tc_prod(X3,X4))
    | ~ c_Wellfounded__Recursion_Owf(X1,X3)
    | ~ c_Wellfounded__Recursion_Owf(X2,X4) ),
    inference(literals_permutation,[status(thm)],[c_0_5525]) ).

cnf(c_0_5525_1,axiom,
    ( ~ c_Wellfounded__Recursion_Owf(X1,X3)
    | c_Wellfounded__Recursion_Owf(c_Wellfounded__Relations_Olex__prod(X1,X2,X3,X4),tc_prod(X3,X4))
    | ~ c_Wellfounded__Recursion_Owf(X2,X4) ),
    inference(literals_permutation,[status(thm)],[c_0_5525]) ).

cnf(c_0_5525_2,axiom,
    ( ~ c_Wellfounded__Recursion_Owf(X2,X4)
    | ~ c_Wellfounded__Recursion_Owf(X1,X3)
    | c_Wellfounded__Recursion_Owf(c_Wellfounded__Relations_Olex__prod(X1,X2,X3,X4),tc_prod(X3,X4)) ),
    inference(literals_permutation,[status(thm)],[c_0_5525]) ).

cnf(c_0_5526_0,axiom,
    ( c_Relation_Otrans(c_Wellfounded__Relations_Olex__prod(X1,X2,X3,X4),tc_prod(X3,X4))
    | ~ c_Relation_Otrans(X1,X3)
    | ~ c_Relation_Otrans(X2,X4) ),
    inference(literals_permutation,[status(thm)],[c_0_5526]) ).

cnf(c_0_5526_1,axiom,
    ( ~ c_Relation_Otrans(X1,X3)
    | c_Relation_Otrans(c_Wellfounded__Relations_Olex__prod(X1,X2,X3,X4),tc_prod(X3,X4))
    | ~ c_Relation_Otrans(X2,X4) ),
    inference(literals_permutation,[status(thm)],[c_0_5526]) ).

cnf(c_0_5526_2,axiom,
    ( ~ c_Relation_Otrans(X2,X4)
    | ~ c_Relation_Otrans(X1,X3)
    | c_Relation_Otrans(c_Wellfounded__Relations_Olex__prod(X1,X2,X3,X4),tc_prod(X3,X4)) ),
    inference(literals_permutation,[status(thm)],[c_0_5526]) ).

cnf(c_0_5528_0,axiom,
    ( X1 = X2
    | c_append(X3,c_List_Olist_OCons(X1,c_List_Olist_ONil,X4),X4) != c_append(X5,c_List_Olist_OCons(X2,c_List_Olist_ONil,X4),X4) ),
    inference(literals_permutation,[status(thm)],[c_0_5528]) ).

cnf(c_0_5528_1,axiom,
    ( c_append(X3,c_List_Olist_OCons(X1,c_List_Olist_ONil,X4),X4) != c_append(X5,c_List_Olist_OCons(X2,c_List_Olist_ONil,X4),X4)
    | X1 = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_5528]) ).

cnf(c_0_5529_0,axiom,
    ( X1 = X2
    | c_append(X1,c_List_Olist_OCons(X3,c_List_Olist_ONil,X4),X4) != c_append(X2,c_List_Olist_OCons(X5,c_List_Olist_ONil,X4),X4) ),
    inference(literals_permutation,[status(thm)],[c_0_5529]) ).

cnf(c_0_5529_1,axiom,
    ( c_append(X1,c_List_Olist_OCons(X3,c_List_Olist_ONil,X4),X4) != c_append(X2,c_List_Olist_OCons(X5,c_List_Olist_ONil,X4),X4)
    | X1 = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_5529]) ).

cnf(c_0_5536_0,axiom,
    ( c_in(c_append(X1,X2,X3),c_List_Olists(X4,X3),tc_List_Olist(X3))
    | ~ c_in(X1,c_List_Olists(X4,X3),tc_List_Olist(X3))
    | ~ c_in(X2,c_List_Olists(X4,X3),tc_List_Olist(X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_5536]) ).

cnf(c_0_5536_1,axiom,
    ( ~ c_in(X1,c_List_Olists(X4,X3),tc_List_Olist(X3))
    | c_in(c_append(X1,X2,X3),c_List_Olists(X4,X3),tc_List_Olist(X3))
    | ~ c_in(X2,c_List_Olists(X4,X3),tc_List_Olist(X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_5536]) ).

cnf(c_0_5536_2,axiom,
    ( ~ c_in(X2,c_List_Olists(X4,X3),tc_List_Olist(X3))
    | ~ c_in(X1,c_List_Olists(X4,X3),tc_List_Olist(X3))
    | c_in(c_append(X1,X2,X3),c_List_Olists(X4,X3),tc_List_Olist(X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_5536]) ).

cnf(c_0_5537_0,axiom,
    ( c_in(X1,c_Finite__Set_OFinites,tc_set(tc_prod(X2,X3)))
    | ~ c_in(c_Relation_Oconverse(X1,X2,X3),c_Finite__Set_OFinites,tc_set(tc_prod(X3,X2))) ),
    inference(literals_permutation,[status(thm)],[c_0_5537]) ).

cnf(c_0_5537_1,axiom,
    ( ~ c_in(c_Relation_Oconverse(X1,X2,X3),c_Finite__Set_OFinites,tc_set(tc_prod(X3,X2)))
    | c_in(X1,c_Finite__Set_OFinites,tc_set(tc_prod(X2,X3))) ),
    inference(literals_permutation,[status(thm)],[c_0_5537]) ).

cnf(c_0_5539_0,axiom,
    ( c_Pair(c_Main_OIdE__1(X1,X2),c_Main_OIdE__1(X1,X2),X2,X2) = X1
    | ~ c_in(X1,c_Relation_OId,tc_prod(X2,X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_5539]) ).

cnf(c_0_5539_1,axiom,
    ( ~ c_in(X1,c_Relation_OId,tc_prod(X2,X2))
    | c_Pair(c_Main_OIdE__1(X1,X2),c_Main_OIdE__1(X1,X2),X2,X2) = X1 ),
    inference(literals_permutation,[status(thm)],[c_0_5539]) ).

cnf(c_0_5540_0,axiom,
    ( c_in(c_List_Olist_OCons(X1,X2,X3),c_List_Olists(X4,X3),tc_List_Olist(X3))
    | ~ c_in(X2,c_List_Olists(X4,X3),tc_List_Olist(X3))
    | ~ c_in(X1,X4,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5540]) ).

cnf(c_0_5540_1,axiom,
    ( ~ c_in(X2,c_List_Olists(X4,X3),tc_List_Olist(X3))
    | c_in(c_List_Olist_OCons(X1,X2,X3),c_List_Olists(X4,X3),tc_List_Olist(X3))
    | ~ c_in(X1,X4,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5540]) ).

cnf(c_0_5540_2,axiom,
    ( ~ c_in(X1,X4,X3)
    | ~ c_in(X2,c_List_Olists(X4,X3),tc_List_Olist(X3))
    | c_in(c_List_Olist_OCons(X1,X2,X3),c_List_Olists(X4,X3),tc_List_Olist(X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_5540]) ).

cnf(c_0_5541_0,axiom,
    ( c_in(c_Relation_Oconverse(X1,X2,X3),c_Finite__Set_OFinites,tc_set(tc_prod(X3,X2)))
    | ~ c_in(X1,c_Finite__Set_OFinites,tc_set(tc_prod(X2,X3))) ),
    inference(literals_permutation,[status(thm)],[c_0_5541]) ).

cnf(c_0_5541_1,axiom,
    ( ~ c_in(X1,c_Finite__Set_OFinites,tc_set(tc_prod(X2,X3)))
    | c_in(c_Relation_Oconverse(X1,X2,X3),c_Finite__Set_OFinites,tc_set(tc_prod(X3,X2))) ),
    inference(literals_permutation,[status(thm)],[c_0_5541]) ).

cnf(c_0_5542_0,axiom,
    ( c_in(X1,c_List_Olists(X2,X3),tc_List_Olist(X3))
    | ~ c_in(c_List_Olist_OCons(X4,X1,X3),c_List_Olists(X2,X3),tc_List_Olist(X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_5542]) ).

cnf(c_0_5542_1,axiom,
    ( ~ c_in(c_List_Olist_OCons(X4,X1,X3),c_List_Olists(X2,X3),tc_List_Olist(X3))
    | c_in(X1,c_List_Olists(X2,X3),tc_List_Olist(X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_5542]) ).

cnf(c_0_5543_0,axiom,
    ( c_in(X1,c_List_Olists(X2,X3),tc_List_Olist(X3))
    | ~ c_in(c_append(X4,X1,X3),c_List_Olists(X2,X3),tc_List_Olist(X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_5543]) ).

cnf(c_0_5543_1,axiom,
    ( ~ c_in(c_append(X4,X1,X3),c_List_Olists(X2,X3),tc_List_Olist(X3))
    | c_in(X1,c_List_Olists(X2,X3),tc_List_Olist(X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_5543]) ).

cnf(c_0_5544_0,axiom,
    ( c_in(X1,c_List_Olists(X2,X3),tc_List_Olist(X3))
    | ~ c_in(c_append(X1,X4,X3),c_List_Olists(X2,X3),tc_List_Olist(X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_5544]) ).

cnf(c_0_5544_1,axiom,
    ( ~ c_in(c_append(X1,X4,X3),c_List_Olists(X2,X3),tc_List_Olist(X3))
    | c_in(X1,c_List_Olists(X2,X3),tc_List_Olist(X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_5544]) ).

cnf(c_0_5545_0,axiom,
    ( c_insert(X1,c_emptyset,X2) = c_insert(X1,X3,X2)
    | ~ c_lessequals(X3,c_insert(X1,c_emptyset,X2),tc_set(X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_5545]) ).

cnf(c_0_5545_1,axiom,
    ( ~ c_lessequals(X3,c_insert(X1,c_emptyset,X2),tc_set(X2))
    | c_insert(X1,c_emptyset,X2) = c_insert(X1,X3,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5545]) ).

cnf(c_0_5546_0,axiom,
    ( c_insert(X1,X2,X3) = c_insert(X1,c_emptyset,X3)
    | ~ c_lessequals(X2,c_insert(X1,c_emptyset,X3),tc_set(X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_5546]) ).

cnf(c_0_5546_1,axiom,
    ( ~ c_lessequals(X2,c_insert(X1,c_emptyset,X3),tc_set(X3))
    | c_insert(X1,X2,X3) = c_insert(X1,c_emptyset,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5546]) ).

cnf(c_0_5547_0,axiom,
    ( c_in(X1,X2,X3)
    | c_in(X1,X4,X3)
    | ~ c_in(X1,c_union(X2,X4,X3),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5547]) ).

cnf(c_0_5547_1,axiom,
    ( c_in(X1,X4,X3)
    | c_in(X1,X2,X3)
    | ~ c_in(X1,c_union(X2,X4,X3),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5547]) ).

cnf(c_0_5547_2,axiom,
    ( ~ c_in(X1,c_union(X2,X4,X3),X3)
    | c_in(X1,X4,X3)
    | c_in(X1,X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5547]) ).

cnf(c_0_5548_0,axiom,
    ( ~ c_in(X1,c_minus(X2,X3,tc_set(X4)),X4)
    | ~ c_in(X1,X3,X4) ),
    inference(literals_permutation,[status(thm)],[c_0_5548]) ).

cnf(c_0_5548_1,axiom,
    ( ~ c_in(X1,X3,X4)
    | ~ c_in(X1,c_minus(X2,X3,tc_set(X4)),X4) ),
    inference(literals_permutation,[status(thm)],[c_0_5548]) ).

cnf(c_0_5549_0,axiom,
    ( c_in(X1,X2,X3)
    | ~ c_in(c_List_Olist_OCons(X1,X4,X3),c_List_Olists(X2,X3),tc_List_Olist(X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_5549]) ).

cnf(c_0_5549_1,axiom,
    ( ~ c_in(c_List_Olist_OCons(X1,X4,X3),c_List_Olists(X2,X3),tc_List_Olist(X3))
    | c_in(X1,X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5549]) ).

cnf(c_0_5550_0,axiom,
    ( c_in(c_union(X1,X2,X3),c_Finite__Set_OFinites,tc_set(X3))
    | ~ c_in(X1,c_Finite__Set_OFinites,tc_set(X3))
    | ~ c_in(X2,c_Finite__Set_OFinites,tc_set(X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_5550]) ).

cnf(c_0_5550_1,axiom,
    ( ~ c_in(X1,c_Finite__Set_OFinites,tc_set(X3))
    | c_in(c_union(X1,X2,X3),c_Finite__Set_OFinites,tc_set(X3))
    | ~ c_in(X2,c_Finite__Set_OFinites,tc_set(X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_5550]) ).

cnf(c_0_5550_2,axiom,
    ( ~ c_in(X2,c_Finite__Set_OFinites,tc_set(X3))
    | ~ c_in(X1,c_Finite__Set_OFinites,tc_set(X3))
    | c_in(c_union(X1,X2,X3),c_Finite__Set_OFinites,tc_set(X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_5550]) ).

cnf(c_0_5551_0,axiom,
    ( c_less(c_0,X1,tc_nat)
    | c_less(c_0,X2,tc_nat)
    | ~ c_less(c_0,c_plus(X1,X2,tc_nat),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_5551]) ).

cnf(c_0_5551_1,axiom,
    ( c_less(c_0,X2,tc_nat)
    | c_less(c_0,X1,tc_nat)
    | ~ c_less(c_0,c_plus(X1,X2,tc_nat),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_5551]) ).

cnf(c_0_5551_2,axiom,
    ( ~ c_less(c_0,c_plus(X1,X2,tc_nat),tc_nat)
    | c_less(c_0,X2,tc_nat)
    | c_less(c_0,X1,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_5551]) ).

cnf(c_0_5552_0,axiom,
    ( c_in(X1,c_List_Olists(X2,X3),tc_List_Olist(X3))
    | ~ c_in(c_Main_Oin__listsI__1(X2,X1,X3),X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5552]) ).

cnf(c_0_5552_1,axiom,
    ( ~ c_in(c_Main_Oin__listsI__1(X2,X1,X3),X2,X3)
    | c_in(X1,c_List_Olists(X2,X3),tc_List_Olist(X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_5552]) ).

cnf(c_0_5553_0,axiom,
    ( c_in(X1,c_Inter(X2,X3),X3)
    | ~ c_in(X1,c_Main_OInterI__1(X1,X2,X3),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5553]) ).

cnf(c_0_5553_1,axiom,
    ( ~ c_in(X1,c_Main_OInterI__1(X1,X2,X3),X3)
    | c_in(X1,c_Inter(X2,X3),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5553]) ).

cnf(c_0_5554_0,axiom,
    ( c_in(X1,c_inter(X2,X3,X4),X4)
    | ~ c_in(X1,X2,X4)
    | ~ c_in(X1,X3,X4) ),
    inference(literals_permutation,[status(thm)],[c_0_5554]) ).

cnf(c_0_5554_1,axiom,
    ( ~ c_in(X1,X2,X4)
    | c_in(X1,c_inter(X2,X3,X4),X4)
    | ~ c_in(X1,X3,X4) ),
    inference(literals_permutation,[status(thm)],[c_0_5554]) ).

cnf(c_0_5554_2,axiom,
    ( ~ c_in(X1,X3,X4)
    | ~ c_in(X1,X2,X4)
    | c_in(X1,c_inter(X2,X3,X4),X4) ),
    inference(literals_permutation,[status(thm)],[c_0_5554]) ).

cnf(c_0_5555_0,axiom,
    ( c_lessequals(X1,c_insert(X2,c_emptyset,X3),tc_set(X3))
    | c_insert(X2,c_emptyset,X3) != c_insert(X4,X1,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5555]) ).

cnf(c_0_5555_1,axiom,
    ( c_insert(X2,c_emptyset,X3) != c_insert(X4,X1,X3)
    | c_lessequals(X1,c_insert(X2,c_emptyset,X3),tc_set(X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_5555]) ).

cnf(c_0_5556_0,axiom,
    ( c_lessequals(X1,c_insert(X2,c_emptyset,X3),tc_set(X3))
    | c_insert(X4,X1,X3) != c_insert(X2,c_emptyset,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5556]) ).

cnf(c_0_5556_1,axiom,
    ( c_insert(X4,X1,X3) != c_insert(X2,c_emptyset,X3)
    | c_lessequals(X1,c_insert(X2,c_emptyset,X3),tc_set(X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_5556]) ).

cnf(c_0_5557_0,axiom,
    ( c_in(c_Union(X1,X2),c_Finite__Set_OFinites,tc_set(X2))
    | ~ c_in(c_Main_Ofinite__Union__1(X1,X2),c_Finite__Set_OFinites,tc_set(X2))
    | ~ c_in(X1,c_Finite__Set_OFinites,tc_set(tc_set(X2))) ),
    inference(literals_permutation,[status(thm)],[c_0_5557]) ).

cnf(c_0_5557_1,axiom,
    ( ~ c_in(c_Main_Ofinite__Union__1(X1,X2),c_Finite__Set_OFinites,tc_set(X2))
    | c_in(c_Union(X1,X2),c_Finite__Set_OFinites,tc_set(X2))
    | ~ c_in(X1,c_Finite__Set_OFinites,tc_set(tc_set(X2))) ),
    inference(literals_permutation,[status(thm)],[c_0_5557]) ).

cnf(c_0_5557_2,axiom,
    ( ~ c_in(X1,c_Finite__Set_OFinites,tc_set(tc_set(X2)))
    | ~ c_in(c_Main_Ofinite__Union__1(X1,X2),c_Finite__Set_OFinites,tc_set(X2))
    | c_in(c_Union(X1,X2),c_Finite__Set_OFinites,tc_set(X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_5557]) ).

cnf(c_0_5558_0,axiom,
    ( c_in(c_Main_OdiagE__1(X1,X2,X3),X1,X3)
    | ~ c_in(X2,c_Relation_Odiag(X1,X3),tc_prod(X3,X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_5558]) ).

cnf(c_0_5558_1,axiom,
    ( ~ c_in(X2,c_Relation_Odiag(X1,X3),tc_prod(X3,X3))
    | c_in(c_Main_OdiagE__1(X1,X2,X3),X1,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5558]) ).

cnf(c_0_5559_0,axiom,
    ( c_in(X1,X2,X3)
    | ~ c_in(X1,c_minus(X2,X4,tc_set(X3)),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5559]) ).

cnf(c_0_5559_1,axiom,
    ( ~ c_in(X1,c_minus(X2,X4,tc_set(X3)),X3)
    | c_in(X1,X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5559]) ).

cnf(c_0_5560_0,axiom,
    ( c_in(X1,c_Finite__Set_OFinites,tc_set(X2))
    | ~ c_in(c_union(X3,X1,X2),c_Finite__Set_OFinites,tc_set(X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_5560]) ).

cnf(c_0_5560_1,axiom,
    ( ~ c_in(c_union(X3,X1,X2),c_Finite__Set_OFinites,tc_set(X2))
    | c_in(X1,c_Finite__Set_OFinites,tc_set(X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_5560]) ).

cnf(c_0_5561_0,axiom,
    ( c_in(X1,c_Finite__Set_OFinites,tc_set(X2))
    | ~ c_in(c_union(X1,X3,X2),c_Finite__Set_OFinites,tc_set(X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_5561]) ).

cnf(c_0_5561_1,axiom,
    ( ~ c_in(c_union(X1,X3,X2),c_Finite__Set_OFinites,tc_set(X2))
    | c_in(X1,c_Finite__Set_OFinites,tc_set(X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_5561]) ).

cnf(c_0_5562_0,axiom,
    ( c_in(X1,X2,X3)
    | ~ c_in(X1,c_List_Oset(X4,X3),X3)
    | ~ c_in(X4,c_List_Olists(X2,X3),tc_List_Olist(X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_5562]) ).

cnf(c_0_5562_1,axiom,
    ( ~ c_in(X1,c_List_Oset(X4,X3),X3)
    | c_in(X1,X2,X3)
    | ~ c_in(X4,c_List_Olists(X2,X3),tc_List_Olist(X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_5562]) ).

cnf(c_0_5562_2,axiom,
    ( ~ c_in(X4,c_List_Olists(X2,X3),tc_List_Olist(X3))
    | ~ c_in(X1,c_List_Oset(X4,X3),X3)
    | c_in(X1,X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5562]) ).

cnf(c_0_5563_0,axiom,
    ( c_lessequals(X1,X2,tc_set(X3))
    | ~ c_in(c_Main_OsubsetI__1(X1,X2,X3),X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5563]) ).

cnf(c_0_5563_1,axiom,
    ( ~ c_in(c_Main_OsubsetI__1(X1,X2,X3),X2,X3)
    | c_lessequals(X1,X2,tc_set(X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_5563]) ).

cnf(c_0_5564_0,axiom,
    ( c_in(X1,c_minus(X2,X3,tc_set(X4)),X4)
    | c_in(X1,X3,X4)
    | ~ c_in(X1,X2,X4) ),
    inference(literals_permutation,[status(thm)],[c_0_5564]) ).

cnf(c_0_5564_1,axiom,
    ( c_in(X1,X3,X4)
    | c_in(X1,c_minus(X2,X3,tc_set(X4)),X4)
    | ~ c_in(X1,X2,X4) ),
    inference(literals_permutation,[status(thm)],[c_0_5564]) ).

cnf(c_0_5564_2,axiom,
    ( ~ c_in(X1,X2,X4)
    | c_in(X1,X3,X4)
    | c_in(X1,c_minus(X2,X3,tc_set(X4)),X4) ),
    inference(literals_permutation,[status(thm)],[c_0_5564]) ).

cnf(c_0_5565_0,axiom,
    ( X1 = X2
    | c_in(X1,X3,X4)
    | ~ c_in(X1,c_insert(X2,X3,X4),X4) ),
    inference(literals_permutation,[status(thm)],[c_0_5565]) ).

cnf(c_0_5565_1,axiom,
    ( c_in(X1,X3,X4)
    | X1 = X2
    | ~ c_in(X1,c_insert(X2,X3,X4),X4) ),
    inference(literals_permutation,[status(thm)],[c_0_5565]) ).

cnf(c_0_5565_2,axiom,
    ( ~ c_in(X1,c_insert(X2,X3,X4),X4)
    | c_in(X1,X3,X4)
    | X1 = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_5565]) ).

cnf(c_0_5566_0,axiom,
    ( c_in(X1,X2,X3)
    | ~ c_in(X1,c_inter(X2,X4,X3),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5566]) ).

cnf(c_0_5566_1,axiom,
    ( ~ c_in(X1,c_inter(X2,X4,X3),X3)
    | c_in(X1,X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5566]) ).

cnf(c_0_5567_0,axiom,
    ( c_in(X1,X2,X3)
    | ~ c_in(X1,c_inter(X4,X2,X3),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5567]) ).

cnf(c_0_5567_1,axiom,
    ( ~ c_in(X1,c_inter(X4,X2,X3),X3)
    | c_in(X1,X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5567]) ).

cnf(c_0_5568_0,axiom,
    ( c_lessequals(X1,c_Zorn_Osucc(X2,X3,X4),tc_set(tc_set(X4)))
    | ~ c_lessequals(X1,X3,tc_set(tc_set(X4))) ),
    inference(literals_permutation,[status(thm)],[c_0_5568]) ).

cnf(c_0_5568_1,axiom,
    ( ~ c_lessequals(X1,X3,tc_set(tc_set(X4)))
    | c_lessequals(X1,c_Zorn_Osucc(X2,X3,X4),tc_set(tc_set(X4))) ),
    inference(literals_permutation,[status(thm)],[c_0_5568]) ).

cnf(c_0_5569_0,axiom,
    ( c_in(c_Main_OUnionE__1(X1,X2,X3),X2,tc_set(X3))
    | ~ c_in(X1,c_Union(X2,X3),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5569]) ).

cnf(c_0_5569_1,axiom,
    ( ~ c_in(X1,c_Union(X2,X3),X3)
    | c_in(c_Main_OUnionE__1(X1,X2,X3),X2,tc_set(X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_5569]) ).

cnf(c_0_5570_0,axiom,
    ( X1 = c_append(c_List_Orev(X2,X3),c_List_Olist_OCons(X4,c_List_Olist_ONil,X3),X3)
    | c_List_Orev(X1,X3) != c_List_Olist_OCons(X4,X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5570]) ).

cnf(c_0_5570_1,axiom,
    ( c_List_Orev(X1,X3) != c_List_Olist_OCons(X4,X2,X3)
    | X1 = c_append(c_List_Orev(X2,X3),c_List_Olist_OCons(X4,c_List_Olist_ONil,X3),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5570]) ).

cnf(c_0_5571_0,axiom,
    ( c_in(X1,c_Main_OUnionE__1(X1,X2,X3),X3)
    | ~ c_in(X1,c_Union(X2,X3),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5571]) ).

cnf(c_0_5571_1,axiom,
    ( ~ c_in(X1,c_Union(X2,X3),X3)
    | c_in(X1,c_Main_OUnionE__1(X1,X2,X3),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5571]) ).

cnf(c_0_5572_0,axiom,
    ( c_in(c_Union(X1,X2),c_Finite__Set_OFinites,tc_set(X2))
    | c_in(c_Main_Ofinite__Union__1(X1,X2),X1,tc_set(X2))
    | ~ c_in(X1,c_Finite__Set_OFinites,tc_set(tc_set(X2))) ),
    inference(literals_permutation,[status(thm)],[c_0_5572]) ).

cnf(c_0_5572_1,axiom,
    ( c_in(c_Main_Ofinite__Union__1(X1,X2),X1,tc_set(X2))
    | c_in(c_Union(X1,X2),c_Finite__Set_OFinites,tc_set(X2))
    | ~ c_in(X1,c_Finite__Set_OFinites,tc_set(tc_set(X2))) ),
    inference(literals_permutation,[status(thm)],[c_0_5572]) ).

cnf(c_0_5572_2,axiom,
    ( ~ c_in(X1,c_Finite__Set_OFinites,tc_set(tc_set(X2)))
    | c_in(c_Main_Ofinite__Union__1(X1,X2),X1,tc_set(X2))
    | c_in(c_Union(X1,X2),c_Finite__Set_OFinites,tc_set(X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_5572]) ).

cnf(c_0_5573_0,axiom,
    ( c_in(X1,X2,X3)
    | ~ c_in(X1,c_Inter(X4,X3),X3)
    | ~ c_in(X2,X4,tc_set(X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_5573]) ).

cnf(c_0_5573_1,axiom,
    ( ~ c_in(X1,c_Inter(X4,X3),X3)
    | c_in(X1,X2,X3)
    | ~ c_in(X2,X4,tc_set(X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_5573]) ).

cnf(c_0_5573_2,axiom,
    ( ~ c_in(X2,X4,tc_set(X3))
    | ~ c_in(X1,c_Inter(X4,X3),X3)
    | c_in(X1,X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5573]) ).

cnf(c_0_5574_0,axiom,
    ( c_lessequals(X1,X2,tc_set(X3))
    | ~ c_lessequals(c_uminus(X2,tc_set(X3)),c_uminus(X1,tc_set(X3)),tc_set(X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_5574]) ).

cnf(c_0_5574_1,axiom,
    ( ~ c_lessequals(c_uminus(X2,tc_set(X3)),c_uminus(X1,tc_set(X3)),tc_set(X3))
    | c_lessequals(X1,X2,tc_set(X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_5574]) ).

cnf(c_0_5575_0,axiom,
    ( c_in(c_Main_Oin__listsI__1(X1,X2,X3),c_List_Oset(X2,X3),X3)
    | c_in(X2,c_List_Olists(X1,X3),tc_List_Olist(X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_5575]) ).

cnf(c_0_5575_1,axiom,
    ( c_in(X2,c_List_Olists(X1,X3),tc_List_Olist(X3))
    | c_in(c_Main_Oin__listsI__1(X1,X2,X3),c_List_Oset(X2,X3),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5575]) ).

cnf(c_0_5576_0,axiom,
    ( c_in(X1,c_Union(X2,X3),X3)
    | ~ c_in(X4,X2,tc_set(X3))
    | ~ c_in(X1,X4,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5576]) ).

cnf(c_0_5576_1,axiom,
    ( ~ c_in(X4,X2,tc_set(X3))
    | c_in(X1,c_Union(X2,X3),X3)
    | ~ c_in(X1,X4,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5576]) ).

cnf(c_0_5576_2,axiom,
    ( ~ c_in(X1,X4,X3)
    | ~ c_in(X4,X2,tc_set(X3))
    | c_in(X1,c_Union(X2,X3),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5576]) ).

cnf(c_0_5577_0,axiom,
    ( c_in(c_inter(X1,X2,X3),c_Finite__Set_OFinites,tc_set(X3))
    | ~ c_in(X2,c_Finite__Set_OFinites,tc_set(X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_5577]) ).

cnf(c_0_5577_1,axiom,
    ( ~ c_in(X2,c_Finite__Set_OFinites,tc_set(X3))
    | c_in(c_inter(X1,X2,X3),c_Finite__Set_OFinites,tc_set(X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_5577]) ).

cnf(c_0_5578_0,axiom,
    ( c_in(c_inter(X1,X2,X3),c_Finite__Set_OFinites,tc_set(X3))
    | ~ c_in(X1,c_Finite__Set_OFinites,tc_set(X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_5578]) ).

cnf(c_0_5578_1,axiom,
    ( ~ c_in(X1,c_Finite__Set_OFinites,tc_set(X3))
    | c_in(c_inter(X1,X2,X3),c_Finite__Set_OFinites,tc_set(X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_5578]) ).

cnf(c_0_5579_0,axiom,
    ( c_in(c_insert(X1,X2,X3),c_Finite__Set_OFinites,tc_set(X3))
    | ~ c_in(X2,c_Finite__Set_OFinites,tc_set(X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_5579]) ).

cnf(c_0_5579_1,axiom,
    ( ~ c_in(X2,c_Finite__Set_OFinites,tc_set(X3))
    | c_in(c_insert(X1,X2,X3),c_Finite__Set_OFinites,tc_set(X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_5579]) ).

cnf(c_0_5580_0,axiom,
    ( X1 = X2
    | ~ c_in(X1,c_insert(X2,c_emptyset,X3),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5580]) ).

cnf(c_0_5580_1,axiom,
    ( ~ c_in(X1,c_insert(X2,c_emptyset,X3),X3)
    | X1 = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_5580]) ).

cnf(c_0_5581_0,axiom,
    ( c_in(c_Main_OInterI__1(X1,X2,X3),X2,tc_set(X3))
    | c_in(X1,c_Inter(X2,X3),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5581]) ).

cnf(c_0_5581_1,axiom,
    ( c_in(X1,c_Inter(X2,X3),X3)
    | c_in(c_Main_OInterI__1(X1,X2,X3),X2,tc_set(X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_5581]) ).

cnf(c_0_5582_0,axiom,
    ( c_in(X1,c_insert(X2,X3,X4),X4)
    | ~ c_in(X1,X3,X4) ),
    inference(literals_permutation,[status(thm)],[c_0_5582]) ).

cnf(c_0_5582_1,axiom,
    ( ~ c_in(X1,X3,X4)
    | c_in(X1,c_insert(X2,X3,X4),X4) ),
    inference(literals_permutation,[status(thm)],[c_0_5582]) ).

cnf(c_0_5583_0,axiom,
    ( c_in(X1,c_union(X2,X3,X4),X4)
    | ~ c_in(X1,X2,X4) ),
    inference(literals_permutation,[status(thm)],[c_0_5583]) ).

cnf(c_0_5583_1,axiom,
    ( ~ c_in(X1,X2,X4)
    | c_in(X1,c_union(X2,X3,X4),X4) ),
    inference(literals_permutation,[status(thm)],[c_0_5583]) ).

cnf(c_0_5584_0,axiom,
    ( c_in(X1,c_union(X2,X3,X4),X4)
    | ~ c_in(X1,X3,X4) ),
    inference(literals_permutation,[status(thm)],[c_0_5584]) ).

cnf(c_0_5584_1,axiom,
    ( ~ c_in(X1,X3,X4)
    | c_in(X1,c_union(X2,X3,X4),X4) ),
    inference(literals_permutation,[status(thm)],[c_0_5584]) ).

cnf(c_0_5587_0,axiom,
    ( c_lessequals(X1,X2,X3)
    | ~ c_lessequals(c_SetInterval_OlessThan(X1,X3),c_SetInterval_OlessThan(X2,X3),tc_set(X3))
    | ~ class_Orderings_Olinorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5587]) ).

cnf(c_0_5587_1,axiom,
    ( ~ c_lessequals(c_SetInterval_OlessThan(X1,X3),c_SetInterval_OlessThan(X2,X3),tc_set(X3))
    | c_lessequals(X1,X2,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5587]) ).

cnf(c_0_5587_2,axiom,
    ( ~ class_Orderings_Olinorder(X3)
    | ~ c_lessequals(c_SetInterval_OlessThan(X1,X3),c_SetInterval_OlessThan(X2,X3),tc_set(X3))
    | c_lessequals(X1,X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5587]) ).

cnf(c_0_5588_0,axiom,
    ( c_lessequals(X1,X2,X3)
    | ~ c_lessequals(c_SetInterval_OgreaterThan(X2,X3),c_SetInterval_OgreaterThan(X1,X3),tc_set(X3))
    | ~ class_Orderings_Olinorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5588]) ).

cnf(c_0_5588_1,axiom,
    ( ~ c_lessequals(c_SetInterval_OgreaterThan(X2,X3),c_SetInterval_OgreaterThan(X1,X3),tc_set(X3))
    | c_lessequals(X1,X2,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5588]) ).

cnf(c_0_5588_2,axiom,
    ( ~ class_Orderings_Olinorder(X3)
    | ~ c_lessequals(c_SetInterval_OgreaterThan(X2,X3),c_SetInterval_OgreaterThan(X1,X3),tc_set(X3))
    | c_lessequals(X1,X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5588]) ).

cnf(c_0_5589_0,axiom,
    ( c_lessequals(X1,X2,X3)
    | ~ c_lessequals(c_SetInterval_OatMost(X1,X3),c_SetInterval_OatMost(X2,X3),tc_set(X3))
    | ~ class_Orderings_Oorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5589]) ).

cnf(c_0_5589_1,axiom,
    ( ~ c_lessequals(c_SetInterval_OatMost(X1,X3),c_SetInterval_OatMost(X2,X3),tc_set(X3))
    | c_lessequals(X1,X2,X3)
    | ~ class_Orderings_Oorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5589]) ).

cnf(c_0_5589_2,axiom,
    ( ~ class_Orderings_Oorder(X3)
    | ~ c_lessequals(c_SetInterval_OatMost(X1,X3),c_SetInterval_OatMost(X2,X3),tc_set(X3))
    | c_lessequals(X1,X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5589]) ).

cnf(c_0_5590_0,axiom,
    ( c_lessequals(X1,X2,X3)
    | ~ c_lessequals(c_SetInterval_OatLeast(X2,X3),c_SetInterval_OatLeast(X1,X3),tc_set(X3))
    | ~ class_Orderings_Oorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5590]) ).

cnf(c_0_5590_1,axiom,
    ( ~ c_lessequals(c_SetInterval_OatLeast(X2,X3),c_SetInterval_OatLeast(X1,X3),tc_set(X3))
    | c_lessequals(X1,X2,X3)
    | ~ class_Orderings_Oorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5590]) ).

cnf(c_0_5590_2,axiom,
    ( ~ class_Orderings_Oorder(X3)
    | ~ c_lessequals(c_SetInterval_OatLeast(X2,X3),c_SetInterval_OatLeast(X1,X3),tc_set(X3))
    | c_lessequals(X1,X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5590]) ).

cnf(c_0_5591_0,axiom,
    ( c_in(X1,X2,X3)
    | ~ c_lessequals(X4,X2,tc_set(X3))
    | ~ c_in(X1,X4,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5591]) ).

cnf(c_0_5591_1,axiom,
    ( ~ c_lessequals(X4,X2,tc_set(X3))
    | c_in(X1,X2,X3)
    | ~ c_in(X1,X4,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5591]) ).

cnf(c_0_5591_2,axiom,
    ( ~ c_in(X1,X4,X3)
    | ~ c_lessequals(X4,X2,tc_set(X3))
    | c_in(X1,X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5591]) ).

cnf(c_0_5592_0,axiom,
    ( c_less(c_0,c_plus(X1,X2,tc_nat),tc_nat)
    | ~ c_less(c_0,X2,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_5592]) ).

cnf(c_0_5592_1,axiom,
    ( ~ c_less(c_0,X2,tc_nat)
    | c_less(c_0,c_plus(X1,X2,tc_nat),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_5592]) ).

cnf(c_0_5593_0,axiom,
    ( c_less(c_0,c_plus(X1,X2,tc_nat),tc_nat)
    | ~ c_less(c_0,X1,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_5593]) ).

cnf(c_0_5593_1,axiom,
    ( ~ c_less(c_0,X1,tc_nat)
    | c_less(c_0,c_plus(X1,X2,tc_nat),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_5593]) ).

cnf(c_0_5594_0,axiom,
    ( c_in(X1,c_Transitive__Closure_Ortrancl(X2,X3),tc_prod(X3,X3))
    | ~ c_in(X1,X2,tc_prod(X3,X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_5594]) ).

cnf(c_0_5594_1,axiom,
    ( ~ c_in(X1,X2,tc_prod(X3,X3))
    | c_in(X1,c_Transitive__Closure_Ortrancl(X2,X3),tc_prod(X3,X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_5594]) ).

cnf(c_0_5595_0,axiom,
    ( c_lessequals(c_uminus(X1,tc_set(X2)),c_uminus(X3,tc_set(X2)),tc_set(X2))
    | ~ c_lessequals(X3,X1,tc_set(X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_5595]) ).

cnf(c_0_5595_1,axiom,
    ( ~ c_lessequals(X3,X1,tc_set(X2))
    | c_lessequals(c_uminus(X1,tc_set(X2)),c_uminus(X3,tc_set(X2)),tc_set(X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_5595]) ).

cnf(c_0_5596_0,axiom,
    ( ~ c_in(X1,c_uminus(X2,tc_set(X3)),X3)
    | ~ c_in(X1,X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5596]) ).

cnf(c_0_5596_1,axiom,
    ( ~ c_in(X1,X2,X3)
    | ~ c_in(X1,c_uminus(X2,tc_set(X3)),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5596]) ).

cnf(c_0_5597_0,axiom,
    ( c_lessequals(X1,X2,tc_set(X3))
    | c_in(c_Main_OsubsetI__1(X1,X2,X3),X1,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5597]) ).

cnf(c_0_5597_1,axiom,
    ( c_in(c_Main_OsubsetI__1(X1,X2,X3),X1,X3)
    | c_lessequals(X1,X2,tc_set(X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_5597]) ).

cnf(c_0_5598_0,axiom,
    ( c_in(X1,c_Finite__Set_OFinites,tc_set(X2))
    | ~ c_in(c_Pow(X1,X2),c_Finite__Set_OFinites,tc_set(tc_set(X2))) ),
    inference(literals_permutation,[status(thm)],[c_0_5598]) ).

cnf(c_0_5598_1,axiom,
    ( ~ c_in(c_Pow(X1,X2),c_Finite__Set_OFinites,tc_set(tc_set(X2)))
    | c_in(X1,c_Finite__Set_OFinites,tc_set(X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_5598]) ).

cnf(c_0_5599_0,axiom,
    ( c_lessequals(c_SetInterval_OlessThan(X1,X2),c_SetInterval_OlessThan(X3,X2),tc_set(X2))
    | ~ c_lessequals(X1,X3,X2)
    | ~ class_Orderings_Olinorder(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5599]) ).

cnf(c_0_5599_1,axiom,
    ( ~ c_lessequals(X1,X3,X2)
    | c_lessequals(c_SetInterval_OlessThan(X1,X2),c_SetInterval_OlessThan(X3,X2),tc_set(X2))
    | ~ class_Orderings_Olinorder(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5599]) ).

cnf(c_0_5599_2,axiom,
    ( ~ class_Orderings_Olinorder(X2)
    | ~ c_lessequals(X1,X3,X2)
    | c_lessequals(c_SetInterval_OlessThan(X1,X2),c_SetInterval_OlessThan(X3,X2),tc_set(X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_5599]) ).

cnf(c_0_5600_0,axiom,
    ( c_lessequals(c_SetInterval_OgreaterThan(X1,X2),c_SetInterval_OgreaterThan(X3,X2),tc_set(X2))
    | ~ c_lessequals(X3,X1,X2)
    | ~ class_Orderings_Olinorder(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5600]) ).

cnf(c_0_5600_1,axiom,
    ( ~ c_lessequals(X3,X1,X2)
    | c_lessequals(c_SetInterval_OgreaterThan(X1,X2),c_SetInterval_OgreaterThan(X3,X2),tc_set(X2))
    | ~ class_Orderings_Olinorder(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5600]) ).

cnf(c_0_5600_2,axiom,
    ( ~ class_Orderings_Olinorder(X2)
    | ~ c_lessequals(X3,X1,X2)
    | c_lessequals(c_SetInterval_OgreaterThan(X1,X2),c_SetInterval_OgreaterThan(X3,X2),tc_set(X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_5600]) ).

cnf(c_0_5601_0,axiom,
    ( c_lessequals(c_SetInterval_OatMost(X1,X2),c_SetInterval_OatMost(X3,X2),tc_set(X2))
    | ~ c_lessequals(X1,X3,X2)
    | ~ class_Orderings_Oorder(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5601]) ).

cnf(c_0_5601_1,axiom,
    ( ~ c_lessequals(X1,X3,X2)
    | c_lessequals(c_SetInterval_OatMost(X1,X2),c_SetInterval_OatMost(X3,X2),tc_set(X2))
    | ~ class_Orderings_Oorder(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5601]) ).

cnf(c_0_5601_2,axiom,
    ( ~ class_Orderings_Oorder(X2)
    | ~ c_lessequals(X1,X3,X2)
    | c_lessequals(c_SetInterval_OatMost(X1,X2),c_SetInterval_OatMost(X3,X2),tc_set(X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_5601]) ).

cnf(c_0_5602_0,axiom,
    ( c_lessequals(c_SetInterval_OatLeast(X1,X2),c_SetInterval_OatLeast(X3,X2),tc_set(X2))
    | ~ c_lessequals(X3,X1,X2)
    | ~ class_Orderings_Oorder(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5602]) ).

cnf(c_0_5602_1,axiom,
    ( ~ c_lessequals(X3,X1,X2)
    | c_lessequals(c_SetInterval_OatLeast(X1,X2),c_SetInterval_OatLeast(X3,X2),tc_set(X2))
    | ~ class_Orderings_Oorder(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5602]) ).

cnf(c_0_5602_2,axiom,
    ( ~ class_Orderings_Oorder(X2)
    | ~ c_lessequals(X3,X1,X2)
    | c_lessequals(c_SetInterval_OatLeast(X1,X2),c_SetInterval_OatLeast(X3,X2),tc_set(X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_5602]) ).

cnf(c_0_5603_0,axiom,
    ( c_Wellfounded__Recursion_Oacyclic(X1,X2)
    | ~ c_Wellfounded__Recursion_Oacyclic(c_Relation_Oconverse(X1,X2,X2),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5603]) ).

cnf(c_0_5603_1,axiom,
    ( ~ c_Wellfounded__Recursion_Oacyclic(c_Relation_Oconverse(X1,X2,X2),X2)
    | c_Wellfounded__Recursion_Oacyclic(X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5603]) ).

cnf(c_0_5604_0,axiom,
    ( X1 = X2
    | ~ c_in(X2,X3,X4)
    | ~ c_in(X1,X3,X4)
    | ~ c_Infinite__Set_Oatmost__one(X3,X4) ),
    inference(literals_permutation,[status(thm)],[c_0_5604]) ).

cnf(c_0_5604_1,axiom,
    ( ~ c_in(X2,X3,X4)
    | X1 = X2
    | ~ c_in(X1,X3,X4)
    | ~ c_Infinite__Set_Oatmost__one(X3,X4) ),
    inference(literals_permutation,[status(thm)],[c_0_5604]) ).

cnf(c_0_5604_2,axiom,
    ( ~ c_in(X1,X3,X4)
    | ~ c_in(X2,X3,X4)
    | X1 = X2
    | ~ c_Infinite__Set_Oatmost__one(X3,X4) ),
    inference(literals_permutation,[status(thm)],[c_0_5604]) ).

cnf(c_0_5604_3,axiom,
    ( ~ c_Infinite__Set_Oatmost__one(X3,X4)
    | ~ c_in(X1,X3,X4)
    | ~ c_in(X2,X3,X4)
    | X1 = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_5604]) ).

cnf(c_0_5605_0,axiom,
    ( c_lessequals(X1,X2,tc_set(X3))
    | ~ c_in(X1,c_Pow(X2,X3),tc_set(X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_5605]) ).

cnf(c_0_5605_1,axiom,
    ( ~ c_in(X1,c_Pow(X2,X3),tc_set(X3))
    | c_lessequals(X1,X2,tc_set(X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_5605]) ).

cnf(c_0_5606_0,axiom,
    ( X1 = X2
    | ~ c_lessequals(X1,X2,tc_set(X3))
    | ~ c_lessequals(X2,X1,tc_set(X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_5606]) ).

cnf(c_0_5606_1,axiom,
    ( ~ c_lessequals(X1,X2,tc_set(X3))
    | X1 = X2
    | ~ c_lessequals(X2,X1,tc_set(X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_5606]) ).

cnf(c_0_5606_2,axiom,
    ( ~ c_lessequals(X2,X1,tc_set(X3))
    | ~ c_lessequals(X1,X2,tc_set(X3))
    | X1 = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_5606]) ).

cnf(c_0_5607_0,axiom,
    ( ~ c_lessequals(X1,X2,tc_set(X3))
    | ~ c_less(X2,X1,tc_set(X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_5607]) ).

cnf(c_0_5607_1,axiom,
    ( ~ c_less(X2,X1,tc_set(X3))
    | ~ c_lessequals(X1,X2,tc_set(X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_5607]) ).

cnf(c_0_5608_0,axiom,
    ( c_in(c_Pow(X1,X2),c_Finite__Set_OFinites,tc_set(tc_set(X2)))
    | ~ c_in(X1,c_Finite__Set_OFinites,tc_set(X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_5608]) ).

cnf(c_0_5608_1,axiom,
    ( ~ c_in(X1,c_Finite__Set_OFinites,tc_set(X2))
    | c_in(c_Pow(X1,X2),c_Finite__Set_OFinites,tc_set(tc_set(X2))) ),
    inference(literals_permutation,[status(thm)],[c_0_5608]) ).

cnf(c_0_5609_0,axiom,
    ( c_less(X1,X2,X3)
    | ~ c_in(X1,c_SetInterval_OlessThan(X2,X3),X3)
    | ~ class_Orderings_Oord(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5609]) ).

cnf(c_0_5609_1,axiom,
    ( ~ c_in(X1,c_SetInterval_OlessThan(X2,X3),X3)
    | c_less(X1,X2,X3)
    | ~ class_Orderings_Oord(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5609]) ).

cnf(c_0_5609_2,axiom,
    ( ~ class_Orderings_Oord(X3)
    | ~ c_in(X1,c_SetInterval_OlessThan(X2,X3),X3)
    | c_less(X1,X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5609]) ).

cnf(c_0_5610_0,axiom,
    ( c_less(X1,X2,X3)
    | ~ c_in(X2,c_SetInterval_OgreaterThan(X1,X3),X3)
    | ~ class_Orderings_Oord(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5610]) ).

cnf(c_0_5610_1,axiom,
    ( ~ c_in(X2,c_SetInterval_OgreaterThan(X1,X3),X3)
    | c_less(X1,X2,X3)
    | ~ class_Orderings_Oord(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5610]) ).

cnf(c_0_5610_2,axiom,
    ( ~ class_Orderings_Oord(X3)
    | ~ c_in(X2,c_SetInterval_OgreaterThan(X1,X3),X3)
    | c_less(X1,X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5610]) ).

cnf(c_0_5611_0,axiom,
    ( c_lessequals(X1,X2,X3)
    | ~ c_in(X1,c_SetInterval_OatMost(X2,X3),X3)
    | ~ class_Orderings_Oord(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5611]) ).

cnf(c_0_5611_1,axiom,
    ( ~ c_in(X1,c_SetInterval_OatMost(X2,X3),X3)
    | c_lessequals(X1,X2,X3)
    | ~ class_Orderings_Oord(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5611]) ).

cnf(c_0_5611_2,axiom,
    ( ~ class_Orderings_Oord(X3)
    | ~ c_in(X1,c_SetInterval_OatMost(X2,X3),X3)
    | c_lessequals(X1,X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5611]) ).

cnf(c_0_5612_0,axiom,
    ( c_lessequals(X1,X2,X3)
    | ~ c_in(X2,c_SetInterval_OatLeast(X1,X3),X3)
    | ~ class_Orderings_Oord(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5612]) ).

cnf(c_0_5612_1,axiom,
    ( ~ c_in(X2,c_SetInterval_OatLeast(X1,X3),X3)
    | c_lessequals(X1,X2,X3)
    | ~ class_Orderings_Oord(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5612]) ).

cnf(c_0_5612_2,axiom,
    ( ~ class_Orderings_Oord(X3)
    | ~ c_in(X2,c_SetInterval_OatLeast(X1,X3),X3)
    | c_lessequals(X1,X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5612]) ).

cnf(c_0_5613_0,axiom,
    ( c_in(X1,c_Pow(X2,X3),tc_set(X3))
    | ~ c_lessequals(X1,X2,tc_set(X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_5613]) ).

cnf(c_0_5613_1,axiom,
    ( ~ c_lessequals(X1,X2,tc_set(X3))
    | c_in(X1,c_Pow(X2,X3),tc_set(X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_5613]) ).

cnf(c_0_5615_0,axiom,
    ( c_in(X1,c_SetInterval_OlessThan(X2,X3),X3)
    | ~ c_less(X1,X2,X3)
    | ~ class_Orderings_Oord(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5615]) ).

cnf(c_0_5615_1,axiom,
    ( ~ c_less(X1,X2,X3)
    | c_in(X1,c_SetInterval_OlessThan(X2,X3),X3)
    | ~ class_Orderings_Oord(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5615]) ).

cnf(c_0_5615_2,axiom,
    ( ~ class_Orderings_Oord(X3)
    | ~ c_less(X1,X2,X3)
    | c_in(X1,c_SetInterval_OlessThan(X2,X3),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5615]) ).

cnf(c_0_5616_0,axiom,
    ( c_in(X1,c_SetInterval_OgreaterThan(X2,X3),X3)
    | ~ c_less(X2,X1,X3)
    | ~ class_Orderings_Oord(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5616]) ).

cnf(c_0_5616_1,axiom,
    ( ~ c_less(X2,X1,X3)
    | c_in(X1,c_SetInterval_OgreaterThan(X2,X3),X3)
    | ~ class_Orderings_Oord(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5616]) ).

cnf(c_0_5616_2,axiom,
    ( ~ class_Orderings_Oord(X3)
    | ~ c_less(X2,X1,X3)
    | c_in(X1,c_SetInterval_OgreaterThan(X2,X3),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5616]) ).

cnf(c_0_5617_0,axiom,
    ( c_in(X1,c_SetInterval_OatMost(X2,X3),X3)
    | ~ c_lessequals(X1,X2,X3)
    | ~ class_Orderings_Oord(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5617]) ).

cnf(c_0_5617_1,axiom,
    ( ~ c_lessequals(X1,X2,X3)
    | c_in(X1,c_SetInterval_OatMost(X2,X3),X3)
    | ~ class_Orderings_Oord(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5617]) ).

cnf(c_0_5617_2,axiom,
    ( ~ class_Orderings_Oord(X3)
    | ~ c_lessequals(X1,X2,X3)
    | c_in(X1,c_SetInterval_OatMost(X2,X3),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5617]) ).

cnf(c_0_5618_0,axiom,
    ( c_in(X1,c_SetInterval_OatLeast(X2,X3),X3)
    | ~ c_lessequals(X2,X1,X3)
    | ~ class_Orderings_Oord(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5618]) ).

cnf(c_0_5618_1,axiom,
    ( ~ c_lessequals(X2,X1,X3)
    | c_in(X1,c_SetInterval_OatLeast(X2,X3),X3)
    | ~ class_Orderings_Oord(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5618]) ).

cnf(c_0_5618_2,axiom,
    ( ~ class_Orderings_Oord(X3)
    | ~ c_lessequals(X2,X1,X3)
    | c_in(X1,c_SetInterval_OatLeast(X2,X3),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5618]) ).

cnf(c_0_5619_0,axiom,
    ( X1 = X2
    | c_Datatype__Universe_ONumb(X1,X3,X4) != c_Datatype__Universe_ONumb(X2,X3,X4) ),
    inference(literals_permutation,[status(thm)],[c_0_5619]) ).

cnf(c_0_5619_1,axiom,
    ( c_Datatype__Universe_ONumb(X1,X3,X4) != c_Datatype__Universe_ONumb(X2,X3,X4)
    | X1 = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_5619]) ).

cnf(c_0_5620_0,axiom,
    ( X1 = X2
    | c_Datatype__Universe_OLeaf(X1,X3,X4) != c_Datatype__Universe_OLeaf(X2,X3,X4) ),
    inference(literals_permutation,[status(thm)],[c_0_5620]) ).

cnf(c_0_5620_1,axiom,
    ( c_Datatype__Universe_OLeaf(X1,X3,X4) != c_Datatype__Universe_OLeaf(X2,X3,X4)
    | X1 = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_5620]) ).

cnf(c_0_5621_0,axiom,
    ( X1 = X2
    | c_Sum__Type_OInr(X1,X3,X4) != c_Sum__Type_OInr(X2,X3,X4) ),
    inference(literals_permutation,[status(thm)],[c_0_5621]) ).

cnf(c_0_5621_1,axiom,
    ( c_Sum__Type_OInr(X1,X3,X4) != c_Sum__Type_OInr(X2,X3,X4)
    | X1 = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_5621]) ).

cnf(c_0_5622_0,axiom,
    ( X1 = X2
    | c_Sum__Type_OInl(X1,X3,X4) != c_Sum__Type_OInl(X2,X3,X4) ),
    inference(literals_permutation,[status(thm)],[c_0_5622]) ).

cnf(c_0_5622_1,axiom,
    ( c_Sum__Type_OInl(X1,X3,X4) != c_Sum__Type_OInl(X2,X3,X4)
    | X1 = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_5622]) ).

cnf(c_0_5623_0,axiom,
    ( X1 = X2
    | c_append(X3,X1,X4) != c_append(X3,X2,X4) ),
    inference(literals_permutation,[status(thm)],[c_0_5623]) ).

cnf(c_0_5623_1,axiom,
    ( c_append(X3,X1,X4) != c_append(X3,X2,X4)
    | X1 = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_5623]) ).

cnf(c_0_5624_0,axiom,
    ( X1 = X2
    | c_List_Olist_OCons(X3,X1,X4) != c_List_Olist_OCons(X5,X2,X4) ),
    inference(literals_permutation,[status(thm)],[c_0_5624]) ).

cnf(c_0_5624_1,axiom,
    ( c_List_Olist_OCons(X3,X1,X4) != c_List_Olist_OCons(X5,X2,X4)
    | X1 = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_5624]) ).

cnf(c_0_5625_0,axiom,
    ( X1 = X2
    | c_List_Olist_OCons(X1,X3,X4) != c_List_Olist_OCons(X2,X5,X4) ),
    inference(literals_permutation,[status(thm)],[c_0_5625]) ).

cnf(c_0_5625_1,axiom,
    ( c_List_Olist_OCons(X1,X3,X4) != c_List_Olist_OCons(X2,X5,X4)
    | X1 = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_5625]) ).

cnf(c_0_5626_0,axiom,
    ( X1 = X2
    | c_append(X1,X3,X4) != c_append(X2,X3,X4) ),
    inference(literals_permutation,[status(thm)],[c_0_5626]) ).

cnf(c_0_5626_1,axiom,
    ( c_append(X1,X3,X4) != c_append(X2,X3,X4)
    | X1 = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_5626]) ).

cnf(c_0_5627_0,axiom,
    ( X1 = X2
    | c_Datatype__Universe_OIn1(X1,X3,X4) != c_Datatype__Universe_OIn1(X2,X3,X4) ),
    inference(literals_permutation,[status(thm)],[c_0_5627]) ).

cnf(c_0_5627_1,axiom,
    ( c_Datatype__Universe_OIn1(X1,X3,X4) != c_Datatype__Universe_OIn1(X2,X3,X4)
    | X1 = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_5627]) ).

cnf(c_0_5628_0,axiom,
    ( X1 = X2
    | c_Datatype__Universe_OIn0(X1,X3,X4) != c_Datatype__Universe_OIn0(X2,X3,X4) ),
    inference(literals_permutation,[status(thm)],[c_0_5628]) ).

cnf(c_0_5628_1,axiom,
    ( c_Datatype__Universe_OIn0(X1,X3,X4) != c_Datatype__Universe_OIn0(X2,X3,X4)
    | X1 = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_5628]) ).

cnf(c_0_5629_0,axiom,
    ( X1 = X2
    | c_Datatype__Universe_OAtom(X1,X3,X4) != c_Datatype__Universe_OAtom(X2,X3,X4) ),
    inference(literals_permutation,[status(thm)],[c_0_5629]) ).

cnf(c_0_5629_1,axiom,
    ( c_Datatype__Universe_OAtom(X1,X3,X4) != c_Datatype__Universe_OAtom(X2,X3,X4)
    | X1 = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_5629]) ).

cnf(c_0_5630_0,axiom,
    ( c_Divides_Oop_Advd(X1,X2,tc_IntDef_Oint)
    | ~ c_Divides_Oop_Advd(c_uminus(X1,tc_IntDef_Oint),X2,tc_IntDef_Oint) ),
    inference(literals_permutation,[status(thm)],[c_0_5630]) ).

cnf(c_0_5630_1,axiom,
    ( ~ c_Divides_Oop_Advd(c_uminus(X1,tc_IntDef_Oint),X2,tc_IntDef_Oint)
    | c_Divides_Oop_Advd(X1,X2,tc_IntDef_Oint) ),
    inference(literals_permutation,[status(thm)],[c_0_5630]) ).

cnf(c_0_5631_0,axiom,
    ( c_Divides_Oop_Advd(X1,X2,tc_IntDef_Oint)
    | ~ c_Divides_Oop_Advd(X1,c_uminus(X2,tc_IntDef_Oint),tc_IntDef_Oint) ),
    inference(literals_permutation,[status(thm)],[c_0_5631]) ).

cnf(c_0_5631_1,axiom,
    ( ~ c_Divides_Oop_Advd(X1,c_uminus(X2,tc_IntDef_Oint),tc_IntDef_Oint)
    | c_Divides_Oop_Advd(X1,X2,tc_IntDef_Oint) ),
    inference(literals_permutation,[status(thm)],[c_0_5631]) ).

cnf(c_0_5638_0,axiom,
    ( X1 = X2
    | c_insert(X2,c_emptyset,X3) != c_insert(X1,X4,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5638]) ).

cnf(c_0_5638_1,axiom,
    ( c_insert(X2,c_emptyset,X3) != c_insert(X1,X4,X3)
    | X1 = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_5638]) ).

cnf(c_0_5639_0,axiom,
    ( X1 = X2
    | c_insert(X1,X3,X4) != c_insert(X2,c_emptyset,X4) ),
    inference(literals_permutation,[status(thm)],[c_0_5639]) ).

cnf(c_0_5639_1,axiom,
    ( c_insert(X1,X3,X4) != c_insert(X2,c_emptyset,X4)
    | X1 = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_5639]) ).

cnf(c_0_5640_0,axiom,
    ( X1 = X2
    | c_insert(X1,c_emptyset,X3) != c_insert(X2,c_emptyset,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5640]) ).

cnf(c_0_5640_1,axiom,
    ( c_insert(X1,c_emptyset,X3) != c_insert(X2,c_emptyset,X3)
    | X1 = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_5640]) ).

cnf(c_0_5641_0,axiom,
    ( c_times(X2,c_Main_Ozmod__eq__0D__dest__1(X2,X1),tc_IntDef_Oint) = X1
    | c_Divides_Oop_Amod(X1,X2,tc_IntDef_Oint) != c_0 ),
    inference(literals_permutation,[status(thm)],[c_0_5641]) ).

cnf(c_0_5641_1,axiom,
    ( c_Divides_Oop_Amod(X1,X2,tc_IntDef_Oint) != c_0
    | c_times(X2,c_Main_Ozmod__eq__0D__dest__1(X2,X1),tc_IntDef_Oint) = X1 ),
    inference(literals_permutation,[status(thm)],[c_0_5641]) ).

cnf(c_0_5642_0,axiom,
    ( c_times(X2,c_Main_Omod__eq__0D__dest__1(X2,X1),tc_nat) = X1
    | c_Divides_Oop_Amod(X1,X2,tc_nat) != c_0 ),
    inference(literals_permutation,[status(thm)],[c_0_5642]) ).

cnf(c_0_5642_1,axiom,
    ( c_Divides_Oop_Amod(X1,X2,tc_nat) != c_0
    | c_times(X2,c_Main_Omod__eq__0D__dest__1(X2,X1),tc_nat) = X1 ),
    inference(literals_permutation,[status(thm)],[c_0_5642]) ).

cnf(c_0_5652_0,axiom,
    ( c_Divides_Oop_Advd(c_uminus(X1,tc_IntDef_Oint),X2,tc_IntDef_Oint)
    | ~ c_Divides_Oop_Advd(X1,X2,tc_IntDef_Oint) ),
    inference(literals_permutation,[status(thm)],[c_0_5652]) ).

cnf(c_0_5652_1,axiom,
    ( ~ c_Divides_Oop_Advd(X1,X2,tc_IntDef_Oint)
    | c_Divides_Oop_Advd(c_uminus(X1,tc_IntDef_Oint),X2,tc_IntDef_Oint) ),
    inference(literals_permutation,[status(thm)],[c_0_5652]) ).

cnf(c_0_5653_0,axiom,
    ( c_Divides_Oop_Advd(X1,c_uminus(X2,tc_IntDef_Oint),tc_IntDef_Oint)
    | ~ c_Divides_Oop_Advd(X1,X2,tc_IntDef_Oint) ),
    inference(literals_permutation,[status(thm)],[c_0_5653]) ).

cnf(c_0_5653_1,axiom,
    ( ~ c_Divides_Oop_Advd(X1,X2,tc_IntDef_Oint)
    | c_Divides_Oop_Advd(X1,c_uminus(X2,tc_IntDef_Oint),tc_IntDef_Oint) ),
    inference(literals_permutation,[status(thm)],[c_0_5653]) ).

cnf(c_0_5654_0,axiom,
    ( X1 = X2
    | c_less(X1,X2,tc_set(X3))
    | ~ c_lessequals(X1,X2,tc_set(X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_5654]) ).

cnf(c_0_5654_1,axiom,
    ( c_less(X1,X2,tc_set(X3))
    | X1 = X2
    | ~ c_lessequals(X1,X2,tc_set(X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_5654]) ).

cnf(c_0_5654_2,axiom,
    ( ~ c_lessequals(X1,X2,tc_set(X3))
    | c_less(X1,X2,tc_set(X3))
    | X1 = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_5654]) ).

cnf(c_0_5660_0,axiom,
    ( c_lessequals(X1,X2,tc_set(X3))
    | ~ c_less(X1,X2,tc_set(X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_5660]) ).

cnf(c_0_5660_1,axiom,
    ( ~ c_less(X1,X2,tc_set(X3))
    | c_lessequals(X1,X2,tc_set(X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_5660]) ).

cnf(c_0_5661_0,axiom,
    ( c_less(X1,X2,tc_nat)
    | ~ c_less(c_Suc(X1),c_Suc(X2),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_5661]) ).

cnf(c_0_5661_1,axiom,
    ( ~ c_less(c_Suc(X1),c_Suc(X2),tc_nat)
    | c_less(X1,X2,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_5661]) ).

cnf(c_0_5662_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_5662]) ).

cnf(c_0_5662_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_5662]) ).

cnf(c_0_5663_0,axiom,
    ( c_less(c_Suc(X1),c_Suc(X2),tc_nat)
    | ~ c_less(X1,X2,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_5663]) ).

cnf(c_0_5663_1,axiom,
    ( ~ c_less(X1,X2,tc_nat)
    | c_less(c_Suc(X1),c_Suc(X2),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_5663]) ).

cnf(c_0_5664_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_5664]) ).

cnf(c_0_5664_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_5664]) ).

cnf(c_0_5665_0,axiom,
    ( c_in(X1,c_uminus(X2,tc_set(X3)),X3)
    | c_in(X1,X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5665]) ).

cnf(c_0_5665_1,axiom,
    ( c_in(X1,X2,X3)
    | c_in(X1,c_uminus(X2,tc_set(X3)),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5665]) ).

cnf(c_0_5666_0,axiom,
    ( c_Wellfounded__Recursion_Oacyclic(c_Relation_Oconverse(X1,X2,X2),X2)
    | ~ c_Wellfounded__Recursion_Oacyclic(X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5666]) ).

cnf(c_0_5666_1,axiom,
    ( ~ c_Wellfounded__Recursion_Oacyclic(X1,X2)
    | c_Wellfounded__Recursion_Oacyclic(c_Relation_Oconverse(X1,X2,X2),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5666]) ).

cnf(c_0_5667_0,axiom,
    ( X1 = c_Datatype_Ooption_OSome(X2,X3)
    | ~ c_in(X2,c_Datatype_Oo2s(X1,X3),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5667]) ).

cnf(c_0_5667_1,axiom,
    ( ~ c_in(X2,c_Datatype_Oo2s(X1,X3),X3)
    | X1 = c_Datatype_Ooption_OSome(X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5667]) ).

cnf(c_0_5670_0,axiom,
    ( c_List_Oremdups(X1,X2) = X1
    | c_Nat_Osize(c_List_Oremdups(X1,X2),tc_List_Olist(X2)) != c_Nat_Osize(X1,tc_List_Olist(X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_5670]) ).

cnf(c_0_5670_1,axiom,
    ( c_Nat_Osize(c_List_Oremdups(X1,X2),tc_List_Olist(X2)) != c_Nat_Osize(X1,tc_List_Olist(X2))
    | c_List_Oremdups(X1,X2) = X1 ),
    inference(literals_permutation,[status(thm)],[c_0_5670]) ).

cnf(c_0_5674_0,axiom,
    ( ~ c_less(X1,X1,X2)
    | ~ class_Orderings_Oorder(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5674]) ).

cnf(c_0_5674_1,axiom,
    ( ~ class_Orderings_Oorder(X2)
    | ~ c_less(X1,X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5674]) ).

cnf(c_0_5675_0,axiom,
    ( X1 = c_List_Olist_ONil
    | c_less(c_0,c_Nat_Osize(X1,tc_List_Olist(X2)),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_5675]) ).

cnf(c_0_5675_1,axiom,
    ( c_less(c_0,c_Nat_Osize(X1,tc_List_Olist(X2)),tc_nat)
    | X1 = c_List_Olist_ONil ),
    inference(literals_permutation,[status(thm)],[c_0_5675]) ).

cnf(c_0_5676_0,axiom,
    ( c_Nat_Osize(c_List_Oremdups(X1,X2),tc_List_Olist(X2)) = c_Nat_Osize(X1,tc_List_Olist(X2))
    | c_List_Oremdups(X1,X2) != X1 ),
    inference(literals_permutation,[status(thm)],[c_0_5676]) ).

cnf(c_0_5676_1,axiom,
    ( c_List_Oremdups(X1,X2) != X1
    | c_Nat_Osize(c_List_Oremdups(X1,X2),tc_List_Olist(X2)) = c_Nat_Osize(X1,tc_List_Olist(X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_5676]) ).

cnf(c_0_5677_0,axiom,
    ( X1 = c_0
    | ~ c_less(X1,c_Suc(c_0),tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_5677]) ).

cnf(c_0_5677_1,axiom,
    ( ~ c_less(X1,c_Suc(c_0),tc_nat)
    | X1 = c_0 ),
    inference(literals_permutation,[status(thm)],[c_0_5677]) ).

cnf(c_0_5678_0,axiom,
    ( X1 = c_List_Olist_ONil
    | c_append(X2,X1,X3) != X2 ),
    inference(literals_permutation,[status(thm)],[c_0_5678]) ).

cnf(c_0_5678_1,axiom,
    ( c_append(X2,X1,X3) != X2
    | X1 = c_List_Olist_ONil ),
    inference(literals_permutation,[status(thm)],[c_0_5678]) ).

cnf(c_0_5679_0,axiom,
    ( X1 = c_List_Olist_ONil
    | c_append(X1,X2,X3) != X2 ),
    inference(literals_permutation,[status(thm)],[c_0_5679]) ).

cnf(c_0_5679_1,axiom,
    ( c_append(X1,X2,X3) != X2
    | X1 = c_List_Olist_ONil ),
    inference(literals_permutation,[status(thm)],[c_0_5679]) ).

cnf(c_0_5680_0,axiom,
    ( X1 = c_List_Olist_ONil
    | c_append(X2,X1,X3) != X2 ),
    inference(literals_permutation,[status(thm)],[c_0_5680]) ).

cnf(c_0_5680_1,axiom,
    ( c_append(X2,X1,X3) != X2
    | X1 = c_List_Olist_ONil ),
    inference(literals_permutation,[status(thm)],[c_0_5680]) ).

cnf(c_0_5681_0,axiom,
    ( X1 = c_List_Olist_ONil
    | c_append(X1,X2,X3) != X2 ),
    inference(literals_permutation,[status(thm)],[c_0_5681]) ).

cnf(c_0_5681_1,axiom,
    ( c_append(X1,X2,X3) != X2
    | X1 = c_List_Olist_ONil ),
    inference(literals_permutation,[status(thm)],[c_0_5681]) ).

cnf(c_0_5682_0,axiom,
    ( X1 = c_emptyset
    | c_union(X2,X1,X3) != c_emptyset ),
    inference(literals_permutation,[status(thm)],[c_0_5682]) ).

cnf(c_0_5682_1,axiom,
    ( c_union(X2,X1,X3) != c_emptyset
    | X1 = c_emptyset ),
    inference(literals_permutation,[status(thm)],[c_0_5682]) ).

cnf(c_0_5683_0,axiom,
    ( X1 = c_emptyset
    | c_union(X1,X2,X3) != c_emptyset ),
    inference(literals_permutation,[status(thm)],[c_0_5683]) ).

cnf(c_0_5683_1,axiom,
    ( c_union(X1,X2,X3) != c_emptyset
    | X1 = c_emptyset ),
    inference(literals_permutation,[status(thm)],[c_0_5683]) ).

cnf(c_0_5684_0,axiom,
    ( X1 = c_List_Olist_ONil
    | c_append(X2,X1,X3) != c_List_Olist_ONil ),
    inference(literals_permutation,[status(thm)],[c_0_5684]) ).

cnf(c_0_5684_1,axiom,
    ( c_append(X2,X1,X3) != c_List_Olist_ONil
    | X1 = c_List_Olist_ONil ),
    inference(literals_permutation,[status(thm)],[c_0_5684]) ).

cnf(c_0_5685_0,axiom,
    ( X1 = c_List_Olist_ONil
    | c_append(X1,X2,X3) != c_List_Olist_ONil ),
    inference(literals_permutation,[status(thm)],[c_0_5685]) ).

cnf(c_0_5685_1,axiom,
    ( c_append(X1,X2,X3) != c_List_Olist_ONil
    | X1 = c_List_Olist_ONil ),
    inference(literals_permutation,[status(thm)],[c_0_5685]) ).

cnf(c_0_5686_0,axiom,
    ( X1 = c_List_Olist_ONil
    | c_append(X2,X1,X3) != c_List_Olist_ONil ),
    inference(literals_permutation,[status(thm)],[c_0_5686]) ).

cnf(c_0_5686_1,axiom,
    ( c_append(X2,X1,X3) != c_List_Olist_ONil
    | X1 = c_List_Olist_ONil ),
    inference(literals_permutation,[status(thm)],[c_0_5686]) ).

cnf(c_0_5687_0,axiom,
    ( X1 = c_List_Olist_ONil
    | c_append(X1,X2,X3) != c_List_Olist_ONil ),
    inference(literals_permutation,[status(thm)],[c_0_5687]) ).

cnf(c_0_5687_1,axiom,
    ( c_append(X1,X2,X3) != c_List_Olist_ONil
    | X1 = c_List_Olist_ONil ),
    inference(literals_permutation,[status(thm)],[c_0_5687]) ).

cnf(c_0_5688_0,axiom,
    ( X1 = c_emptyset
    | c_Equiv__Relations_Oquotient(X1,X2,X3) != c_emptyset ),
    inference(literals_permutation,[status(thm)],[c_0_5688]) ).

cnf(c_0_5688_1,axiom,
    ( c_Equiv__Relations_Oquotient(X1,X2,X3) != c_emptyset
    | X1 = c_emptyset ),
    inference(literals_permutation,[status(thm)],[c_0_5688]) ).

cnf(c_0_5689_0,axiom,
    ( X1 = c_emptyset
    | c_Equiv__Relations_Oquotient(X1,X2,X3) != c_emptyset ),
    inference(literals_permutation,[status(thm)],[c_0_5689]) ).

cnf(c_0_5689_1,axiom,
    ( c_Equiv__Relations_Oquotient(X1,X2,X3) != c_emptyset
    | X1 = c_emptyset ),
    inference(literals_permutation,[status(thm)],[c_0_5689]) ).

cnf(c_0_5695_0,axiom,
    ( X1 = c_0
    | c_plus(X2,X1,tc_nat) != c_0 ),
    inference(literals_permutation,[status(thm)],[c_0_5695]) ).

cnf(c_0_5695_1,axiom,
    ( c_plus(X2,X1,tc_nat) != c_0
    | X1 = c_0 ),
    inference(literals_permutation,[status(thm)],[c_0_5695]) ).

cnf(c_0_5696_0,axiom,
    ( X1 = c_0
    | c_plus(X1,X2,tc_nat) != c_0 ),
    inference(literals_permutation,[status(thm)],[c_0_5696]) ).

cnf(c_0_5696_1,axiom,
    ( c_plus(X1,X2,tc_nat) != c_0
    | X1 = c_0 ),
    inference(literals_permutation,[status(thm)],[c_0_5696]) ).

cnf(c_0_5699_0,axiom,
    ( X1 = c_0
    | ~ c_less(X1,c_1,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_5699]) ).

cnf(c_0_5699_1,axiom,
    ( ~ c_less(X1,c_1,tc_nat)
    | X1 = c_0 ),
    inference(literals_permutation,[status(thm)],[c_0_5699]) ).

cnf(c_0_5700_0,axiom,
    ( X1 = c_0
    | ~ c_lessequals(X1,c_0,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_5700]) ).

cnf(c_0_5700_1,axiom,
    ( ~ c_lessequals(X1,c_0,tc_nat)
    | X1 = c_0 ),
    inference(literals_permutation,[status(thm)],[c_0_5700]) ).

cnf(c_0_5701_0,axiom,
    ( X1 = c_0
    | ~ c_Divides_Oop_Advd(c_0,X1,tc_IntDef_Oint) ),
    inference(literals_permutation,[status(thm)],[c_0_5701]) ).

cnf(c_0_5701_1,axiom,
    ( ~ c_Divides_Oop_Advd(c_0,X1,tc_IntDef_Oint)
    | X1 = c_0 ),
    inference(literals_permutation,[status(thm)],[c_0_5701]) ).

cnf(c_0_5702_0,axiom,
    ( X1 = c_0
    | ~ c_Divides_Oop_Advd(c_0,X1,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_5702]) ).

cnf(c_0_5702_1,axiom,
    ( ~ c_Divides_Oop_Advd(c_0,X1,tc_nat)
    | X1 = c_0 ),
    inference(literals_permutation,[status(thm)],[c_0_5702]) ).

cnf(c_0_5707_0,axiom,
    ( c_Wellfounded__Recursion_Owf(c_List_Olex(X1,X2),tc_List_Olist(X2))
    | ~ c_Wellfounded__Recursion_Owf(X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5707]) ).

cnf(c_0_5707_1,axiom,
    ( ~ c_Wellfounded__Recursion_Owf(X1,X2)
    | c_Wellfounded__Recursion_Owf(c_List_Olex(X1,X2),tc_List_Olist(X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_5707]) ).

cnf(c_0_5708_0,axiom,
    ( c_Wellfounded__Recursion_Owf(c_List_Olenlex(X1,X2),tc_List_Olist(X2))
    | ~ c_Wellfounded__Recursion_Owf(X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5708]) ).

cnf(c_0_5708_1,axiom,
    ( ~ c_Wellfounded__Recursion_Owf(X1,X2)
    | c_Wellfounded__Recursion_Owf(c_List_Olenlex(X1,X2),tc_List_Olist(X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_5708]) ).

cnf(c_0_5709_0,axiom,
    ( X1 = X2
    | c_uminus(X1,tc_set(X3)) != c_uminus(X2,tc_set(X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_5709]) ).

cnf(c_0_5709_1,axiom,
    ( c_uminus(X1,tc_set(X3)) != c_uminus(X2,tc_set(X3))
    | X1 = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_5709]) ).

cnf(c_0_5710_0,axiom,
    ( c_lessequals(X1,X1,X2)
    | ~ class_Orderings_Oorder(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5710]) ).

cnf(c_0_5710_1,axiom,
    ( ~ class_Orderings_Oorder(X2)
    | c_lessequals(X1,X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5710]) ).

cnf(c_0_5722_0,axiom,
    ( X1 = X2
    | c_SetInterval_OlessThan(X1,X3) != c_SetInterval_OlessThan(X2,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5722]) ).

cnf(c_0_5722_1,axiom,
    ( c_SetInterval_OlessThan(X1,X3) != c_SetInterval_OlessThan(X2,X3)
    | X1 = X2
    | ~ class_Orderings_Olinorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5722]) ).

cnf(c_0_5722_2,axiom,
    ( ~ class_Orderings_Olinorder(X3)
    | c_SetInterval_OlessThan(X1,X3) != c_SetInterval_OlessThan(X2,X3)
    | X1 = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_5722]) ).

cnf(c_0_5723_0,axiom,
    ( X1 = X2
    | c_SetInterval_OgreaterThan(X1,X3) != c_SetInterval_OgreaterThan(X2,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5723]) ).

cnf(c_0_5723_1,axiom,
    ( c_SetInterval_OgreaterThan(X1,X3) != c_SetInterval_OgreaterThan(X2,X3)
    | X1 = X2
    | ~ class_Orderings_Olinorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5723]) ).

cnf(c_0_5723_2,axiom,
    ( ~ class_Orderings_Olinorder(X3)
    | c_SetInterval_OgreaterThan(X1,X3) != c_SetInterval_OgreaterThan(X2,X3)
    | X1 = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_5723]) ).

cnf(c_0_5724_0,axiom,
    ( X1 = X2
    | c_SetInterval_OatMost(X1,X3) != c_SetInterval_OatMost(X2,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5724]) ).

cnf(c_0_5724_1,axiom,
    ( c_SetInterval_OatMost(X1,X3) != c_SetInterval_OatMost(X2,X3)
    | X1 = X2
    | ~ class_Orderings_Olinorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5724]) ).

cnf(c_0_5724_2,axiom,
    ( ~ class_Orderings_Olinorder(X3)
    | c_SetInterval_OatMost(X1,X3) != c_SetInterval_OatMost(X2,X3)
    | X1 = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_5724]) ).

cnf(c_0_5725_0,axiom,
    ( X1 = X2
    | c_SetInterval_OatLeast(X1,X3) != c_SetInterval_OatLeast(X2,X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5725]) ).

cnf(c_0_5725_1,axiom,
    ( c_SetInterval_OatLeast(X1,X3) != c_SetInterval_OatLeast(X2,X3)
    | X1 = X2
    | ~ class_Orderings_Olinorder(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5725]) ).

cnf(c_0_5725_2,axiom,
    ( ~ class_Orderings_Olinorder(X3)
    | c_SetInterval_OatLeast(X1,X3) != c_SetInterval_OatLeast(X2,X3)
    | X1 = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_5725]) ).

cnf(c_0_5727_0,axiom,
    ( X1 = c_0
    | c_less(c_0,X1,tc_nat) ),
    inference(literals_permutation,[status(thm)],[c_0_5727]) ).

cnf(c_0_5727_1,axiom,
    ( c_less(c_0,X1,tc_nat)
    | X1 = c_0 ),
    inference(literals_permutation,[status(thm)],[c_0_5727]) ).

cnf(c_0_5742_0,axiom,
    ( X1 = X2
    | c_List_Orev(X1,X3) != c_List_Orev(X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5742]) ).

cnf(c_0_5742_1,axiom,
    ( c_List_Orev(X1,X3) != c_List_Orev(X2,X3)
    | X1 = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_5742]) ).

cnf(c_0_5743_0,axiom,
    ( X1 = X2
    | c_List_Ochar_OChar(X3,X1) != c_List_Ochar_OChar(X4,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5743]) ).

cnf(c_0_5743_1,axiom,
    ( c_List_Ochar_OChar(X3,X1) != c_List_Ochar_OChar(X4,X2)
    | X1 = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_5743]) ).

cnf(c_0_5744_0,axiom,
    ( X1 = X2
    | c_List_Ochar_OChar(X1,X3) != c_List_Ochar_OChar(X2,X4) ),
    inference(literals_permutation,[status(thm)],[c_0_5744]) ).

cnf(c_0_5744_1,axiom,
    ( c_List_Ochar_OChar(X1,X3) != c_List_Ochar_OChar(X2,X4)
    | X1 = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_5744]) ).

cnf(c_0_5745_0,axiom,
    ( X1 = X2
    | c_Datatype_Ooption_OSome(X1,X3) != c_Datatype_Ooption_OSome(X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5745]) ).

cnf(c_0_5745_1,axiom,
    ( c_Datatype_Ooption_OSome(X1,X3) != c_Datatype_Ooption_OSome(X2,X3)
    | X1 = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_5745]) ).

cnf(c_0_5746_0,axiom,
    ( class_Finite__Set_Ofinite(tc_sum(X1,X2))
    | ~ class_Finite__Set_Ofinite(X1)
    | ~ class_Finite__Set_Ofinite(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5746]) ).

cnf(c_0_5746_1,axiom,
    ( ~ class_Finite__Set_Ofinite(X1)
    | class_Finite__Set_Ofinite(tc_sum(X1,X2))
    | ~ class_Finite__Set_Ofinite(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5746]) ).

cnf(c_0_5746_2,axiom,
    ( ~ class_Finite__Set_Ofinite(X2)
    | ~ class_Finite__Set_Ofinite(X1)
    | class_Finite__Set_Ofinite(tc_sum(X1,X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_5746]) ).

cnf(c_0_5747_0,axiom,
    ( class_Finite__Set_Ofinite(tc_prod(X1,X2))
    | ~ class_Finite__Set_Ofinite(X1)
    | ~ class_Finite__Set_Ofinite(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5747]) ).

cnf(c_0_5747_1,axiom,
    ( ~ class_Finite__Set_Ofinite(X1)
    | class_Finite__Set_Ofinite(tc_prod(X1,X2))
    | ~ class_Finite__Set_Ofinite(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5747]) ).

cnf(c_0_5747_2,axiom,
    ( ~ class_Finite__Set_Ofinite(X2)
    | ~ class_Finite__Set_Ofinite(X1)
    | class_Finite__Set_Ofinite(tc_prod(X1,X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_5747]) ).

cnf(c_0_5748_0,axiom,
    ( class_Finite__Set_Ofinite(tc_fun(X1,X2))
    | ~ class_Finite__Set_Ofinite(X1)
    | ~ class_Finite__Set_Ofinite(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5748]) ).

cnf(c_0_5748_1,axiom,
    ( ~ class_Finite__Set_Ofinite(X1)
    | class_Finite__Set_Ofinite(tc_fun(X1,X2))
    | ~ class_Finite__Set_Ofinite(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5748]) ).

cnf(c_0_5748_2,axiom,
    ( ~ class_Finite__Set_Ofinite(X2)
    | ~ class_Finite__Set_Ofinite(X1)
    | class_Finite__Set_Ofinite(tc_fun(X1,X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_5748]) ).

cnf(c_0_5749_0,axiom,
    ( c_Datatype_Ooption_OSome(c_Main_Onot__Some__eq__iff1__1(X1,X2),X2) = X1
    | X1 = c_Datatype_Ooption_ONone ),
    inference(literals_permutation,[status(thm)],[c_0_5749]) ).

cnf(c_0_5749_1,axiom,
    ( X1 = c_Datatype_Ooption_ONone
    | c_Datatype_Ooption_OSome(c_Main_Onot__Some__eq__iff1__1(X1,X2),X2) = X1 ),
    inference(literals_permutation,[status(thm)],[c_0_5749]) ).

cnf(c_0_5750_0,axiom,
    ( c_Datatype_Ooption_OSome(c_Main_Onot__None__eq__iff1__1(X1,X2),X2) = X1
    | X1 = c_Datatype_Ooption_ONone ),
    inference(literals_permutation,[status(thm)],[c_0_5750]) ).

cnf(c_0_5750_1,axiom,
    ( X1 = c_Datatype_Ooption_ONone
    | c_Datatype_Ooption_OSome(c_Main_Onot__None__eq__iff1__1(X1,X2),X2) = X1 ),
    inference(literals_permutation,[status(thm)],[c_0_5750]) ).

cnf(c_0_5752_0,axiom,
    ( X1 = c_List_Olist_ONil
    | c_Nat_Osize(X1,tc_List_Olist(X2)) != c_0 ),
    inference(literals_permutation,[status(thm)],[c_0_5752]) ).

cnf(c_0_5752_1,axiom,
    ( c_Nat_Osize(X1,tc_List_Olist(X2)) != c_0
    | X1 = c_List_Olist_ONil ),
    inference(literals_permutation,[status(thm)],[c_0_5752]) ).

cnf(c_0_5754_0,axiom,
    ( X1 = c_List_Olist_ONil
    | c_List_Oset(X1,X2) != c_emptyset ),
    inference(literals_permutation,[status(thm)],[c_0_5754]) ).

cnf(c_0_5754_1,axiom,
    ( c_List_Oset(X1,X2) != c_emptyset
    | X1 = c_List_Olist_ONil ),
    inference(literals_permutation,[status(thm)],[c_0_5754]) ).

cnf(c_0_5755_0,axiom,
    ( X1 = c_List_Olist_ONil
    | c_List_Oset(X1,X2) != c_emptyset ),
    inference(literals_permutation,[status(thm)],[c_0_5755]) ).

cnf(c_0_5755_1,axiom,
    ( c_List_Oset(X1,X2) != c_emptyset
    | X1 = c_List_Olist_ONil ),
    inference(literals_permutation,[status(thm)],[c_0_5755]) ).

cnf(c_0_5756_0,axiom,
    ( X1 = c_List_Olist_ONil
    | c_List_Orev(X1,X2) != c_List_Olist_ONil ),
    inference(literals_permutation,[status(thm)],[c_0_5756]) ).

cnf(c_0_5756_1,axiom,
    ( c_List_Orev(X1,X2) != c_List_Olist_ONil
    | X1 = c_List_Olist_ONil ),
    inference(literals_permutation,[status(thm)],[c_0_5756]) ).

cnf(c_0_5757_0,axiom,
    ( X1 = c_List_Olist_ONil
    | c_List_Orev(X1,X2) != c_List_Olist_ONil ),
    inference(literals_permutation,[status(thm)],[c_0_5757]) ).

cnf(c_0_5757_1,axiom,
    ( c_List_Orev(X1,X2) != c_List_Olist_ONil
    | X1 = c_List_Olist_ONil ),
    inference(literals_permutation,[status(thm)],[c_0_5757]) ).

cnf(c_0_5761_0,axiom,
    ( class_Finite__Set_Ofinite(tc_set(X1))
    | ~ class_Finite__Set_Ofinite(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5761]) ).

cnf(c_0_5761_1,axiom,
    ( ~ class_Finite__Set_Ofinite(X1)
    | class_Finite__Set_Ofinite(tc_set(X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_5761]) ).

cnf(c_0_5762_0,axiom,
    ( class_Finite__Set_Ofinite(tc_Datatype_Ooption(X1))
    | ~ class_Finite__Set_Ofinite(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5762]) ).

cnf(c_0_5762_1,axiom,
    ( ~ class_Finite__Set_Ofinite(X1)
    | class_Finite__Set_Ofinite(tc_Datatype_Ooption(X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_5762]) ).

cnf(c_0_5763_0,axiom,
    ( X1 = X2
    | c_Suc(X1) != c_Suc(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5763]) ).

cnf(c_0_5763_1,axiom,
    ( c_Suc(X1) != c_Suc(X2)
    | X1 = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_5763]) ).

cnf(c_0_5764_0,axiom,
    ( X1 = X2
    | c_IntDef_Oint(X1) != c_IntDef_Oint(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5764]) ).

cnf(c_0_5764_1,axiom,
    ( c_IntDef_Oint(X1) != c_IntDef_Oint(X2)
    | X1 = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_5764]) ).

cnf(c_0_5770_0,axiom,
    ( class_Orderings_Olinorder(X1)
    | ~ class_Wellfounded__Recursion_Owellorder(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5770]) ).

cnf(c_0_5770_1,axiom,
    ( ~ class_Wellfounded__Recursion_Owellorder(X1)
    | class_Orderings_Olinorder(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5770]) ).

cnf(c_0_5771_0,axiom,
    ( class_LOrder_Olorder(X1)
    | ~ class_Wellfounded__Recursion_Owellorder(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5771]) ).

cnf(c_0_5771_1,axiom,
    ( ~ class_Wellfounded__Recursion_Owellorder(X1)
    | class_LOrder_Olorder(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5771]) ).

cnf(c_0_5772_0,axiom,
    ( class_LOrder_Ojoin__semilorder(X1)
    | ~ class_Wellfounded__Recursion_Owellorder(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5772]) ).

cnf(c_0_5772_1,axiom,
    ( ~ class_Wellfounded__Recursion_Owellorder(X1)
    | class_LOrder_Ojoin__semilorder(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5772]) ).

cnf(c_0_5773_0,axiom,
    ( class_LOrder_Omeet__semilorder(X1)
    | ~ class_Wellfounded__Recursion_Owellorder(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5773]) ).

cnf(c_0_5773_1,axiom,
    ( ~ class_Wellfounded__Recursion_Owellorder(X1)
    | class_LOrder_Omeet__semilorder(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5773]) ).

cnf(c_0_5774_0,axiom,
    ( class_Orderings_Oorder(X1)
    | ~ class_Wellfounded__Recursion_Owellorder(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5774]) ).

cnf(c_0_5774_1,axiom,
    ( ~ class_Wellfounded__Recursion_Owellorder(X1)
    | class_Orderings_Oorder(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5774]) ).

cnf(c_0_5775_0,axiom,
    ( class_Orderings_Oord(X1)
    | ~ class_Wellfounded__Recursion_Owellorder(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5775]) ).

cnf(c_0_5775_1,axiom,
    ( ~ class_Wellfounded__Recursion_Owellorder(X1)
    | class_Orderings_Oord(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5775]) ).

cnf(c_0_5776_0,axiom,
    ( class_OrderedGroup_Omonoid__mult(X1)
    | ~ class_Ring__and__Field_Osemiring__1__cancel(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5776]) ).

cnf(c_0_5776_1,axiom,
    ( ~ class_Ring__and__Field_Osemiring__1__cancel(X1)
    | class_OrderedGroup_Omonoid__mult(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5776]) ).

cnf(c_0_5777_0,axiom,
    ( class_HOL_Oplus(X1)
    | ~ class_Ring__and__Field_Osemiring__1__cancel(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5777]) ).

cnf(c_0_5777_1,axiom,
    ( ~ class_Ring__and__Field_Osemiring__1__cancel(X1)
    | class_HOL_Oplus(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5777]) ).

cnf(c_0_5778_0,axiom,
    ( class_OrderedGroup_Osemigroup__add(X1)
    | ~ class_Ring__and__Field_Osemiring__1__cancel(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5778]) ).

cnf(c_0_5778_1,axiom,
    ( ~ class_Ring__and__Field_Osemiring__1__cancel(X1)
    | class_OrderedGroup_Osemigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5778]) ).

cnf(c_0_5779_0,axiom,
    ( class_OrderedGroup_Oab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Osemiring__1__cancel(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5779]) ).

cnf(c_0_5779_1,axiom,
    ( ~ class_Ring__and__Field_Osemiring__1__cancel(X1)
    | class_OrderedGroup_Oab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5779]) ).

cnf(c_0_5780_0,axiom,
    ( class_HOL_Ozero(X1)
    | ~ class_Ring__and__Field_Osemiring__1__cancel(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5780]) ).

cnf(c_0_5780_1,axiom,
    ( ~ class_Ring__and__Field_Osemiring__1__cancel(X1)
    | class_HOL_Ozero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5780]) ).

cnf(c_0_5781_0,axiom,
    ( class_OrderedGroup_Ocomm__monoid__add(X1)
    | ~ class_Ring__and__Field_Osemiring__1__cancel(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5781]) ).

cnf(c_0_5781_1,axiom,
    ( ~ class_Ring__and__Field_Osemiring__1__cancel(X1)
    | class_OrderedGroup_Ocomm__monoid__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5781]) ).

cnf(c_0_5782_0,axiom,
    ( class_Ring__and__Field_Osemiring(X1)
    | ~ class_Ring__and__Field_Osemiring__1__cancel(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5782]) ).

cnf(c_0_5782_1,axiom,
    ( ~ class_Ring__and__Field_Osemiring__1__cancel(X1)
    | class_Ring__and__Field_Osemiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5782]) ).

cnf(c_0_5783_0,axiom,
    ( class_Ring__and__Field_Osemiring__0(X1)
    | ~ class_Ring__and__Field_Osemiring__1__cancel(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5783]) ).

cnf(c_0_5783_1,axiom,
    ( ~ class_Ring__and__Field_Osemiring__1__cancel(X1)
    | class_Ring__and__Field_Osemiring__0(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5783]) ).

cnf(c_0_5784_0,axiom,
    ( class_Ring__and__Field_Osemiring__0__cancel(X1)
    | ~ class_Ring__and__Field_Osemiring__1__cancel(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5784]) ).

cnf(c_0_5784_1,axiom,
    ( ~ class_Ring__and__Field_Osemiring__1__cancel(X1)
    | class_Ring__and__Field_Osemiring__0__cancel(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5784]) ).

cnf(c_0_5785_0,axiom,
    ( class_OrderedGroup_Ocancel__semigroup__add(X1)
    | ~ class_Ring__and__Field_Osemiring__1__cancel(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5785]) ).

cnf(c_0_5785_1,axiom,
    ( ~ class_Ring__and__Field_Osemiring__1__cancel(X1)
    | class_OrderedGroup_Ocancel__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5785]) ).

cnf(c_0_5786_0,axiom,
    ( class_OrderedGroup_Ocancel__ab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Osemiring__1__cancel(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5786]) ).

cnf(c_0_5786_1,axiom,
    ( ~ class_Ring__and__Field_Osemiring__1__cancel(X1)
    | class_OrderedGroup_Ocancel__ab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5786]) ).

cnf(c_0_5787_0,axiom,
    ( class_HOL_Otimes(X1)
    | ~ class_Ring__and__Field_Osemiring__1__cancel(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5787]) ).

cnf(c_0_5787_1,axiom,
    ( ~ class_Ring__and__Field_Osemiring__1__cancel(X1)
    | class_HOL_Otimes(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5787]) ).

cnf(c_0_5788_0,axiom,
    ( class_OrderedGroup_Osemigroup__mult(X1)
    | ~ class_Ring__and__Field_Osemiring__1__cancel(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5788]) ).

cnf(c_0_5788_1,axiom,
    ( ~ class_Ring__and__Field_Osemiring__1__cancel(X1)
    | class_OrderedGroup_Osemigroup__mult(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5788]) ).

cnf(c_0_5789_0,axiom,
    ( class_HOL_Oone(X1)
    | ~ class_Ring__and__Field_Osemiring__1__cancel(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5789]) ).

cnf(c_0_5789_1,axiom,
    ( ~ class_Ring__and__Field_Osemiring__1__cancel(X1)
    | class_HOL_Oone(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5789]) ).

cnf(c_0_5790_0,axiom,
    ( class_Ring__and__Field_Oaxclass__0__neq__1(X1)
    | ~ class_Ring__and__Field_Osemiring__1__cancel(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5790]) ).

cnf(c_0_5790_1,axiom,
    ( ~ class_Ring__and__Field_Osemiring__1__cancel(X1)
    | class_Ring__and__Field_Oaxclass__0__neq__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5790]) ).

cnf(c_0_5791_0,axiom,
    ( class_Ring__and__Field_Osemiring__1(X1)
    | ~ class_Ring__and__Field_Osemiring__1__cancel(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5791]) ).

cnf(c_0_5791_1,axiom,
    ( ~ class_Ring__and__Field_Osemiring__1__cancel(X1)
    | class_Ring__and__Field_Osemiring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5791]) ).

cnf(c_0_5792_0,axiom,
    ( class_OrderedGroup_Osemigroup__add(X1)
    | ~ class_Ring__and__Field_Osemiring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5792]) ).

cnf(c_0_5792_1,axiom,
    ( ~ class_Ring__and__Field_Osemiring__1(X1)
    | class_OrderedGroup_Osemigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5792]) ).

cnf(c_0_5793_0,axiom,
    ( class_OrderedGroup_Oab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Osemiring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5793]) ).

cnf(c_0_5793_1,axiom,
    ( ~ class_Ring__and__Field_Osemiring__1(X1)
    | class_OrderedGroup_Oab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5793]) ).

cnf(c_0_5794_0,axiom,
    ( class_OrderedGroup_Ocomm__monoid__add(X1)
    | ~ class_Ring__and__Field_Osemiring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5794]) ).

cnf(c_0_5794_1,axiom,
    ( ~ class_Ring__and__Field_Osemiring__1(X1)
    | class_OrderedGroup_Ocomm__monoid__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5794]) ).

cnf(c_0_5795_0,axiom,
    ( class_HOL_Otimes(X1)
    | ~ class_Ring__and__Field_Osemiring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5795]) ).

cnf(c_0_5795_1,axiom,
    ( ~ class_Ring__and__Field_Osemiring__1(X1)
    | class_HOL_Otimes(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5795]) ).

cnf(c_0_5796_0,axiom,
    ( class_OrderedGroup_Osemigroup__mult(X1)
    | ~ class_Ring__and__Field_Osemiring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5796]) ).

cnf(c_0_5796_1,axiom,
    ( ~ class_Ring__and__Field_Osemiring__1(X1)
    | class_OrderedGroup_Osemigroup__mult(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5796]) ).

cnf(c_0_5797_0,axiom,
    ( class_Ring__and__Field_Osemiring(X1)
    | ~ class_Ring__and__Field_Osemiring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5797]) ).

cnf(c_0_5797_1,axiom,
    ( ~ class_Ring__and__Field_Osemiring__1(X1)
    | class_Ring__and__Field_Osemiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5797]) ).

cnf(c_0_5798_0,axiom,
    ( class_Ring__and__Field_Osemiring__0(X1)
    | ~ class_Ring__and__Field_Osemiring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5798]) ).

cnf(c_0_5798_1,axiom,
    ( ~ class_Ring__and__Field_Osemiring__1(X1)
    | class_Ring__and__Field_Osemiring__0(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5798]) ).

cnf(c_0_5799_0,axiom,
    ( class_HOL_Oone(X1)
    | ~ class_Ring__and__Field_Osemiring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5799]) ).

cnf(c_0_5799_1,axiom,
    ( ~ class_Ring__and__Field_Osemiring__1(X1)
    | class_HOL_Oone(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5799]) ).

cnf(c_0_5800_0,axiom,
    ( class_OrderedGroup_Omonoid__mult(X1)
    | ~ class_Ring__and__Field_Osemiring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5800]) ).

cnf(c_0_5800_1,axiom,
    ( ~ class_Ring__and__Field_Osemiring__1(X1)
    | class_OrderedGroup_Omonoid__mult(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5800]) ).

cnf(c_0_5801_0,axiom,
    ( class_HOL_Oplus(X1)
    | ~ class_Ring__and__Field_Osemiring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5801]) ).

cnf(c_0_5801_1,axiom,
    ( ~ class_Ring__and__Field_Osemiring__1(X1)
    | class_HOL_Oplus(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5801]) ).

cnf(c_0_5802_0,axiom,
    ( class_HOL_Ozero(X1)
    | ~ class_Ring__and__Field_Osemiring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5802]) ).

cnf(c_0_5802_1,axiom,
    ( ~ class_Ring__and__Field_Osemiring__1(X1)
    | class_HOL_Ozero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5802]) ).

cnf(c_0_5803_0,axiom,
    ( class_Ring__and__Field_Oaxclass__0__neq__1(X1)
    | ~ class_Ring__and__Field_Osemiring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5803]) ).

cnf(c_0_5803_1,axiom,
    ( ~ class_Ring__and__Field_Osemiring__1(X1)
    | class_Ring__and__Field_Oaxclass__0__neq__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5803]) ).

cnf(c_0_5804_0,axiom,
    ( class_OrderedGroup_Ocancel__ab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Osemiring__0__cancel(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5804]) ).

cnf(c_0_5804_1,axiom,
    ( ~ class_Ring__and__Field_Osemiring__0__cancel(X1)
    | class_OrderedGroup_Ocancel__ab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5804]) ).

cnf(c_0_5805_0,axiom,
    ( class_HOL_Ozero(X1)
    | ~ class_Ring__and__Field_Osemiring__0__cancel(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5805]) ).

cnf(c_0_5805_1,axiom,
    ( ~ class_Ring__and__Field_Osemiring__0__cancel(X1)
    | class_HOL_Ozero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5805]) ).

cnf(c_0_5806_0,axiom,
    ( class_HOL_Oplus(X1)
    | ~ class_Ring__and__Field_Osemiring__0__cancel(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5806]) ).

cnf(c_0_5806_1,axiom,
    ( ~ class_Ring__and__Field_Osemiring__0__cancel(X1)
    | class_HOL_Oplus(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5806]) ).

cnf(c_0_5807_0,axiom,
    ( class_OrderedGroup_Osemigroup__add(X1)
    | ~ class_Ring__and__Field_Osemiring__0__cancel(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5807]) ).

cnf(c_0_5807_1,axiom,
    ( ~ class_Ring__and__Field_Osemiring__0__cancel(X1)
    | class_OrderedGroup_Osemigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5807]) ).

cnf(c_0_5808_0,axiom,
    ( class_OrderedGroup_Oab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Osemiring__0__cancel(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5808]) ).

cnf(c_0_5808_1,axiom,
    ( ~ class_Ring__and__Field_Osemiring__0__cancel(X1)
    | class_OrderedGroup_Oab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5808]) ).

cnf(c_0_5809_0,axiom,
    ( class_OrderedGroup_Ocomm__monoid__add(X1)
    | ~ class_Ring__and__Field_Osemiring__0__cancel(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5809]) ).

cnf(c_0_5809_1,axiom,
    ( ~ class_Ring__and__Field_Osemiring__0__cancel(X1)
    | class_OrderedGroup_Ocomm__monoid__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5809]) ).

cnf(c_0_5810_0,axiom,
    ( class_HOL_Otimes(X1)
    | ~ class_Ring__and__Field_Osemiring__0__cancel(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5810]) ).

cnf(c_0_5810_1,axiom,
    ( ~ class_Ring__and__Field_Osemiring__0__cancel(X1)
    | class_HOL_Otimes(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5810]) ).

cnf(c_0_5811_0,axiom,
    ( class_OrderedGroup_Osemigroup__mult(X1)
    | ~ class_Ring__and__Field_Osemiring__0__cancel(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5811]) ).

cnf(c_0_5811_1,axiom,
    ( ~ class_Ring__and__Field_Osemiring__0__cancel(X1)
    | class_OrderedGroup_Osemigroup__mult(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5811]) ).

cnf(c_0_5812_0,axiom,
    ( class_OrderedGroup_Ocancel__semigroup__add(X1)
    | ~ class_Ring__and__Field_Osemiring__0__cancel(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5812]) ).

cnf(c_0_5812_1,axiom,
    ( ~ class_Ring__and__Field_Osemiring__0__cancel(X1)
    | class_OrderedGroup_Ocancel__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5812]) ).

cnf(c_0_5813_0,axiom,
    ( class_Ring__and__Field_Osemiring(X1)
    | ~ class_Ring__and__Field_Osemiring__0__cancel(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5813]) ).

cnf(c_0_5813_1,axiom,
    ( ~ class_Ring__and__Field_Osemiring__0__cancel(X1)
    | class_Ring__and__Field_Osemiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5813]) ).

cnf(c_0_5814_0,axiom,
    ( class_Ring__and__Field_Osemiring__0(X1)
    | ~ class_Ring__and__Field_Osemiring__0__cancel(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5814]) ).

cnf(c_0_5814_1,axiom,
    ( ~ class_Ring__and__Field_Osemiring__0__cancel(X1)
    | class_Ring__and__Field_Osemiring__0(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5814]) ).

cnf(c_0_5815_0,axiom,
    ( class_HOL_Ozero(X1)
    | ~ class_Ring__and__Field_Osemiring__0(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5815]) ).

cnf(c_0_5815_1,axiom,
    ( ~ class_Ring__and__Field_Osemiring__0(X1)
    | class_HOL_Ozero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5815]) ).

cnf(c_0_5816_0,axiom,
    ( class_OrderedGroup_Ocomm__monoid__add(X1)
    | ~ class_Ring__and__Field_Osemiring__0(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5816]) ).

cnf(c_0_5816_1,axiom,
    ( ~ class_Ring__and__Field_Osemiring__0(X1)
    | class_OrderedGroup_Ocomm__monoid__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5816]) ).

cnf(c_0_5817_0,axiom,
    ( class_HOL_Otimes(X1)
    | ~ class_Ring__and__Field_Osemiring__0(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5817]) ).

cnf(c_0_5817_1,axiom,
    ( ~ class_Ring__and__Field_Osemiring__0(X1)
    | class_HOL_Otimes(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5817]) ).

cnf(c_0_5818_0,axiom,
    ( class_OrderedGroup_Osemigroup__mult(X1)
    | ~ class_Ring__and__Field_Osemiring__0(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5818]) ).

cnf(c_0_5818_1,axiom,
    ( ~ class_Ring__and__Field_Osemiring__0(X1)
    | class_OrderedGroup_Osemigroup__mult(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5818]) ).

cnf(c_0_5819_0,axiom,
    ( class_HOL_Oplus(X1)
    | ~ class_Ring__and__Field_Osemiring__0(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5819]) ).

cnf(c_0_5819_1,axiom,
    ( ~ class_Ring__and__Field_Osemiring__0(X1)
    | class_HOL_Oplus(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5819]) ).

cnf(c_0_5820_0,axiom,
    ( class_OrderedGroup_Osemigroup__add(X1)
    | ~ class_Ring__and__Field_Osemiring__0(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5820]) ).

cnf(c_0_5820_1,axiom,
    ( ~ class_Ring__and__Field_Osemiring__0(X1)
    | class_OrderedGroup_Osemigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5820]) ).

cnf(c_0_5821_0,axiom,
    ( class_OrderedGroup_Oab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Osemiring__0(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5821]) ).

cnf(c_0_5821_1,axiom,
    ( ~ class_Ring__and__Field_Osemiring__0(X1)
    | class_OrderedGroup_Oab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5821]) ).

cnf(c_0_5822_0,axiom,
    ( class_Ring__and__Field_Osemiring(X1)
    | ~ class_Ring__and__Field_Osemiring__0(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5822]) ).

cnf(c_0_5822_1,axiom,
    ( ~ class_Ring__and__Field_Osemiring__0(X1)
    | class_Ring__and__Field_Osemiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5822]) ).

cnf(c_0_5823_0,axiom,
    ( class_HOL_Otimes(X1)
    | ~ class_Ring__and__Field_Osemiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5823]) ).

cnf(c_0_5823_1,axiom,
    ( ~ class_Ring__and__Field_Osemiring(X1)
    | class_HOL_Otimes(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5823]) ).

cnf(c_0_5824_0,axiom,
    ( class_OrderedGroup_Osemigroup__mult(X1)
    | ~ class_Ring__and__Field_Osemiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5824]) ).

cnf(c_0_5824_1,axiom,
    ( ~ class_Ring__and__Field_Osemiring(X1)
    | class_OrderedGroup_Osemigroup__mult(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5824]) ).

cnf(c_0_5825_0,axiom,
    ( class_HOL_Oplus(X1)
    | ~ class_Ring__and__Field_Osemiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5825]) ).

cnf(c_0_5825_1,axiom,
    ( ~ class_Ring__and__Field_Osemiring(X1)
    | class_HOL_Oplus(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5825]) ).

cnf(c_0_5826_0,axiom,
    ( class_OrderedGroup_Osemigroup__add(X1)
    | ~ class_Ring__and__Field_Osemiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5826]) ).

cnf(c_0_5826_1,axiom,
    ( ~ class_Ring__and__Field_Osemiring(X1)
    | class_OrderedGroup_Osemigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5826]) ).

cnf(c_0_5827_0,axiom,
    ( class_OrderedGroup_Oab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Osemiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5827]) ).

cnf(c_0_5827_1,axiom,
    ( ~ class_Ring__and__Field_Osemiring(X1)
    | class_OrderedGroup_Oab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5827]) ).

cnf(c_0_5828_0,axiom,
    ( class_HOL_Otimes(X1)
    | ~ class_Ring__and__Field_Oring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5828]) ).

cnf(c_0_5828_1,axiom,
    ( ~ class_Ring__and__Field_Oring__1(X1)
    | class_HOL_Otimes(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5828]) ).

cnf(c_0_5829_0,axiom,
    ( class_OrderedGroup_Osemigroup__mult(X1)
    | ~ class_Ring__and__Field_Oring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5829]) ).

cnf(c_0_5829_1,axiom,
    ( ~ class_Ring__and__Field_Oring__1(X1)
    | class_OrderedGroup_Osemigroup__mult(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5829]) ).

cnf(c_0_5830_0,axiom,
    ( class_Ring__and__Field_Osemiring(X1)
    | ~ class_Ring__and__Field_Oring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5830]) ).

cnf(c_0_5830_1,axiom,
    ( ~ class_Ring__and__Field_Oring__1(X1)
    | class_Ring__and__Field_Osemiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5830]) ).

cnf(c_0_5831_0,axiom,
    ( class_Ring__and__Field_Osemiring__0(X1)
    | ~ class_Ring__and__Field_Oring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5831]) ).

cnf(c_0_5831_1,axiom,
    ( ~ class_Ring__and__Field_Oring__1(X1)
    | class_Ring__and__Field_Osemiring__0(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5831]) ).

cnf(c_0_5832_0,axiom,
    ( class_OrderedGroup_Ocancel__semigroup__add(X1)
    | ~ class_Ring__and__Field_Oring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5832]) ).

cnf(c_0_5832_1,axiom,
    ( ~ class_Ring__and__Field_Oring__1(X1)
    | class_OrderedGroup_Ocancel__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5832]) ).

cnf(c_0_5833_0,axiom,
    ( class_OrderedGroup_Ocancel__ab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Oring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5833]) ).

cnf(c_0_5833_1,axiom,
    ( ~ class_Ring__and__Field_Oring__1(X1)
    | class_OrderedGroup_Ocancel__ab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5833]) ).

cnf(c_0_5834_0,axiom,
    ( class_Ring__and__Field_Osemiring__0__cancel(X1)
    | ~ class_Ring__and__Field_Oring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5834]) ).

cnf(c_0_5834_1,axiom,
    ( ~ class_Ring__and__Field_Oring__1(X1)
    | class_Ring__and__Field_Osemiring__0__cancel(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5834]) ).

cnf(c_0_5835_0,axiom,
    ( class_HOL_Ominus(X1)
    | ~ class_Ring__and__Field_Oring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5835]) ).

cnf(c_0_5835_1,axiom,
    ( ~ class_Ring__and__Field_Oring__1(X1)
    | class_HOL_Ominus(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5835]) ).

cnf(c_0_5836_0,axiom,
    ( class_Ring__and__Field_Osemiring__1__cancel(X1)
    | ~ class_Ring__and__Field_Oring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5836]) ).

cnf(c_0_5836_1,axiom,
    ( ~ class_Ring__and__Field_Oring__1(X1)
    | class_Ring__and__Field_Osemiring__1__cancel(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5836]) ).

cnf(c_0_5837_0,axiom,
    ( class_HOL_Oone(X1)
    | ~ class_Ring__and__Field_Oring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5837]) ).

cnf(c_0_5837_1,axiom,
    ( ~ class_Ring__and__Field_Oring__1(X1)
    | class_HOL_Oone(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5837]) ).

cnf(c_0_5838_0,axiom,
    ( class_OrderedGroup_Omonoid__mult(X1)
    | ~ class_Ring__and__Field_Oring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5838]) ).

cnf(c_0_5838_1,axiom,
    ( ~ class_Ring__and__Field_Oring__1(X1)
    | class_OrderedGroup_Omonoid__mult(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5838]) ).

cnf(c_0_5839_0,axiom,
    ( class_Ring__and__Field_Oaxclass__0__neq__1(X1)
    | ~ class_Ring__and__Field_Oring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5839]) ).

cnf(c_0_5839_1,axiom,
    ( ~ class_Ring__and__Field_Oring__1(X1)
    | class_Ring__and__Field_Oaxclass__0__neq__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5839]) ).

cnf(c_0_5840_0,axiom,
    ( class_Ring__and__Field_Osemiring__1(X1)
    | ~ class_Ring__and__Field_Oring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5840]) ).

cnf(c_0_5840_1,axiom,
    ( ~ class_Ring__and__Field_Oring__1(X1)
    | class_Ring__and__Field_Osemiring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5840]) ).

cnf(c_0_5841_0,axiom,
    ( class_HOL_Ozero(X1)
    | ~ class_Ring__and__Field_Oring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5841]) ).

cnf(c_0_5841_1,axiom,
    ( ~ class_Ring__and__Field_Oring__1(X1)
    | class_HOL_Ozero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5841]) ).

cnf(c_0_5842_0,axiom,
    ( class_HOL_Oplus(X1)
    | ~ class_Ring__and__Field_Oring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5842]) ).

cnf(c_0_5842_1,axiom,
    ( ~ class_Ring__and__Field_Oring__1(X1)
    | class_HOL_Oplus(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5842]) ).

cnf(c_0_5843_0,axiom,
    ( class_OrderedGroup_Osemigroup__add(X1)
    | ~ class_Ring__and__Field_Oring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5843]) ).

cnf(c_0_5843_1,axiom,
    ( ~ class_Ring__and__Field_Oring__1(X1)
    | class_OrderedGroup_Osemigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5843]) ).

cnf(c_0_5844_0,axiom,
    ( class_OrderedGroup_Oab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Oring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5844]) ).

cnf(c_0_5844_1,axiom,
    ( ~ class_Ring__and__Field_Oring__1(X1)
    | class_OrderedGroup_Oab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5844]) ).

cnf(c_0_5845_0,axiom,
    ( class_OrderedGroup_Ocomm__monoid__add(X1)
    | ~ class_Ring__and__Field_Oring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5845]) ).

cnf(c_0_5845_1,axiom,
    ( ~ class_Ring__and__Field_Oring__1(X1)
    | class_OrderedGroup_Ocomm__monoid__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5845]) ).

cnf(c_0_5846_0,axiom,
    ( class_OrderedGroup_Oab__group__add(X1)
    | ~ class_Ring__and__Field_Oring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5846]) ).

cnf(c_0_5846_1,axiom,
    ( ~ class_Ring__and__Field_Oring__1(X1)
    | class_OrderedGroup_Oab__group__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5846]) ).

cnf(c_0_5847_0,axiom,
    ( class_Ring__and__Field_Oring(X1)
    | ~ class_Ring__and__Field_Oring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5847]) ).

cnf(c_0_5847_1,axiom,
    ( ~ class_Ring__and__Field_Oring__1(X1)
    | class_Ring__and__Field_Oring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5847]) ).

cnf(c_0_5848_0,axiom,
    ( class_HOL_Ozero(X1)
    | ~ class_Ring__and__Field_Oring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5848]) ).

cnf(c_0_5848_1,axiom,
    ( ~ class_Ring__and__Field_Oring(X1)
    | class_HOL_Ozero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5848]) ).

cnf(c_0_5849_0,axiom,
    ( class_OrderedGroup_Ocomm__monoid__add(X1)
    | ~ class_Ring__and__Field_Oring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5849]) ).

cnf(c_0_5849_1,axiom,
    ( ~ class_Ring__and__Field_Oring(X1)
    | class_OrderedGroup_Ocomm__monoid__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5849]) ).

cnf(c_0_5850_0,axiom,
    ( class_HOL_Ominus(X1)
    | ~ class_Ring__and__Field_Oring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5850]) ).

cnf(c_0_5850_1,axiom,
    ( ~ class_Ring__and__Field_Oring(X1)
    | class_HOL_Ominus(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5850]) ).

cnf(c_0_5851_0,axiom,
    ( class_OrderedGroup_Oab__group__add(X1)
    | ~ class_Ring__and__Field_Oring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5851]) ).

cnf(c_0_5851_1,axiom,
    ( ~ class_Ring__and__Field_Oring(X1)
    | class_OrderedGroup_Oab__group__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5851]) ).

cnf(c_0_5852_0,axiom,
    ( class_HOL_Otimes(X1)
    | ~ class_Ring__and__Field_Oring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5852]) ).

cnf(c_0_5852_1,axiom,
    ( ~ class_Ring__and__Field_Oring(X1)
    | class_HOL_Otimes(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5852]) ).

cnf(c_0_5853_0,axiom,
    ( class_OrderedGroup_Osemigroup__mult(X1)
    | ~ class_Ring__and__Field_Oring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5853]) ).

cnf(c_0_5853_1,axiom,
    ( ~ class_Ring__and__Field_Oring(X1)
    | class_OrderedGroup_Osemigroup__mult(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5853]) ).

cnf(c_0_5854_0,axiom,
    ( class_HOL_Oplus(X1)
    | ~ class_Ring__and__Field_Oring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5854]) ).

cnf(c_0_5854_1,axiom,
    ( ~ class_Ring__and__Field_Oring(X1)
    | class_HOL_Oplus(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5854]) ).

cnf(c_0_5855_0,axiom,
    ( class_OrderedGroup_Osemigroup__add(X1)
    | ~ class_Ring__and__Field_Oring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5855]) ).

cnf(c_0_5855_1,axiom,
    ( ~ class_Ring__and__Field_Oring(X1)
    | class_OrderedGroup_Osemigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5855]) ).

cnf(c_0_5856_0,axiom,
    ( class_Ring__and__Field_Osemiring__0(X1)
    | ~ class_Ring__and__Field_Oring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5856]) ).

cnf(c_0_5856_1,axiom,
    ( ~ class_Ring__and__Field_Oring(X1)
    | class_Ring__and__Field_Osemiring__0(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5856]) ).

cnf(c_0_5857_0,axiom,
    ( class_Ring__and__Field_Osemiring__0__cancel(X1)
    | ~ class_Ring__and__Field_Oring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5857]) ).

cnf(c_0_5857_1,axiom,
    ( ~ class_Ring__and__Field_Oring(X1)
    | class_Ring__and__Field_Osemiring__0__cancel(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5857]) ).

cnf(c_0_5858_0,axiom,
    ( class_OrderedGroup_Ocancel__semigroup__add(X1)
    | ~ class_Ring__and__Field_Oring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5858]) ).

cnf(c_0_5858_1,axiom,
    ( ~ class_Ring__and__Field_Oring(X1)
    | class_OrderedGroup_Ocancel__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5858]) ).

cnf(c_0_5859_0,axiom,
    ( class_OrderedGroup_Ocancel__ab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Oring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5859]) ).

cnf(c_0_5859_1,axiom,
    ( ~ class_Ring__and__Field_Oring(X1)
    | class_OrderedGroup_Ocancel__ab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5859]) ).

cnf(c_0_5860_0,axiom,
    ( class_OrderedGroup_Oab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Oring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5860]) ).

cnf(c_0_5860_1,axiom,
    ( ~ class_Ring__and__Field_Oring(X1)
    | class_OrderedGroup_Oab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5860]) ).

cnf(c_0_5861_0,axiom,
    ( class_Ring__and__Field_Osemiring(X1)
    | ~ class_Ring__and__Field_Oring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5861]) ).

cnf(c_0_5861_1,axiom,
    ( ~ class_Ring__and__Field_Oring(X1)
    | class_Ring__and__Field_Osemiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5861]) ).

cnf(c_0_5862_0,axiom,
    ( class_OrderedGroup_Opordered__ab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Opordered__semiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5862]) ).

cnf(c_0_5862_1,axiom,
    ( ~ class_Ring__and__Field_Opordered__semiring(X1)
    | class_OrderedGroup_Opordered__ab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5862]) ).

cnf(c_0_5863_0,axiom,
    ( class_HOL_Ozero(X1)
    | ~ class_Ring__and__Field_Opordered__semiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5863]) ).

cnf(c_0_5863_1,axiom,
    ( ~ class_Ring__and__Field_Opordered__semiring(X1)
    | class_HOL_Ozero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5863]) ).

cnf(c_0_5864_0,axiom,
    ( class_HOL_Oplus(X1)
    | ~ class_Ring__and__Field_Opordered__semiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5864]) ).

cnf(c_0_5864_1,axiom,
    ( ~ class_Ring__and__Field_Opordered__semiring(X1)
    | class_HOL_Oplus(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5864]) ).

cnf(c_0_5865_0,axiom,
    ( class_OrderedGroup_Osemigroup__add(X1)
    | ~ class_Ring__and__Field_Opordered__semiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5865]) ).

cnf(c_0_5865_1,axiom,
    ( ~ class_Ring__and__Field_Opordered__semiring(X1)
    | class_OrderedGroup_Osemigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5865]) ).

cnf(c_0_5866_0,axiom,
    ( class_OrderedGroup_Oab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Opordered__semiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5866]) ).

cnf(c_0_5866_1,axiom,
    ( ~ class_Ring__and__Field_Opordered__semiring(X1)
    | class_OrderedGroup_Oab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5866]) ).

cnf(c_0_5867_0,axiom,
    ( class_OrderedGroup_Ocomm__monoid__add(X1)
    | ~ class_Ring__and__Field_Opordered__semiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5867]) ).

cnf(c_0_5867_1,axiom,
    ( ~ class_Ring__and__Field_Opordered__semiring(X1)
    | class_OrderedGroup_Ocomm__monoid__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5867]) ).

cnf(c_0_5868_0,axiom,
    ( class_HOL_Otimes(X1)
    | ~ class_Ring__and__Field_Opordered__semiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5868]) ).

cnf(c_0_5868_1,axiom,
    ( ~ class_Ring__and__Field_Opordered__semiring(X1)
    | class_HOL_Otimes(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5868]) ).

cnf(c_0_5869_0,axiom,
    ( class_OrderedGroup_Osemigroup__mult(X1)
    | ~ class_Ring__and__Field_Opordered__semiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5869]) ).

cnf(c_0_5869_1,axiom,
    ( ~ class_Ring__and__Field_Opordered__semiring(X1)
    | class_OrderedGroup_Osemigroup__mult(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5869]) ).

cnf(c_0_5870_0,axiom,
    ( class_Orderings_Oord(X1)
    | ~ class_Ring__and__Field_Opordered__semiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5870]) ).

cnf(c_0_5870_1,axiom,
    ( ~ class_Ring__and__Field_Opordered__semiring(X1)
    | class_Orderings_Oord(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5870]) ).

cnf(c_0_5871_0,axiom,
    ( class_Orderings_Oorder(X1)
    | ~ class_Ring__and__Field_Opordered__semiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5871]) ).

cnf(c_0_5871_1,axiom,
    ( ~ class_Ring__and__Field_Opordered__semiring(X1)
    | class_Orderings_Oorder(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5871]) ).

cnf(c_0_5872_0,axiom,
    ( class_Ring__and__Field_Osemiring(X1)
    | ~ class_Ring__and__Field_Opordered__semiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5872]) ).

cnf(c_0_5872_1,axiom,
    ( ~ class_Ring__and__Field_Opordered__semiring(X1)
    | class_Ring__and__Field_Osemiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5872]) ).

cnf(c_0_5873_0,axiom,
    ( class_Ring__and__Field_Osemiring__0(X1)
    | ~ class_Ring__and__Field_Opordered__semiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5873]) ).

cnf(c_0_5873_1,axiom,
    ( ~ class_Ring__and__Field_Opordered__semiring(X1)
    | class_Ring__and__Field_Osemiring__0(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5873]) ).

cnf(c_0_5874_0,axiom,
    ( class_HOL_Otimes(X1)
    | ~ class_Ring__and__Field_Opordered__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5874]) ).

cnf(c_0_5874_1,axiom,
    ( ~ class_Ring__and__Field_Opordered__ring(X1)
    | class_HOL_Otimes(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5874]) ).

cnf(c_0_5875_0,axiom,
    ( class_OrderedGroup_Osemigroup__mult(X1)
    | ~ class_Ring__and__Field_Opordered__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5875]) ).

cnf(c_0_5875_1,axiom,
    ( ~ class_Ring__and__Field_Opordered__ring(X1)
    | class_OrderedGroup_Osemigroup__mult(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5875]) ).

cnf(c_0_5876_0,axiom,
    ( class_Ring__and__Field_Osemiring(X1)
    | ~ class_Ring__and__Field_Opordered__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5876]) ).

cnf(c_0_5876_1,axiom,
    ( ~ class_Ring__and__Field_Opordered__ring(X1)
    | class_Ring__and__Field_Osemiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5876]) ).

cnf(c_0_5877_0,axiom,
    ( class_Ring__and__Field_Osemiring__0(X1)
    | ~ class_Ring__and__Field_Opordered__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5877]) ).

cnf(c_0_5877_1,axiom,
    ( ~ class_Ring__and__Field_Opordered__ring(X1)
    | class_Ring__and__Field_Osemiring__0(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5877]) ).

cnf(c_0_5878_0,axiom,
    ( class_OrderedGroup_Ocancel__semigroup__add(X1)
    | ~ class_Ring__and__Field_Opordered__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5878]) ).

cnf(c_0_5878_1,axiom,
    ( ~ class_Ring__and__Field_Opordered__ring(X1)
    | class_OrderedGroup_Ocancel__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5878]) ).

cnf(c_0_5879_0,axiom,
    ( class_OrderedGroup_Ocancel__ab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Opordered__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5879]) ).

cnf(c_0_5879_1,axiom,
    ( ~ class_Ring__and__Field_Opordered__ring(X1)
    | class_OrderedGroup_Ocancel__ab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5879]) ).

cnf(c_0_5880_0,axiom,
    ( class_Ring__and__Field_Osemiring__0__cancel(X1)
    | ~ class_Ring__and__Field_Opordered__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5880]) ).

cnf(c_0_5880_1,axiom,
    ( ~ class_Ring__and__Field_Opordered__ring(X1)
    | class_Ring__and__Field_Osemiring__0__cancel(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5880]) ).

cnf(c_0_5881_0,axiom,
    ( class_Ring__and__Field_Opordered__cancel__semiring(X1)
    | ~ class_Ring__and__Field_Opordered__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5881]) ).

cnf(c_0_5881_1,axiom,
    ( ~ class_Ring__and__Field_Opordered__ring(X1)
    | class_Ring__and__Field_Opordered__cancel__semiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5881]) ).

cnf(c_0_5882_0,axiom,
    ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Opordered__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5882]) ).

cnf(c_0_5882_1,axiom,
    ( ~ class_Ring__and__Field_Opordered__ring(X1)
    | class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5882]) ).

cnf(c_0_5883_0,axiom,
    ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
    | ~ class_Ring__and__Field_Opordered__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5883]) ).

cnf(c_0_5883_1,axiom,
    ( ~ class_Ring__and__Field_Opordered__ring(X1)
    | class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5883]) ).

cnf(c_0_5884_0,axiom,
    ( class_HOL_Ominus(X1)
    | ~ class_Ring__and__Field_Opordered__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5884]) ).

cnf(c_0_5884_1,axiom,
    ( ~ class_Ring__and__Field_Opordered__ring(X1)
    | class_HOL_Ominus(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5884]) ).

cnf(c_0_5885_0,axiom,
    ( class_OrderedGroup_Opordered__ab__group__add(X1)
    | ~ class_Ring__and__Field_Opordered__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5885]) ).

cnf(c_0_5885_1,axiom,
    ( ~ class_Ring__and__Field_Opordered__ring(X1)
    | class_OrderedGroup_Opordered__ab__group__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5885]) ).

cnf(c_0_5886_0,axiom,
    ( class_Orderings_Oord(X1)
    | ~ class_Ring__and__Field_Opordered__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5886]) ).

cnf(c_0_5886_1,axiom,
    ( ~ class_Ring__and__Field_Opordered__ring(X1)
    | class_Orderings_Oord(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5886]) ).

cnf(c_0_5887_0,axiom,
    ( class_Orderings_Oorder(X1)
    | ~ class_Ring__and__Field_Opordered__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5887]) ).

cnf(c_0_5887_1,axiom,
    ( ~ class_Ring__and__Field_Opordered__ring(X1)
    | class_Orderings_Oorder(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5887]) ).

cnf(c_0_5888_0,axiom,
    ( class_OrderedGroup_Opordered__ab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Opordered__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5888]) ).

cnf(c_0_5888_1,axiom,
    ( ~ class_Ring__and__Field_Opordered__ring(X1)
    | class_OrderedGroup_Opordered__ab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5888]) ).

cnf(c_0_5889_0,axiom,
    ( class_Ring__and__Field_Opordered__semiring(X1)
    | ~ class_Ring__and__Field_Opordered__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5889]) ).

cnf(c_0_5889_1,axiom,
    ( ~ class_Ring__and__Field_Opordered__ring(X1)
    | class_Ring__and__Field_Opordered__semiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5889]) ).

cnf(c_0_5890_0,axiom,
    ( class_HOL_Ozero(X1)
    | ~ class_Ring__and__Field_Opordered__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5890]) ).

cnf(c_0_5890_1,axiom,
    ( ~ class_Ring__and__Field_Opordered__ring(X1)
    | class_HOL_Ozero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5890]) ).

cnf(c_0_5891_0,axiom,
    ( class_HOL_Oplus(X1)
    | ~ class_Ring__and__Field_Opordered__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5891]) ).

cnf(c_0_5891_1,axiom,
    ( ~ class_Ring__and__Field_Opordered__ring(X1)
    | class_HOL_Oplus(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5891]) ).

cnf(c_0_5892_0,axiom,
    ( class_OrderedGroup_Osemigroup__add(X1)
    | ~ class_Ring__and__Field_Opordered__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5892]) ).

cnf(c_0_5892_1,axiom,
    ( ~ class_Ring__and__Field_Opordered__ring(X1)
    | class_OrderedGroup_Osemigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5892]) ).

cnf(c_0_5893_0,axiom,
    ( class_OrderedGroup_Oab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Opordered__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5893]) ).

cnf(c_0_5893_1,axiom,
    ( ~ class_Ring__and__Field_Opordered__ring(X1)
    | class_OrderedGroup_Oab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5893]) ).

cnf(c_0_5894_0,axiom,
    ( class_OrderedGroup_Ocomm__monoid__add(X1)
    | ~ class_Ring__and__Field_Opordered__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5894]) ).

cnf(c_0_5894_1,axiom,
    ( ~ class_Ring__and__Field_Opordered__ring(X1)
    | class_OrderedGroup_Ocomm__monoid__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5894]) ).

cnf(c_0_5895_0,axiom,
    ( class_OrderedGroup_Oab__group__add(X1)
    | ~ class_Ring__and__Field_Opordered__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5895]) ).

cnf(c_0_5895_1,axiom,
    ( ~ class_Ring__and__Field_Opordered__ring(X1)
    | class_OrderedGroup_Oab__group__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5895]) ).

cnf(c_0_5896_0,axiom,
    ( class_Ring__and__Field_Oring(X1)
    | ~ class_Ring__and__Field_Opordered__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5896]) ).

cnf(c_0_5896_1,axiom,
    ( ~ class_Ring__and__Field_Opordered__ring(X1)
    | class_Ring__and__Field_Oring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5896]) ).

cnf(c_0_5897_0,axiom,
    ( class_OrderedGroup_Osemigroup__add(X1)
    | ~ class_Ring__and__Field_Opordered__comm__semiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5897]) ).

cnf(c_0_5897_1,axiom,
    ( ~ class_Ring__and__Field_Opordered__comm__semiring(X1)
    | class_OrderedGroup_Osemigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5897]) ).

cnf(c_0_5898_0,axiom,
    ( class_OrderedGroup_Oab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Opordered__comm__semiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5898]) ).

cnf(c_0_5898_1,axiom,
    ( ~ class_Ring__and__Field_Opordered__comm__semiring(X1)
    | class_OrderedGroup_Oab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5898]) ).

cnf(c_0_5899_0,axiom,
    ( class_OrderedGroup_Ocomm__monoid__add(X1)
    | ~ class_Ring__and__Field_Opordered__comm__semiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5899]) ).

cnf(c_0_5899_1,axiom,
    ( ~ class_Ring__and__Field_Opordered__comm__semiring(X1)
    | class_OrderedGroup_Ocomm__monoid__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5899]) ).

cnf(c_0_5900_0,axiom,
    ( class_HOL_Otimes(X1)
    | ~ class_Ring__and__Field_Opordered__comm__semiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5900]) ).

cnf(c_0_5900_1,axiom,
    ( ~ class_Ring__and__Field_Opordered__comm__semiring(X1)
    | class_HOL_Otimes(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5900]) ).

cnf(c_0_5901_0,axiom,
    ( class_OrderedGroup_Osemigroup__mult(X1)
    | ~ class_Ring__and__Field_Opordered__comm__semiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5901]) ).

cnf(c_0_5901_1,axiom,
    ( ~ class_Ring__and__Field_Opordered__comm__semiring(X1)
    | class_OrderedGroup_Osemigroup__mult(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5901]) ).

cnf(c_0_5902_0,axiom,
    ( class_Ring__and__Field_Osemiring(X1)
    | ~ class_Ring__and__Field_Opordered__comm__semiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5902]) ).

cnf(c_0_5902_1,axiom,
    ( ~ class_Ring__and__Field_Opordered__comm__semiring(X1)
    | class_Ring__and__Field_Osemiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5902]) ).

cnf(c_0_5903_0,axiom,
    ( class_Ring__and__Field_Osemiring__0(X1)
    | ~ class_Ring__and__Field_Opordered__comm__semiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5903]) ).

cnf(c_0_5903_1,axiom,
    ( ~ class_Ring__and__Field_Opordered__comm__semiring(X1)
    | class_Ring__and__Field_Osemiring__0(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5903]) ).

cnf(c_0_5904_0,axiom,
    ( class_OrderedGroup_Oab__semigroup__mult(X1)
    | ~ class_Ring__and__Field_Opordered__comm__semiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5904]) ).

cnf(c_0_5904_1,axiom,
    ( ~ class_Ring__and__Field_Opordered__comm__semiring(X1)
    | class_OrderedGroup_Oab__semigroup__mult(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5904]) ).

cnf(c_0_5905_0,axiom,
    ( class_Ring__and__Field_Opordered__semiring(X1)
    | ~ class_Ring__and__Field_Opordered__comm__semiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5905]) ).

cnf(c_0_5905_1,axiom,
    ( ~ class_Ring__and__Field_Opordered__comm__semiring(X1)
    | class_Ring__and__Field_Opordered__semiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5905]) ).

cnf(c_0_5906_0,axiom,
    ( class_Orderings_Oord(X1)
    | ~ class_Ring__and__Field_Opordered__comm__semiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5906]) ).

cnf(c_0_5906_1,axiom,
    ( ~ class_Ring__and__Field_Opordered__comm__semiring(X1)
    | class_Orderings_Oord(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5906]) ).

cnf(c_0_5907_0,axiom,
    ( class_Orderings_Oorder(X1)
    | ~ class_Ring__and__Field_Opordered__comm__semiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5907]) ).

cnf(c_0_5907_1,axiom,
    ( ~ class_Ring__and__Field_Opordered__comm__semiring(X1)
    | class_Orderings_Oorder(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5907]) ).

cnf(c_0_5908_0,axiom,
    ( class_OrderedGroup_Opordered__ab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Opordered__comm__semiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5908]) ).

cnf(c_0_5908_1,axiom,
    ( ~ class_Ring__and__Field_Opordered__comm__semiring(X1)
    | class_OrderedGroup_Opordered__ab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5908]) ).

cnf(c_0_5909_0,axiom,
    ( class_HOL_Ozero(X1)
    | ~ class_Ring__and__Field_Opordered__comm__semiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5909]) ).

cnf(c_0_5909_1,axiom,
    ( ~ class_Ring__and__Field_Opordered__comm__semiring(X1)
    | class_HOL_Ozero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5909]) ).

cnf(c_0_5910_0,axiom,
    ( class_HOL_Oplus(X1)
    | ~ class_Ring__and__Field_Opordered__comm__semiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5910]) ).

cnf(c_0_5910_1,axiom,
    ( ~ class_Ring__and__Field_Opordered__comm__semiring(X1)
    | class_HOL_Oplus(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5910]) ).

cnf(c_0_5911_0,axiom,
    ( class_Ring__and__Field_Ocomm__semiring(X1)
    | ~ class_Ring__and__Field_Opordered__comm__semiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5911]) ).

cnf(c_0_5911_1,axiom,
    ( ~ class_Ring__and__Field_Opordered__comm__semiring(X1)
    | class_Ring__and__Field_Ocomm__semiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5911]) ).

cnf(c_0_5912_0,axiom,
    ( class_Ring__and__Field_Ocomm__semiring__0(X1)
    | ~ class_Ring__and__Field_Opordered__comm__semiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5912]) ).

cnf(c_0_5912_1,axiom,
    ( ~ class_Ring__and__Field_Opordered__comm__semiring(X1)
    | class_Ring__and__Field_Ocomm__semiring__0(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5912]) ).

cnf(c_0_5913_0,axiom,
    ( class_Ring__and__Field_Osemiring__0(X1)
    | ~ class_Ring__and__Field_Opordered__comm__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5913]) ).

cnf(c_0_5913_1,axiom,
    ( ~ class_Ring__and__Field_Opordered__comm__ring(X1)
    | class_Ring__and__Field_Osemiring__0(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5913]) ).

cnf(c_0_5914_0,axiom,
    ( class_Ring__and__Field_Osemiring__0__cancel(X1)
    | ~ class_Ring__and__Field_Opordered__comm__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5914]) ).

cnf(c_0_5914_1,axiom,
    ( ~ class_Ring__and__Field_Opordered__comm__ring(X1)
    | class_Ring__and__Field_Osemiring__0__cancel(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5914]) ).

cnf(c_0_5915_0,axiom,
    ( class_OrderedGroup_Oab__semigroup__mult(X1)
    | ~ class_Ring__and__Field_Opordered__comm__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5915]) ).

cnf(c_0_5915_1,axiom,
    ( ~ class_Ring__and__Field_Opordered__comm__ring(X1)
    | class_OrderedGroup_Oab__semigroup__mult(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5915]) ).

cnf(c_0_5916_0,axiom,
    ( class_Ring__and__Field_Ocomm__semiring(X1)
    | ~ class_Ring__and__Field_Opordered__comm__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5916]) ).

cnf(c_0_5916_1,axiom,
    ( ~ class_Ring__and__Field_Opordered__comm__ring(X1)
    | class_Ring__and__Field_Ocomm__semiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5916]) ).

cnf(c_0_5917_0,axiom,
    ( class_Ring__and__Field_Ocomm__semiring__0(X1)
    | ~ class_Ring__and__Field_Opordered__comm__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5917]) ).

cnf(c_0_5917_1,axiom,
    ( ~ class_Ring__and__Field_Opordered__comm__ring(X1)
    | class_Ring__and__Field_Ocomm__semiring__0(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5917]) ).

cnf(c_0_5918_0,axiom,
    ( class_Ring__and__Field_Ocomm__semiring__0__cancel(X1)
    | ~ class_Ring__and__Field_Opordered__comm__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5918]) ).

cnf(c_0_5918_1,axiom,
    ( ~ class_Ring__and__Field_Opordered__comm__ring(X1)
    | class_Ring__and__Field_Ocomm__semiring__0__cancel(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5918]) ).

cnf(c_0_5919_0,axiom,
    ( class_HOL_Ominus(X1)
    | ~ class_Ring__and__Field_Opordered__comm__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5919]) ).

cnf(c_0_5919_1,axiom,
    ( ~ class_Ring__and__Field_Opordered__comm__ring(X1)
    | class_HOL_Ominus(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5919]) ).

cnf(c_0_5920_0,axiom,
    ( class_Orderings_Oord(X1)
    | ~ class_Ring__and__Field_Opordered__comm__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5920]) ).

cnf(c_0_5920_1,axiom,
    ( ~ class_Ring__and__Field_Opordered__comm__ring(X1)
    | class_Orderings_Oord(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5920]) ).

cnf(c_0_5921_0,axiom,
    ( class_Orderings_Oorder(X1)
    | ~ class_Ring__and__Field_Opordered__comm__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5921]) ).

cnf(c_0_5921_1,axiom,
    ( ~ class_Ring__and__Field_Opordered__comm__ring(X1)
    | class_Orderings_Oorder(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5921]) ).

cnf(c_0_5922_0,axiom,
    ( class_OrderedGroup_Opordered__ab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Opordered__comm__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5922]) ).

cnf(c_0_5922_1,axiom,
    ( ~ class_Ring__and__Field_Opordered__comm__ring(X1)
    | class_OrderedGroup_Opordered__ab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5922]) ).

cnf(c_0_5923_0,axiom,
    ( class_Ring__and__Field_Opordered__semiring(X1)
    | ~ class_Ring__and__Field_Opordered__comm__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5923]) ).

cnf(c_0_5923_1,axiom,
    ( ~ class_Ring__and__Field_Opordered__comm__ring(X1)
    | class_Ring__and__Field_Opordered__semiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5923]) ).

cnf(c_0_5924_0,axiom,
    ( class_Ring__and__Field_Opordered__comm__semiring(X1)
    | ~ class_Ring__and__Field_Opordered__comm__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5924]) ).

cnf(c_0_5924_1,axiom,
    ( ~ class_Ring__and__Field_Opordered__comm__ring(X1)
    | class_Ring__and__Field_Opordered__comm__semiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5924]) ).

cnf(c_0_5925_0,axiom,
    ( class_OrderedGroup_Oab__group__add(X1)
    | ~ class_Ring__and__Field_Opordered__comm__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5925]) ).

cnf(c_0_5925_1,axiom,
    ( ~ class_Ring__and__Field_Opordered__comm__ring(X1)
    | class_OrderedGroup_Oab__group__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5925]) ).

cnf(c_0_5926_0,axiom,
    ( class_HOL_Oplus(X1)
    | ~ class_Ring__and__Field_Opordered__comm__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5926]) ).

cnf(c_0_5926_1,axiom,
    ( ~ class_Ring__and__Field_Opordered__comm__ring(X1)
    | class_HOL_Oplus(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5926]) ).

cnf(c_0_5927_0,axiom,
    ( class_OrderedGroup_Osemigroup__add(X1)
    | ~ class_Ring__and__Field_Opordered__comm__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5927]) ).

cnf(c_0_5927_1,axiom,
    ( ~ class_Ring__and__Field_Opordered__comm__ring(X1)
    | class_OrderedGroup_Osemigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5927]) ).

cnf(c_0_5928_0,axiom,
    ( class_OrderedGroup_Ocancel__semigroup__add(X1)
    | ~ class_Ring__and__Field_Opordered__comm__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5928]) ).

cnf(c_0_5928_1,axiom,
    ( ~ class_Ring__and__Field_Opordered__comm__ring(X1)
    | class_OrderedGroup_Ocancel__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5928]) ).

cnf(c_0_5929_0,axiom,
    ( class_OrderedGroup_Oab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Opordered__comm__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5929]) ).

cnf(c_0_5929_1,axiom,
    ( ~ class_Ring__and__Field_Opordered__comm__ring(X1)
    | class_OrderedGroup_Oab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5929]) ).

cnf(c_0_5930_0,axiom,
    ( class_OrderedGroup_Ocancel__ab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Opordered__comm__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5930]) ).

cnf(c_0_5930_1,axiom,
    ( ~ class_Ring__and__Field_Opordered__comm__ring(X1)
    | class_OrderedGroup_Ocancel__ab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5930]) ).

cnf(c_0_5931_0,axiom,
    ( class_HOL_Ozero(X1)
    | ~ class_Ring__and__Field_Opordered__comm__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5931]) ).

cnf(c_0_5931_1,axiom,
    ( ~ class_Ring__and__Field_Opordered__comm__ring(X1)
    | class_HOL_Ozero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5931]) ).

cnf(c_0_5932_0,axiom,
    ( class_OrderedGroup_Ocomm__monoid__add(X1)
    | ~ class_Ring__and__Field_Opordered__comm__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5932]) ).

cnf(c_0_5932_1,axiom,
    ( ~ class_Ring__and__Field_Opordered__comm__ring(X1)
    | class_OrderedGroup_Ocomm__monoid__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5932]) ).

cnf(c_0_5933_0,axiom,
    ( class_HOL_Otimes(X1)
    | ~ class_Ring__and__Field_Opordered__comm__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5933]) ).

cnf(c_0_5933_1,axiom,
    ( ~ class_Ring__and__Field_Opordered__comm__ring(X1)
    | class_HOL_Otimes(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5933]) ).

cnf(c_0_5934_0,axiom,
    ( class_OrderedGroup_Osemigroup__mult(X1)
    | ~ class_Ring__and__Field_Opordered__comm__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5934]) ).

cnf(c_0_5934_1,axiom,
    ( ~ class_Ring__and__Field_Opordered__comm__ring(X1)
    | class_OrderedGroup_Osemigroup__mult(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5934]) ).

cnf(c_0_5935_0,axiom,
    ( class_Ring__and__Field_Osemiring(X1)
    | ~ class_Ring__and__Field_Opordered__comm__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5935]) ).

cnf(c_0_5935_1,axiom,
    ( ~ class_Ring__and__Field_Opordered__comm__ring(X1)
    | class_Ring__and__Field_Osemiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5935]) ).

cnf(c_0_5936_0,axiom,
    ( class_Ring__and__Field_Oring(X1)
    | ~ class_Ring__and__Field_Opordered__comm__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5936]) ).

cnf(c_0_5936_1,axiom,
    ( ~ class_Ring__and__Field_Opordered__comm__ring(X1)
    | class_Ring__and__Field_Oring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5936]) ).

cnf(c_0_5937_0,axiom,
    ( class_Ring__and__Field_Ocomm__ring(X1)
    | ~ class_Ring__and__Field_Opordered__comm__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5937]) ).

cnf(c_0_5937_1,axiom,
    ( ~ class_Ring__and__Field_Opordered__comm__ring(X1)
    | class_Ring__and__Field_Ocomm__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5937]) ).

cnf(c_0_5938_0,axiom,
    ( class_OrderedGroup_Osemigroup__add(X1)
    | ~ class_Ring__and__Field_Opordered__cancel__semiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5938]) ).

cnf(c_0_5938_1,axiom,
    ( ~ class_Ring__and__Field_Opordered__cancel__semiring(X1)
    | class_OrderedGroup_Osemigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5938]) ).

cnf(c_0_5939_0,axiom,
    ( class_OrderedGroup_Oab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Opordered__cancel__semiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5939]) ).

cnf(c_0_5939_1,axiom,
    ( ~ class_Ring__and__Field_Opordered__cancel__semiring(X1)
    | class_OrderedGroup_Oab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5939]) ).

cnf(c_0_5940_0,axiom,
    ( class_OrderedGroup_Opordered__ab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Opordered__cancel__semiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5940]) ).

cnf(c_0_5940_1,axiom,
    ( ~ class_Ring__and__Field_Opordered__cancel__semiring(X1)
    | class_OrderedGroup_Opordered__ab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5940]) ).

cnf(c_0_5941_0,axiom,
    ( class_HOL_Ozero(X1)
    | ~ class_Ring__and__Field_Opordered__cancel__semiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5941]) ).

cnf(c_0_5941_1,axiom,
    ( ~ class_Ring__and__Field_Opordered__cancel__semiring(X1)
    | class_HOL_Ozero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5941]) ).

cnf(c_0_5942_0,axiom,
    ( class_OrderedGroup_Ocomm__monoid__add(X1)
    | ~ class_Ring__and__Field_Opordered__cancel__semiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5942]) ).

cnf(c_0_5942_1,axiom,
    ( ~ class_Ring__and__Field_Opordered__cancel__semiring(X1)
    | class_OrderedGroup_Ocomm__monoid__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5942]) ).

cnf(c_0_5943_0,axiom,
    ( class_HOL_Otimes(X1)
    | ~ class_Ring__and__Field_Opordered__cancel__semiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5943]) ).

cnf(c_0_5943_1,axiom,
    ( ~ class_Ring__and__Field_Opordered__cancel__semiring(X1)
    | class_HOL_Otimes(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5943]) ).

cnf(c_0_5944_0,axiom,
    ( class_OrderedGroup_Osemigroup__mult(X1)
    | ~ class_Ring__and__Field_Opordered__cancel__semiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5944]) ).

cnf(c_0_5944_1,axiom,
    ( ~ class_Ring__and__Field_Opordered__cancel__semiring(X1)
    | class_OrderedGroup_Osemigroup__mult(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5944]) ).

cnf(c_0_5945_0,axiom,
    ( class_Ring__and__Field_Osemiring(X1)
    | ~ class_Ring__and__Field_Opordered__cancel__semiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5945]) ).

cnf(c_0_5945_1,axiom,
    ( ~ class_Ring__and__Field_Opordered__cancel__semiring(X1)
    | class_Ring__and__Field_Osemiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5945]) ).

cnf(c_0_5946_0,axiom,
    ( class_Ring__and__Field_Osemiring__0__cancel(X1)
    | ~ class_Ring__and__Field_Opordered__cancel__semiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5946]) ).

cnf(c_0_5946_1,axiom,
    ( ~ class_Ring__and__Field_Opordered__cancel__semiring(X1)
    | class_Ring__and__Field_Osemiring__0__cancel(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5946]) ).

cnf(c_0_5947_0,axiom,
    ( class_OrderedGroup_Ocancel__semigroup__add(X1)
    | ~ class_Ring__and__Field_Opordered__cancel__semiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5947]) ).

cnf(c_0_5947_1,axiom,
    ( ~ class_Ring__and__Field_Opordered__cancel__semiring(X1)
    | class_OrderedGroup_Ocancel__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5947]) ).

cnf(c_0_5948_0,axiom,
    ( class_OrderedGroup_Ocancel__ab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Opordered__cancel__semiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5948]) ).

cnf(c_0_5948_1,axiom,
    ( ~ class_Ring__and__Field_Opordered__cancel__semiring(X1)
    | class_OrderedGroup_Ocancel__ab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5948]) ).

cnf(c_0_5949_0,axiom,
    ( class_Orderings_Oord(X1)
    | ~ class_Ring__and__Field_Opordered__cancel__semiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5949]) ).

cnf(c_0_5949_1,axiom,
    ( ~ class_Ring__and__Field_Opordered__cancel__semiring(X1)
    | class_Orderings_Oord(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5949]) ).

cnf(c_0_5950_0,axiom,
    ( class_Orderings_Oorder(X1)
    | ~ class_Ring__and__Field_Opordered__cancel__semiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5950]) ).

cnf(c_0_5950_1,axiom,
    ( ~ class_Ring__and__Field_Opordered__cancel__semiring(X1)
    | class_Orderings_Oorder(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5950]) ).

cnf(c_0_5951_0,axiom,
    ( class_HOL_Oplus(X1)
    | ~ class_Ring__and__Field_Opordered__cancel__semiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5951]) ).

cnf(c_0_5951_1,axiom,
    ( ~ class_Ring__and__Field_Opordered__cancel__semiring(X1)
    | class_HOL_Oplus(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5951]) ).

cnf(c_0_5952_0,axiom,
    ( class_Ring__and__Field_Osemiring__0(X1)
    | ~ class_Ring__and__Field_Opordered__cancel__semiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5952]) ).

cnf(c_0_5952_1,axiom,
    ( ~ class_Ring__and__Field_Opordered__cancel__semiring(X1)
    | class_Ring__and__Field_Osemiring__0(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5952]) ).

cnf(c_0_5953_0,axiom,
    ( class_Ring__and__Field_Opordered__semiring(X1)
    | ~ class_Ring__and__Field_Opordered__cancel__semiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5953]) ).

cnf(c_0_5953_1,axiom,
    ( ~ class_Ring__and__Field_Opordered__cancel__semiring(X1)
    | class_Ring__and__Field_Opordered__semiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5953]) ).

cnf(c_0_5954_0,axiom,
    ( class_HOL_Ozero(X1)
    | ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5954]) ).

cnf(c_0_5954_1,axiom,
    ( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X1)
    | class_HOL_Ozero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5954]) ).

cnf(c_0_5955_0,axiom,
    ( class_OrderedGroup_Ocomm__monoid__add(X1)
    | ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5955]) ).

cnf(c_0_5955_1,axiom,
    ( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X1)
    | class_OrderedGroup_Ocomm__monoid__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5955]) ).

cnf(c_0_5956_0,axiom,
    ( class_HOL_Otimes(X1)
    | ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5956]) ).

cnf(c_0_5956_1,axiom,
    ( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X1)
    | class_HOL_Otimes(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5956]) ).

cnf(c_0_5957_0,axiom,
    ( class_OrderedGroup_Osemigroup__mult(X1)
    | ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5957]) ).

cnf(c_0_5957_1,axiom,
    ( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X1)
    | class_OrderedGroup_Osemigroup__mult(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5957]) ).

cnf(c_0_5958_0,axiom,
    ( class_Ring__and__Field_Osemiring(X1)
    | ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5958]) ).

cnf(c_0_5958_1,axiom,
    ( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X1)
    | class_Ring__and__Field_Osemiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5958]) ).

cnf(c_0_5959_0,axiom,
    ( class_Ring__and__Field_Osemiring__0(X1)
    | ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5959]) ).

cnf(c_0_5959_1,axiom,
    ( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X1)
    | class_Ring__and__Field_Osemiring__0(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5959]) ).

cnf(c_0_5960_0,axiom,
    ( class_OrderedGroup_Oab__semigroup__mult(X1)
    | ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5960]) ).

cnf(c_0_5960_1,axiom,
    ( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X1)
    | class_OrderedGroup_Oab__semigroup__mult(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5960]) ).

cnf(c_0_5961_0,axiom,
    ( class_Ring__and__Field_Osemiring__0__cancel(X1)
    | ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5961]) ).

cnf(c_0_5961_1,axiom,
    ( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X1)
    | class_Ring__and__Field_Osemiring__0__cancel(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5961]) ).

cnf(c_0_5962_0,axiom,
    ( class_Ring__and__Field_Ocomm__semiring(X1)
    | ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5962]) ).

cnf(c_0_5962_1,axiom,
    ( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X1)
    | class_Ring__and__Field_Ocomm__semiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5962]) ).

cnf(c_0_5963_0,axiom,
    ( class_Ring__and__Field_Opordered__cancel__semiring(X1)
    | ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5963]) ).

cnf(c_0_5963_1,axiom,
    ( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X1)
    | class_Ring__and__Field_Opordered__cancel__semiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5963]) ).

cnf(c_0_5964_0,axiom,
    ( class_Ring__and__Field_Opordered__semiring(X1)
    | ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5964]) ).

cnf(c_0_5964_1,axiom,
    ( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X1)
    | class_Ring__and__Field_Opordered__semiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5964]) ).

cnf(c_0_5965_0,axiom,
    ( class_OrderedGroup_Ocancel__semigroup__add(X1)
    | ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5965]) ).

cnf(c_0_5965_1,axiom,
    ( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X1)
    | class_OrderedGroup_Ocancel__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5965]) ).

cnf(c_0_5966_0,axiom,
    ( class_OrderedGroup_Ocancel__ab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5966]) ).

cnf(c_0_5966_1,axiom,
    ( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X1)
    | class_OrderedGroup_Ocancel__ab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5966]) ).

cnf(c_0_5967_0,axiom,
    ( class_Orderings_Oord(X1)
    | ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5967]) ).

cnf(c_0_5967_1,axiom,
    ( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X1)
    | class_Orderings_Oord(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5967]) ).

cnf(c_0_5968_0,axiom,
    ( class_Orderings_Oorder(X1)
    | ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5968]) ).

cnf(c_0_5968_1,axiom,
    ( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X1)
    | class_Orderings_Oorder(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5968]) ).

cnf(c_0_5969_0,axiom,
    ( class_HOL_Oplus(X1)
    | ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5969]) ).

cnf(c_0_5969_1,axiom,
    ( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X1)
    | class_HOL_Oplus(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5969]) ).

cnf(c_0_5970_0,axiom,
    ( class_OrderedGroup_Osemigroup__add(X1)
    | ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5970]) ).

cnf(c_0_5970_1,axiom,
    ( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X1)
    | class_OrderedGroup_Osemigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5970]) ).

cnf(c_0_5971_0,axiom,
    ( class_OrderedGroup_Oab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5971]) ).

cnf(c_0_5971_1,axiom,
    ( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X1)
    | class_OrderedGroup_Oab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5971]) ).

cnf(c_0_5972_0,axiom,
    ( class_OrderedGroup_Opordered__ab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5972]) ).

cnf(c_0_5972_1,axiom,
    ( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X1)
    | class_OrderedGroup_Opordered__ab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5972]) ).

cnf(c_0_5973_0,axiom,
    ( class_Ring__and__Field_Ocomm__semiring__0(X1)
    | ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5973]) ).

cnf(c_0_5973_1,axiom,
    ( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X1)
    | class_Ring__and__Field_Ocomm__semiring__0(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5973]) ).

cnf(c_0_5974_0,axiom,
    ( class_Ring__and__Field_Opordered__comm__semiring(X1)
    | ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5974]) ).

cnf(c_0_5974_1,axiom,
    ( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X1)
    | class_Ring__and__Field_Opordered__comm__semiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5974]) ).

cnf(c_0_5975_0,axiom,
    ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5975]) ).

cnf(c_0_5975_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__semiring__strict(X1)
    | class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5975]) ).

cnf(c_0_5976_0,axiom,
    ( class_HOL_Ozero(X1)
    | ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5976]) ).

cnf(c_0_5976_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__semiring__strict(X1)
    | class_HOL_Ozero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5976]) ).

cnf(c_0_5977_0,axiom,
    ( class_HOL_Oplus(X1)
    | ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5977]) ).

cnf(c_0_5977_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__semiring__strict(X1)
    | class_HOL_Oplus(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5977]) ).

cnf(c_0_5978_0,axiom,
    ( class_OrderedGroup_Osemigroup__add(X1)
    | ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5978]) ).

cnf(c_0_5978_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__semiring__strict(X1)
    | class_OrderedGroup_Osemigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5978]) ).

cnf(c_0_5979_0,axiom,
    ( class_OrderedGroup_Oab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5979]) ).

cnf(c_0_5979_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__semiring__strict(X1)
    | class_OrderedGroup_Oab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5979]) ).

cnf(c_0_5980_0,axiom,
    ( class_OrderedGroup_Ocomm__monoid__add(X1)
    | ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5980]) ).

cnf(c_0_5980_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__semiring__strict(X1)
    | class_OrderedGroup_Ocomm__monoid__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5980]) ).

cnf(c_0_5981_0,axiom,
    ( class_HOL_Otimes(X1)
    | ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5981]) ).

cnf(c_0_5981_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__semiring__strict(X1)
    | class_HOL_Otimes(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5981]) ).

cnf(c_0_5982_0,axiom,
    ( class_Ring__and__Field_Opordered__semiring(X1)
    | ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5982]) ).

cnf(c_0_5982_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__semiring__strict(X1)
    | class_Ring__and__Field_Opordered__semiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5982]) ).

cnf(c_0_5983_0,axiom,
    ( class_Ring__and__Field_Opordered__cancel__semiring(X1)
    | ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5983]) ).

cnf(c_0_5983_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__semiring__strict(X1)
    | class_Ring__and__Field_Opordered__cancel__semiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5983]) ).

cnf(c_0_5984_0,axiom,
    ( class_Ring__and__Field_Osemiring__0__cancel(X1)
    | ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5984]) ).

cnf(c_0_5984_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__semiring__strict(X1)
    | class_Ring__and__Field_Osemiring__0__cancel(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5984]) ).

cnf(c_0_5985_0,axiom,
    ( class_OrderedGroup_Ocancel__semigroup__add(X1)
    | ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5985]) ).

cnf(c_0_5985_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__semiring__strict(X1)
    | class_OrderedGroup_Ocancel__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5985]) ).

cnf(c_0_5986_0,axiom,
    ( class_OrderedGroup_Osemigroup__mult(X1)
    | ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5986]) ).

cnf(c_0_5986_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__semiring__strict(X1)
    | class_OrderedGroup_Osemigroup__mult(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5986]) ).

cnf(c_0_5987_0,axiom,
    ( class_OrderedGroup_Ocancel__ab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5987]) ).

cnf(c_0_5987_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__semiring__strict(X1)
    | class_OrderedGroup_Ocancel__ab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5987]) ).

cnf(c_0_5988_0,axiom,
    ( class_Orderings_Oord(X1)
    | ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5988]) ).

cnf(c_0_5988_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__semiring__strict(X1)
    | class_Orderings_Oord(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5988]) ).

cnf(c_0_5989_0,axiom,
    ( class_Orderings_Oorder(X1)
    | ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5989]) ).

cnf(c_0_5989_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__semiring__strict(X1)
    | class_Orderings_Oorder(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5989]) ).

cnf(c_0_5990_0,axiom,
    ( class_OrderedGroup_Opordered__ab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5990]) ).

cnf(c_0_5990_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__semiring__strict(X1)
    | class_OrderedGroup_Opordered__ab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5990]) ).

cnf(c_0_5991_0,axiom,
    ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5991]) ).

cnf(c_0_5991_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__semiring__strict(X1)
    | class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5991]) ).

cnf(c_0_5992_0,axiom,
    ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
    | ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5992]) ).

cnf(c_0_5992_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__semiring__strict(X1)
    | class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5992]) ).

cnf(c_0_5993_0,axiom,
    ( class_LOrder_Omeet__semilorder(X1)
    | ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5993]) ).

cnf(c_0_5993_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__semiring__strict(X1)
    | class_LOrder_Omeet__semilorder(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5993]) ).

cnf(c_0_5994_0,axiom,
    ( class_LOrder_Ojoin__semilorder(X1)
    | ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5994]) ).

cnf(c_0_5994_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__semiring__strict(X1)
    | class_LOrder_Ojoin__semilorder(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5994]) ).

cnf(c_0_5995_0,axiom,
    ( class_LOrder_Olorder(X1)
    | ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5995]) ).

cnf(c_0_5995_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__semiring__strict(X1)
    | class_LOrder_Olorder(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5995]) ).

cnf(c_0_5996_0,axiom,
    ( class_Orderings_Olinorder(X1)
    | ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5996]) ).

cnf(c_0_5996_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__semiring__strict(X1)
    | class_Orderings_Olinorder(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5996]) ).

cnf(c_0_5997_0,axiom,
    ( class_Ring__and__Field_Osemiring(X1)
    | ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5997]) ).

cnf(c_0_5997_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__semiring__strict(X1)
    | class_Ring__and__Field_Osemiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5997]) ).

cnf(c_0_5998_0,axiom,
    ( class_Ring__and__Field_Osemiring__0(X1)
    | ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5998]) ).

cnf(c_0_5998_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__semiring__strict(X1)
    | class_Ring__and__Field_Osemiring__0(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5998]) ).

cnf(c_0_5999_0,axiom,
    ( class_Ring__and__Field_Ocomm__semiring__0(X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5999]) ).

cnf(c_0_5999_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__semidom(X1)
    | class_Ring__and__Field_Ocomm__semiring__0(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5999]) ).

cnf(c_0_6000_0,axiom,
    ( class_Ring__and__Field_Ocomm__semiring__0__cancel(X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6000]) ).

cnf(c_0_6000_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__semidom(X1)
    | class_Ring__and__Field_Ocomm__semiring__0__cancel(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6000]) ).

cnf(c_0_6001_0,axiom,
    ( class_HOL_Oone(X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6001]) ).

cnf(c_0_6001_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__semidom(X1)
    | class_HOL_Oone(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6001]) ).

cnf(c_0_6002_0,axiom,
    ( class_OrderedGroup_Omonoid__mult(X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6002]) ).

cnf(c_0_6002_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__semidom(X1)
    | class_OrderedGroup_Omonoid__mult(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6002]) ).

cnf(c_0_6003_0,axiom,
    ( class_Ring__and__Field_Oaxclass__0__neq__1(X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6003]) ).

cnf(c_0_6003_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__semidom(X1)
    | class_Ring__and__Field_Oaxclass__0__neq__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6003]) ).

cnf(c_0_6004_0,axiom,
    ( class_Ring__and__Field_Osemiring__1(X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6004]) ).

cnf(c_0_6004_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__semidom(X1)
    | class_Ring__and__Field_Osemiring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6004]) ).

cnf(c_0_6005_0,axiom,
    ( class_Orderings_Oord(X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6005]) ).

cnf(c_0_6005_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__semidom(X1)
    | class_Orderings_Oord(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6005]) ).

cnf(c_0_6006_0,axiom,
    ( class_Orderings_Oorder(X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6006]) ).

cnf(c_0_6006_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__semidom(X1)
    | class_Orderings_Oorder(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6006]) ).

cnf(c_0_6007_0,axiom,
    ( class_OrderedGroup_Opordered__ab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6007]) ).

cnf(c_0_6007_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__semidom(X1)
    | class_OrderedGroup_Opordered__ab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6007]) ).

cnf(c_0_6008_0,axiom,
    ( class_Ring__and__Field_Opordered__semiring(X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6008]) ).

cnf(c_0_6008_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__semidom(X1)
    | class_Ring__and__Field_Opordered__semiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6008]) ).

cnf(c_0_6009_0,axiom,
    ( class_Ring__and__Field_Opordered__comm__semiring(X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6009]) ).

cnf(c_0_6009_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__semidom(X1)
    | class_Ring__and__Field_Opordered__comm__semiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6009]) ).

cnf(c_0_6010_0,axiom,
    ( class_Ring__and__Field_Opordered__cancel__semiring(X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6010]) ).

cnf(c_0_6010_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__semidom(X1)
    | class_Ring__and__Field_Opordered__cancel__semiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6010]) ).

cnf(c_0_6011_0,axiom,
    ( class_Ring__and__Field_Opordered__cancel__comm__semiring(X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6011]) ).

cnf(c_0_6011_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__semidom(X1)
    | class_Ring__and__Field_Opordered__cancel__comm__semiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6011]) ).

cnf(c_0_6012_0,axiom,
    ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6012]) ).

cnf(c_0_6012_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__semidom(X1)
    | class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6012]) ).

cnf(c_0_6013_0,axiom,
    ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6013]) ).

cnf(c_0_6013_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__semidom(X1)
    | class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6013]) ).

cnf(c_0_6014_0,axiom,
    ( class_LOrder_Omeet__semilorder(X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6014]) ).

cnf(c_0_6014_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__semidom(X1)
    | class_LOrder_Omeet__semilorder(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6014]) ).

cnf(c_0_6015_0,axiom,
    ( class_Ring__and__Field_Osemiring__1__cancel(X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6015]) ).

cnf(c_0_6015_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__semidom(X1)
    | class_Ring__and__Field_Osemiring__1__cancel(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6015]) ).

cnf(c_0_6016_0,axiom,
    ( class_LOrder_Ojoin__semilorder(X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6016]) ).

cnf(c_0_6016_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__semidom(X1)
    | class_LOrder_Ojoin__semilorder(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6016]) ).

cnf(c_0_6017_0,axiom,
    ( class_LOrder_Olorder(X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6017]) ).

cnf(c_0_6017_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__semidom(X1)
    | class_LOrder_Olorder(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6017]) ).

cnf(c_0_6018_0,axiom,
    ( class_Orderings_Olinorder(X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6018]) ).

cnf(c_0_6018_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__semidom(X1)
    | class_Orderings_Olinorder(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6018]) ).

cnf(c_0_6019_0,axiom,
    ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6019]) ).

cnf(c_0_6019_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__semidom(X1)
    | class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6019]) ).

cnf(c_0_6020_0,axiom,
    ( class_Ring__and__Field_Oordered__semiring__strict(X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6020]) ).

cnf(c_0_6020_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__semidom(X1)
    | class_Ring__and__Field_Oordered__semiring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6020]) ).

cnf(c_0_6021_0,axiom,
    ( class_Ring__and__Field_Oordered__comm__semiring__strict(X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6021]) ).

cnf(c_0_6021_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__semidom(X1)
    | class_Ring__and__Field_Oordered__comm__semiring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6021]) ).

cnf(c_0_6022_0,axiom,
    ( class_HOL_Oplus(X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6022]) ).

cnf(c_0_6022_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__semidom(X1)
    | class_HOL_Oplus(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6022]) ).

cnf(c_0_6023_0,axiom,
    ( class_OrderedGroup_Osemigroup__add(X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6023]) ).

cnf(c_0_6023_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__semidom(X1)
    | class_OrderedGroup_Osemigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6023]) ).

cnf(c_0_6024_0,axiom,
    ( class_OrderedGroup_Ocancel__semigroup__add(X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6024]) ).

cnf(c_0_6024_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__semidom(X1)
    | class_OrderedGroup_Ocancel__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6024]) ).

cnf(c_0_6025_0,axiom,
    ( class_OrderedGroup_Oab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6025]) ).

cnf(c_0_6025_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__semidom(X1)
    | class_OrderedGroup_Oab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6025]) ).

cnf(c_0_6026_0,axiom,
    ( class_OrderedGroup_Ocomm__monoid__mult(X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6026]) ).

cnf(c_0_6026_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__semidom(X1)
    | class_OrderedGroup_Ocomm__monoid__mult(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6026]) ).

cnf(c_0_6027_0,axiom,
    ( class_OrderedGroup_Ocancel__ab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6027]) ).

cnf(c_0_6027_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__semidom(X1)
    | class_OrderedGroup_Ocancel__ab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6027]) ).

cnf(c_0_6028_0,axiom,
    ( class_HOL_Ozero(X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6028]) ).

cnf(c_0_6028_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__semidom(X1)
    | class_HOL_Ozero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6028]) ).

cnf(c_0_6029_0,axiom,
    ( class_OrderedGroup_Ocomm__monoid__add(X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6029]) ).

cnf(c_0_6029_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__semidom(X1)
    | class_OrderedGroup_Ocomm__monoid__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6029]) ).

cnf(c_0_6030_0,axiom,
    ( class_HOL_Otimes(X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6030]) ).

cnf(c_0_6030_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__semidom(X1)
    | class_HOL_Otimes(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6030]) ).

cnf(c_0_6031_0,axiom,
    ( class_OrderedGroup_Osemigroup__mult(X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6031]) ).

cnf(c_0_6031_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__semidom(X1)
    | class_OrderedGroup_Osemigroup__mult(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6031]) ).

cnf(c_0_6032_0,axiom,
    ( class_Ring__and__Field_Osemiring(X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6032]) ).

cnf(c_0_6032_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__semidom(X1)
    | class_Ring__and__Field_Osemiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6032]) ).

cnf(c_0_6033_0,axiom,
    ( class_Ring__and__Field_Osemiring__0(X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6033]) ).

cnf(c_0_6033_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__semidom(X1)
    | class_Ring__and__Field_Osemiring__0(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6033]) ).

cnf(c_0_6034_0,axiom,
    ( class_Ring__and__Field_Osemiring__0__cancel(X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6034]) ).

cnf(c_0_6034_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__semidom(X1)
    | class_Ring__and__Field_Osemiring__0__cancel(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6034]) ).

cnf(c_0_6035_0,axiom,
    ( class_OrderedGroup_Oab__semigroup__mult(X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6035]) ).

cnf(c_0_6035_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__semidom(X1)
    | class_OrderedGroup_Oab__semigroup__mult(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6035]) ).

cnf(c_0_6036_0,axiom,
    ( class_Ring__and__Field_Ocomm__semiring(X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6036]) ).

cnf(c_0_6036_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__semidom(X1)
    | class_Ring__and__Field_Ocomm__semiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6036]) ).

cnf(c_0_6037_0,axiom,
    ( class_Ring__and__Field_Ocomm__semiring__1(X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6037]) ).

cnf(c_0_6037_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__semidom(X1)
    | class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6037]) ).

cnf(c_0_6038_0,axiom,
    ( class_Ring__and__Field_Ocomm__semiring__1__cancel(X1)
    | ~ class_Ring__and__Field_Oordered__semidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6038]) ).

cnf(c_0_6038_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__semidom(X1)
    | class_Ring__and__Field_Ocomm__semiring__1__cancel(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6038]) ).

cnf(c_0_6039_0,axiom,
    ( class_HOL_Otimes(X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6039]) ).

cnf(c_0_6039_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__ring__strict(X1)
    | class_HOL_Otimes(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6039]) ).

cnf(c_0_6040_0,axiom,
    ( class_OrderedGroup_Osemigroup__mult(X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6040]) ).

cnf(c_0_6040_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__ring__strict(X1)
    | class_OrderedGroup_Osemigroup__mult(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6040]) ).

cnf(c_0_6041_0,axiom,
    ( class_Ring__and__Field_Osemiring(X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6041]) ).

cnf(c_0_6041_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__ring__strict(X1)
    | class_Ring__and__Field_Osemiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6041]) ).

cnf(c_0_6042_0,axiom,
    ( class_Ring__and__Field_Osemiring__0(X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6042]) ).

cnf(c_0_6042_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__ring__strict(X1)
    | class_Ring__and__Field_Osemiring__0(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6042]) ).

cnf(c_0_6043_0,axiom,
    ( class_OrderedGroup_Ocancel__semigroup__add(X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6043]) ).

cnf(c_0_6043_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__ring__strict(X1)
    | class_OrderedGroup_Ocancel__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6043]) ).

cnf(c_0_6044_0,axiom,
    ( class_OrderedGroup_Ocancel__ab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6044]) ).

cnf(c_0_6044_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__ring__strict(X1)
    | class_OrderedGroup_Ocancel__ab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6044]) ).

cnf(c_0_6045_0,axiom,
    ( class_Ring__and__Field_Oaxclass__no__zero__divisors(X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6045]) ).

cnf(c_0_6045_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__ring__strict(X1)
    | class_Ring__and__Field_Oaxclass__no__zero__divisors(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6045]) ).

cnf(c_0_6046_0,axiom,
    ( class_OrderedGroup_Olordered__ab__group__join(X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6046]) ).

cnf(c_0_6046_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__ring__strict(X1)
    | class_OrderedGroup_Olordered__ab__group__join(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6046]) ).

cnf(c_0_6047_0,axiom,
    ( class_OrderedGroup_Olordered__ab__group__meet(X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6047]) ).

cnf(c_0_6047_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__ring__strict(X1)
    | class_OrderedGroup_Olordered__ab__group__meet(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6047]) ).

cnf(c_0_6048_0,axiom,
    ( class_OrderedGroup_Olordered__ab__group__abs(X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6048]) ).

cnf(c_0_6048_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__ring__strict(X1)
    | class_OrderedGroup_Olordered__ab__group__abs(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6048]) ).

cnf(c_0_6049_0,axiom,
    ( class_Ring__and__Field_Opordered__ring(X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6049]) ).

cnf(c_0_6049_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__ring__strict(X1)
    | class_Ring__and__Field_Opordered__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6049]) ).

cnf(c_0_6050_0,axiom,
    ( class_Ring__and__Field_Olordered__ring(X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6050]) ).

cnf(c_0_6050_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__ring__strict(X1)
    | class_Ring__and__Field_Olordered__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6050]) ).

cnf(c_0_6051_0,axiom,
    ( class_OrderedGroup_Opordered__ab__group__add(X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6051]) ).

cnf(c_0_6051_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__ring__strict(X1)
    | class_OrderedGroup_Opordered__ab__group__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6051]) ).

cnf(c_0_6052_0,axiom,
    ( class_Ring__and__Field_Osemiring__0__cancel(X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6052]) ).

cnf(c_0_6052_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__ring__strict(X1)
    | class_Ring__and__Field_Osemiring__0__cancel(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6052]) ).

cnf(c_0_6053_0,axiom,
    ( class_OrderedGroup_Olordered__ab__group(X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6053]) ).

cnf(c_0_6053_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__ring__strict(X1)
    | class_OrderedGroup_Olordered__ab__group(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6053]) ).

cnf(c_0_6054_0,axiom,
    ( class_Ring__and__Field_Oaxclass__abs__if(X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6054]) ).

cnf(c_0_6054_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__ring__strict(X1)
    | class_Ring__and__Field_Oaxclass__abs__if(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6054]) ).

cnf(c_0_6055_0,axiom,
    ( class_Orderings_Oord(X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6055]) ).

cnf(c_0_6055_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__ring__strict(X1)
    | class_Orderings_Oord(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6055]) ).

cnf(c_0_6056_0,axiom,
    ( class_Orderings_Oorder(X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6056]) ).

cnf(c_0_6056_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__ring__strict(X1)
    | class_Orderings_Oorder(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6056]) ).

cnf(c_0_6057_0,axiom,
    ( class_OrderedGroup_Opordered__ab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6057]) ).

cnf(c_0_6057_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__ring__strict(X1)
    | class_OrderedGroup_Opordered__ab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6057]) ).

cnf(c_0_6058_0,axiom,
    ( class_Ring__and__Field_Opordered__semiring(X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6058]) ).

cnf(c_0_6058_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__ring__strict(X1)
    | class_Ring__and__Field_Opordered__semiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6058]) ).

cnf(c_0_6059_0,axiom,
    ( class_Ring__and__Field_Opordered__cancel__semiring(X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6059]) ).

cnf(c_0_6059_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__ring__strict(X1)
    | class_Ring__and__Field_Opordered__cancel__semiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6059]) ).

cnf(c_0_6060_0,axiom,
    ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6060]) ).

cnf(c_0_6060_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__ring__strict(X1)
    | class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6060]) ).

cnf(c_0_6061_0,axiom,
    ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6061]) ).

cnf(c_0_6061_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__ring__strict(X1)
    | class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6061]) ).

cnf(c_0_6062_0,axiom,
    ( class_LOrder_Omeet__semilorder(X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6062]) ).

cnf(c_0_6062_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__ring__strict(X1)
    | class_LOrder_Omeet__semilorder(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6062]) ).

cnf(c_0_6063_0,axiom,
    ( class_HOL_Ominus(X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6063]) ).

cnf(c_0_6063_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__ring__strict(X1)
    | class_HOL_Ominus(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6063]) ).

cnf(c_0_6064_0,axiom,
    ( class_LOrder_Ojoin__semilorder(X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6064]) ).

cnf(c_0_6064_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__ring__strict(X1)
    | class_LOrder_Ojoin__semilorder(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6064]) ).

cnf(c_0_6065_0,axiom,
    ( class_LOrder_Olorder(X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6065]) ).

cnf(c_0_6065_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__ring__strict(X1)
    | class_LOrder_Olorder(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6065]) ).

cnf(c_0_6066_0,axiom,
    ( class_Orderings_Olinorder(X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6066]) ).

cnf(c_0_6066_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__ring__strict(X1)
    | class_Orderings_Olinorder(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6066]) ).

cnf(c_0_6067_0,axiom,
    ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6067]) ).

cnf(c_0_6067_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__ring__strict(X1)
    | class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6067]) ).

cnf(c_0_6068_0,axiom,
    ( class_Ring__and__Field_Oordered__semiring__strict(X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6068]) ).

cnf(c_0_6068_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__ring__strict(X1)
    | class_Ring__and__Field_Oordered__semiring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6068]) ).

cnf(c_0_6069_0,axiom,
    ( class_HOL_Ozero(X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6069]) ).

cnf(c_0_6069_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__ring__strict(X1)
    | class_HOL_Ozero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6069]) ).

cnf(c_0_6070_0,axiom,
    ( class_HOL_Oplus(X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6070]) ).

cnf(c_0_6070_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__ring__strict(X1)
    | class_HOL_Oplus(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6070]) ).

cnf(c_0_6071_0,axiom,
    ( class_OrderedGroup_Osemigroup__add(X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6071]) ).

cnf(c_0_6071_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__ring__strict(X1)
    | class_OrderedGroup_Osemigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6071]) ).

cnf(c_0_6072_0,axiom,
    ( class_OrderedGroup_Oab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6072]) ).

cnf(c_0_6072_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__ring__strict(X1)
    | class_OrderedGroup_Oab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6072]) ).

cnf(c_0_6073_0,axiom,
    ( class_OrderedGroup_Ocomm__monoid__add(X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6073]) ).

cnf(c_0_6073_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__ring__strict(X1)
    | class_OrderedGroup_Ocomm__monoid__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6073]) ).

cnf(c_0_6074_0,axiom,
    ( class_OrderedGroup_Oab__group__add(X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6074]) ).

cnf(c_0_6074_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__ring__strict(X1)
    | class_OrderedGroup_Oab__group__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6074]) ).

cnf(c_0_6075_0,axiom,
    ( class_Ring__and__Field_Oring(X1)
    | ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6075]) ).

cnf(c_0_6075_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__ring__strict(X1)
    | class_Ring__and__Field_Oring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6075]) ).

cnf(c_0_6076_0,axiom,
    ( class_Ring__and__Field_Osemiring__1__cancel(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6076]) ).

cnf(c_0_6076_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(X1)
    | class_Ring__and__Field_Osemiring__1__cancel(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6076]) ).

cnf(c_0_6077_0,axiom,
    ( class_OrderedGroup_Ocomm__monoid__mult(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6077]) ).

cnf(c_0_6077_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(X1)
    | class_OrderedGroup_Ocomm__monoid__mult(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6077]) ).

cnf(c_0_6078_0,axiom,
    ( class_Ring__and__Field_Ocomm__semiring__1(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6078]) ).

cnf(c_0_6078_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(X1)
    | class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6078]) ).

cnf(c_0_6079_0,axiom,
    ( class_Ring__and__Field_Ocomm__semiring__1__cancel(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6079]) ).

cnf(c_0_6079_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(X1)
    | class_Ring__and__Field_Ocomm__semiring__1__cancel(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6079]) ).

cnf(c_0_6080_0,axiom,
    ( class_Ring__and__Field_Oidom(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6080]) ).

cnf(c_0_6080_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(X1)
    | class_Ring__and__Field_Oidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6080]) ).

cnf(c_0_6081_0,axiom,
    ( class_Ring__and__Field_Oaxclass__no__zero__divisors(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6081]) ).

cnf(c_0_6081_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(X1)
    | class_Ring__and__Field_Oaxclass__no__zero__divisors(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6081]) ).

cnf(c_0_6082_0,axiom,
    ( class_Ring__and__Field_Oordered__semidom(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6082]) ).

cnf(c_0_6082_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(X1)
    | class_Ring__and__Field_Oordered__semidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6082]) ).

cnf(c_0_6083_0,axiom,
    ( class_OrderedGroup_Opordered__ab__group__add(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6083]) ).

cnf(c_0_6083_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(X1)
    | class_OrderedGroup_Opordered__ab__group__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6083]) ).

cnf(c_0_6084_0,axiom,
    ( class_OrderedGroup_Olordered__ab__group(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6084]) ).

cnf(c_0_6084_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(X1)
    | class_OrderedGroup_Olordered__ab__group(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6084]) ).

cnf(c_0_6085_0,axiom,
    ( class_OrderedGroup_Olordered__ab__group__join(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6085]) ).

cnf(c_0_6085_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(X1)
    | class_OrderedGroup_Olordered__ab__group__join(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6085]) ).

cnf(c_0_6086_0,axiom,
    ( class_OrderedGroup_Olordered__ab__group__meet(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6086]) ).

cnf(c_0_6086_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(X1)
    | class_OrderedGroup_Olordered__ab__group__meet(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6086]) ).

cnf(c_0_6087_0,axiom,
    ( class_OrderedGroup_Olordered__ab__group__abs(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6087]) ).

cnf(c_0_6087_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(X1)
    | class_OrderedGroup_Olordered__ab__group__abs(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6087]) ).

cnf(c_0_6088_0,axiom,
    ( class_HOL_Ominus(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6088]) ).

cnf(c_0_6088_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(X1)
    | class_HOL_Ominus(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6088]) ).

cnf(c_0_6089_0,axiom,
    ( class_Ring__and__Field_Opordered__ring(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6089]) ).

cnf(c_0_6089_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(X1)
    | class_Ring__and__Field_Opordered__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6089]) ).

cnf(c_0_6090_0,axiom,
    ( class_Ring__and__Field_Olordered__ring(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6090]) ).

cnf(c_0_6090_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(X1)
    | class_Ring__and__Field_Olordered__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6090]) ).

cnf(c_0_6091_0,axiom,
    ( class_Ring__and__Field_Oordered__ring__strict(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6091]) ).

cnf(c_0_6091_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(X1)
    | class_Ring__and__Field_Oordered__ring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6091]) ).

cnf(c_0_6092_0,axiom,
    ( class_Ring__and__Field_Oaxclass__abs__if(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6092]) ).

cnf(c_0_6092_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(X1)
    | class_Ring__and__Field_Oaxclass__abs__if(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6092]) ).

cnf(c_0_6093_0,axiom,
    ( class_Orderings_Oord(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6093]) ).

cnf(c_0_6093_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(X1)
    | class_Orderings_Oord(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6093]) ).

cnf(c_0_6094_0,axiom,
    ( class_Orderings_Oorder(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6094]) ).

cnf(c_0_6094_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(X1)
    | class_Orderings_Oorder(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6094]) ).

cnf(c_0_6095_0,axiom,
    ( class_OrderedGroup_Opordered__ab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6095]) ).

cnf(c_0_6095_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(X1)
    | class_OrderedGroup_Opordered__ab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6095]) ).

cnf(c_0_6096_0,axiom,
    ( class_Ring__and__Field_Opordered__semiring(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6096]) ).

cnf(c_0_6096_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(X1)
    | class_Ring__and__Field_Opordered__semiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6096]) ).

cnf(c_0_6097_0,axiom,
    ( class_Ring__and__Field_Opordered__comm__semiring(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6097]) ).

cnf(c_0_6097_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(X1)
    | class_Ring__and__Field_Opordered__comm__semiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6097]) ).

cnf(c_0_6098_0,axiom,
    ( class_Ring__and__Field_Opordered__cancel__semiring(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6098]) ).

cnf(c_0_6098_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(X1)
    | class_Ring__and__Field_Opordered__cancel__semiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6098]) ).

cnf(c_0_6099_0,axiom,
    ( class_OrderedGroup_Oab__group__add(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6099]) ).

cnf(c_0_6099_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(X1)
    | class_OrderedGroup_Oab__group__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6099]) ).

cnf(c_0_6100_0,axiom,
    ( class_Ring__and__Field_Opordered__cancel__comm__semiring(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6100]) ).

cnf(c_0_6100_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(X1)
    | class_Ring__and__Field_Opordered__cancel__comm__semiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6100]) ).

cnf(c_0_6101_0,axiom,
    ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6101]) ).

cnf(c_0_6101_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(X1)
    | class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6101]) ).

cnf(c_0_6102_0,axiom,
    ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6102]) ).

cnf(c_0_6102_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(X1)
    | class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6102]) ).

cnf(c_0_6103_0,axiom,
    ( class_LOrder_Omeet__semilorder(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6103]) ).

cnf(c_0_6103_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(X1)
    | class_LOrder_Omeet__semilorder(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6103]) ).

cnf(c_0_6104_0,axiom,
    ( class_LOrder_Ojoin__semilorder(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6104]) ).

cnf(c_0_6104_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(X1)
    | class_LOrder_Ojoin__semilorder(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6104]) ).

cnf(c_0_6105_0,axiom,
    ( class_LOrder_Olorder(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6105]) ).

cnf(c_0_6105_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(X1)
    | class_LOrder_Olorder(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6105]) ).

cnf(c_0_6106_0,axiom,
    ( class_Orderings_Olinorder(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6106]) ).

cnf(c_0_6106_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(X1)
    | class_Orderings_Olinorder(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6106]) ).

cnf(c_0_6107_0,axiom,
    ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6107]) ).

cnf(c_0_6107_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(X1)
    | class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6107]) ).

cnf(c_0_6108_0,axiom,
    ( class_Ring__and__Field_Oordered__semiring__strict(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6108]) ).

cnf(c_0_6108_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(X1)
    | class_Ring__and__Field_Oordered__semiring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6108]) ).

cnf(c_0_6109_0,axiom,
    ( class_Ring__and__Field_Oordered__comm__semiring__strict(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6109]) ).

cnf(c_0_6109_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(X1)
    | class_Ring__and__Field_Oordered__comm__semiring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6109]) ).

cnf(c_0_6110_0,axiom,
    ( class_Ring__and__Field_Oring(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6110]) ).

cnf(c_0_6110_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(X1)
    | class_Ring__and__Field_Oring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6110]) ).

cnf(c_0_6111_0,axiom,
    ( class_HOL_Oplus(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6111]) ).

cnf(c_0_6111_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(X1)
    | class_HOL_Oplus(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6111]) ).

cnf(c_0_6112_0,axiom,
    ( class_OrderedGroup_Osemigroup__add(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6112]) ).

cnf(c_0_6112_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(X1)
    | class_OrderedGroup_Osemigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6112]) ).

cnf(c_0_6113_0,axiom,
    ( class_OrderedGroup_Ocancel__semigroup__add(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6113]) ).

cnf(c_0_6113_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(X1)
    | class_OrderedGroup_Ocancel__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6113]) ).

cnf(c_0_6114_0,axiom,
    ( class_OrderedGroup_Oab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6114]) ).

cnf(c_0_6114_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(X1)
    | class_OrderedGroup_Oab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6114]) ).

cnf(c_0_6115_0,axiom,
    ( class_OrderedGroup_Ocancel__ab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6115]) ).

cnf(c_0_6115_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(X1)
    | class_OrderedGroup_Ocancel__ab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6115]) ).

cnf(c_0_6116_0,axiom,
    ( class_HOL_Ozero(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6116]) ).

cnf(c_0_6116_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(X1)
    | class_HOL_Ozero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6116]) ).

cnf(c_0_6117_0,axiom,
    ( class_OrderedGroup_Ocomm__monoid__add(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6117]) ).

cnf(c_0_6117_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(X1)
    | class_OrderedGroup_Ocomm__monoid__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6117]) ).

cnf(c_0_6118_0,axiom,
    ( class_HOL_Otimes(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6118]) ).

cnf(c_0_6118_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(X1)
    | class_HOL_Otimes(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6118]) ).

cnf(c_0_6119_0,axiom,
    ( class_OrderedGroup_Osemigroup__mult(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6119]) ).

cnf(c_0_6119_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(X1)
    | class_OrderedGroup_Osemigroup__mult(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6119]) ).

cnf(c_0_6120_0,axiom,
    ( class_Ring__and__Field_Osemiring(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6120]) ).

cnf(c_0_6120_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(X1)
    | class_Ring__and__Field_Osemiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6120]) ).

cnf(c_0_6121_0,axiom,
    ( class_Ring__and__Field_Oring__1(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6121]) ).

cnf(c_0_6121_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(X1)
    | class_Ring__and__Field_Oring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6121]) ).

cnf(c_0_6122_0,axiom,
    ( class_Ring__and__Field_Osemiring__0(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6122]) ).

cnf(c_0_6122_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(X1)
    | class_Ring__and__Field_Osemiring__0(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6122]) ).

cnf(c_0_6123_0,axiom,
    ( class_Ring__and__Field_Osemiring__0__cancel(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6123]) ).

cnf(c_0_6123_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(X1)
    | class_Ring__and__Field_Osemiring__0__cancel(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6123]) ).

cnf(c_0_6124_0,axiom,
    ( class_OrderedGroup_Oab__semigroup__mult(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6124]) ).

cnf(c_0_6124_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(X1)
    | class_OrderedGroup_Oab__semigroup__mult(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6124]) ).

cnf(c_0_6125_0,axiom,
    ( class_Ring__and__Field_Ocomm__semiring(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6125]) ).

cnf(c_0_6125_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(X1)
    | class_Ring__and__Field_Ocomm__semiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6125]) ).

cnf(c_0_6126_0,axiom,
    ( class_Ring__and__Field_Ocomm__semiring__0(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6126]) ).

cnf(c_0_6126_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(X1)
    | class_Ring__and__Field_Ocomm__semiring__0(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6126]) ).

cnf(c_0_6127_0,axiom,
    ( class_Ring__and__Field_Ocomm__semiring__0__cancel(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6127]) ).

cnf(c_0_6127_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(X1)
    | class_Ring__and__Field_Ocomm__semiring__0__cancel(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6127]) ).

cnf(c_0_6128_0,axiom,
    ( class_HOL_Oone(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6128]) ).

cnf(c_0_6128_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(X1)
    | class_HOL_Oone(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6128]) ).

cnf(c_0_6129_0,axiom,
    ( class_OrderedGroup_Omonoid__mult(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6129]) ).

cnf(c_0_6129_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(X1)
    | class_OrderedGroup_Omonoid__mult(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6129]) ).

cnf(c_0_6130_0,axiom,
    ( class_Ring__and__Field_Oaxclass__0__neq__1(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6130]) ).

cnf(c_0_6130_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(X1)
    | class_Ring__and__Field_Oaxclass__0__neq__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6130]) ).

cnf(c_0_6131_0,axiom,
    ( class_Ring__and__Field_Osemiring__1(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6131]) ).

cnf(c_0_6131_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(X1)
    | class_Ring__and__Field_Osemiring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6131]) ).

cnf(c_0_6132_0,axiom,
    ( class_Ring__and__Field_Ocomm__ring(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6132]) ).

cnf(c_0_6132_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(X1)
    | class_Ring__and__Field_Ocomm__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6132]) ).

cnf(c_0_6133_0,axiom,
    ( class_Ring__and__Field_Ocomm__ring__1(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6133]) ).

cnf(c_0_6133_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(X1)
    | class_Ring__and__Field_Ocomm__ring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6133]) ).

cnf(c_0_6134_0,axiom,
    ( class_Ring__and__Field_Ocomm__semiring__1__cancel(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6134]) ).

cnf(c_0_6134_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(X1)
    | class_Ring__and__Field_Ocomm__semiring__1__cancel(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6134]) ).

cnf(c_0_6135_0,axiom,
    ( class_HOL_Ominus(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6135]) ).

cnf(c_0_6135_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(X1)
    | class_HOL_Ominus(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6135]) ).

cnf(c_0_6136_0,axiom,
    ( class_OrderedGroup_Oab__group__add(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6136]) ).

cnf(c_0_6136_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(X1)
    | class_OrderedGroup_Oab__group__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6136]) ).

cnf(c_0_6137_0,axiom,
    ( class_Ring__and__Field_Oordered__semidom(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6137]) ).

cnf(c_0_6137_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(X1)
    | class_Ring__and__Field_Oordered__semidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6137]) ).

cnf(c_0_6138_0,axiom,
    ( class_Ring__and__Field_Oring(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6138]) ).

cnf(c_0_6138_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(X1)
    | class_Ring__and__Field_Oring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6138]) ).

cnf(c_0_6139_0,axiom,
    ( class_Orderings_Oord(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6139]) ).

cnf(c_0_6139_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(X1)
    | class_Orderings_Oord(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6139]) ).

cnf(c_0_6140_0,axiom,
    ( class_Orderings_Oorder(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6140]) ).

cnf(c_0_6140_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(X1)
    | class_Orderings_Oorder(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6140]) ).

cnf(c_0_6141_0,axiom,
    ( class_OrderedGroup_Opordered__ab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6141]) ).

cnf(c_0_6141_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(X1)
    | class_OrderedGroup_Opordered__ab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6141]) ).

cnf(c_0_6142_0,axiom,
    ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6142]) ).

cnf(c_0_6142_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(X1)
    | class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6142]) ).

cnf(c_0_6143_0,axiom,
    ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6143]) ).

cnf(c_0_6143_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(X1)
    | class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6143]) ).

cnf(c_0_6144_0,axiom,
    ( class_OrderedGroup_Opordered__ab__group__add(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6144]) ).

cnf(c_0_6144_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(X1)
    | class_OrderedGroup_Opordered__ab__group__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6144]) ).

cnf(c_0_6145_0,axiom,
    ( class_LOrder_Omeet__semilorder(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6145]) ).

cnf(c_0_6145_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(X1)
    | class_LOrder_Omeet__semilorder(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6145]) ).

cnf(c_0_6146_0,axiom,
    ( class_LOrder_Ojoin__semilorder(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6146]) ).

cnf(c_0_6146_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(X1)
    | class_LOrder_Ojoin__semilorder(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6146]) ).

cnf(c_0_6147_0,axiom,
    ( class_LOrder_Olorder(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6147]) ).

cnf(c_0_6147_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(X1)
    | class_LOrder_Olorder(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6147]) ).

cnf(c_0_6148_0,axiom,
    ( class_OrderedGroup_Olordered__ab__group(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6148]) ).

cnf(c_0_6148_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(X1)
    | class_OrderedGroup_Olordered__ab__group(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6148]) ).

cnf(c_0_6149_0,axiom,
    ( class_Ring__and__Field_Oring__1(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6149]) ).

cnf(c_0_6149_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(X1)
    | class_Ring__and__Field_Oring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6149]) ).

cnf(c_0_6150_0,axiom,
    ( class_OrderedGroup_Olordered__ab__group__join(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6150]) ).

cnf(c_0_6150_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(X1)
    | class_OrderedGroup_Olordered__ab__group__join(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6150]) ).

cnf(c_0_6151_0,axiom,
    ( class_OrderedGroup_Olordered__ab__group__meet(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6151]) ).

cnf(c_0_6151_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(X1)
    | class_OrderedGroup_Olordered__ab__group__meet(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6151]) ).

cnf(c_0_6152_0,axiom,
    ( class_OrderedGroup_Olordered__ab__group__abs(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6152]) ).

cnf(c_0_6152_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(X1)
    | class_OrderedGroup_Olordered__ab__group__abs(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6152]) ).

cnf(c_0_6153_0,axiom,
    ( class_Ring__and__Field_Opordered__semiring(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6153]) ).

cnf(c_0_6153_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(X1)
    | class_Ring__and__Field_Opordered__semiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6153]) ).

cnf(c_0_6154_0,axiom,
    ( class_Ring__and__Field_Opordered__cancel__semiring(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6154]) ).

cnf(c_0_6154_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(X1)
    | class_Ring__and__Field_Opordered__cancel__semiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6154]) ).

cnf(c_0_6155_0,axiom,
    ( class_Ring__and__Field_Opordered__ring(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6155]) ).

cnf(c_0_6155_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(X1)
    | class_Ring__and__Field_Opordered__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6155]) ).

cnf(c_0_6156_0,axiom,
    ( class_Ring__and__Field_Olordered__ring(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6156]) ).

cnf(c_0_6156_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(X1)
    | class_Ring__and__Field_Olordered__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6156]) ).

cnf(c_0_6157_0,axiom,
    ( class_Ring__and__Field_Oaxclass__abs__if(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6157]) ).

cnf(c_0_6157_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(X1)
    | class_Ring__and__Field_Oaxclass__abs__if(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6157]) ).

cnf(c_0_6158_0,axiom,
    ( class_Orderings_Olinorder(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6158]) ).

cnf(c_0_6158_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(X1)
    | class_Orderings_Olinorder(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6158]) ).

cnf(c_0_6159_0,axiom,
    ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6159]) ).

cnf(c_0_6159_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(X1)
    | class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6159]) ).

cnf(c_0_6160_0,axiom,
    ( class_Ring__and__Field_Ocomm__ring(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6160]) ).

cnf(c_0_6160_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(X1)
    | class_Ring__and__Field_Ocomm__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6160]) ).

cnf(c_0_6161_0,axiom,
    ( class_Ring__and__Field_Oordered__semiring__strict(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6161]) ).

cnf(c_0_6161_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(X1)
    | class_Ring__and__Field_Oordered__semiring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6161]) ).

cnf(c_0_6162_0,axiom,
    ( class_Ring__and__Field_Oordered__ring__strict(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6162]) ).

cnf(c_0_6162_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(X1)
    | class_Ring__and__Field_Oordered__ring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6162]) ).

cnf(c_0_6163_0,axiom,
    ( class_Ring__and__Field_Opordered__comm__semiring(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6163]) ).

cnf(c_0_6163_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(X1)
    | class_Ring__and__Field_Opordered__comm__semiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6163]) ).

cnf(c_0_6164_0,axiom,
    ( class_Ring__and__Field_Opordered__cancel__comm__semiring(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6164]) ).

cnf(c_0_6164_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(X1)
    | class_Ring__and__Field_Opordered__cancel__comm__semiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6164]) ).

cnf(c_0_6165_0,axiom,
    ( class_Ring__and__Field_Oordered__comm__semiring__strict(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6165]) ).

cnf(c_0_6165_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(X1)
    | class_Ring__and__Field_Oordered__comm__semiring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6165]) ).

cnf(c_0_6166_0,axiom,
    ( class_Ring__and__Field_Oordered__idom(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6166]) ).

cnf(c_0_6166_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(X1)
    | class_Ring__and__Field_Oordered__idom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6166]) ).

cnf(c_0_6167_0,axiom,
    ( class_HOL_Otimes(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6167]) ).

cnf(c_0_6167_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(X1)
    | class_HOL_Otimes(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6167]) ).

cnf(c_0_6168_0,axiom,
    ( class_HOL_Ozero(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6168]) ).

cnf(c_0_6168_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(X1)
    | class_HOL_Ozero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6168]) ).

cnf(c_0_6169_0,axiom,
    ( class_Ring__and__Field_Oaxclass__no__zero__divisors(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6169]) ).

cnf(c_0_6169_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(X1)
    | class_Ring__and__Field_Oaxclass__no__zero__divisors(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6169]) ).

cnf(c_0_6170_0,axiom,
    ( class_HOL_Oplus(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6170]) ).

cnf(c_0_6170_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(X1)
    | class_HOL_Oplus(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6170]) ).

cnf(c_0_6171_0,axiom,
    ( class_Ring__and__Field_Ocomm__ring__1(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6171]) ).

cnf(c_0_6171_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(X1)
    | class_Ring__and__Field_Ocomm__ring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6171]) ).

cnf(c_0_6172_0,axiom,
    ( class_OrderedGroup_Osemigroup__add(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6172]) ).

cnf(c_0_6172_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(X1)
    | class_OrderedGroup_Osemigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6172]) ).

cnf(c_0_6173_0,axiom,
    ( class_OrderedGroup_Ocancel__semigroup__add(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6173]) ).

cnf(c_0_6173_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(X1)
    | class_OrderedGroup_Ocancel__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6173]) ).

cnf(c_0_6174_0,axiom,
    ( class_OrderedGroup_Oab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6174]) ).

cnf(c_0_6174_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(X1)
    | class_OrderedGroup_Oab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6174]) ).

cnf(c_0_6175_0,axiom,
    ( class_OrderedGroup_Ocancel__ab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6175]) ).

cnf(c_0_6175_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(X1)
    | class_OrderedGroup_Ocancel__ab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6175]) ).

cnf(c_0_6176_0,axiom,
    ( class_OrderedGroup_Ocomm__monoid__add(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6176]) ).

cnf(c_0_6176_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(X1)
    | class_OrderedGroup_Ocomm__monoid__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6176]) ).

cnf(c_0_6177_0,axiom,
    ( class_OrderedGroup_Osemigroup__mult(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6177]) ).

cnf(c_0_6177_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(X1)
    | class_OrderedGroup_Osemigroup__mult(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6177]) ).

cnf(c_0_6178_0,axiom,
    ( class_Ring__and__Field_Osemiring(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6178]) ).

cnf(c_0_6178_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(X1)
    | class_Ring__and__Field_Osemiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6178]) ).

cnf(c_0_6179_0,axiom,
    ( class_Ring__and__Field_Osemiring__0(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6179]) ).

cnf(c_0_6179_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(X1)
    | class_Ring__and__Field_Osemiring__0(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6179]) ).

cnf(c_0_6180_0,axiom,
    ( class_Ring__and__Field_Osemiring__0__cancel(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6180]) ).

cnf(c_0_6180_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(X1)
    | class_Ring__and__Field_Osemiring__0__cancel(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6180]) ).

cnf(c_0_6181_0,axiom,
    ( class_OrderedGroup_Oab__semigroup__mult(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6181]) ).

cnf(c_0_6181_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(X1)
    | class_OrderedGroup_Oab__semigroup__mult(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6181]) ).

cnf(c_0_6182_0,axiom,
    ( class_Ring__and__Field_Oidom(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6182]) ).

cnf(c_0_6182_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(X1)
    | class_Ring__and__Field_Oidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6182]) ).

cnf(c_0_6183_0,axiom,
    ( class_Ring__and__Field_Ocomm__semiring(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6183]) ).

cnf(c_0_6183_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(X1)
    | class_Ring__and__Field_Ocomm__semiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6183]) ).

cnf(c_0_6184_0,axiom,
    ( class_Ring__and__Field_Ocomm__semiring__0(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6184]) ).

cnf(c_0_6184_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(X1)
    | class_Ring__and__Field_Ocomm__semiring__0(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6184]) ).

cnf(c_0_6185_0,axiom,
    ( class_Ring__and__Field_Ocomm__semiring__0__cancel(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6185]) ).

cnf(c_0_6185_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(X1)
    | class_Ring__and__Field_Ocomm__semiring__0__cancel(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6185]) ).

cnf(c_0_6186_0,axiom,
    ( class_HOL_Oone(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6186]) ).

cnf(c_0_6186_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(X1)
    | class_HOL_Oone(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6186]) ).

cnf(c_0_6187_0,axiom,
    ( class_OrderedGroup_Omonoid__mult(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6187]) ).

cnf(c_0_6187_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(X1)
    | class_OrderedGroup_Omonoid__mult(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6187]) ).

cnf(c_0_6188_0,axiom,
    ( class_Ring__and__Field_Oaxclass__0__neq__1(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6188]) ).

cnf(c_0_6188_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(X1)
    | class_Ring__and__Field_Oaxclass__0__neq__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6188]) ).

cnf(c_0_6189_0,axiom,
    ( class_Ring__and__Field_Osemiring__1(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6189]) ).

cnf(c_0_6189_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(X1)
    | class_Ring__and__Field_Osemiring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6189]) ).

cnf(c_0_6190_0,axiom,
    ( class_Ring__and__Field_Osemiring__1__cancel(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6190]) ).

cnf(c_0_6190_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(X1)
    | class_Ring__and__Field_Osemiring__1__cancel(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6190]) ).

cnf(c_0_6191_0,axiom,
    ( class_OrderedGroup_Ocomm__monoid__mult(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6191]) ).

cnf(c_0_6191_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(X1)
    | class_OrderedGroup_Ocomm__monoid__mult(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6191]) ).

cnf(c_0_6192_0,axiom,
    ( class_Ring__and__Field_Ocomm__semiring__1(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6192]) ).

cnf(c_0_6192_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(X1)
    | class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6192]) ).

cnf(c_0_6193_0,axiom,
    ( class_HOL_Oinverse(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6193]) ).

cnf(c_0_6193_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(X1)
    | class_HOL_Oinverse(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6193]) ).

cnf(c_0_6194_0,axiom,
    ( class_Ring__and__Field_Ofield(X1)
    | ~ class_Ring__and__Field_Oordered__field(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6194]) ).

cnf(c_0_6194_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(X1)
    | class_Ring__and__Field_Ofield(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6194]) ).

cnf(c_0_6195_0,axiom,
    ( class_OrderedGroup_Osemigroup__add(X1)
    | ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6195]) ).

cnf(c_0_6195_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X1)
    | class_OrderedGroup_Osemigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6195]) ).

cnf(c_0_6196_0,axiom,
    ( class_OrderedGroup_Oab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6196]) ).

cnf(c_0_6196_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X1)
    | class_OrderedGroup_Oab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6196]) ).

cnf(c_0_6197_0,axiom,
    ( class_OrderedGroup_Ocomm__monoid__add(X1)
    | ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6197]) ).

cnf(c_0_6197_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X1)
    | class_OrderedGroup_Ocomm__monoid__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6197]) ).

cnf(c_0_6198_0,axiom,
    ( class_HOL_Otimes(X1)
    | ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6198]) ).

cnf(c_0_6198_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X1)
    | class_HOL_Otimes(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6198]) ).

cnf(c_0_6199_0,axiom,
    ( class_OrderedGroup_Osemigroup__mult(X1)
    | ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6199]) ).

cnf(c_0_6199_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X1)
    | class_OrderedGroup_Osemigroup__mult(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6199]) ).

cnf(c_0_6200_0,axiom,
    ( class_Ring__and__Field_Osemiring(X1)
    | ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6200]) ).

cnf(c_0_6200_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X1)
    | class_Ring__and__Field_Osemiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6200]) ).

cnf(c_0_6201_0,axiom,
    ( class_Ring__and__Field_Osemiring__0(X1)
    | ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6201]) ).

cnf(c_0_6201_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X1)
    | class_Ring__and__Field_Osemiring__0(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6201]) ).

cnf(c_0_6202_0,axiom,
    ( class_Ring__and__Field_Opordered__comm__semiring(X1)
    | ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6202]) ).

cnf(c_0_6202_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X1)
    | class_Ring__and__Field_Opordered__comm__semiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6202]) ).

cnf(c_0_6203_0,axiom,
    ( class_Ring__and__Field_Opordered__cancel__comm__semiring(X1)
    | ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6203]) ).

cnf(c_0_6203_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X1)
    | class_Ring__and__Field_Opordered__cancel__comm__semiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6203]) ).

cnf(c_0_6204_0,axiom,
    ( class_Ring__and__Field_Opordered__semiring(X1)
    | ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6204]) ).

cnf(c_0_6204_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X1)
    | class_Ring__and__Field_Opordered__semiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6204]) ).

cnf(c_0_6205_0,axiom,
    ( class_Ring__and__Field_Osemiring__0__cancel(X1)
    | ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6205]) ).

cnf(c_0_6205_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X1)
    | class_Ring__and__Field_Osemiring__0__cancel(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6205]) ).

cnf(c_0_6206_0,axiom,
    ( class_Ring__and__Field_Opordered__cancel__semiring(X1)
    | ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6206]) ).

cnf(c_0_6206_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X1)
    | class_Ring__and__Field_Opordered__cancel__semiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6206]) ).

cnf(c_0_6207_0,axiom,
    ( class_Ring__and__Field_Oordered__semiring__strict(X1)
    | ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6207]) ).

cnf(c_0_6207_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X1)
    | class_Ring__and__Field_Oordered__semiring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6207]) ).

cnf(c_0_6208_0,axiom,
    ( class_OrderedGroup_Ocancel__semigroup__add(X1)
    | ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6208]) ).

cnf(c_0_6208_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X1)
    | class_OrderedGroup_Ocancel__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6208]) ).

cnf(c_0_6209_0,axiom,
    ( class_OrderedGroup_Ocancel__ab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6209]) ).

cnf(c_0_6209_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X1)
    | class_OrderedGroup_Ocancel__ab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6209]) ).

cnf(c_0_6210_0,axiom,
    ( class_Orderings_Oord(X1)
    | ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6210]) ).

cnf(c_0_6210_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X1)
    | class_Orderings_Oord(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6210]) ).

cnf(c_0_6211_0,axiom,
    ( class_Orderings_Oorder(X1)
    | ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6211]) ).

cnf(c_0_6211_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X1)
    | class_Orderings_Oorder(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6211]) ).

cnf(c_0_6212_0,axiom,
    ( class_OrderedGroup_Oab__semigroup__mult(X1)
    | ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6212]) ).

cnf(c_0_6212_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X1)
    | class_OrderedGroup_Oab__semigroup__mult(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6212]) ).

cnf(c_0_6213_0,axiom,
    ( class_OrderedGroup_Opordered__ab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6213]) ).

cnf(c_0_6213_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X1)
    | class_OrderedGroup_Opordered__ab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6213]) ).

cnf(c_0_6214_0,axiom,
    ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6214]) ).

cnf(c_0_6214_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X1)
    | class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6214]) ).

cnf(c_0_6215_0,axiom,
    ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
    | ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6215]) ).

cnf(c_0_6215_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X1)
    | class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6215]) ).

cnf(c_0_6216_0,axiom,
    ( class_LOrder_Omeet__semilorder(X1)
    | ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6216]) ).

cnf(c_0_6216_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X1)
    | class_LOrder_Omeet__semilorder(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6216]) ).

cnf(c_0_6217_0,axiom,
    ( class_LOrder_Ojoin__semilorder(X1)
    | ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6217]) ).

cnf(c_0_6217_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X1)
    | class_LOrder_Ojoin__semilorder(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6217]) ).

cnf(c_0_6218_0,axiom,
    ( class_LOrder_Olorder(X1)
    | ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6218]) ).

cnf(c_0_6218_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X1)
    | class_LOrder_Olorder(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6218]) ).

cnf(c_0_6219_0,axiom,
    ( class_Orderings_Olinorder(X1)
    | ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6219]) ).

cnf(c_0_6219_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X1)
    | class_Orderings_Olinorder(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6219]) ).

cnf(c_0_6220_0,axiom,
    ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6220]) ).

cnf(c_0_6220_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X1)
    | class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6220]) ).

cnf(c_0_6221_0,axiom,
    ( class_HOL_Ozero(X1)
    | ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6221]) ).

cnf(c_0_6221_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X1)
    | class_HOL_Ozero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6221]) ).

cnf(c_0_6222_0,axiom,
    ( class_HOL_Oplus(X1)
    | ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6222]) ).

cnf(c_0_6222_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X1)
    | class_HOL_Oplus(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6222]) ).

cnf(c_0_6223_0,axiom,
    ( class_Ring__and__Field_Ocomm__semiring(X1)
    | ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6223]) ).

cnf(c_0_6223_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X1)
    | class_Ring__and__Field_Ocomm__semiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6223]) ).

cnf(c_0_6224_0,axiom,
    ( class_Ring__and__Field_Ocomm__semiring__0(X1)
    | ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6224]) ).

cnf(c_0_6224_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X1)
    | class_Ring__and__Field_Ocomm__semiring__0(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6224]) ).

cnf(c_0_6225_0,axiom,
    ( class_OrderedGroup_Opordered__ab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Olordered__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6225]) ).

cnf(c_0_6225_1,axiom,
    ( ~ class_Ring__and__Field_Olordered__ring(X1)
    | class_OrderedGroup_Opordered__ab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6225]) ).

cnf(c_0_6226_0,axiom,
    ( class_Ring__and__Field_Opordered__semiring(X1)
    | ~ class_Ring__and__Field_Olordered__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6226]) ).

cnf(c_0_6226_1,axiom,
    ( ~ class_Ring__and__Field_Olordered__ring(X1)
    | class_Ring__and__Field_Opordered__semiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6226]) ).

cnf(c_0_6227_0,axiom,
    ( class_Ring__and__Field_Opordered__cancel__semiring(X1)
    | ~ class_Ring__and__Field_Olordered__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6227]) ).

cnf(c_0_6227_1,axiom,
    ( ~ class_Ring__and__Field_Olordered__ring(X1)
    | class_Ring__and__Field_Opordered__cancel__semiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6227]) ).

cnf(c_0_6228_0,axiom,
    ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Olordered__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6228]) ).

cnf(c_0_6228_1,axiom,
    ( ~ class_Ring__and__Field_Olordered__ring(X1)
    | class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6228]) ).

cnf(c_0_6229_0,axiom,
    ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
    | ~ class_Ring__and__Field_Olordered__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6229]) ).

cnf(c_0_6229_1,axiom,
    ( ~ class_Ring__and__Field_Olordered__ring(X1)
    | class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6229]) ).

cnf(c_0_6230_0,axiom,
    ( class_HOL_Ominus(X1)
    | ~ class_Ring__and__Field_Olordered__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6230]) ).

cnf(c_0_6230_1,axiom,
    ( ~ class_Ring__and__Field_Olordered__ring(X1)
    | class_HOL_Ominus(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6230]) ).

cnf(c_0_6231_0,axiom,
    ( class_OrderedGroup_Olordered__ab__group__join(X1)
    | ~ class_Ring__and__Field_Olordered__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6231]) ).

cnf(c_0_6231_1,axiom,
    ( ~ class_Ring__and__Field_Olordered__ring(X1)
    | class_OrderedGroup_Olordered__ab__group__join(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6231]) ).

cnf(c_0_6232_0,axiom,
    ( class_OrderedGroup_Oab__group__add(X1)
    | ~ class_Ring__and__Field_Olordered__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6232]) ).

cnf(c_0_6232_1,axiom,
    ( ~ class_Ring__and__Field_Olordered__ring(X1)
    | class_OrderedGroup_Oab__group__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6232]) ).

cnf(c_0_6233_0,axiom,
    ( class_OrderedGroup_Olordered__ab__group__meet(X1)
    | ~ class_Ring__and__Field_Olordered__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6233]) ).

cnf(c_0_6233_1,axiom,
    ( ~ class_Ring__and__Field_Olordered__ring(X1)
    | class_OrderedGroup_Olordered__ab__group__meet(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6233]) ).

cnf(c_0_6234_0,axiom,
    ( class_LOrder_Omeet__semilorder(X1)
    | ~ class_Ring__and__Field_Olordered__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6234]) ).

cnf(c_0_6234_1,axiom,
    ( ~ class_Ring__and__Field_Olordered__ring(X1)
    | class_LOrder_Omeet__semilorder(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6234]) ).

cnf(c_0_6235_0,axiom,
    ( class_LOrder_Ojoin__semilorder(X1)
    | ~ class_Ring__and__Field_Olordered__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6235]) ).

cnf(c_0_6235_1,axiom,
    ( ~ class_Ring__and__Field_Olordered__ring(X1)
    | class_LOrder_Ojoin__semilorder(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6235]) ).

cnf(c_0_6236_0,axiom,
    ( class_LOrder_Olorder(X1)
    | ~ class_Ring__and__Field_Olordered__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6236]) ).

cnf(c_0_6236_1,axiom,
    ( ~ class_Ring__and__Field_Olordered__ring(X1)
    | class_LOrder_Olorder(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6236]) ).

cnf(c_0_6237_0,axiom,
    ( class_OrderedGroup_Olordered__ab__group(X1)
    | ~ class_Ring__and__Field_Olordered__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6237]) ).

cnf(c_0_6237_1,axiom,
    ( ~ class_Ring__and__Field_Olordered__ring(X1)
    | class_OrderedGroup_Olordered__ab__group(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6237]) ).

cnf(c_0_6238_0,axiom,
    ( class_OrderedGroup_Olordered__ab__group__abs(X1)
    | ~ class_Ring__and__Field_Olordered__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6238]) ).

cnf(c_0_6238_1,axiom,
    ( ~ class_Ring__and__Field_Olordered__ring(X1)
    | class_OrderedGroup_Olordered__ab__group__abs(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6238]) ).

cnf(c_0_6239_0,axiom,
    ( class_HOL_Oplus(X1)
    | ~ class_Ring__and__Field_Olordered__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6239]) ).

cnf(c_0_6239_1,axiom,
    ( ~ class_Ring__and__Field_Olordered__ring(X1)
    | class_HOL_Oplus(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6239]) ).

cnf(c_0_6240_0,axiom,
    ( class_OrderedGroup_Osemigroup__add(X1)
    | ~ class_Ring__and__Field_Olordered__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6240]) ).

cnf(c_0_6240_1,axiom,
    ( ~ class_Ring__and__Field_Olordered__ring(X1)
    | class_OrderedGroup_Osemigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6240]) ).

cnf(c_0_6241_0,axiom,
    ( class_OrderedGroup_Ocancel__semigroup__add(X1)
    | ~ class_Ring__and__Field_Olordered__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6241]) ).

cnf(c_0_6241_1,axiom,
    ( ~ class_Ring__and__Field_Olordered__ring(X1)
    | class_OrderedGroup_Ocancel__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6241]) ).

cnf(c_0_6242_0,axiom,
    ( class_OrderedGroup_Oab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Olordered__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6242]) ).

cnf(c_0_6242_1,axiom,
    ( ~ class_Ring__and__Field_Olordered__ring(X1)
    | class_OrderedGroup_Oab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6242]) ).

cnf(c_0_6243_0,axiom,
    ( class_OrderedGroup_Opordered__ab__group__add(X1)
    | ~ class_Ring__and__Field_Olordered__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6243]) ).

cnf(c_0_6243_1,axiom,
    ( ~ class_Ring__and__Field_Olordered__ring(X1)
    | class_OrderedGroup_Opordered__ab__group__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6243]) ).

cnf(c_0_6244_0,axiom,
    ( class_OrderedGroup_Ocancel__ab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Olordered__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6244]) ).

cnf(c_0_6244_1,axiom,
    ( ~ class_Ring__and__Field_Olordered__ring(X1)
    | class_OrderedGroup_Ocancel__ab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6244]) ).

cnf(c_0_6245_0,axiom,
    ( class_HOL_Ozero(X1)
    | ~ class_Ring__and__Field_Olordered__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6245]) ).

cnf(c_0_6245_1,axiom,
    ( ~ class_Ring__and__Field_Olordered__ring(X1)
    | class_HOL_Ozero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6245]) ).

cnf(c_0_6246_0,axiom,
    ( class_OrderedGroup_Ocomm__monoid__add(X1)
    | ~ class_Ring__and__Field_Olordered__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6246]) ).

cnf(c_0_6246_1,axiom,
    ( ~ class_Ring__and__Field_Olordered__ring(X1)
    | class_OrderedGroup_Ocomm__monoid__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6246]) ).

cnf(c_0_6247_0,axiom,
    ( class_HOL_Otimes(X1)
    | ~ class_Ring__and__Field_Olordered__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6247]) ).

cnf(c_0_6247_1,axiom,
    ( ~ class_Ring__and__Field_Olordered__ring(X1)
    | class_HOL_Otimes(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6247]) ).

cnf(c_0_6248_0,axiom,
    ( class_OrderedGroup_Osemigroup__mult(X1)
    | ~ class_Ring__and__Field_Olordered__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6248]) ).

cnf(c_0_6248_1,axiom,
    ( ~ class_Ring__and__Field_Olordered__ring(X1)
    | class_OrderedGroup_Osemigroup__mult(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6248]) ).

cnf(c_0_6249_0,axiom,
    ( class_Ring__and__Field_Osemiring(X1)
    | ~ class_Ring__and__Field_Olordered__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6249]) ).

cnf(c_0_6249_1,axiom,
    ( ~ class_Ring__and__Field_Olordered__ring(X1)
    | class_Ring__and__Field_Osemiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6249]) ).

cnf(c_0_6250_0,axiom,
    ( class_Ring__and__Field_Osemiring__0(X1)
    | ~ class_Ring__and__Field_Olordered__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6250]) ).

cnf(c_0_6250_1,axiom,
    ( ~ class_Ring__and__Field_Olordered__ring(X1)
    | class_Ring__and__Field_Osemiring__0(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6250]) ).

cnf(c_0_6251_0,axiom,
    ( class_Ring__and__Field_Osemiring__0__cancel(X1)
    | ~ class_Ring__and__Field_Olordered__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6251]) ).

cnf(c_0_6251_1,axiom,
    ( ~ class_Ring__and__Field_Olordered__ring(X1)
    | class_Ring__and__Field_Osemiring__0__cancel(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6251]) ).

cnf(c_0_6252_0,axiom,
    ( class_Orderings_Oord(X1)
    | ~ class_Ring__and__Field_Olordered__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6252]) ).

cnf(c_0_6252_1,axiom,
    ( ~ class_Ring__and__Field_Olordered__ring(X1)
    | class_Orderings_Oord(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6252]) ).

cnf(c_0_6253_0,axiom,
    ( class_Orderings_Oorder(X1)
    | ~ class_Ring__and__Field_Olordered__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6253]) ).

cnf(c_0_6253_1,axiom,
    ( ~ class_Ring__and__Field_Olordered__ring(X1)
    | class_Orderings_Oorder(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6253]) ).

cnf(c_0_6254_0,axiom,
    ( class_Ring__and__Field_Oring(X1)
    | ~ class_Ring__and__Field_Olordered__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6254]) ).

cnf(c_0_6254_1,axiom,
    ( ~ class_Ring__and__Field_Olordered__ring(X1)
    | class_Ring__and__Field_Oring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6254]) ).

cnf(c_0_6255_0,axiom,
    ( class_Ring__and__Field_Opordered__ring(X1)
    | ~ class_Ring__and__Field_Olordered__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6255]) ).

cnf(c_0_6255_1,axiom,
    ( ~ class_Ring__and__Field_Olordered__ring(X1)
    | class_Ring__and__Field_Opordered__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6255]) ).

cnf(c_0_6256_0,axiom,
    ( class_Ring__and__Field_Osemiring__1__cancel(X1)
    | ~ class_Ring__and__Field_Oidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6256]) ).

cnf(c_0_6256_1,axiom,
    ( ~ class_Ring__and__Field_Oidom(X1)
    | class_Ring__and__Field_Osemiring__1__cancel(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6256]) ).

cnf(c_0_6257_0,axiom,
    ( class_OrderedGroup_Ocomm__monoid__mult(X1)
    | ~ class_Ring__and__Field_Oidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6257]) ).

cnf(c_0_6257_1,axiom,
    ( ~ class_Ring__and__Field_Oidom(X1)
    | class_OrderedGroup_Ocomm__monoid__mult(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6257]) ).

cnf(c_0_6258_0,axiom,
    ( class_Ring__and__Field_Ocomm__semiring__1(X1)
    | ~ class_Ring__and__Field_Oidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6258]) ).

cnf(c_0_6258_1,axiom,
    ( ~ class_Ring__and__Field_Oidom(X1)
    | class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6258]) ).

cnf(c_0_6259_0,axiom,
    ( class_Ring__and__Field_Ocomm__semiring__1__cancel(X1)
    | ~ class_Ring__and__Field_Oidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6259]) ).

cnf(c_0_6259_1,axiom,
    ( ~ class_Ring__and__Field_Oidom(X1)
    | class_Ring__and__Field_Ocomm__semiring__1__cancel(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6259]) ).

cnf(c_0_6260_0,axiom,
    ( class_HOL_Ominus(X1)
    | ~ class_Ring__and__Field_Oidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6260]) ).

cnf(c_0_6260_1,axiom,
    ( ~ class_Ring__and__Field_Oidom(X1)
    | class_HOL_Ominus(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6260]) ).

cnf(c_0_6261_0,axiom,
    ( class_OrderedGroup_Oab__group__add(X1)
    | ~ class_Ring__and__Field_Oidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6261]) ).

cnf(c_0_6261_1,axiom,
    ( ~ class_Ring__and__Field_Oidom(X1)
    | class_OrderedGroup_Oab__group__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6261]) ).

cnf(c_0_6262_0,axiom,
    ( class_Ring__and__Field_Oaxclass__no__zero__divisors(X1)
    | ~ class_Ring__and__Field_Oidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6262]) ).

cnf(c_0_6262_1,axiom,
    ( ~ class_Ring__and__Field_Oidom(X1)
    | class_Ring__and__Field_Oaxclass__no__zero__divisors(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6262]) ).

cnf(c_0_6263_0,axiom,
    ( class_Ring__and__Field_Oring(X1)
    | ~ class_Ring__and__Field_Oidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6263]) ).

cnf(c_0_6263_1,axiom,
    ( ~ class_Ring__and__Field_Oidom(X1)
    | class_Ring__and__Field_Oring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6263]) ).

cnf(c_0_6264_0,axiom,
    ( class_HOL_Oplus(X1)
    | ~ class_Ring__and__Field_Oidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6264]) ).

cnf(c_0_6264_1,axiom,
    ( ~ class_Ring__and__Field_Oidom(X1)
    | class_HOL_Oplus(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6264]) ).

cnf(c_0_6265_0,axiom,
    ( class_OrderedGroup_Osemigroup__add(X1)
    | ~ class_Ring__and__Field_Oidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6265]) ).

cnf(c_0_6265_1,axiom,
    ( ~ class_Ring__and__Field_Oidom(X1)
    | class_OrderedGroup_Osemigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6265]) ).

cnf(c_0_6266_0,axiom,
    ( class_OrderedGroup_Ocancel__semigroup__add(X1)
    | ~ class_Ring__and__Field_Oidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6266]) ).

cnf(c_0_6266_1,axiom,
    ( ~ class_Ring__and__Field_Oidom(X1)
    | class_OrderedGroup_Ocancel__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6266]) ).

cnf(c_0_6267_0,axiom,
    ( class_OrderedGroup_Oab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Oidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6267]) ).

cnf(c_0_6267_1,axiom,
    ( ~ class_Ring__and__Field_Oidom(X1)
    | class_OrderedGroup_Oab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6267]) ).

cnf(c_0_6268_0,axiom,
    ( class_OrderedGroup_Ocancel__ab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Oidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6268]) ).

cnf(c_0_6268_1,axiom,
    ( ~ class_Ring__and__Field_Oidom(X1)
    | class_OrderedGroup_Ocancel__ab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6268]) ).

cnf(c_0_6269_0,axiom,
    ( class_HOL_Ozero(X1)
    | ~ class_Ring__and__Field_Oidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6269]) ).

cnf(c_0_6269_1,axiom,
    ( ~ class_Ring__and__Field_Oidom(X1)
    | class_HOL_Ozero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6269]) ).

cnf(c_0_6270_0,axiom,
    ( class_OrderedGroup_Ocomm__monoid__add(X1)
    | ~ class_Ring__and__Field_Oidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6270]) ).

cnf(c_0_6270_1,axiom,
    ( ~ class_Ring__and__Field_Oidom(X1)
    | class_OrderedGroup_Ocomm__monoid__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6270]) ).

cnf(c_0_6271_0,axiom,
    ( class_HOL_Otimes(X1)
    | ~ class_Ring__and__Field_Oidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6271]) ).

cnf(c_0_6271_1,axiom,
    ( ~ class_Ring__and__Field_Oidom(X1)
    | class_HOL_Otimes(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6271]) ).

cnf(c_0_6272_0,axiom,
    ( class_OrderedGroup_Osemigroup__mult(X1)
    | ~ class_Ring__and__Field_Oidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6272]) ).

cnf(c_0_6272_1,axiom,
    ( ~ class_Ring__and__Field_Oidom(X1)
    | class_OrderedGroup_Osemigroup__mult(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6272]) ).

cnf(c_0_6273_0,axiom,
    ( class_Ring__and__Field_Osemiring(X1)
    | ~ class_Ring__and__Field_Oidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6273]) ).

cnf(c_0_6273_1,axiom,
    ( ~ class_Ring__and__Field_Oidom(X1)
    | class_Ring__and__Field_Osemiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6273]) ).

cnf(c_0_6274_0,axiom,
    ( class_Ring__and__Field_Oring__1(X1)
    | ~ class_Ring__and__Field_Oidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6274]) ).

cnf(c_0_6274_1,axiom,
    ( ~ class_Ring__and__Field_Oidom(X1)
    | class_Ring__and__Field_Oring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6274]) ).

cnf(c_0_6275_0,axiom,
    ( class_Ring__and__Field_Osemiring__0(X1)
    | ~ class_Ring__and__Field_Oidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6275]) ).

cnf(c_0_6275_1,axiom,
    ( ~ class_Ring__and__Field_Oidom(X1)
    | class_Ring__and__Field_Osemiring__0(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6275]) ).

cnf(c_0_6276_0,axiom,
    ( class_Ring__and__Field_Osemiring__0__cancel(X1)
    | ~ class_Ring__and__Field_Oidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6276]) ).

cnf(c_0_6276_1,axiom,
    ( ~ class_Ring__and__Field_Oidom(X1)
    | class_Ring__and__Field_Osemiring__0__cancel(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6276]) ).

cnf(c_0_6277_0,axiom,
    ( class_OrderedGroup_Oab__semigroup__mult(X1)
    | ~ class_Ring__and__Field_Oidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6277]) ).

cnf(c_0_6277_1,axiom,
    ( ~ class_Ring__and__Field_Oidom(X1)
    | class_OrderedGroup_Oab__semigroup__mult(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6277]) ).

cnf(c_0_6278_0,axiom,
    ( class_Ring__and__Field_Ocomm__semiring(X1)
    | ~ class_Ring__and__Field_Oidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6278]) ).

cnf(c_0_6278_1,axiom,
    ( ~ class_Ring__and__Field_Oidom(X1)
    | class_Ring__and__Field_Ocomm__semiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6278]) ).

cnf(c_0_6279_0,axiom,
    ( class_Ring__and__Field_Ocomm__semiring__0(X1)
    | ~ class_Ring__and__Field_Oidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6279]) ).

cnf(c_0_6279_1,axiom,
    ( ~ class_Ring__and__Field_Oidom(X1)
    | class_Ring__and__Field_Ocomm__semiring__0(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6279]) ).

cnf(c_0_6280_0,axiom,
    ( class_Ring__and__Field_Ocomm__semiring__0__cancel(X1)
    | ~ class_Ring__and__Field_Oidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6280]) ).

cnf(c_0_6280_1,axiom,
    ( ~ class_Ring__and__Field_Oidom(X1)
    | class_Ring__and__Field_Ocomm__semiring__0__cancel(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6280]) ).

cnf(c_0_6281_0,axiom,
    ( class_HOL_Oone(X1)
    | ~ class_Ring__and__Field_Oidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6281]) ).

cnf(c_0_6281_1,axiom,
    ( ~ class_Ring__and__Field_Oidom(X1)
    | class_HOL_Oone(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6281]) ).

cnf(c_0_6282_0,axiom,
    ( class_OrderedGroup_Omonoid__mult(X1)
    | ~ class_Ring__and__Field_Oidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6282]) ).

cnf(c_0_6282_1,axiom,
    ( ~ class_Ring__and__Field_Oidom(X1)
    | class_OrderedGroup_Omonoid__mult(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6282]) ).

cnf(c_0_6283_0,axiom,
    ( class_Ring__and__Field_Oaxclass__0__neq__1(X1)
    | ~ class_Ring__and__Field_Oidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6283]) ).

cnf(c_0_6283_1,axiom,
    ( ~ class_Ring__and__Field_Oidom(X1)
    | class_Ring__and__Field_Oaxclass__0__neq__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6283]) ).

cnf(c_0_6284_0,axiom,
    ( class_Ring__and__Field_Osemiring__1(X1)
    | ~ class_Ring__and__Field_Oidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6284]) ).

cnf(c_0_6284_1,axiom,
    ( ~ class_Ring__and__Field_Oidom(X1)
    | class_Ring__and__Field_Osemiring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6284]) ).

cnf(c_0_6285_0,axiom,
    ( class_Ring__and__Field_Ocomm__ring(X1)
    | ~ class_Ring__and__Field_Oidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6285]) ).

cnf(c_0_6285_1,axiom,
    ( ~ class_Ring__and__Field_Oidom(X1)
    | class_Ring__and__Field_Ocomm__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6285]) ).

cnf(c_0_6286_0,axiom,
    ( class_Ring__and__Field_Ocomm__ring__1(X1)
    | ~ class_Ring__and__Field_Oidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6286]) ).

cnf(c_0_6286_1,axiom,
    ( ~ class_Ring__and__Field_Oidom(X1)
    | class_Ring__and__Field_Ocomm__ring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6286]) ).

cnf(c_0_6287_0,axiom,
    ( class_Ring__and__Field_Osemiring__1__cancel(X1)
    | ~ class_Ring__and__Field_Ofield(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6287]) ).

cnf(c_0_6287_1,axiom,
    ( ~ class_Ring__and__Field_Ofield(X1)
    | class_Ring__and__Field_Osemiring__1__cancel(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6287]) ).

cnf(c_0_6288_0,axiom,
    ( class_OrderedGroup_Ocomm__monoid__mult(X1)
    | ~ class_Ring__and__Field_Ofield(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6288]) ).

cnf(c_0_6288_1,axiom,
    ( ~ class_Ring__and__Field_Ofield(X1)
    | class_OrderedGroup_Ocomm__monoid__mult(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6288]) ).

cnf(c_0_6289_0,axiom,
    ( class_Ring__and__Field_Ocomm__semiring__1(X1)
    | ~ class_Ring__and__Field_Ofield(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6289]) ).

cnf(c_0_6289_1,axiom,
    ( ~ class_Ring__and__Field_Ofield(X1)
    | class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6289]) ).

cnf(c_0_6290_0,axiom,
    ( class_Ring__and__Field_Ocomm__semiring__1__cancel(X1)
    | ~ class_Ring__and__Field_Ofield(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6290]) ).

cnf(c_0_6290_1,axiom,
    ( ~ class_Ring__and__Field_Ofield(X1)
    | class_Ring__and__Field_Ocomm__semiring__1__cancel(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6290]) ).

cnf(c_0_6291_0,axiom,
    ( class_HOL_Ominus(X1)
    | ~ class_Ring__and__Field_Ofield(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6291]) ).

cnf(c_0_6291_1,axiom,
    ( ~ class_Ring__and__Field_Ofield(X1)
    | class_HOL_Ominus(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6291]) ).

cnf(c_0_6292_0,axiom,
    ( class_OrderedGroup_Oab__group__add(X1)
    | ~ class_Ring__and__Field_Ofield(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6292]) ).

cnf(c_0_6292_1,axiom,
    ( ~ class_Ring__and__Field_Ofield(X1)
    | class_OrderedGroup_Oab__group__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6292]) ).

cnf(c_0_6293_0,axiom,
    ( class_Ring__and__Field_Oaxclass__no__zero__divisors(X1)
    | ~ class_Ring__and__Field_Ofield(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6293]) ).

cnf(c_0_6293_1,axiom,
    ( ~ class_Ring__and__Field_Ofield(X1)
    | class_Ring__and__Field_Oaxclass__no__zero__divisors(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6293]) ).

cnf(c_0_6294_0,axiom,
    ( class_Ring__and__Field_Oidom(X1)
    | ~ class_Ring__and__Field_Ofield(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6294]) ).

cnf(c_0_6294_1,axiom,
    ( ~ class_Ring__and__Field_Ofield(X1)
    | class_Ring__and__Field_Oidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6294]) ).

cnf(c_0_6295_0,axiom,
    ( class_HOL_Oinverse(X1)
    | ~ class_Ring__and__Field_Ofield(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6295]) ).

cnf(c_0_6295_1,axiom,
    ( ~ class_Ring__and__Field_Ofield(X1)
    | class_HOL_Oinverse(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6295]) ).

cnf(c_0_6296_0,axiom,
    ( class_Ring__and__Field_Oring(X1)
    | ~ class_Ring__and__Field_Ofield(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6296]) ).

cnf(c_0_6296_1,axiom,
    ( ~ class_Ring__and__Field_Ofield(X1)
    | class_Ring__and__Field_Oring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6296]) ).

cnf(c_0_6297_0,axiom,
    ( class_HOL_Oplus(X1)
    | ~ class_Ring__and__Field_Ofield(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6297]) ).

cnf(c_0_6297_1,axiom,
    ( ~ class_Ring__and__Field_Ofield(X1)
    | class_HOL_Oplus(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6297]) ).

cnf(c_0_6298_0,axiom,
    ( class_OrderedGroup_Osemigroup__add(X1)
    | ~ class_Ring__and__Field_Ofield(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6298]) ).

cnf(c_0_6298_1,axiom,
    ( ~ class_Ring__and__Field_Ofield(X1)
    | class_OrderedGroup_Osemigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6298]) ).

cnf(c_0_6299_0,axiom,
    ( class_OrderedGroup_Ocancel__semigroup__add(X1)
    | ~ class_Ring__and__Field_Ofield(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6299]) ).

cnf(c_0_6299_1,axiom,
    ( ~ class_Ring__and__Field_Ofield(X1)
    | class_OrderedGroup_Ocancel__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6299]) ).

cnf(c_0_6300_0,axiom,
    ( class_OrderedGroup_Oab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Ofield(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6300]) ).

cnf(c_0_6300_1,axiom,
    ( ~ class_Ring__and__Field_Ofield(X1)
    | class_OrderedGroup_Oab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6300]) ).

cnf(c_0_6301_0,axiom,
    ( class_OrderedGroup_Ocancel__ab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Ofield(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6301]) ).

cnf(c_0_6301_1,axiom,
    ( ~ class_Ring__and__Field_Ofield(X1)
    | class_OrderedGroup_Ocancel__ab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6301]) ).

cnf(c_0_6302_0,axiom,
    ( class_HOL_Ozero(X1)
    | ~ class_Ring__and__Field_Ofield(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6302]) ).

cnf(c_0_6302_1,axiom,
    ( ~ class_Ring__and__Field_Ofield(X1)
    | class_HOL_Ozero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6302]) ).

cnf(c_0_6303_0,axiom,
    ( class_OrderedGroup_Ocomm__monoid__add(X1)
    | ~ class_Ring__and__Field_Ofield(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6303]) ).

cnf(c_0_6303_1,axiom,
    ( ~ class_Ring__and__Field_Ofield(X1)
    | class_OrderedGroup_Ocomm__monoid__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6303]) ).

cnf(c_0_6304_0,axiom,
    ( class_HOL_Otimes(X1)
    | ~ class_Ring__and__Field_Ofield(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6304]) ).

cnf(c_0_6304_1,axiom,
    ( ~ class_Ring__and__Field_Ofield(X1)
    | class_HOL_Otimes(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6304]) ).

cnf(c_0_6305_0,axiom,
    ( class_OrderedGroup_Osemigroup__mult(X1)
    | ~ class_Ring__and__Field_Ofield(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6305]) ).

cnf(c_0_6305_1,axiom,
    ( ~ class_Ring__and__Field_Ofield(X1)
    | class_OrderedGroup_Osemigroup__mult(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6305]) ).

cnf(c_0_6306_0,axiom,
    ( class_Ring__and__Field_Osemiring(X1)
    | ~ class_Ring__and__Field_Ofield(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6306]) ).

cnf(c_0_6306_1,axiom,
    ( ~ class_Ring__and__Field_Ofield(X1)
    | class_Ring__and__Field_Osemiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6306]) ).

cnf(c_0_6307_0,axiom,
    ( class_Ring__and__Field_Oring__1(X1)
    | ~ class_Ring__and__Field_Ofield(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6307]) ).

cnf(c_0_6307_1,axiom,
    ( ~ class_Ring__and__Field_Ofield(X1)
    | class_Ring__and__Field_Oring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6307]) ).

cnf(c_0_6308_0,axiom,
    ( class_Ring__and__Field_Osemiring__0(X1)
    | ~ class_Ring__and__Field_Ofield(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6308]) ).

cnf(c_0_6308_1,axiom,
    ( ~ class_Ring__and__Field_Ofield(X1)
    | class_Ring__and__Field_Osemiring__0(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6308]) ).

cnf(c_0_6309_0,axiom,
    ( class_Ring__and__Field_Osemiring__0__cancel(X1)
    | ~ class_Ring__and__Field_Ofield(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6309]) ).

cnf(c_0_6309_1,axiom,
    ( ~ class_Ring__and__Field_Ofield(X1)
    | class_Ring__and__Field_Osemiring__0__cancel(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6309]) ).

cnf(c_0_6310_0,axiom,
    ( class_OrderedGroup_Oab__semigroup__mult(X1)
    | ~ class_Ring__and__Field_Ofield(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6310]) ).

cnf(c_0_6310_1,axiom,
    ( ~ class_Ring__and__Field_Ofield(X1)
    | class_OrderedGroup_Oab__semigroup__mult(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6310]) ).

cnf(c_0_6311_0,axiom,
    ( class_Ring__and__Field_Ocomm__semiring(X1)
    | ~ class_Ring__and__Field_Ofield(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6311]) ).

cnf(c_0_6311_1,axiom,
    ( ~ class_Ring__and__Field_Ofield(X1)
    | class_Ring__and__Field_Ocomm__semiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6311]) ).

cnf(c_0_6312_0,axiom,
    ( class_Ring__and__Field_Ocomm__semiring__0(X1)
    | ~ class_Ring__and__Field_Ofield(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6312]) ).

cnf(c_0_6312_1,axiom,
    ( ~ class_Ring__and__Field_Ofield(X1)
    | class_Ring__and__Field_Ocomm__semiring__0(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6312]) ).

cnf(c_0_6313_0,axiom,
    ( class_Ring__and__Field_Ocomm__semiring__0__cancel(X1)
    | ~ class_Ring__and__Field_Ofield(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6313]) ).

cnf(c_0_6313_1,axiom,
    ( ~ class_Ring__and__Field_Ofield(X1)
    | class_Ring__and__Field_Ocomm__semiring__0__cancel(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6313]) ).

cnf(c_0_6314_0,axiom,
    ( class_HOL_Oone(X1)
    | ~ class_Ring__and__Field_Ofield(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6314]) ).

cnf(c_0_6314_1,axiom,
    ( ~ class_Ring__and__Field_Ofield(X1)
    | class_HOL_Oone(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6314]) ).

cnf(c_0_6315_0,axiom,
    ( class_OrderedGroup_Omonoid__mult(X1)
    | ~ class_Ring__and__Field_Ofield(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6315]) ).

cnf(c_0_6315_1,axiom,
    ( ~ class_Ring__and__Field_Ofield(X1)
    | class_OrderedGroup_Omonoid__mult(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6315]) ).

cnf(c_0_6316_0,axiom,
    ( class_Ring__and__Field_Oaxclass__0__neq__1(X1)
    | ~ class_Ring__and__Field_Ofield(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6316]) ).

cnf(c_0_6316_1,axiom,
    ( ~ class_Ring__and__Field_Ofield(X1)
    | class_Ring__and__Field_Oaxclass__0__neq__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6316]) ).

cnf(c_0_6317_0,axiom,
    ( class_Ring__and__Field_Osemiring__1(X1)
    | ~ class_Ring__and__Field_Ofield(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6317]) ).

cnf(c_0_6317_1,axiom,
    ( ~ class_Ring__and__Field_Ofield(X1)
    | class_Ring__and__Field_Osemiring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6317]) ).

cnf(c_0_6318_0,axiom,
    ( class_Ring__and__Field_Ocomm__ring(X1)
    | ~ class_Ring__and__Field_Ofield(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6318]) ).

cnf(c_0_6318_1,axiom,
    ( ~ class_Ring__and__Field_Ofield(X1)
    | class_Ring__and__Field_Ocomm__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6318]) ).

cnf(c_0_6319_0,axiom,
    ( class_Ring__and__Field_Ocomm__ring__1(X1)
    | ~ class_Ring__and__Field_Ofield(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6319]) ).

cnf(c_0_6319_1,axiom,
    ( ~ class_Ring__and__Field_Ofield(X1)
    | class_Ring__and__Field_Ocomm__ring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6319]) ).

cnf(c_0_6320_0,axiom,
    ( class_HOL_Oinverse(X1)
    | ~ class_Ring__and__Field_Odivision__by__zero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6320]) ).

cnf(c_0_6320_1,axiom,
    ( ~ class_Ring__and__Field_Odivision__by__zero(X1)
    | class_HOL_Oinverse(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6320]) ).

cnf(c_0_6321_0,axiom,
    ( class_HOL_Ozero(X1)
    | ~ class_Ring__and__Field_Odivision__by__zero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6321]) ).

cnf(c_0_6321_1,axiom,
    ( ~ class_Ring__and__Field_Odivision__by__zero(X1)
    | class_HOL_Ozero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6321]) ).

cnf(c_0_6322_0,axiom,
    ( class_OrderedGroup_Ocomm__monoid__add(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6322]) ).

cnf(c_0_6322_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X1)
    | class_OrderedGroup_Ocomm__monoid__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6322]) ).

cnf(c_0_6323_0,axiom,
    ( class_Ring__and__Field_Osemiring(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6323]) ).

cnf(c_0_6323_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X1)
    | class_Ring__and__Field_Osemiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6323]) ).

cnf(c_0_6324_0,axiom,
    ( class_Ring__and__Field_Osemiring__0(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6324]) ).

cnf(c_0_6324_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X1)
    | class_Ring__and__Field_Osemiring__0(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6324]) ).

cnf(c_0_6325_0,axiom,
    ( class_Ring__and__Field_Oaxclass__0__neq__1(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6325]) ).

cnf(c_0_6325_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X1)
    | class_Ring__and__Field_Oaxclass__0__neq__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6325]) ).

cnf(c_0_6326_0,axiom,
    ( class_Ring__and__Field_Osemiring__1(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6326]) ).

cnf(c_0_6326_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X1)
    | class_Ring__and__Field_Osemiring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6326]) ).

cnf(c_0_6327_0,axiom,
    ( class_OrderedGroup_Oab__semigroup__mult(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6327]) ).

cnf(c_0_6327_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X1)
    | class_OrderedGroup_Oab__semigroup__mult(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6327]) ).

cnf(c_0_6328_0,axiom,
    ( class_OrderedGroup_Ocomm__monoid__mult(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6328]) ).

cnf(c_0_6328_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X1)
    | class_OrderedGroup_Ocomm__monoid__mult(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6328]) ).

cnf(c_0_6329_0,axiom,
    ( class_Ring__and__Field_Ocomm__semiring__0__cancel(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6329]) ).

cnf(c_0_6329_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X1)
    | class_Ring__and__Field_Ocomm__semiring__0__cancel(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6329]) ).

cnf(c_0_6330_0,axiom,
    ( class_Ring__and__Field_Osemiring__0__cancel(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6330]) ).

cnf(c_0_6330_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X1)
    | class_Ring__and__Field_Osemiring__0__cancel(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6330]) ).

cnf(c_0_6331_0,axiom,
    ( class_Ring__and__Field_Osemiring__1__cancel(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6331]) ).

cnf(c_0_6331_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X1)
    | class_Ring__and__Field_Osemiring__1__cancel(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6331]) ).

cnf(c_0_6332_0,axiom,
    ( class_Ring__and__Field_Ocomm__semiring(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6332]) ).

cnf(c_0_6332_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X1)
    | class_Ring__and__Field_Ocomm__semiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6332]) ).

cnf(c_0_6333_0,axiom,
    ( class_OrderedGroup_Ocancel__semigroup__add(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6333]) ).

cnf(c_0_6333_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X1)
    | class_OrderedGroup_Ocancel__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6333]) ).

cnf(c_0_6334_0,axiom,
    ( class_OrderedGroup_Ocancel__ab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6334]) ).

cnf(c_0_6334_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X1)
    | class_OrderedGroup_Ocancel__ab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6334]) ).

cnf(c_0_6335_0,axiom,
    ( class_HOL_Otimes(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6335]) ).

cnf(c_0_6335_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X1)
    | class_HOL_Otimes(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6335]) ).

cnf(c_0_6336_0,axiom,
    ( class_OrderedGroup_Osemigroup__mult(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6336]) ).

cnf(c_0_6336_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X1)
    | class_OrderedGroup_Osemigroup__mult(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6336]) ).

cnf(c_0_6337_0,axiom,
    ( class_HOL_Oone(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6337]) ).

cnf(c_0_6337_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X1)
    | class_HOL_Oone(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6337]) ).

cnf(c_0_6338_0,axiom,
    ( class_OrderedGroup_Omonoid__mult(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6338]) ).

cnf(c_0_6338_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X1)
    | class_OrderedGroup_Omonoid__mult(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6338]) ).

cnf(c_0_6339_0,axiom,
    ( class_HOL_Oplus(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6339]) ).

cnf(c_0_6339_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X1)
    | class_HOL_Oplus(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6339]) ).

cnf(c_0_6340_0,axiom,
    ( class_OrderedGroup_Osemigroup__add(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6340]) ).

cnf(c_0_6340_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X1)
    | class_OrderedGroup_Osemigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6340]) ).

cnf(c_0_6341_0,axiom,
    ( class_OrderedGroup_Oab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6341]) ).

cnf(c_0_6341_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X1)
    | class_OrderedGroup_Oab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6341]) ).

cnf(c_0_6342_0,axiom,
    ( class_HOL_Ozero(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6342]) ).

cnf(c_0_6342_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X1)
    | class_HOL_Ozero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6342]) ).

cnf(c_0_6343_0,axiom,
    ( class_Ring__and__Field_Ocomm__semiring__0(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6343]) ).

cnf(c_0_6343_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X1)
    | class_Ring__and__Field_Ocomm__semiring__0(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6343]) ).

cnf(c_0_6344_0,axiom,
    ( class_Ring__and__Field_Ocomm__semiring__1(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6344]) ).

cnf(c_0_6344_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X1)
    | class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6344]) ).

cnf(c_0_6345_0,axiom,
    ( class_HOL_Otimes(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6345]) ).

cnf(c_0_6345_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
    | class_HOL_Otimes(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6345]) ).

cnf(c_0_6346_0,axiom,
    ( class_OrderedGroup_Osemigroup__mult(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6346]) ).

cnf(c_0_6346_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
    | class_OrderedGroup_Osemigroup__mult(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6346]) ).

cnf(c_0_6347_0,axiom,
    ( class_Ring__and__Field_Osemiring(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6347]) ).

cnf(c_0_6347_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
    | class_Ring__and__Field_Osemiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6347]) ).

cnf(c_0_6348_0,axiom,
    ( class_Ring__and__Field_Osemiring__0(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6348]) ).

cnf(c_0_6348_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
    | class_Ring__and__Field_Osemiring__0(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6348]) ).

cnf(c_0_6349_0,axiom,
    ( class_OrderedGroup_Oab__semigroup__mult(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6349]) ).

cnf(c_0_6349_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
    | class_OrderedGroup_Oab__semigroup__mult(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6349]) ).

cnf(c_0_6350_0,axiom,
    ( class_Ring__and__Field_Ocomm__semiring(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6350]) ).

cnf(c_0_6350_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
    | class_Ring__and__Field_Ocomm__semiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6350]) ).

cnf(c_0_6351_0,axiom,
    ( class_Ring__and__Field_Ocomm__semiring__0(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6351]) ).

cnf(c_0_6351_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
    | class_Ring__and__Field_Ocomm__semiring__0(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6351]) ).

cnf(c_0_6352_0,axiom,
    ( class_HOL_Oone(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6352]) ).

cnf(c_0_6352_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
    | class_HOL_Oone(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6352]) ).

cnf(c_0_6353_0,axiom,
    ( class_Ring__and__Field_Osemiring__1(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6353]) ).

cnf(c_0_6353_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
    | class_Ring__and__Field_Osemiring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6353]) ).

cnf(c_0_6354_0,axiom,
    ( class_OrderedGroup_Omonoid__mult(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6354]) ).

cnf(c_0_6354_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
    | class_OrderedGroup_Omonoid__mult(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6354]) ).

cnf(c_0_6355_0,axiom,
    ( class_OrderedGroup_Ocomm__monoid__mult(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6355]) ).

cnf(c_0_6355_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
    | class_OrderedGroup_Ocomm__monoid__mult(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6355]) ).

cnf(c_0_6356_0,axiom,
    ( class_HOL_Oplus(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6356]) ).

cnf(c_0_6356_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
    | class_HOL_Oplus(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6356]) ).

cnf(c_0_6357_0,axiom,
    ( class_OrderedGroup_Osemigroup__add(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6357]) ).

cnf(c_0_6357_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
    | class_OrderedGroup_Osemigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6357]) ).

cnf(c_0_6358_0,axiom,
    ( class_OrderedGroup_Oab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6358]) ).

cnf(c_0_6358_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
    | class_OrderedGroup_Oab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6358]) ).

cnf(c_0_6359_0,axiom,
    ( class_OrderedGroup_Ocomm__monoid__add(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6359]) ).

cnf(c_0_6359_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
    | class_OrderedGroup_Ocomm__monoid__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6359]) ).

cnf(c_0_6360_0,axiom,
    ( class_HOL_Ozero(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6360]) ).

cnf(c_0_6360_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
    | class_HOL_Ozero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6360]) ).

cnf(c_0_6361_0,axiom,
    ( class_Ring__and__Field_Oaxclass__0__neq__1(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6361]) ).

cnf(c_0_6361_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
    | class_Ring__and__Field_Oaxclass__0__neq__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6361]) ).

cnf(c_0_6362_0,axiom,
    ( class_OrderedGroup_Osemigroup__add(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6362]) ).

cnf(c_0_6362_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X1)
    | class_OrderedGroup_Osemigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6362]) ).

cnf(c_0_6363_0,axiom,
    ( class_OrderedGroup_Oab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6363]) ).

cnf(c_0_6363_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X1)
    | class_OrderedGroup_Oab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6363]) ).

cnf(c_0_6364_0,axiom,
    ( class_OrderedGroup_Ocomm__monoid__add(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6364]) ).

cnf(c_0_6364_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X1)
    | class_OrderedGroup_Ocomm__monoid__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6364]) ).

cnf(c_0_6365_0,axiom,
    ( class_HOL_Otimes(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6365]) ).

cnf(c_0_6365_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X1)
    | class_HOL_Otimes(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6365]) ).

cnf(c_0_6366_0,axiom,
    ( class_OrderedGroup_Osemigroup__mult(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6366]) ).

cnf(c_0_6366_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X1)
    | class_OrderedGroup_Osemigroup__mult(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6366]) ).

cnf(c_0_6367_0,axiom,
    ( class_Ring__and__Field_Osemiring(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6367]) ).

cnf(c_0_6367_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X1)
    | class_Ring__and__Field_Osemiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6367]) ).

cnf(c_0_6368_0,axiom,
    ( class_Ring__and__Field_Osemiring__0(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6368]) ).

cnf(c_0_6368_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X1)
    | class_Ring__and__Field_Osemiring__0(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6368]) ).

cnf(c_0_6369_0,axiom,
    ( class_OrderedGroup_Oab__semigroup__mult(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6369]) ).

cnf(c_0_6369_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X1)
    | class_OrderedGroup_Oab__semigroup__mult(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6369]) ).

cnf(c_0_6370_0,axiom,
    ( class_Ring__and__Field_Osemiring__0__cancel(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6370]) ).

cnf(c_0_6370_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X1)
    | class_Ring__and__Field_Osemiring__0__cancel(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6370]) ).

cnf(c_0_6371_0,axiom,
    ( class_OrderedGroup_Ocancel__semigroup__add(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6371]) ).

cnf(c_0_6371_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X1)
    | class_OrderedGroup_Ocancel__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6371]) ).

cnf(c_0_6372_0,axiom,
    ( class_OrderedGroup_Ocancel__ab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6372]) ).

cnf(c_0_6372_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X1)
    | class_OrderedGroup_Ocancel__ab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6372]) ).

cnf(c_0_6373_0,axiom,
    ( class_HOL_Ozero(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6373]) ).

cnf(c_0_6373_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X1)
    | class_HOL_Ozero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6373]) ).

cnf(c_0_6374_0,axiom,
    ( class_HOL_Oplus(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6374]) ).

cnf(c_0_6374_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X1)
    | class_HOL_Oplus(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6374]) ).

cnf(c_0_6375_0,axiom,
    ( class_Ring__and__Field_Ocomm__semiring(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6375]) ).

cnf(c_0_6375_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X1)
    | class_Ring__and__Field_Ocomm__semiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6375]) ).

cnf(c_0_6376_0,axiom,
    ( class_Ring__and__Field_Ocomm__semiring__0(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6376]) ).

cnf(c_0_6376_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X1)
    | class_Ring__and__Field_Ocomm__semiring__0(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6376]) ).

cnf(c_0_6377_0,axiom,
    ( class_HOL_Ozero(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__0(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6377]) ).

cnf(c_0_6377_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__0(X1)
    | class_HOL_Ozero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6377]) ).

cnf(c_0_6378_0,axiom,
    ( class_OrderedGroup_Ocomm__monoid__add(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__0(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6378]) ).

cnf(c_0_6378_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__0(X1)
    | class_OrderedGroup_Ocomm__monoid__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6378]) ).

cnf(c_0_6379_0,axiom,
    ( class_HOL_Otimes(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__0(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6379]) ).

cnf(c_0_6379_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__0(X1)
    | class_HOL_Otimes(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6379]) ).

cnf(c_0_6380_0,axiom,
    ( class_OrderedGroup_Osemigroup__mult(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__0(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6380]) ).

cnf(c_0_6380_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__0(X1)
    | class_OrderedGroup_Osemigroup__mult(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6380]) ).

cnf(c_0_6381_0,axiom,
    ( class_HOL_Oplus(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__0(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6381]) ).

cnf(c_0_6381_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__0(X1)
    | class_HOL_Oplus(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6381]) ).

cnf(c_0_6382_0,axiom,
    ( class_OrderedGroup_Osemigroup__add(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__0(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6382]) ).

cnf(c_0_6382_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__0(X1)
    | class_OrderedGroup_Osemigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6382]) ).

cnf(c_0_6383_0,axiom,
    ( class_OrderedGroup_Oab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__0(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6383]) ).

cnf(c_0_6383_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__0(X1)
    | class_OrderedGroup_Oab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6383]) ).

cnf(c_0_6384_0,axiom,
    ( class_Ring__and__Field_Osemiring(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__0(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6384]) ).

cnf(c_0_6384_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__0(X1)
    | class_Ring__and__Field_Osemiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6384]) ).

cnf(c_0_6385_0,axiom,
    ( class_Ring__and__Field_Osemiring__0(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__0(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6385]) ).

cnf(c_0_6385_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__0(X1)
    | class_Ring__and__Field_Osemiring__0(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6385]) ).

cnf(c_0_6386_0,axiom,
    ( class_OrderedGroup_Oab__semigroup__mult(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__0(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6386]) ).

cnf(c_0_6386_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__0(X1)
    | class_OrderedGroup_Oab__semigroup__mult(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6386]) ).

cnf(c_0_6387_0,axiom,
    ( class_Ring__and__Field_Ocomm__semiring(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__0(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6387]) ).

cnf(c_0_6387_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__0(X1)
    | class_Ring__and__Field_Ocomm__semiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6387]) ).

cnf(c_0_6388_0,axiom,
    ( class_Ring__and__Field_Osemiring(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6388]) ).

cnf(c_0_6388_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring(X1)
    | class_Ring__and__Field_Osemiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6388]) ).

cnf(c_0_6389_0,axiom,
    ( class_HOL_Otimes(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6389]) ).

cnf(c_0_6389_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring(X1)
    | class_HOL_Otimes(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6389]) ).

cnf(c_0_6390_0,axiom,
    ( class_OrderedGroup_Osemigroup__mult(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6390]) ).

cnf(c_0_6390_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring(X1)
    | class_OrderedGroup_Osemigroup__mult(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6390]) ).

cnf(c_0_6391_0,axiom,
    ( class_OrderedGroup_Oab__semigroup__mult(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6391]) ).

cnf(c_0_6391_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring(X1)
    | class_OrderedGroup_Oab__semigroup__mult(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6391]) ).

cnf(c_0_6392_0,axiom,
    ( class_HOL_Oplus(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6392]) ).

cnf(c_0_6392_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring(X1)
    | class_HOL_Oplus(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6392]) ).

cnf(c_0_6393_0,axiom,
    ( class_OrderedGroup_Osemigroup__add(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6393]) ).

cnf(c_0_6393_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring(X1)
    | class_OrderedGroup_Osemigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6393]) ).

cnf(c_0_6394_0,axiom,
    ( class_OrderedGroup_Oab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6394]) ).

cnf(c_0_6394_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring(X1)
    | class_OrderedGroup_Oab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6394]) ).

cnf(c_0_6395_0,axiom,
    ( class_Ring__and__Field_Osemiring__0(X1)
    | ~ class_Ring__and__Field_Ocomm__ring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6395]) ).

cnf(c_0_6395_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__ring__1(X1)
    | class_Ring__and__Field_Osemiring__0(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6395]) ).

cnf(c_0_6396_0,axiom,
    ( class_Ring__and__Field_Osemiring__0__cancel(X1)
    | ~ class_Ring__and__Field_Ocomm__ring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6396]) ).

cnf(c_0_6396_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__ring__1(X1)
    | class_Ring__and__Field_Osemiring__0__cancel(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6396]) ).

cnf(c_0_6397_0,axiom,
    ( class_OrderedGroup_Oab__semigroup__mult(X1)
    | ~ class_Ring__and__Field_Ocomm__ring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6397]) ).

cnf(c_0_6397_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__ring__1(X1)
    | class_OrderedGroup_Oab__semigroup__mult(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6397]) ).

cnf(c_0_6398_0,axiom,
    ( class_Ring__and__Field_Ocomm__semiring(X1)
    | ~ class_Ring__and__Field_Ocomm__ring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6398]) ).

cnf(c_0_6398_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__ring__1(X1)
    | class_Ring__and__Field_Ocomm__semiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6398]) ).

cnf(c_0_6399_0,axiom,
    ( class_Ring__and__Field_Ocomm__semiring__0(X1)
    | ~ class_Ring__and__Field_Ocomm__ring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6399]) ).

cnf(c_0_6399_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__ring__1(X1)
    | class_Ring__and__Field_Ocomm__semiring__0(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6399]) ).

cnf(c_0_6400_0,axiom,
    ( class_Ring__and__Field_Ocomm__semiring__0__cancel(X1)
    | ~ class_Ring__and__Field_Ocomm__ring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6400]) ).

cnf(c_0_6400_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__ring__1(X1)
    | class_Ring__and__Field_Ocomm__semiring__0__cancel(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6400]) ).

cnf(c_0_6401_0,axiom,
    ( class_HOL_Ominus(X1)
    | ~ class_Ring__and__Field_Ocomm__ring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6401]) ).

cnf(c_0_6401_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__ring__1(X1)
    | class_HOL_Ominus(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6401]) ).

cnf(c_0_6402_0,axiom,
    ( class_Ring__and__Field_Ocomm__semiring__1__cancel(X1)
    | ~ class_Ring__and__Field_Ocomm__ring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6402]) ).

cnf(c_0_6402_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__ring__1(X1)
    | class_Ring__and__Field_Ocomm__semiring__1__cancel(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6402]) ).

cnf(c_0_6403_0,axiom,
    ( class_Ring__and__Field_Osemiring__1__cancel(X1)
    | ~ class_Ring__and__Field_Ocomm__ring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6403]) ).

cnf(c_0_6403_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__ring__1(X1)
    | class_Ring__and__Field_Osemiring__1__cancel(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6403]) ).

cnf(c_0_6404_0,axiom,
    ( class_Ring__and__Field_Oring__1(X1)
    | ~ class_Ring__and__Field_Ocomm__ring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6404]) ).

cnf(c_0_6404_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__ring__1(X1)
    | class_Ring__and__Field_Oring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6404]) ).

cnf(c_0_6405_0,axiom,
    ( class_HOL_Oone(X1)
    | ~ class_Ring__and__Field_Ocomm__ring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6405]) ).

cnf(c_0_6405_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__ring__1(X1)
    | class_HOL_Oone(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6405]) ).

cnf(c_0_6406_0,axiom,
    ( class_OrderedGroup_Omonoid__mult(X1)
    | ~ class_Ring__and__Field_Ocomm__ring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6406]) ).

cnf(c_0_6406_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__ring__1(X1)
    | class_OrderedGroup_Omonoid__mult(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6406]) ).

cnf(c_0_6407_0,axiom,
    ( class_Ring__and__Field_Oaxclass__0__neq__1(X1)
    | ~ class_Ring__and__Field_Ocomm__ring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6407]) ).

cnf(c_0_6407_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__ring__1(X1)
    | class_Ring__and__Field_Oaxclass__0__neq__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6407]) ).

cnf(c_0_6408_0,axiom,
    ( class_Ring__and__Field_Osemiring__1(X1)
    | ~ class_Ring__and__Field_Ocomm__ring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6408]) ).

cnf(c_0_6408_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__ring__1(X1)
    | class_Ring__and__Field_Osemiring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6408]) ).

cnf(c_0_6409_0,axiom,
    ( class_OrderedGroup_Ocomm__monoid__mult(X1)
    | ~ class_Ring__and__Field_Ocomm__ring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6409]) ).

cnf(c_0_6409_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__ring__1(X1)
    | class_OrderedGroup_Ocomm__monoid__mult(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6409]) ).

cnf(c_0_6410_0,axiom,
    ( class_Ring__and__Field_Ocomm__semiring__1(X1)
    | ~ class_Ring__and__Field_Ocomm__ring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6410]) ).

cnf(c_0_6410_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__ring__1(X1)
    | class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6410]) ).

cnf(c_0_6411_0,axiom,
    ( class_OrderedGroup_Oab__group__add(X1)
    | ~ class_Ring__and__Field_Ocomm__ring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6411]) ).

cnf(c_0_6411_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__ring__1(X1)
    | class_OrderedGroup_Oab__group__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6411]) ).

cnf(c_0_6412_0,axiom,
    ( class_HOL_Oplus(X1)
    | ~ class_Ring__and__Field_Ocomm__ring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6412]) ).

cnf(c_0_6412_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__ring__1(X1)
    | class_HOL_Oplus(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6412]) ).

cnf(c_0_6413_0,axiom,
    ( class_OrderedGroup_Osemigroup__add(X1)
    | ~ class_Ring__and__Field_Ocomm__ring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6413]) ).

cnf(c_0_6413_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__ring__1(X1)
    | class_OrderedGroup_Osemigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6413]) ).

cnf(c_0_6414_0,axiom,
    ( class_OrderedGroup_Ocancel__semigroup__add(X1)
    | ~ class_Ring__and__Field_Ocomm__ring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6414]) ).

cnf(c_0_6414_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__ring__1(X1)
    | class_OrderedGroup_Ocancel__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6414]) ).

cnf(c_0_6415_0,axiom,
    ( class_OrderedGroup_Oab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Ocomm__ring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6415]) ).

cnf(c_0_6415_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__ring__1(X1)
    | class_OrderedGroup_Oab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6415]) ).

cnf(c_0_6416_0,axiom,
    ( class_OrderedGroup_Ocancel__ab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Ocomm__ring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6416]) ).

cnf(c_0_6416_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__ring__1(X1)
    | class_OrderedGroup_Ocancel__ab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6416]) ).

cnf(c_0_6417_0,axiom,
    ( class_HOL_Ozero(X1)
    | ~ class_Ring__and__Field_Ocomm__ring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6417]) ).

cnf(c_0_6417_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__ring__1(X1)
    | class_HOL_Ozero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6417]) ).

cnf(c_0_6418_0,axiom,
    ( class_OrderedGroup_Ocomm__monoid__add(X1)
    | ~ class_Ring__and__Field_Ocomm__ring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6418]) ).

cnf(c_0_6418_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__ring__1(X1)
    | class_OrderedGroup_Ocomm__monoid__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6418]) ).

cnf(c_0_6419_0,axiom,
    ( class_HOL_Otimes(X1)
    | ~ class_Ring__and__Field_Ocomm__ring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6419]) ).

cnf(c_0_6419_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__ring__1(X1)
    | class_HOL_Otimes(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6419]) ).

cnf(c_0_6420_0,axiom,
    ( class_OrderedGroup_Osemigroup__mult(X1)
    | ~ class_Ring__and__Field_Ocomm__ring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6420]) ).

cnf(c_0_6420_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__ring__1(X1)
    | class_OrderedGroup_Osemigroup__mult(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6420]) ).

cnf(c_0_6421_0,axiom,
    ( class_Ring__and__Field_Osemiring(X1)
    | ~ class_Ring__and__Field_Ocomm__ring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6421]) ).

cnf(c_0_6421_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__ring__1(X1)
    | class_Ring__and__Field_Osemiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6421]) ).

cnf(c_0_6422_0,axiom,
    ( class_Ring__and__Field_Oring(X1)
    | ~ class_Ring__and__Field_Ocomm__ring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6422]) ).

cnf(c_0_6422_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__ring__1(X1)
    | class_Ring__and__Field_Oring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6422]) ).

cnf(c_0_6423_0,axiom,
    ( class_Ring__and__Field_Ocomm__ring(X1)
    | ~ class_Ring__and__Field_Ocomm__ring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6423]) ).

cnf(c_0_6423_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__ring__1(X1)
    | class_Ring__and__Field_Ocomm__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6423]) ).

cnf(c_0_6424_0,axiom,
    ( class_OrderedGroup_Osemigroup__add(X1)
    | ~ class_Ring__and__Field_Ocomm__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6424]) ).

cnf(c_0_6424_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__ring(X1)
    | class_OrderedGroup_Osemigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6424]) ).

cnf(c_0_6425_0,axiom,
    ( class_OrderedGroup_Oab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Ocomm__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6425]) ).

cnf(c_0_6425_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__ring(X1)
    | class_OrderedGroup_Oab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6425]) ).

cnf(c_0_6426_0,axiom,
    ( class_OrderedGroup_Ocomm__monoid__add(X1)
    | ~ class_Ring__and__Field_Ocomm__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6426]) ).

cnf(c_0_6426_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__ring(X1)
    | class_OrderedGroup_Ocomm__monoid__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6426]) ).

cnf(c_0_6427_0,axiom,
    ( class_HOL_Otimes(X1)
    | ~ class_Ring__and__Field_Ocomm__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6427]) ).

cnf(c_0_6427_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__ring(X1)
    | class_HOL_Otimes(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6427]) ).

cnf(c_0_6428_0,axiom,
    ( class_OrderedGroup_Osemigroup__mult(X1)
    | ~ class_Ring__and__Field_Ocomm__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6428]) ).

cnf(c_0_6428_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__ring(X1)
    | class_OrderedGroup_Osemigroup__mult(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6428]) ).

cnf(c_0_6429_0,axiom,
    ( class_Ring__and__Field_Osemiring(X1)
    | ~ class_Ring__and__Field_Ocomm__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6429]) ).

cnf(c_0_6429_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__ring(X1)
    | class_Ring__and__Field_Osemiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6429]) ).

cnf(c_0_6430_0,axiom,
    ( class_Ring__and__Field_Osemiring__0(X1)
    | ~ class_Ring__and__Field_Ocomm__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6430]) ).

cnf(c_0_6430_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__ring(X1)
    | class_Ring__and__Field_Osemiring__0(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6430]) ).

cnf(c_0_6431_0,axiom,
    ( class_OrderedGroup_Oab__semigroup__mult(X1)
    | ~ class_Ring__and__Field_Ocomm__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6431]) ).

cnf(c_0_6431_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__ring(X1)
    | class_OrderedGroup_Oab__semigroup__mult(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6431]) ).

cnf(c_0_6432_0,axiom,
    ( class_Ring__and__Field_Ocomm__semiring__0__cancel(X1)
    | ~ class_Ring__and__Field_Ocomm__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6432]) ).

cnf(c_0_6432_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__ring(X1)
    | class_Ring__and__Field_Ocomm__semiring__0__cancel(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6432]) ).

cnf(c_0_6433_0,axiom,
    ( class_Ring__and__Field_Osemiring__0__cancel(X1)
    | ~ class_Ring__and__Field_Ocomm__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6433]) ).

cnf(c_0_6433_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__ring(X1)
    | class_Ring__and__Field_Osemiring__0__cancel(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6433]) ).

cnf(c_0_6434_0,axiom,
    ( class_Ring__and__Field_Oring(X1)
    | ~ class_Ring__and__Field_Ocomm__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6434]) ).

cnf(c_0_6434_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__ring(X1)
    | class_Ring__and__Field_Oring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6434]) ).

cnf(c_0_6435_0,axiom,
    ( class_OrderedGroup_Ocancel__semigroup__add(X1)
    | ~ class_Ring__and__Field_Ocomm__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6435]) ).

cnf(c_0_6435_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__ring(X1)
    | class_OrderedGroup_Ocancel__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6435]) ).

cnf(c_0_6436_0,axiom,
    ( class_OrderedGroup_Ocancel__ab__semigroup__add(X1)
    | ~ class_Ring__and__Field_Ocomm__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6436]) ).

cnf(c_0_6436_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__ring(X1)
    | class_OrderedGroup_Ocancel__ab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6436]) ).

cnf(c_0_6437_0,axiom,
    ( class_HOL_Ominus(X1)
    | ~ class_Ring__and__Field_Ocomm__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6437]) ).

cnf(c_0_6437_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__ring(X1)
    | class_HOL_Ominus(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6437]) ).

cnf(c_0_6438_0,axiom,
    ( class_OrderedGroup_Oab__group__add(X1)
    | ~ class_Ring__and__Field_Ocomm__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6438]) ).

cnf(c_0_6438_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__ring(X1)
    | class_OrderedGroup_Oab__group__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6438]) ).

cnf(c_0_6439_0,axiom,
    ( class_HOL_Ozero(X1)
    | ~ class_Ring__and__Field_Ocomm__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6439]) ).

cnf(c_0_6439_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__ring(X1)
    | class_HOL_Ozero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6439]) ).

cnf(c_0_6440_0,axiom,
    ( class_HOL_Oplus(X1)
    | ~ class_Ring__and__Field_Ocomm__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6440]) ).

cnf(c_0_6440_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__ring(X1)
    | class_HOL_Oplus(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6440]) ).

cnf(c_0_6441_0,axiom,
    ( class_Ring__and__Field_Ocomm__semiring(X1)
    | ~ class_Ring__and__Field_Ocomm__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6441]) ).

cnf(c_0_6441_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__ring(X1)
    | class_Ring__and__Field_Ocomm__semiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6441]) ).

cnf(c_0_6442_0,axiom,
    ( class_Ring__and__Field_Ocomm__semiring__0(X1)
    | ~ class_Ring__and__Field_Ocomm__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6442]) ).

cnf(c_0_6442_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__ring(X1)
    | class_Ring__and__Field_Ocomm__semiring__0(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6442]) ).

cnf(c_0_6443_0,axiom,
    ( class_HOL_Otimes(X1)
    | ~ class_Ring__and__Field_Oaxclass__no__zero__divisors(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6443]) ).

cnf(c_0_6443_1,axiom,
    ( ~ class_Ring__and__Field_Oaxclass__no__zero__divisors(X1)
    | class_HOL_Otimes(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6443]) ).

cnf(c_0_6444_0,axiom,
    ( class_HOL_Ozero(X1)
    | ~ class_Ring__and__Field_Oaxclass__no__zero__divisors(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6444]) ).

cnf(c_0_6444_1,axiom,
    ( ~ class_Ring__and__Field_Oaxclass__no__zero__divisors(X1)
    | class_HOL_Ozero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6444]) ).

cnf(c_0_6445_0,axiom,
    ( class_HOL_Ozero(X1)
    | ~ class_Ring__and__Field_Oaxclass__abs__if(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6445]) ).

cnf(c_0_6445_1,axiom,
    ( ~ class_Ring__and__Field_Oaxclass__abs__if(X1)
    | class_HOL_Ozero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6445]) ).

cnf(c_0_6446_0,axiom,
    ( class_Orderings_Oord(X1)
    | ~ class_Ring__and__Field_Oaxclass__abs__if(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6446]) ).

cnf(c_0_6446_1,axiom,
    ( ~ class_Ring__and__Field_Oaxclass__abs__if(X1)
    | class_Orderings_Oord(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6446]) ).

cnf(c_0_6447_0,axiom,
    ( class_HOL_Ominus(X1)
    | ~ class_Ring__and__Field_Oaxclass__abs__if(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6447]) ).

cnf(c_0_6447_1,axiom,
    ( ~ class_Ring__and__Field_Oaxclass__abs__if(X1)
    | class_HOL_Ominus(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6447]) ).

cnf(c_0_6448_0,axiom,
    ( class_HOL_Oone(X1)
    | ~ class_Ring__and__Field_Oaxclass__0__neq__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6448]) ).

cnf(c_0_6448_1,axiom,
    ( ~ class_Ring__and__Field_Oaxclass__0__neq__1(X1)
    | class_HOL_Oone(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6448]) ).

cnf(c_0_6449_0,axiom,
    ( class_HOL_Ozero(X1)
    | ~ class_Ring__and__Field_Oaxclass__0__neq__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6449]) ).

cnf(c_0_6449_1,axiom,
    ( ~ class_Ring__and__Field_Oaxclass__0__neq__1(X1)
    | class_HOL_Ozero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6449]) ).

cnf(c_0_6450_0,axiom,
    ( class_OrderedGroup_Oab__semigroup__mult(X1)
    | ~ class_Power_Orecpower(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6450]) ).

cnf(c_0_6450_1,axiom,
    ( ~ class_Power_Orecpower(X1)
    | class_OrderedGroup_Oab__semigroup__mult(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6450]) ).

cnf(c_0_6451_0,axiom,
    ( class_OrderedGroup_Osemigroup__mult(X1)
    | ~ class_Power_Orecpower(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6451]) ).

cnf(c_0_6451_1,axiom,
    ( ~ class_Power_Orecpower(X1)
    | class_OrderedGroup_Osemigroup__mult(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6451]) ).

cnf(c_0_6452_0,axiom,
    ( class_HOL_Otimes(X1)
    | ~ class_Power_Orecpower(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6452]) ).

cnf(c_0_6452_1,axiom,
    ( ~ class_Power_Orecpower(X1)
    | class_HOL_Otimes(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6452]) ).

cnf(c_0_6453_0,axiom,
    ( class_OrderedGroup_Oab__semigroup__add(X1)
    | ~ class_Power_Orecpower(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6453]) ).

cnf(c_0_6453_1,axiom,
    ( ~ class_Power_Orecpower(X1)
    | class_OrderedGroup_Oab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6453]) ).

cnf(c_0_6454_0,axiom,
    ( class_OrderedGroup_Osemigroup__add(X1)
    | ~ class_Power_Orecpower(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6454]) ).

cnf(c_0_6454_1,axiom,
    ( ~ class_Power_Orecpower(X1)
    | class_OrderedGroup_Osemigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6454]) ).

cnf(c_0_6455_0,axiom,
    ( class_HOL_Oplus(X1)
    | ~ class_Power_Orecpower(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6455]) ).

cnf(c_0_6455_1,axiom,
    ( ~ class_Power_Orecpower(X1)
    | class_HOL_Oplus(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6455]) ).

cnf(c_0_6456_0,axiom,
    ( class_Ring__and__Field_Oaxclass__0__neq__1(X1)
    | ~ class_Power_Orecpower(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6456]) ).

cnf(c_0_6456_1,axiom,
    ( ~ class_Power_Orecpower(X1)
    | class_Ring__and__Field_Oaxclass__0__neq__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6456]) ).

cnf(c_0_6457_0,axiom,
    ( class_Ring__and__Field_Ocomm__semiring__1__cancel(X1)
    | ~ class_Power_Orecpower(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6457]) ).

cnf(c_0_6457_1,axiom,
    ( ~ class_Power_Orecpower(X1)
    | class_Ring__and__Field_Ocomm__semiring__1__cancel(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6457]) ).

cnf(c_0_6458_0,axiom,
    ( class_Ring__and__Field_Ocomm__semiring__0__cancel(X1)
    | ~ class_Power_Orecpower(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6458]) ).

cnf(c_0_6458_1,axiom,
    ( ~ class_Power_Orecpower(X1)
    | class_Ring__and__Field_Ocomm__semiring__0__cancel(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6458]) ).

cnf(c_0_6459_0,axiom,
    ( class_Ring__and__Field_Osemiring__1__cancel(X1)
    | ~ class_Power_Orecpower(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6459]) ).

cnf(c_0_6459_1,axiom,
    ( ~ class_Power_Orecpower(X1)
    | class_Ring__and__Field_Osemiring__1__cancel(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6459]) ).

cnf(c_0_6460_0,axiom,
    ( class_Ring__and__Field_Osemiring__0__cancel(X1)
    | ~ class_Power_Orecpower(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6460]) ).

cnf(c_0_6460_1,axiom,
    ( ~ class_Power_Orecpower(X1)
    | class_Ring__and__Field_Osemiring__0__cancel(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6460]) ).

cnf(c_0_6461_0,axiom,
    ( class_OrderedGroup_Ocancel__ab__semigroup__add(X1)
    | ~ class_Power_Orecpower(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6461]) ).

cnf(c_0_6461_1,axiom,
    ( ~ class_Power_Orecpower(X1)
    | class_OrderedGroup_Ocancel__ab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6461]) ).

cnf(c_0_6462_0,axiom,
    ( class_HOL_Oone(X1)
    | ~ class_Power_Orecpower(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6462]) ).

cnf(c_0_6462_1,axiom,
    ( ~ class_Power_Orecpower(X1)
    | class_HOL_Oone(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6462]) ).

cnf(c_0_6463_0,axiom,
    ( class_OrderedGroup_Ocancel__semigroup__add(X1)
    | ~ class_Power_Orecpower(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6463]) ).

cnf(c_0_6463_1,axiom,
    ( ~ class_Power_Orecpower(X1)
    | class_OrderedGroup_Ocancel__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6463]) ).

cnf(c_0_6464_0,axiom,
    ( class_Ring__and__Field_Ocomm__semiring__1(X1)
    | ~ class_Power_Orecpower(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6464]) ).

cnf(c_0_6464_1,axiom,
    ( ~ class_Power_Orecpower(X1)
    | class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6464]) ).

cnf(c_0_6465_0,axiom,
    ( class_Ring__and__Field_Osemiring__1(X1)
    | ~ class_Power_Orecpower(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6465]) ).

cnf(c_0_6465_1,axiom,
    ( ~ class_Power_Orecpower(X1)
    | class_Ring__and__Field_Osemiring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6465]) ).

cnf(c_0_6466_0,axiom,
    ( class_OrderedGroup_Ocomm__monoid__mult(X1)
    | ~ class_Power_Orecpower(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6466]) ).

cnf(c_0_6466_1,axiom,
    ( ~ class_Power_Orecpower(X1)
    | class_OrderedGroup_Ocomm__monoid__mult(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6466]) ).

cnf(c_0_6467_0,axiom,
    ( class_OrderedGroup_Omonoid__mult(X1)
    | ~ class_Power_Orecpower(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6467]) ).

cnf(c_0_6467_1,axiom,
    ( ~ class_Power_Orecpower(X1)
    | class_OrderedGroup_Omonoid__mult(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6467]) ).

cnf(c_0_6468_0,axiom,
    ( class_Ring__and__Field_Ocomm__semiring__0(X1)
    | ~ class_Power_Orecpower(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6468]) ).

cnf(c_0_6468_1,axiom,
    ( ~ class_Power_Orecpower(X1)
    | class_Ring__and__Field_Ocomm__semiring__0(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6468]) ).

cnf(c_0_6469_0,axiom,
    ( class_Ring__and__Field_Osemiring__0(X1)
    | ~ class_Power_Orecpower(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6469]) ).

cnf(c_0_6469_1,axiom,
    ( ~ class_Power_Orecpower(X1)
    | class_Ring__and__Field_Osemiring__0(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6469]) ).

cnf(c_0_6470_0,axiom,
    ( class_OrderedGroup_Ocomm__monoid__add(X1)
    | ~ class_Power_Orecpower(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6470]) ).

cnf(c_0_6470_1,axiom,
    ( ~ class_Power_Orecpower(X1)
    | class_OrderedGroup_Ocomm__monoid__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6470]) ).

cnf(c_0_6471_0,axiom,
    ( class_Ring__and__Field_Ocomm__semiring(X1)
    | ~ class_Power_Orecpower(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6471]) ).

cnf(c_0_6471_1,axiom,
    ( ~ class_Power_Orecpower(X1)
    | class_Ring__and__Field_Ocomm__semiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6471]) ).

cnf(c_0_6472_0,axiom,
    ( class_Ring__and__Field_Osemiring(X1)
    | ~ class_Power_Orecpower(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6472]) ).

cnf(c_0_6472_1,axiom,
    ( ~ class_Power_Orecpower(X1)
    | class_Ring__and__Field_Osemiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6472]) ).

cnf(c_0_6473_0,axiom,
    ( class_HOL_Ozero(X1)
    | ~ class_Power_Orecpower(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6473]) ).

cnf(c_0_6473_1,axiom,
    ( ~ class_Power_Orecpower(X1)
    | class_HOL_Ozero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6473]) ).

cnf(c_0_6474_0,axiom,
    ( class_Nat_Opower(X1)
    | ~ class_Power_Orecpower(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6474]) ).

cnf(c_0_6474_1,axiom,
    ( ~ class_Power_Orecpower(X1)
    | class_Nat_Opower(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6474]) ).

cnf(c_0_6475_0,axiom,
    ( class_Orderings_Oord(X1)
    | ~ class_Orderings_Oorder(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6475]) ).

cnf(c_0_6475_1,axiom,
    ( ~ class_Orderings_Oorder(X1)
    | class_Orderings_Oord(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6475]) ).

cnf(c_0_6476_0,axiom,
    ( class_Orderings_Oorder(X1)
    | ~ class_Orderings_Olinorder(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6476]) ).

cnf(c_0_6476_1,axiom,
    ( ~ class_Orderings_Olinorder(X1)
    | class_Orderings_Oorder(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6476]) ).

cnf(c_0_6477_0,axiom,
    ( class_Orderings_Oord(X1)
    | ~ class_Orderings_Olinorder(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6477]) ).

cnf(c_0_6477_1,axiom,
    ( ~ class_Orderings_Olinorder(X1)
    | class_Orderings_Oord(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6477]) ).

cnf(c_0_6478_0,axiom,
    ( class_LOrder_Omeet__semilorder(X1)
    | ~ class_Orderings_Olinorder(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6478]) ).

cnf(c_0_6478_1,axiom,
    ( ~ class_Orderings_Olinorder(X1)
    | class_LOrder_Omeet__semilorder(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6478]) ).

cnf(c_0_6479_0,axiom,
    ( class_LOrder_Ojoin__semilorder(X1)
    | ~ class_Orderings_Olinorder(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6479]) ).

cnf(c_0_6479_1,axiom,
    ( ~ class_Orderings_Olinorder(X1)
    | class_LOrder_Ojoin__semilorder(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6479]) ).

cnf(c_0_6480_0,axiom,
    ( class_LOrder_Olorder(X1)
    | ~ class_Orderings_Olinorder(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6480]) ).

cnf(c_0_6480_1,axiom,
    ( ~ class_Orderings_Olinorder(X1)
    | class_LOrder_Olorder(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6480]) ).

cnf(c_0_6481_0,axiom,
    ( class_HOL_Otimes(X1)
    | ~ class_OrderedGroup_Osemigroup__mult(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6481]) ).

cnf(c_0_6481_1,axiom,
    ( ~ class_OrderedGroup_Osemigroup__mult(X1)
    | class_HOL_Otimes(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6481]) ).

cnf(c_0_6482_0,axiom,
    ( class_HOL_Oplus(X1)
    | ~ class_OrderedGroup_Osemigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6482]) ).

cnf(c_0_6482_1,axiom,
    ( ~ class_OrderedGroup_Osemigroup__add(X1)
    | class_HOL_Oplus(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6482]) ).

cnf(c_0_6483_0,axiom,
    ( class_OrderedGroup_Ocancel__semigroup__add(X1)
    | ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6483]) ).

cnf(c_0_6483_1,axiom,
    ( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1)
    | class_OrderedGroup_Ocancel__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6483]) ).

cnf(c_0_6484_0,axiom,
    ( class_OrderedGroup_Ocancel__ab__semigroup__add(X1)
    | ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6484]) ).

cnf(c_0_6484_1,axiom,
    ( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1)
    | class_OrderedGroup_Ocancel__ab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6484]) ).

cnf(c_0_6485_0,axiom,
    ( class_HOL_Oplus(X1)
    | ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6485]) ).

cnf(c_0_6485_1,axiom,
    ( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1)
    | class_HOL_Oplus(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6485]) ).

cnf(c_0_6486_0,axiom,
    ( class_OrderedGroup_Osemigroup__add(X1)
    | ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6486]) ).

cnf(c_0_6486_1,axiom,
    ( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1)
    | class_OrderedGroup_Osemigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6486]) ).

cnf(c_0_6487_0,axiom,
    ( class_OrderedGroup_Oab__semigroup__add(X1)
    | ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6487]) ).

cnf(c_0_6487_1,axiom,
    ( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1)
    | class_OrderedGroup_Oab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6487]) ).

cnf(c_0_6488_0,axiom,
    ( class_Orderings_Oord(X1)
    | ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6488]) ).

cnf(c_0_6488_1,axiom,
    ( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1)
    | class_Orderings_Oord(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6488]) ).

cnf(c_0_6489_0,axiom,
    ( class_Orderings_Oorder(X1)
    | ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6489]) ).

cnf(c_0_6489_1,axiom,
    ( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1)
    | class_Orderings_Oorder(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6489]) ).

cnf(c_0_6490_0,axiom,
    ( class_OrderedGroup_Opordered__ab__semigroup__add(X1)
    | ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6490]) ).

cnf(c_0_6490_1,axiom,
    ( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1)
    | class_OrderedGroup_Opordered__ab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6490]) ).

cnf(c_0_6491_0,axiom,
    ( class_HOL_Oplus(X1)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6491]) ).

cnf(c_0_6491_1,axiom,
    ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
    | class_HOL_Oplus(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6491]) ).

cnf(c_0_6492_0,axiom,
    ( class_OrderedGroup_Osemigroup__add(X1)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6492]) ).

cnf(c_0_6492_1,axiom,
    ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
    | class_OrderedGroup_Osemigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6492]) ).

cnf(c_0_6493_0,axiom,
    ( class_OrderedGroup_Ocancel__semigroup__add(X1)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6493]) ).

cnf(c_0_6493_1,axiom,
    ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
    | class_OrderedGroup_Ocancel__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6493]) ).

cnf(c_0_6494_0,axiom,
    ( class_OrderedGroup_Oab__semigroup__add(X1)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6494]) ).

cnf(c_0_6494_1,axiom,
    ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
    | class_OrderedGroup_Oab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6494]) ).

cnf(c_0_6495_0,axiom,
    ( class_OrderedGroup_Ocancel__ab__semigroup__add(X1)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6495]) ).

cnf(c_0_6495_1,axiom,
    ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
    | class_OrderedGroup_Ocancel__ab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6495]) ).

cnf(c_0_6496_0,axiom,
    ( class_Orderings_Oord(X1)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6496]) ).

cnf(c_0_6496_1,axiom,
    ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
    | class_Orderings_Oord(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6496]) ).

cnf(c_0_6497_0,axiom,
    ( class_Orderings_Oorder(X1)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6497]) ).

cnf(c_0_6497_1,axiom,
    ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
    | class_Orderings_Oorder(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6497]) ).

cnf(c_0_6498_0,axiom,
    ( class_OrderedGroup_Opordered__ab__semigroup__add(X1)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6498]) ).

cnf(c_0_6498_1,axiom,
    ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
    | class_OrderedGroup_Opordered__ab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6498]) ).

cnf(c_0_6499_0,axiom,
    ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6499]) ).

cnf(c_0_6499_1,axiom,
    ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
    | class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6499]) ).

cnf(c_0_6500_0,axiom,
    ( class_HOL_Oplus(X1)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6500]) ).

cnf(c_0_6500_1,axiom,
    ( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X1)
    | class_HOL_Oplus(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6500]) ).

cnf(c_0_6501_0,axiom,
    ( class_OrderedGroup_Osemigroup__add(X1)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6501]) ).

cnf(c_0_6501_1,axiom,
    ( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X1)
    | class_OrderedGroup_Osemigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6501]) ).

cnf(c_0_6502_0,axiom,
    ( class_OrderedGroup_Oab__semigroup__add(X1)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6502]) ).

cnf(c_0_6502_1,axiom,
    ( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X1)
    | class_OrderedGroup_Oab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6502]) ).

cnf(c_0_6503_0,axiom,
    ( class_Orderings_Oord(X1)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6503]) ).

cnf(c_0_6503_1,axiom,
    ( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X1)
    | class_Orderings_Oord(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6503]) ).

cnf(c_0_6504_0,axiom,
    ( class_Orderings_Oorder(X1)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6504]) ).

cnf(c_0_6504_1,axiom,
    ( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X1)
    | class_Orderings_Oorder(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6504]) ).

cnf(c_0_6505_0,axiom,
    ( class_OrderedGroup_Opordered__ab__semigroup__add(X1)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6505]) ).

cnf(c_0_6505_1,axiom,
    ( ~ class_OrderedGroup_Opordered__ab__group__add(X1)
    | class_OrderedGroup_Opordered__ab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6505]) ).

cnf(c_0_6506_0,axiom,
    ( class_HOL_Oplus(X1)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6506]) ).

cnf(c_0_6506_1,axiom,
    ( ~ class_OrderedGroup_Opordered__ab__group__add(X1)
    | class_HOL_Oplus(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6506]) ).

cnf(c_0_6507_0,axiom,
    ( class_OrderedGroup_Osemigroup__add(X1)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6507]) ).

cnf(c_0_6507_1,axiom,
    ( ~ class_OrderedGroup_Opordered__ab__group__add(X1)
    | class_OrderedGroup_Osemigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6507]) ).

cnf(c_0_6508_0,axiom,
    ( class_OrderedGroup_Ocancel__semigroup__add(X1)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6508]) ).

cnf(c_0_6508_1,axiom,
    ( ~ class_OrderedGroup_Opordered__ab__group__add(X1)
    | class_OrderedGroup_Ocancel__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6508]) ).

cnf(c_0_6509_0,axiom,
    ( class_OrderedGroup_Oab__semigroup__add(X1)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6509]) ).

cnf(c_0_6509_1,axiom,
    ( ~ class_OrderedGroup_Opordered__ab__group__add(X1)
    | class_OrderedGroup_Oab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6509]) ).

cnf(c_0_6510_0,axiom,
    ( class_OrderedGroup_Ocancel__ab__semigroup__add(X1)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6510]) ).

cnf(c_0_6510_1,axiom,
    ( ~ class_OrderedGroup_Opordered__ab__group__add(X1)
    | class_OrderedGroup_Ocancel__ab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6510]) ).

cnf(c_0_6511_0,axiom,
    ( class_HOL_Ozero(X1)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6511]) ).

cnf(c_0_6511_1,axiom,
    ( ~ class_OrderedGroup_Opordered__ab__group__add(X1)
    | class_HOL_Ozero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6511]) ).

cnf(c_0_6512_0,axiom,
    ( class_OrderedGroup_Ocomm__monoid__add(X1)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6512]) ).

cnf(c_0_6512_1,axiom,
    ( ~ class_OrderedGroup_Opordered__ab__group__add(X1)
    | class_OrderedGroup_Ocomm__monoid__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6512]) ).

cnf(c_0_6513_0,axiom,
    ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6513]) ).

cnf(c_0_6513_1,axiom,
    ( ~ class_OrderedGroup_Opordered__ab__group__add(X1)
    | class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6513]) ).

cnf(c_0_6514_0,axiom,
    ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6514]) ).

cnf(c_0_6514_1,axiom,
    ( ~ class_OrderedGroup_Opordered__ab__group__add(X1)
    | class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6514]) ).

cnf(c_0_6515_0,axiom,
    ( class_Orderings_Oord(X1)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6515]) ).

cnf(c_0_6515_1,axiom,
    ( ~ class_OrderedGroup_Opordered__ab__group__add(X1)
    | class_Orderings_Oord(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6515]) ).

cnf(c_0_6516_0,axiom,
    ( class_Orderings_Oorder(X1)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6516]) ).

cnf(c_0_6516_1,axiom,
    ( ~ class_OrderedGroup_Opordered__ab__group__add(X1)
    | class_Orderings_Oorder(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6516]) ).

cnf(c_0_6517_0,axiom,
    ( class_HOL_Ominus(X1)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6517]) ).

cnf(c_0_6517_1,axiom,
    ( ~ class_OrderedGroup_Opordered__ab__group__add(X1)
    | class_HOL_Ominus(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6517]) ).

cnf(c_0_6518_0,axiom,
    ( class_OrderedGroup_Oab__group__add(X1)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6518]) ).

cnf(c_0_6518_1,axiom,
    ( ~ class_OrderedGroup_Opordered__ab__group__add(X1)
    | class_OrderedGroup_Oab__group__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6518]) ).

cnf(c_0_6519_0,axiom,
    ( class_Orderings_Olinorder(X1)
    | ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6519]) ).

cnf(c_0_6519_1,axiom,
    ( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X1)
    | class_Orderings_Olinorder(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6519]) ).

cnf(c_0_6520_0,axiom,
    ( class_HOL_Oplus(X1)
    | ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6520]) ).

cnf(c_0_6520_1,axiom,
    ( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X1)
    | class_HOL_Oplus(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6520]) ).

cnf(c_0_6521_0,axiom,
    ( class_OrderedGroup_Osemigroup__add(X1)
    | ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6521]) ).

cnf(c_0_6521_1,axiom,
    ( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X1)
    | class_OrderedGroup_Osemigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6521]) ).

cnf(c_0_6522_0,axiom,
    ( class_OrderedGroup_Ocancel__semigroup__add(X1)
    | ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6522]) ).

cnf(c_0_6522_1,axiom,
    ( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X1)
    | class_OrderedGroup_Ocancel__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6522]) ).

cnf(c_0_6523_0,axiom,
    ( class_OrderedGroup_Oab__semigroup__add(X1)
    | ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6523]) ).

cnf(c_0_6523_1,axiom,
    ( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X1)
    | class_OrderedGroup_Oab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6523]) ).

cnf(c_0_6524_0,axiom,
    ( class_OrderedGroup_Ocancel__ab__semigroup__add(X1)
    | ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6524]) ).

cnf(c_0_6524_1,axiom,
    ( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X1)
    | class_OrderedGroup_Ocancel__ab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6524]) ).

cnf(c_0_6525_0,axiom,
    ( class_Orderings_Oord(X1)
    | ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6525]) ).

cnf(c_0_6525_1,axiom,
    ( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X1)
    | class_Orderings_Oord(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6525]) ).

cnf(c_0_6526_0,axiom,
    ( class_Orderings_Oorder(X1)
    | ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6526]) ).

cnf(c_0_6526_1,axiom,
    ( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X1)
    | class_Orderings_Oorder(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6526]) ).

cnf(c_0_6527_0,axiom,
    ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
    | ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6527]) ).

cnf(c_0_6527_1,axiom,
    ( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X1)
    | class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6527]) ).

cnf(c_0_6528_0,axiom,
    ( class_LOrder_Omeet__semilorder(X1)
    | ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6528]) ).

cnf(c_0_6528_1,axiom,
    ( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X1)
    | class_LOrder_Omeet__semilorder(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6528]) ).

cnf(c_0_6529_0,axiom,
    ( class_LOrder_Ojoin__semilorder(X1)
    | ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6529]) ).

cnf(c_0_6529_1,axiom,
    ( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X1)
    | class_LOrder_Ojoin__semilorder(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6529]) ).

cnf(c_0_6530_0,axiom,
    ( class_LOrder_Olorder(X1)
    | ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6530]) ).

cnf(c_0_6530_1,axiom,
    ( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X1)
    | class_LOrder_Olorder(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6530]) ).

cnf(c_0_6531_0,axiom,
    ( class_OrderedGroup_Opordered__ab__semigroup__add(X1)
    | ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6531]) ).

cnf(c_0_6531_1,axiom,
    ( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X1)
    | class_OrderedGroup_Opordered__ab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6531]) ).

cnf(c_0_6532_0,axiom,
    ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1)
    | ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6532]) ).

cnf(c_0_6532_1,axiom,
    ( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X1)
    | class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6532]) ).

cnf(c_0_6533_0,axiom,
    ( class_HOL_Otimes(X1)
    | ~ class_OrderedGroup_Omonoid__mult(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6533]) ).

cnf(c_0_6533_1,axiom,
    ( ~ class_OrderedGroup_Omonoid__mult(X1)
    | class_HOL_Otimes(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6533]) ).

cnf(c_0_6534_0,axiom,
    ( class_OrderedGroup_Osemigroup__mult(X1)
    | ~ class_OrderedGroup_Omonoid__mult(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6534]) ).

cnf(c_0_6534_1,axiom,
    ( ~ class_OrderedGroup_Omonoid__mult(X1)
    | class_OrderedGroup_Osemigroup__mult(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6534]) ).

cnf(c_0_6535_0,axiom,
    ( class_HOL_Oone(X1)
    | ~ class_OrderedGroup_Omonoid__mult(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6535]) ).

cnf(c_0_6535_1,axiom,
    ( ~ class_OrderedGroup_Omonoid__mult(X1)
    | class_HOL_Oone(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6535]) ).

cnf(c_0_6536_0,axiom,
    ( class_Orderings_Oord(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__meet(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6536]) ).

cnf(c_0_6536_1,axiom,
    ( ~ class_OrderedGroup_Olordered__ab__group__meet(X1)
    | class_Orderings_Oord(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6536]) ).

cnf(c_0_6537_0,axiom,
    ( class_Orderings_Oorder(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__meet(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6537]) ).

cnf(c_0_6537_1,axiom,
    ( ~ class_OrderedGroup_Olordered__ab__group__meet(X1)
    | class_Orderings_Oorder(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6537]) ).

cnf(c_0_6538_0,axiom,
    ( class_OrderedGroup_Opordered__ab__semigroup__add(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__meet(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6538]) ).

cnf(c_0_6538_1,axiom,
    ( ~ class_OrderedGroup_Olordered__ab__group__meet(X1)
    | class_OrderedGroup_Opordered__ab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6538]) ).

cnf(c_0_6539_0,axiom,
    ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__meet(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6539]) ).

cnf(c_0_6539_1,axiom,
    ( ~ class_OrderedGroup_Olordered__ab__group__meet(X1)
    | class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6539]) ).

cnf(c_0_6540_0,axiom,
    ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__meet(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6540]) ).

cnf(c_0_6540_1,axiom,
    ( ~ class_OrderedGroup_Olordered__ab__group__meet(X1)
    | class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6540]) ).

cnf(c_0_6541_0,axiom,
    ( class_HOL_Ozero(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__meet(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6541]) ).

cnf(c_0_6541_1,axiom,
    ( ~ class_OrderedGroup_Olordered__ab__group__meet(X1)
    | class_HOL_Ozero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6541]) ).

cnf(c_0_6542_0,axiom,
    ( class_OrderedGroup_Ocomm__monoid__add(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__meet(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6542]) ).

cnf(c_0_6542_1,axiom,
    ( ~ class_OrderedGroup_Olordered__ab__group__meet(X1)
    | class_OrderedGroup_Ocomm__monoid__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6542]) ).

cnf(c_0_6543_0,axiom,
    ( class_HOL_Ominus(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__meet(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6543]) ).

cnf(c_0_6543_1,axiom,
    ( ~ class_OrderedGroup_Olordered__ab__group__meet(X1)
    | class_HOL_Ominus(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6543]) ).

cnf(c_0_6544_0,axiom,
    ( class_LOrder_Ojoin__semilorder(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__meet(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6544]) ).

cnf(c_0_6544_1,axiom,
    ( ~ class_OrderedGroup_Olordered__ab__group__meet(X1)
    | class_LOrder_Ojoin__semilorder(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6544]) ).

cnf(c_0_6545_0,axiom,
    ( class_LOrder_Olorder(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__meet(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6545]) ).

cnf(c_0_6545_1,axiom,
    ( ~ class_OrderedGroup_Olordered__ab__group__meet(X1)
    | class_LOrder_Olorder(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6545]) ).

cnf(c_0_6546_0,axiom,
    ( class_OrderedGroup_Olordered__ab__group(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__meet(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6546]) ).

cnf(c_0_6546_1,axiom,
    ( ~ class_OrderedGroup_Olordered__ab__group__meet(X1)
    | class_OrderedGroup_Olordered__ab__group(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6546]) ).

cnf(c_0_6547_0,axiom,
    ( class_LOrder_Omeet__semilorder(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__meet(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6547]) ).

cnf(c_0_6547_1,axiom,
    ( ~ class_OrderedGroup_Olordered__ab__group__meet(X1)
    | class_LOrder_Omeet__semilorder(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6547]) ).

cnf(c_0_6548_0,axiom,
    ( class_HOL_Oplus(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__meet(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6548]) ).

cnf(c_0_6548_1,axiom,
    ( ~ class_OrderedGroup_Olordered__ab__group__meet(X1)
    | class_HOL_Oplus(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6548]) ).

cnf(c_0_6549_0,axiom,
    ( class_OrderedGroup_Osemigroup__add(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__meet(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6549]) ).

cnf(c_0_6549_1,axiom,
    ( ~ class_OrderedGroup_Olordered__ab__group__meet(X1)
    | class_OrderedGroup_Osemigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6549]) ).

cnf(c_0_6550_0,axiom,
    ( class_OrderedGroup_Ocancel__semigroup__add(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__meet(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6550]) ).

cnf(c_0_6550_1,axiom,
    ( ~ class_OrderedGroup_Olordered__ab__group__meet(X1)
    | class_OrderedGroup_Ocancel__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6550]) ).

cnf(c_0_6551_0,axiom,
    ( class_OrderedGroup_Oab__semigroup__add(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__meet(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6551]) ).

cnf(c_0_6551_1,axiom,
    ( ~ class_OrderedGroup_Olordered__ab__group__meet(X1)
    | class_OrderedGroup_Oab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6551]) ).

cnf(c_0_6552_0,axiom,
    ( class_OrderedGroup_Ocancel__ab__semigroup__add(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__meet(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6552]) ).

cnf(c_0_6552_1,axiom,
    ( ~ class_OrderedGroup_Olordered__ab__group__meet(X1)
    | class_OrderedGroup_Ocancel__ab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6552]) ).

cnf(c_0_6553_0,axiom,
    ( class_OrderedGroup_Oab__group__add(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__meet(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6553]) ).

cnf(c_0_6553_1,axiom,
    ( ~ class_OrderedGroup_Olordered__ab__group__meet(X1)
    | class_OrderedGroup_Oab__group__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6553]) ).

cnf(c_0_6554_0,axiom,
    ( class_OrderedGroup_Opordered__ab__group__add(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__meet(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6554]) ).

cnf(c_0_6554_1,axiom,
    ( ~ class_OrderedGroup_Olordered__ab__group__meet(X1)
    | class_OrderedGroup_Opordered__ab__group__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6554]) ).

cnf(c_0_6555_0,axiom,
    ( class_Orderings_Oord(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__join(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6555]) ).

cnf(c_0_6555_1,axiom,
    ( ~ class_OrderedGroup_Olordered__ab__group__join(X1)
    | class_Orderings_Oord(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6555]) ).

cnf(c_0_6556_0,axiom,
    ( class_Orderings_Oorder(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__join(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6556]) ).

cnf(c_0_6556_1,axiom,
    ( ~ class_OrderedGroup_Olordered__ab__group__join(X1)
    | class_Orderings_Oorder(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6556]) ).

cnf(c_0_6557_0,axiom,
    ( class_OrderedGroup_Opordered__ab__semigroup__add(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__join(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6557]) ).

cnf(c_0_6557_1,axiom,
    ( ~ class_OrderedGroup_Olordered__ab__group__join(X1)
    | class_OrderedGroup_Opordered__ab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6557]) ).

cnf(c_0_6558_0,axiom,
    ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__join(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6558]) ).

cnf(c_0_6558_1,axiom,
    ( ~ class_OrderedGroup_Olordered__ab__group__join(X1)
    | class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6558]) ).

cnf(c_0_6559_0,axiom,
    ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__join(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6559]) ).

cnf(c_0_6559_1,axiom,
    ( ~ class_OrderedGroup_Olordered__ab__group__join(X1)
    | class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6559]) ).

cnf(c_0_6560_0,axiom,
    ( class_HOL_Ozero(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__join(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6560]) ).

cnf(c_0_6560_1,axiom,
    ( ~ class_OrderedGroup_Olordered__ab__group__join(X1)
    | class_HOL_Ozero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6560]) ).

cnf(c_0_6561_0,axiom,
    ( class_OrderedGroup_Ocomm__monoid__add(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__join(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6561]) ).

cnf(c_0_6561_1,axiom,
    ( ~ class_OrderedGroup_Olordered__ab__group__join(X1)
    | class_OrderedGroup_Ocomm__monoid__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6561]) ).

cnf(c_0_6562_0,axiom,
    ( class_HOL_Ominus(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__join(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6562]) ).

cnf(c_0_6562_1,axiom,
    ( ~ class_OrderedGroup_Olordered__ab__group__join(X1)
    | class_HOL_Ominus(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6562]) ).

cnf(c_0_6563_0,axiom,
    ( class_LOrder_Omeet__semilorder(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__join(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6563]) ).

cnf(c_0_6563_1,axiom,
    ( ~ class_OrderedGroup_Olordered__ab__group__join(X1)
    | class_LOrder_Omeet__semilorder(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6563]) ).

cnf(c_0_6564_0,axiom,
    ( class_LOrder_Olorder(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__join(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6564]) ).

cnf(c_0_6564_1,axiom,
    ( ~ class_OrderedGroup_Olordered__ab__group__join(X1)
    | class_LOrder_Olorder(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6564]) ).

cnf(c_0_6565_0,axiom,
    ( class_OrderedGroup_Olordered__ab__group(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__join(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6565]) ).

cnf(c_0_6565_1,axiom,
    ( ~ class_OrderedGroup_Olordered__ab__group__join(X1)
    | class_OrderedGroup_Olordered__ab__group(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6565]) ).

cnf(c_0_6566_0,axiom,
    ( class_LOrder_Ojoin__semilorder(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__join(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6566]) ).

cnf(c_0_6566_1,axiom,
    ( ~ class_OrderedGroup_Olordered__ab__group__join(X1)
    | class_LOrder_Ojoin__semilorder(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6566]) ).

cnf(c_0_6567_0,axiom,
    ( class_HOL_Oplus(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__join(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6567]) ).

cnf(c_0_6567_1,axiom,
    ( ~ class_OrderedGroup_Olordered__ab__group__join(X1)
    | class_HOL_Oplus(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6567]) ).

cnf(c_0_6568_0,axiom,
    ( class_OrderedGroup_Osemigroup__add(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__join(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6568]) ).

cnf(c_0_6568_1,axiom,
    ( ~ class_OrderedGroup_Olordered__ab__group__join(X1)
    | class_OrderedGroup_Osemigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6568]) ).

cnf(c_0_6569_0,axiom,
    ( class_OrderedGroup_Ocancel__semigroup__add(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__join(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6569]) ).

cnf(c_0_6569_1,axiom,
    ( ~ class_OrderedGroup_Olordered__ab__group__join(X1)
    | class_OrderedGroup_Ocancel__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6569]) ).

cnf(c_0_6570_0,axiom,
    ( class_OrderedGroup_Oab__semigroup__add(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__join(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6570]) ).

cnf(c_0_6570_1,axiom,
    ( ~ class_OrderedGroup_Olordered__ab__group__join(X1)
    | class_OrderedGroup_Oab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6570]) ).

cnf(c_0_6571_0,axiom,
    ( class_OrderedGroup_Ocancel__ab__semigroup__add(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__join(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6571]) ).

cnf(c_0_6571_1,axiom,
    ( ~ class_OrderedGroup_Olordered__ab__group__join(X1)
    | class_OrderedGroup_Ocancel__ab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6571]) ).

cnf(c_0_6572_0,axiom,
    ( class_OrderedGroup_Oab__group__add(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__join(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6572]) ).

cnf(c_0_6572_1,axiom,
    ( ~ class_OrderedGroup_Olordered__ab__group__join(X1)
    | class_OrderedGroup_Oab__group__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6572]) ).

cnf(c_0_6573_0,axiom,
    ( class_OrderedGroup_Opordered__ab__group__add(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__join(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6573]) ).

cnf(c_0_6573_1,axiom,
    ( ~ class_OrderedGroup_Olordered__ab__group__join(X1)
    | class_OrderedGroup_Opordered__ab__group__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6573]) ).

cnf(c_0_6574_0,axiom,
    ( class_OrderedGroup_Ocancel__ab__semigroup__add(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__abs(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6574]) ).

cnf(c_0_6574_1,axiom,
    ( ~ class_OrderedGroup_Olordered__ab__group__abs(X1)
    | class_OrderedGroup_Ocancel__ab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6574]) ).

cnf(c_0_6575_0,axiom,
    ( class_OrderedGroup_Opordered__ab__semigroup__add(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__abs(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6575]) ).

cnf(c_0_6575_1,axiom,
    ( ~ class_OrderedGroup_Olordered__ab__group__abs(X1)
    | class_OrderedGroup_Opordered__ab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6575]) ).

cnf(c_0_6576_0,axiom,
    ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__abs(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6576]) ).

cnf(c_0_6576_1,axiom,
    ( ~ class_OrderedGroup_Olordered__ab__group__abs(X1)
    | class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6576]) ).

cnf(c_0_6577_0,axiom,
    ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__abs(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6577]) ).

cnf(c_0_6577_1,axiom,
    ( ~ class_OrderedGroup_Olordered__ab__group__abs(X1)
    | class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6577]) ).

cnf(c_0_6578_0,axiom,
    ( class_HOL_Ozero(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__abs(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6578]) ).

cnf(c_0_6578_1,axiom,
    ( ~ class_OrderedGroup_Olordered__ab__group__abs(X1)
    | class_HOL_Ozero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6578]) ).

cnf(c_0_6579_0,axiom,
    ( class_OrderedGroup_Ocomm__monoid__add(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__abs(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6579]) ).

cnf(c_0_6579_1,axiom,
    ( ~ class_OrderedGroup_Olordered__ab__group__abs(X1)
    | class_OrderedGroup_Ocomm__monoid__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6579]) ).

cnf(c_0_6580_0,axiom,
    ( class_HOL_Ominus(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__abs(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6580]) ).

cnf(c_0_6580_1,axiom,
    ( ~ class_OrderedGroup_Olordered__ab__group__abs(X1)
    | class_HOL_Ominus(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6580]) ).

cnf(c_0_6581_0,axiom,
    ( class_OrderedGroup_Oab__group__add(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__abs(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6581]) ).

cnf(c_0_6581_1,axiom,
    ( ~ class_OrderedGroup_Olordered__ab__group__abs(X1)
    | class_OrderedGroup_Oab__group__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6581]) ).

cnf(c_0_6582_0,axiom,
    ( class_Orderings_Oord(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__abs(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6582]) ).

cnf(c_0_6582_1,axiom,
    ( ~ class_OrderedGroup_Olordered__ab__group__abs(X1)
    | class_Orderings_Oord(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6582]) ).

cnf(c_0_6583_0,axiom,
    ( class_Orderings_Oorder(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__abs(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6583]) ).

cnf(c_0_6583_1,axiom,
    ( ~ class_OrderedGroup_Olordered__ab__group__abs(X1)
    | class_Orderings_Oorder(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6583]) ).

cnf(c_0_6584_0,axiom,
    ( class_LOrder_Omeet__semilorder(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__abs(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6584]) ).

cnf(c_0_6584_1,axiom,
    ( ~ class_OrderedGroup_Olordered__ab__group__abs(X1)
    | class_LOrder_Omeet__semilorder(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6584]) ).

cnf(c_0_6585_0,axiom,
    ( class_LOrder_Ojoin__semilorder(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__abs(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6585]) ).

cnf(c_0_6585_1,axiom,
    ( ~ class_OrderedGroup_Olordered__ab__group__abs(X1)
    | class_LOrder_Ojoin__semilorder(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6585]) ).

cnf(c_0_6586_0,axiom,
    ( class_LOrder_Olorder(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__abs(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6586]) ).

cnf(c_0_6586_1,axiom,
    ( ~ class_OrderedGroup_Olordered__ab__group__abs(X1)
    | class_LOrder_Olorder(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6586]) ).

cnf(c_0_6587_0,axiom,
    ( class_HOL_Oplus(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__abs(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6587]) ).

cnf(c_0_6587_1,axiom,
    ( ~ class_OrderedGroup_Olordered__ab__group__abs(X1)
    | class_HOL_Oplus(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6587]) ).

cnf(c_0_6588_0,axiom,
    ( class_OrderedGroup_Osemigroup__add(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__abs(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6588]) ).

cnf(c_0_6588_1,axiom,
    ( ~ class_OrderedGroup_Olordered__ab__group__abs(X1)
    | class_OrderedGroup_Osemigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6588]) ).

cnf(c_0_6589_0,axiom,
    ( class_OrderedGroup_Ocancel__semigroup__add(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__abs(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6589]) ).

cnf(c_0_6589_1,axiom,
    ( ~ class_OrderedGroup_Olordered__ab__group__abs(X1)
    | class_OrderedGroup_Ocancel__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6589]) ).

cnf(c_0_6590_0,axiom,
    ( class_OrderedGroup_Oab__semigroup__add(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__abs(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6590]) ).

cnf(c_0_6590_1,axiom,
    ( ~ class_OrderedGroup_Olordered__ab__group__abs(X1)
    | class_OrderedGroup_Oab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6590]) ).

cnf(c_0_6591_0,axiom,
    ( class_OrderedGroup_Opordered__ab__group__add(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__abs(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6591]) ).

cnf(c_0_6591_1,axiom,
    ( ~ class_OrderedGroup_Olordered__ab__group__abs(X1)
    | class_OrderedGroup_Opordered__ab__group__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6591]) ).

cnf(c_0_6592_0,axiom,
    ( class_OrderedGroup_Olordered__ab__group(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__abs(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6592]) ).

cnf(c_0_6592_1,axiom,
    ( ~ class_OrderedGroup_Olordered__ab__group__abs(X1)
    | class_OrderedGroup_Olordered__ab__group(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6592]) ).

cnf(c_0_6593_0,axiom,
    ( class_Orderings_Oord(X1)
    | ~ class_OrderedGroup_Olordered__ab__group(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6593]) ).

cnf(c_0_6593_1,axiom,
    ( ~ class_OrderedGroup_Olordered__ab__group(X1)
    | class_Orderings_Oord(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6593]) ).

cnf(c_0_6594_0,axiom,
    ( class_Orderings_Oorder(X1)
    | ~ class_OrderedGroup_Olordered__ab__group(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6594]) ).

cnf(c_0_6594_1,axiom,
    ( ~ class_OrderedGroup_Olordered__ab__group(X1)
    | class_Orderings_Oorder(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6594]) ).

cnf(c_0_6595_0,axiom,
    ( class_OrderedGroup_Opordered__ab__semigroup__add(X1)
    | ~ class_OrderedGroup_Olordered__ab__group(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6595]) ).

cnf(c_0_6595_1,axiom,
    ( ~ class_OrderedGroup_Olordered__ab__group(X1)
    | class_OrderedGroup_Opordered__ab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6595]) ).

cnf(c_0_6596_0,axiom,
    ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1)
    | ~ class_OrderedGroup_Olordered__ab__group(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6596]) ).

cnf(c_0_6596_1,axiom,
    ( ~ class_OrderedGroup_Olordered__ab__group(X1)
    | class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6596]) ).

cnf(c_0_6597_0,axiom,
    ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
    | ~ class_OrderedGroup_Olordered__ab__group(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6597]) ).

cnf(c_0_6597_1,axiom,
    ( ~ class_OrderedGroup_Olordered__ab__group(X1)
    | class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6597]) ).

cnf(c_0_6598_0,axiom,
    ( class_HOL_Ozero(X1)
    | ~ class_OrderedGroup_Olordered__ab__group(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6598]) ).

cnf(c_0_6598_1,axiom,
    ( ~ class_OrderedGroup_Olordered__ab__group(X1)
    | class_HOL_Ozero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6598]) ).

cnf(c_0_6599_0,axiom,
    ( class_OrderedGroup_Ocomm__monoid__add(X1)
    | ~ class_OrderedGroup_Olordered__ab__group(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6599]) ).

cnf(c_0_6599_1,axiom,
    ( ~ class_OrderedGroup_Olordered__ab__group(X1)
    | class_OrderedGroup_Ocomm__monoid__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6599]) ).

cnf(c_0_6600_0,axiom,
    ( class_HOL_Ominus(X1)
    | ~ class_OrderedGroup_Olordered__ab__group(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6600]) ).

cnf(c_0_6600_1,axiom,
    ( ~ class_OrderedGroup_Olordered__ab__group(X1)
    | class_HOL_Ominus(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6600]) ).

cnf(c_0_6601_0,axiom,
    ( class_LOrder_Omeet__semilorder(X1)
    | ~ class_OrderedGroup_Olordered__ab__group(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6601]) ).

cnf(c_0_6601_1,axiom,
    ( ~ class_OrderedGroup_Olordered__ab__group(X1)
    | class_LOrder_Omeet__semilorder(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6601]) ).

cnf(c_0_6602_0,axiom,
    ( class_LOrder_Ojoin__semilorder(X1)
    | ~ class_OrderedGroup_Olordered__ab__group(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6602]) ).

cnf(c_0_6602_1,axiom,
    ( ~ class_OrderedGroup_Olordered__ab__group(X1)
    | class_LOrder_Ojoin__semilorder(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6602]) ).

cnf(c_0_6603_0,axiom,
    ( class_LOrder_Olorder(X1)
    | ~ class_OrderedGroup_Olordered__ab__group(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6603]) ).

cnf(c_0_6603_1,axiom,
    ( ~ class_OrderedGroup_Olordered__ab__group(X1)
    | class_LOrder_Olorder(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6603]) ).

cnf(c_0_6604_0,axiom,
    ( class_HOL_Oplus(X1)
    | ~ class_OrderedGroup_Olordered__ab__group(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6604]) ).

cnf(c_0_6604_1,axiom,
    ( ~ class_OrderedGroup_Olordered__ab__group(X1)
    | class_HOL_Oplus(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6604]) ).

cnf(c_0_6605_0,axiom,
    ( class_OrderedGroup_Osemigroup__add(X1)
    | ~ class_OrderedGroup_Olordered__ab__group(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6605]) ).

cnf(c_0_6605_1,axiom,
    ( ~ class_OrderedGroup_Olordered__ab__group(X1)
    | class_OrderedGroup_Osemigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6605]) ).

cnf(c_0_6606_0,axiom,
    ( class_OrderedGroup_Ocancel__semigroup__add(X1)
    | ~ class_OrderedGroup_Olordered__ab__group(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6606]) ).

cnf(c_0_6606_1,axiom,
    ( ~ class_OrderedGroup_Olordered__ab__group(X1)
    | class_OrderedGroup_Ocancel__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6606]) ).

cnf(c_0_6607_0,axiom,
    ( class_OrderedGroup_Oab__semigroup__add(X1)
    | ~ class_OrderedGroup_Olordered__ab__group(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6607]) ).

cnf(c_0_6607_1,axiom,
    ( ~ class_OrderedGroup_Olordered__ab__group(X1)
    | class_OrderedGroup_Oab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6607]) ).

cnf(c_0_6608_0,axiom,
    ( class_OrderedGroup_Ocancel__ab__semigroup__add(X1)
    | ~ class_OrderedGroup_Olordered__ab__group(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6608]) ).

cnf(c_0_6608_1,axiom,
    ( ~ class_OrderedGroup_Olordered__ab__group(X1)
    | class_OrderedGroup_Ocancel__ab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6608]) ).

cnf(c_0_6609_0,axiom,
    ( class_OrderedGroup_Oab__group__add(X1)
    | ~ class_OrderedGroup_Olordered__ab__group(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6609]) ).

cnf(c_0_6609_1,axiom,
    ( ~ class_OrderedGroup_Olordered__ab__group(X1)
    | class_OrderedGroup_Oab__group__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6609]) ).

cnf(c_0_6610_0,axiom,
    ( class_OrderedGroup_Opordered__ab__group__add(X1)
    | ~ class_OrderedGroup_Olordered__ab__group(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6610]) ).

cnf(c_0_6610_1,axiom,
    ( ~ class_OrderedGroup_Olordered__ab__group(X1)
    | class_OrderedGroup_Opordered__ab__group__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6610]) ).

cnf(c_0_6611_0,axiom,
    ( class_OrderedGroup_Omonoid__mult(X1)
    | ~ class_OrderedGroup_Ocomm__monoid__mult(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6611]) ).

cnf(c_0_6611_1,axiom,
    ( ~ class_OrderedGroup_Ocomm__monoid__mult(X1)
    | class_OrderedGroup_Omonoid__mult(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6611]) ).

cnf(c_0_6612_0,axiom,
    ( class_HOL_Otimes(X1)
    | ~ class_OrderedGroup_Ocomm__monoid__mult(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6612]) ).

cnf(c_0_6612_1,axiom,
    ( ~ class_OrderedGroup_Ocomm__monoid__mult(X1)
    | class_HOL_Otimes(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6612]) ).

cnf(c_0_6613_0,axiom,
    ( class_OrderedGroup_Osemigroup__mult(X1)
    | ~ class_OrderedGroup_Ocomm__monoid__mult(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6613]) ).

cnf(c_0_6613_1,axiom,
    ( ~ class_OrderedGroup_Ocomm__monoid__mult(X1)
    | class_OrderedGroup_Osemigroup__mult(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6613]) ).

cnf(c_0_6614_0,axiom,
    ( class_OrderedGroup_Oab__semigroup__mult(X1)
    | ~ class_OrderedGroup_Ocomm__monoid__mult(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6614]) ).

cnf(c_0_6614_1,axiom,
    ( ~ class_OrderedGroup_Ocomm__monoid__mult(X1)
    | class_OrderedGroup_Oab__semigroup__mult(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6614]) ).

cnf(c_0_6615_0,axiom,
    ( class_HOL_Oone(X1)
    | ~ class_OrderedGroup_Ocomm__monoid__mult(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6615]) ).

cnf(c_0_6615_1,axiom,
    ( ~ class_OrderedGroup_Ocomm__monoid__mult(X1)
    | class_HOL_Oone(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6615]) ).

cnf(c_0_6616_0,axiom,
    ( class_HOL_Oplus(X1)
    | ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6616]) ).

cnf(c_0_6616_1,axiom,
    ( ~ class_OrderedGroup_Ocomm__monoid__add(X1)
    | class_HOL_Oplus(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6616]) ).

cnf(c_0_6617_0,axiom,
    ( class_OrderedGroup_Osemigroup__add(X1)
    | ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6617]) ).

cnf(c_0_6617_1,axiom,
    ( ~ class_OrderedGroup_Ocomm__monoid__add(X1)
    | class_OrderedGroup_Osemigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6617]) ).

cnf(c_0_6618_0,axiom,
    ( class_OrderedGroup_Oab__semigroup__add(X1)
    | ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6618]) ).

cnf(c_0_6618_1,axiom,
    ( ~ class_OrderedGroup_Ocomm__monoid__add(X1)
    | class_OrderedGroup_Oab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6618]) ).

cnf(c_0_6619_0,axiom,
    ( class_HOL_Ozero(X1)
    | ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6619]) ).

cnf(c_0_6619_1,axiom,
    ( ~ class_OrderedGroup_Ocomm__monoid__add(X1)
    | class_HOL_Ozero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6619]) ).

cnf(c_0_6620_0,axiom,
    ( class_HOL_Oplus(X1)
    | ~ class_OrderedGroup_Ocancel__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6620]) ).

cnf(c_0_6620_1,axiom,
    ( ~ class_OrderedGroup_Ocancel__semigroup__add(X1)
    | class_HOL_Oplus(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6620]) ).

cnf(c_0_6621_0,axiom,
    ( class_OrderedGroup_Osemigroup__add(X1)
    | ~ class_OrderedGroup_Ocancel__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6621]) ).

cnf(c_0_6621_1,axiom,
    ( ~ class_OrderedGroup_Ocancel__semigroup__add(X1)
    | class_OrderedGroup_Osemigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6621]) ).

cnf(c_0_6622_0,axiom,
    ( class_OrderedGroup_Ocancel__semigroup__add(X1)
    | ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6622]) ).

cnf(c_0_6622_1,axiom,
    ( ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X1)
    | class_OrderedGroup_Ocancel__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6622]) ).

cnf(c_0_6623_0,axiom,
    ( class_HOL_Oplus(X1)
    | ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6623]) ).

cnf(c_0_6623_1,axiom,
    ( ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X1)
    | class_HOL_Oplus(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6623]) ).

cnf(c_0_6624_0,axiom,
    ( class_OrderedGroup_Osemigroup__add(X1)
    | ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6624]) ).

cnf(c_0_6624_1,axiom,
    ( ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X1)
    | class_OrderedGroup_Osemigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6624]) ).

cnf(c_0_6625_0,axiom,
    ( class_OrderedGroup_Oab__semigroup__add(X1)
    | ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6625]) ).

cnf(c_0_6625_1,axiom,
    ( ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X1)
    | class_OrderedGroup_Oab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6625]) ).

cnf(c_0_6626_0,axiom,
    ( class_HOL_Otimes(X1)
    | ~ class_OrderedGroup_Oab__semigroup__mult(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6626]) ).

cnf(c_0_6626_1,axiom,
    ( ~ class_OrderedGroup_Oab__semigroup__mult(X1)
    | class_HOL_Otimes(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6626]) ).

cnf(c_0_6627_0,axiom,
    ( class_OrderedGroup_Osemigroup__mult(X1)
    | ~ class_OrderedGroup_Oab__semigroup__mult(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6627]) ).

cnf(c_0_6627_1,axiom,
    ( ~ class_OrderedGroup_Oab__semigroup__mult(X1)
    | class_OrderedGroup_Osemigroup__mult(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6627]) ).

cnf(c_0_6628_0,axiom,
    ( class_HOL_Oplus(X1)
    | ~ class_OrderedGroup_Oab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6628]) ).

cnf(c_0_6628_1,axiom,
    ( ~ class_OrderedGroup_Oab__semigroup__add(X1)
    | class_HOL_Oplus(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6628]) ).

cnf(c_0_6629_0,axiom,
    ( class_OrderedGroup_Osemigroup__add(X1)
    | ~ class_OrderedGroup_Oab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6629]) ).

cnf(c_0_6629_1,axiom,
    ( ~ class_OrderedGroup_Oab__semigroup__add(X1)
    | class_OrderedGroup_Osemigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6629]) ).

cnf(c_0_6630_0,axiom,
    ( class_OrderedGroup_Ocancel__semigroup__add(X1)
    | ~ class_OrderedGroup_Oab__group__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6630]) ).

cnf(c_0_6630_1,axiom,
    ( ~ class_OrderedGroup_Oab__group__add(X1)
    | class_OrderedGroup_Ocancel__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6630]) ).

cnf(c_0_6631_0,axiom,
    ( class_OrderedGroup_Ocancel__ab__semigroup__add(X1)
    | ~ class_OrderedGroup_Oab__group__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6631]) ).

cnf(c_0_6631_1,axiom,
    ( ~ class_OrderedGroup_Oab__group__add(X1)
    | class_OrderedGroup_Ocancel__ab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6631]) ).

cnf(c_0_6632_0,axiom,
    ( class_HOL_Oplus(X1)
    | ~ class_OrderedGroup_Oab__group__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6632]) ).

cnf(c_0_6632_1,axiom,
    ( ~ class_OrderedGroup_Oab__group__add(X1)
    | class_HOL_Oplus(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6632]) ).

cnf(c_0_6633_0,axiom,
    ( class_OrderedGroup_Osemigroup__add(X1)
    | ~ class_OrderedGroup_Oab__group__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6633]) ).

cnf(c_0_6633_1,axiom,
    ( ~ class_OrderedGroup_Oab__group__add(X1)
    | class_OrderedGroup_Osemigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6633]) ).

cnf(c_0_6634_0,axiom,
    ( class_OrderedGroup_Oab__semigroup__add(X1)
    | ~ class_OrderedGroup_Oab__group__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6634]) ).

cnf(c_0_6634_1,axiom,
    ( ~ class_OrderedGroup_Oab__group__add(X1)
    | class_OrderedGroup_Oab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6634]) ).

cnf(c_0_6635_0,axiom,
    ( class_HOL_Ozero(X1)
    | ~ class_OrderedGroup_Oab__group__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6635]) ).

cnf(c_0_6635_1,axiom,
    ( ~ class_OrderedGroup_Oab__group__add(X1)
    | class_HOL_Ozero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6635]) ).

cnf(c_0_6636_0,axiom,
    ( class_OrderedGroup_Ocomm__monoid__add(X1)
    | ~ class_OrderedGroup_Oab__group__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6636]) ).

cnf(c_0_6636_1,axiom,
    ( ~ class_OrderedGroup_Oab__group__add(X1)
    | class_OrderedGroup_Ocomm__monoid__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6636]) ).

cnf(c_0_6637_0,axiom,
    ( class_HOL_Ominus(X1)
    | ~ class_OrderedGroup_Oab__group__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6637]) ).

cnf(c_0_6637_1,axiom,
    ( ~ class_OrderedGroup_Oab__group__add(X1)
    | class_HOL_Ominus(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6637]) ).

cnf(c_0_6638_0,axiom,
    ( class_OrderedGroup_Ocomm__monoid__add(X1)
    | ~ class_Numeral_Onumber__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6638]) ).

cnf(c_0_6638_1,axiom,
    ( ~ class_Numeral_Onumber__ring(X1)
    | class_OrderedGroup_Ocomm__monoid__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6638]) ).

cnf(c_0_6639_0,axiom,
    ( class_HOL_Ozero(X1)
    | ~ class_Numeral_Onumber__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6639]) ).

cnf(c_0_6639_1,axiom,
    ( ~ class_Numeral_Onumber__ring(X1)
    | class_HOL_Ozero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6639]) ).

cnf(c_0_6640_0,axiom,
    ( class_Ring__and__Field_Ocomm__semiring(X1)
    | ~ class_Numeral_Onumber__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6640]) ).

cnf(c_0_6640_1,axiom,
    ( ~ class_Numeral_Onumber__ring(X1)
    | class_Ring__and__Field_Ocomm__semiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6640]) ).

cnf(c_0_6641_0,axiom,
    ( class_Ring__and__Field_Osemiring(X1)
    | ~ class_Numeral_Onumber__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6641]) ).

cnf(c_0_6641_1,axiom,
    ( ~ class_Numeral_Onumber__ring(X1)
    | class_Ring__and__Field_Osemiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6641]) ).

cnf(c_0_6642_0,axiom,
    ( class_OrderedGroup_Oab__semigroup__mult(X1)
    | ~ class_Numeral_Onumber__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6642]) ).

cnf(c_0_6642_1,axiom,
    ( ~ class_Numeral_Onumber__ring(X1)
    | class_OrderedGroup_Oab__semigroup__mult(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6642]) ).

cnf(c_0_6643_0,axiom,
    ( class_OrderedGroup_Osemigroup__mult(X1)
    | ~ class_Numeral_Onumber__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6643]) ).

cnf(c_0_6643_1,axiom,
    ( ~ class_Numeral_Onumber__ring(X1)
    | class_OrderedGroup_Osemigroup__mult(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6643]) ).

cnf(c_0_6644_0,axiom,
    ( class_Numeral_Onumber(X1)
    | ~ class_Numeral_Onumber__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6644]) ).

cnf(c_0_6644_1,axiom,
    ( ~ class_Numeral_Onumber__ring(X1)
    | class_Numeral_Onumber(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6644]) ).

cnf(c_0_6645_0,axiom,
    ( class_HOL_Otimes(X1)
    | ~ class_Numeral_Onumber__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6645]) ).

cnf(c_0_6645_1,axiom,
    ( ~ class_Numeral_Onumber__ring(X1)
    | class_HOL_Otimes(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6645]) ).

cnf(c_0_6646_0,axiom,
    ( class_Ring__and__Field_Ocomm__ring__1(X1)
    | ~ class_Numeral_Onumber__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6646]) ).

cnf(c_0_6646_1,axiom,
    ( ~ class_Numeral_Onumber__ring(X1)
    | class_Ring__and__Field_Ocomm__ring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6646]) ).

cnf(c_0_6647_0,axiom,
    ( class_Ring__and__Field_Ocomm__semiring__1__cancel(X1)
    | ~ class_Numeral_Onumber__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6647]) ).

cnf(c_0_6647_1,axiom,
    ( ~ class_Numeral_Onumber__ring(X1)
    | class_Ring__and__Field_Ocomm__semiring__1__cancel(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6647]) ).

cnf(c_0_6648_0,axiom,
    ( class_Ring__and__Field_Oring__1(X1)
    | ~ class_Numeral_Onumber__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6648]) ).

cnf(c_0_6648_1,axiom,
    ( ~ class_Numeral_Onumber__ring(X1)
    | class_Ring__and__Field_Oring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6648]) ).

cnf(c_0_6649_0,axiom,
    ( class_Ring__and__Field_Osemiring__1__cancel(X1)
    | ~ class_Numeral_Onumber__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6649]) ).

cnf(c_0_6649_1,axiom,
    ( ~ class_Numeral_Onumber__ring(X1)
    | class_Ring__and__Field_Osemiring__1__cancel(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6649]) ).

cnf(c_0_6650_0,axiom,
    ( class_Ring__and__Field_Ocomm__semiring__1(X1)
    | ~ class_Numeral_Onumber__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6650]) ).

cnf(c_0_6650_1,axiom,
    ( ~ class_Numeral_Onumber__ring(X1)
    | class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6650]) ).

cnf(c_0_6651_0,axiom,
    ( class_Ring__and__Field_Osemiring__1(X1)
    | ~ class_Numeral_Onumber__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6651]) ).

cnf(c_0_6651_1,axiom,
    ( ~ class_Numeral_Onumber__ring(X1)
    | class_Ring__and__Field_Osemiring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6651]) ).

cnf(c_0_6652_0,axiom,
    ( class_OrderedGroup_Ocomm__monoid__mult(X1)
    | ~ class_Numeral_Onumber__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6652]) ).

cnf(c_0_6652_1,axiom,
    ( ~ class_Numeral_Onumber__ring(X1)
    | class_OrderedGroup_Ocomm__monoid__mult(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6652]) ).

cnf(c_0_6653_0,axiom,
    ( class_OrderedGroup_Omonoid__mult(X1)
    | ~ class_Numeral_Onumber__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6653]) ).

cnf(c_0_6653_1,axiom,
    ( ~ class_Numeral_Onumber__ring(X1)
    | class_OrderedGroup_Omonoid__mult(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6653]) ).

cnf(c_0_6654_0,axiom,
    ( class_Ring__and__Field_Oaxclass__0__neq__1(X1)
    | ~ class_Numeral_Onumber__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6654]) ).

cnf(c_0_6654_1,axiom,
    ( ~ class_Numeral_Onumber__ring(X1)
    | class_Ring__and__Field_Oaxclass__0__neq__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6654]) ).

cnf(c_0_6655_0,axiom,
    ( class_HOL_Oone(X1)
    | ~ class_Numeral_Onumber__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6655]) ).

cnf(c_0_6655_1,axiom,
    ( ~ class_Numeral_Onumber__ring(X1)
    | class_HOL_Oone(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6655]) ).

cnf(c_0_6656_0,axiom,
    ( class_OrderedGroup_Oab__semigroup__add(X1)
    | ~ class_Numeral_Onumber__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6656]) ).

cnf(c_0_6656_1,axiom,
    ( ~ class_Numeral_Onumber__ring(X1)
    | class_OrderedGroup_Oab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6656]) ).

cnf(c_0_6657_0,axiom,
    ( class_Ring__and__Field_Ocomm__ring(X1)
    | ~ class_Numeral_Onumber__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6657]) ).

cnf(c_0_6657_1,axiom,
    ( ~ class_Numeral_Onumber__ring(X1)
    | class_Ring__and__Field_Ocomm__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6657]) ).

cnf(c_0_6658_0,axiom,
    ( class_Ring__and__Field_Ocomm__semiring__0__cancel(X1)
    | ~ class_Numeral_Onumber__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6658]) ).

cnf(c_0_6658_1,axiom,
    ( ~ class_Numeral_Onumber__ring(X1)
    | class_Ring__and__Field_Ocomm__semiring__0__cancel(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6658]) ).

cnf(c_0_6659_0,axiom,
    ( class_Ring__and__Field_Oring(X1)
    | ~ class_Numeral_Onumber__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6659]) ).

cnf(c_0_6659_1,axiom,
    ( ~ class_Numeral_Onumber__ring(X1)
    | class_Ring__and__Field_Oring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6659]) ).

cnf(c_0_6660_0,axiom,
    ( class_Ring__and__Field_Osemiring__0__cancel(X1)
    | ~ class_Numeral_Onumber__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6660]) ).

cnf(c_0_6660_1,axiom,
    ( ~ class_Numeral_Onumber__ring(X1)
    | class_Ring__and__Field_Osemiring__0__cancel(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6660]) ).

cnf(c_0_6661_0,axiom,
    ( class_OrderedGroup_Oab__group__add(X1)
    | ~ class_Numeral_Onumber__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6661]) ).

cnf(c_0_6661_1,axiom,
    ( ~ class_Numeral_Onumber__ring(X1)
    | class_OrderedGroup_Oab__group__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6661]) ).

cnf(c_0_6662_0,axiom,
    ( class_OrderedGroup_Ocancel__ab__semigroup__add(X1)
    | ~ class_Numeral_Onumber__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6662]) ).

cnf(c_0_6662_1,axiom,
    ( ~ class_Numeral_Onumber__ring(X1)
    | class_OrderedGroup_Ocancel__ab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6662]) ).

cnf(c_0_6663_0,axiom,
    ( class_OrderedGroup_Ocancel__semigroup__add(X1)
    | ~ class_Numeral_Onumber__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6663]) ).

cnf(c_0_6663_1,axiom,
    ( ~ class_Numeral_Onumber__ring(X1)
    | class_OrderedGroup_Ocancel__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6663]) ).

cnf(c_0_6664_0,axiom,
    ( class_HOL_Ominus(X1)
    | ~ class_Numeral_Onumber__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6664]) ).

cnf(c_0_6664_1,axiom,
    ( ~ class_Numeral_Onumber__ring(X1)
    | class_HOL_Ominus(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6664]) ).

cnf(c_0_6665_0,axiom,
    ( class_Ring__and__Field_Ocomm__semiring__0(X1)
    | ~ class_Numeral_Onumber__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6665]) ).

cnf(c_0_6665_1,axiom,
    ( ~ class_Numeral_Onumber__ring(X1)
    | class_Ring__and__Field_Ocomm__semiring__0(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6665]) ).

cnf(c_0_6666_0,axiom,
    ( class_Ring__and__Field_Osemiring__0(X1)
    | ~ class_Numeral_Onumber__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6666]) ).

cnf(c_0_6666_1,axiom,
    ( ~ class_Numeral_Onumber__ring(X1)
    | class_Ring__and__Field_Osemiring__0(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6666]) ).

cnf(c_0_6667_0,axiom,
    ( class_OrderedGroup_Osemigroup__add(X1)
    | ~ class_Numeral_Onumber__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6667]) ).

cnf(c_0_6667_1,axiom,
    ( ~ class_Numeral_Onumber__ring(X1)
    | class_OrderedGroup_Osemigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6667]) ).

cnf(c_0_6668_0,axiom,
    ( class_HOL_Oplus(X1)
    | ~ class_Numeral_Onumber__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6668]) ).

cnf(c_0_6668_1,axiom,
    ( ~ class_Numeral_Onumber__ring(X1)
    | class_HOL_Oplus(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6668]) ).

cnf(c_0_6669_0,axiom,
    ( class_Orderings_Oorder(X1)
    | ~ class_LOrder_Omeet__semilorder(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6669]) ).

cnf(c_0_6669_1,axiom,
    ( ~ class_LOrder_Omeet__semilorder(X1)
    | class_Orderings_Oorder(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6669]) ).

cnf(c_0_6670_0,axiom,
    ( class_Orderings_Oord(X1)
    | ~ class_LOrder_Omeet__semilorder(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6670]) ).

cnf(c_0_6670_1,axiom,
    ( ~ class_LOrder_Omeet__semilorder(X1)
    | class_Orderings_Oord(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6670]) ).

cnf(c_0_6671_0,axiom,
    ( class_LOrder_Ojoin__semilorder(X1)
    | ~ class_LOrder_Olorder(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6671]) ).

cnf(c_0_6671_1,axiom,
    ( ~ class_LOrder_Olorder(X1)
    | class_LOrder_Ojoin__semilorder(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6671]) ).

cnf(c_0_6672_0,axiom,
    ( class_Orderings_Oorder(X1)
    | ~ class_LOrder_Olorder(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6672]) ).

cnf(c_0_6672_1,axiom,
    ( ~ class_LOrder_Olorder(X1)
    | class_Orderings_Oorder(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6672]) ).

cnf(c_0_6673_0,axiom,
    ( class_Orderings_Oord(X1)
    | ~ class_LOrder_Olorder(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6673]) ).

cnf(c_0_6673_1,axiom,
    ( ~ class_LOrder_Olorder(X1)
    | class_Orderings_Oord(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6673]) ).

cnf(c_0_6674_0,axiom,
    ( class_LOrder_Omeet__semilorder(X1)
    | ~ class_LOrder_Olorder(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6674]) ).

cnf(c_0_6674_1,axiom,
    ( ~ class_LOrder_Olorder(X1)
    | class_LOrder_Omeet__semilorder(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6674]) ).

cnf(c_0_6675_0,axiom,
    ( class_Orderings_Oorder(X1)
    | ~ class_LOrder_Ojoin__semilorder(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6675]) ).

cnf(c_0_6675_1,axiom,
    ( ~ class_LOrder_Ojoin__semilorder(X1)
    | class_Orderings_Oorder(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6675]) ).

cnf(c_0_6676_0,axiom,
    ( class_Orderings_Oord(X1)
    | ~ class_LOrder_Ojoin__semilorder(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6676]) ).

cnf(c_0_6676_1,axiom,
    ( ~ class_LOrder_Ojoin__semilorder(X1)
    | class_Orderings_Oord(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6676]) ).

cnf(c_0_5506_0,axiom,
    ~ c_in(c_Pair(c_List_Olist_ONil,X1,tc_List_Olist(X2),tc_List_Olist(X2)),c_List_Olex(X3,X2),tc_prod(tc_List_Olist(X2),tc_List_Olist(X2))),
    inference(literals_permutation,[status(thm)],[c_0_5506]) ).

cnf(c_0_5507_0,axiom,
    ~ c_in(c_Pair(X1,c_List_Olist_ONil,tc_List_Olist(X2),tc_List_Olist(X2)),c_List_Olex(X3,X2),tc_prod(tc_List_Olist(X2),tc_List_Olist(X2))),
    inference(literals_permutation,[status(thm)],[c_0_5507]) ).

cnf(c_0_5530_0,axiom,
    c_Datatype__Universe_OScons(X1,X2,X3,X4) != c_Datatype__Universe_ONumb(X5,X3,X4),
    inference(literals_permutation,[status(thm)],[c_0_5530]) ).

cnf(c_0_5531_0,axiom,
    c_Datatype__Universe_OScons(X1,X2,X3,X4) != c_Datatype__Universe_OLeaf(X5,X3,X4),
    inference(literals_permutation,[status(thm)],[c_0_5531]) ).

cnf(c_0_5532_0,axiom,
    c_Datatype__Universe_OScons(X1,X2,X3,X4) != c_Datatype__Universe_OAtom(X5,X3,X4),
    inference(literals_permutation,[status(thm)],[c_0_5532]) ).

cnf(c_0_5533_0,axiom,
    c_Datatype__Universe_ONumb(X1,X2,X3) != c_Datatype__Universe_OScons(X4,X5,X2,X3),
    inference(literals_permutation,[status(thm)],[c_0_5533]) ).

cnf(c_0_5534_0,axiom,
    c_Datatype__Universe_OLeaf(X1,X2,X3) != c_Datatype__Universe_OScons(X4,X5,X2,X3),
    inference(literals_permutation,[status(thm)],[c_0_5534]) ).

cnf(c_0_5535_0,axiom,
    c_Datatype__Universe_OAtom(X1,X2,X3) != c_Datatype__Universe_OScons(X4,X5,X2,X3),
    inference(literals_permutation,[status(thm)],[c_0_5535]) ).

cnf(c_0_5585_0,axiom,
    ~ c_less(c_plus(X1,X2,tc_nat),X2,tc_nat),
    inference(literals_permutation,[status(thm)],[c_0_5585]) ).

cnf(c_0_5586_0,axiom,
    ~ c_less(c_plus(X1,X2,tc_nat),X1,tc_nat),
    inference(literals_permutation,[status(thm)],[c_0_5586]) ).

cnf(c_0_5632_0,axiom,
    c_Sum__Type_OInr(X1,X2,X3) != c_Sum__Type_OInl(X4,X3,X2),
    inference(literals_permutation,[status(thm)],[c_0_5632]) ).

cnf(c_0_5633_0,axiom,
    c_Sum__Type_OInl(X1,X2,X3) != c_Sum__Type_OInr(X4,X3,X2),
    inference(literals_permutation,[status(thm)],[c_0_5633]) ).

cnf(c_0_5634_0,axiom,
    c_Datatype__Universe_ONumb(X1,X2,X3) != c_Datatype__Universe_OLeaf(X4,X2,X3),
    inference(literals_permutation,[status(thm)],[c_0_5634]) ).

cnf(c_0_5635_0,axiom,
    c_Datatype__Universe_OLeaf(X1,X2,X3) != c_Datatype__Universe_ONumb(X4,X2,X3),
    inference(literals_permutation,[status(thm)],[c_0_5635]) ).

cnf(c_0_5636_0,axiom,
    c_Datatype__Universe_OIn1(X1,X2,X3) != c_Datatype__Universe_OIn0(X4,X2,X3),
    inference(literals_permutation,[status(thm)],[c_0_5636]) ).

cnf(c_0_5637_0,axiom,
    c_Datatype__Universe_OIn0(X1,X2,X3) != c_Datatype__Universe_OIn1(X4,X2,X3),
    inference(literals_permutation,[status(thm)],[c_0_5637]) ).

cnf(c_0_5668_0,axiom,
    ~ c_less(c_0,c_Nat_Osize(c_List_Olist_ONil,tc_List_Olist(X1)),tc_nat),
    inference(literals_permutation,[status(thm)],[c_0_5668]) ).

cnf(c_0_5673_0,axiom,
    ~ c_less(X1,c_emptyset,tc_set(X2)),
    inference(literals_permutation,[status(thm)],[c_0_5673]) ).

cnf(c_0_5690_0,axiom,
    c_List_Olist_OCons(X1,X2,X3) != c_List_Olist_ONil,
    inference(literals_permutation,[status(thm)],[c_0_5690]) ).

cnf(c_0_5691_0,axiom,
    c_List_Olist_OCons(X1,X2,X3) != c_List_Olist_ONil,
    inference(literals_permutation,[status(thm)],[c_0_5691]) ).

cnf(c_0_5692_0,axiom,
    ~ c_in(c_UNIV,c_Finite__Set_OFinites,tc_set(tc_nat)),
    inference(literals_permutation,[status(thm)],[c_0_5692]) ).

cnf(c_0_5697_0,axiom,
    ~ c_less(X1,X1,tc_nat),
    inference(literals_permutation,[status(thm)],[c_0_5697]) ).

cnf(c_0_5698_0,axiom,
    ~ c_in(X1,c_emptyset,X2),
    inference(literals_permutation,[status(thm)],[c_0_5698]) ).

cnf(c_0_5703_0,axiom,
    ~ c_less(X1,c_0,tc_nat),
    inference(literals_permutation,[status(thm)],[c_0_5703]) ).

cnf(c_0_5706_0,axiom,
    ~ c_less(c_0,c_0,tc_nat),
    inference(literals_permutation,[status(thm)],[c_0_5706]) ).

cnf(c_0_5758_0,axiom,
    c_Datatype_Ooption_OSome(X1,X2) != c_Datatype_Ooption_ONone,
    inference(literals_permutation,[status(thm)],[c_0_5758]) ).

cnf(c_0_5759_0,axiom,
    c_Datatype_Ooption_OSome(X1,X2) != c_Datatype_Ooption_ONone,
    inference(literals_permutation,[status(thm)],[c_0_5759]) ).

cnf(c_0_6683_0,axiom,
    c_Suc(X1) != c_0,
    inference(literals_permutation,[status(thm)],[c_0_6683]) ).

cnf(c_0_6684_0,axiom,
    c_Suc(X1) != c_0,
    inference(literals_permutation,[status(thm)],[c_0_6684]) ).

cnf(c_0_6800_0,axiom,
    c_UNIV != c_emptyset,
    inference(literals_permutation,[status(thm)],[c_0_6800]) ).

cnf(c_0_6801_0,axiom,
    c_Numeral_Obit_OB1 != c_Numeral_Obit_OB0,
    inference(literals_permutation,[status(thm)],[c_0_6801]) ).

cnf(c_0_6802_0,axiom,
    c_Numeral_Obit_OB1 != c_Numeral_Obit_OB0,
    inference(literals_permutation,[status(thm)],[c_0_6802]) ).

cnf(c_0_6803_0,axiom,
    c_Extraction_Osumbool_ORight != c_Extraction_Osumbool_OLeft,
    inference(literals_permutation,[status(thm)],[c_0_6803]) ).

cnf(c_0_6804_0,axiom,
    c_Extraction_Osumbool_ORight != c_Extraction_Osumbool_OLeft,
    inference(literals_permutation,[status(thm)],[c_0_6804]) ).

cnf(c_0_5502_0,axiom,
    c_Divides_Oop_Advd(c_GCD_Ogcd(c_Pair(X1,X2,tc_nat,tc_nat)),X2,tc_nat),
    inference(literals_permutation,[status(thm)],[c_0_5502]) ).

cnf(c_0_5503_0,axiom,
    c_Divides_Oop_Advd(c_GCD_Ogcd(c_Pair(X1,X2,tc_nat,tc_nat)),X1,tc_nat),
    inference(literals_permutation,[status(thm)],[c_0_5503]) ).

cnf(c_0_5524_0,axiom,
    c_in(c_Pair(X1,X1,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2)),
    inference(literals_permutation,[status(thm)],[c_0_5524]) ).

cnf(c_0_5527_0,axiom,
    c_in(c_Pair(X1,X1,X2,X2),c_Relation_OId,tc_prod(X2,X2)),
    inference(literals_permutation,[status(thm)],[c_0_5527]) ).

cnf(c_0_5538_0,axiom,
    c_List_Orev(c_append(c_List_Orev(X1,X2),c_List_Olist_OCons(X3,c_List_Olist_ONil,X2),X2),X2) = c_List_Olist_OCons(X3,X1,X2),
    inference(literals_permutation,[status(thm)],[c_0_5538]) ).

cnf(c_0_5614_0,axiom,
    c_lessequals(c_Nat_Osize(c_List_Oremdups(X1,X2),tc_List_Olist(X2)),c_Nat_Osize(X1,tc_List_Olist(X2)),tc_nat),
    inference(literals_permutation,[status(thm)],[c_0_5614]) ).

cnf(c_0_5643_0,axiom,
    c_in(X1,c_insert(X1,X2,X3),X3),
    inference(literals_permutation,[status(thm)],[c_0_5643]) ).

cnf(c_0_5644_0,axiom,
    c_in(c_SetInterval_OgreaterThanLessThan(X1,X2,tc_IntDef_Oint),c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)),
    inference(literals_permutation,[status(thm)],[c_0_5644]) ).

cnf(c_0_5645_0,axiom,
    c_in(c_SetInterval_OgreaterThanLessThan(X1,X2,tc_nat),c_Finite__Set_OFinites,tc_set(tc_nat)),
    inference(literals_permutation,[status(thm)],[c_0_5645]) ).

cnf(c_0_5646_0,axiom,
    c_in(c_SetInterval_OgreaterThanAtMost(X1,X2,tc_IntDef_Oint),c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)),
    inference(literals_permutation,[status(thm)],[c_0_5646]) ).

cnf(c_0_5647_0,axiom,
    c_in(c_SetInterval_OgreaterThanAtMost(X1,X2,tc_nat),c_Finite__Set_OFinites,tc_set(tc_nat)),
    inference(literals_permutation,[status(thm)],[c_0_5647]) ).

cnf(c_0_5648_0,axiom,
    c_in(c_SetInterval_OatLeastLessThan(X1,X2,tc_IntDef_Oint),c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)),
    inference(literals_permutation,[status(thm)],[c_0_5648]) ).

cnf(c_0_5649_0,axiom,
    c_in(c_SetInterval_OatLeastLessThan(X1,X2,tc_nat),c_Finite__Set_OFinites,tc_set(tc_nat)),
    inference(literals_permutation,[status(thm)],[c_0_5649]) ).

cnf(c_0_5650_0,axiom,
    c_in(c_SetInterval_OatLeastAtMost(X1,X2,tc_IntDef_Oint),c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)),
    inference(literals_permutation,[status(thm)],[c_0_5650]) ).

cnf(c_0_5651_0,axiom,
    c_in(c_SetInterval_OatLeastAtMost(X1,X2,tc_nat),c_Finite__Set_OFinites,tc_set(tc_nat)),
    inference(literals_permutation,[status(thm)],[c_0_5651]) ).

cnf(c_0_5655_0,axiom,
    c_in(X1,c_insert(X1,c_emptyset,X2),X2),
    inference(literals_permutation,[status(thm)],[c_0_5655]) ).

cnf(c_0_5656_0,axiom,
    c_Divides_Oop_Advd(X1,c_times(X2,X1,tc_IntDef_Oint),tc_IntDef_Oint),
    inference(literals_permutation,[status(thm)],[c_0_5656]) ).

cnf(c_0_5657_0,axiom,
    c_Divides_Oop_Advd(X1,c_times(X1,X2,tc_IntDef_Oint),tc_IntDef_Oint),
    inference(literals_permutation,[status(thm)],[c_0_5657]) ).

cnf(c_0_5658_0,axiom,
    c_Divides_Oop_Advd(X1,c_times(X2,X1,tc_nat),tc_nat),
    inference(literals_permutation,[status(thm)],[c_0_5658]) ).

cnf(c_0_5659_0,axiom,
    c_Divides_Oop_Advd(X1,c_times(X1,X2,tc_nat),tc_nat),
    inference(literals_permutation,[status(thm)],[c_0_5659]) ).

cnf(c_0_5669_0,axiom,
    c_in(X1,c_Datatype_Oo2s(c_Datatype_Ooption_OSome(X1,X2),X2),X2),
    inference(literals_permutation,[status(thm)],[c_0_5669]) ).

cnf(c_0_5671_0,axiom,
    c_less(c_uminus(c_IntDef_Oint(c_Suc(X1)),tc_IntDef_Oint),c_IntDef_Oint(X2),tc_IntDef_Oint),
    inference(literals_permutation,[status(thm)],[c_0_5671]) ).

cnf(c_0_5672_0,axiom,
    c_lessequals(c_uminus(c_IntDef_Oint(X1),tc_IntDef_Oint),c_IntDef_Oint(X2),tc_IntDef_Oint),
    inference(literals_permutation,[status(thm)],[c_0_5672]) ).

cnf(c_0_5693_0,axiom,
    c_in(c_List_Olist_ONil,c_List_Olists(X1,X2),tc_List_Olist(X2)),
    inference(literals_permutation,[status(thm)],[c_0_5693]) ).

cnf(c_0_5694_0,axiom,
    c_in(c_List_Oset(X1,X2),c_Finite__Set_OFinites,tc_set(X2)),
    inference(literals_permutation,[status(thm)],[c_0_5694]) ).

cnf(c_0_5704_0,axiom,
    c_in(c_SetInterval_OlessThan(X1,tc_nat),c_Finite__Set_OFinites,tc_set(tc_nat)),
    inference(literals_permutation,[status(thm)],[c_0_5704]) ).

cnf(c_0_5705_0,axiom,
    c_in(c_SetInterval_OatMost(X1,tc_nat),c_Finite__Set_OFinites,tc_set(tc_nat)),
    inference(literals_permutation,[status(thm)],[c_0_5705]) ).

cnf(c_0_5711_0,axiom,
    c_lessequals(X1,X1,tc_set(X2)),
    inference(literals_permutation,[status(thm)],[c_0_5711]) ).

cnf(c_0_5712_0,axiom,
    c_lessequals(c_emptyset,X1,tc_set(X2)),
    inference(literals_permutation,[status(thm)],[c_0_5712]) ).

cnf(c_0_5713_0,axiom,
    c_less(X1,c_Suc(X1),tc_nat),
    inference(literals_permutation,[status(thm)],[c_0_5713]) ).

cnf(c_0_5714_0,axiom,
    c_less(c_0,c_Suc(X1),tc_nat),
    inference(literals_permutation,[status(thm)],[c_0_5714]) ).

cnf(c_0_5715_0,axiom,
    c_in(c_emptyset,c_Finite__Set_OFinites,tc_set(X1)),
    inference(literals_permutation,[status(thm)],[c_0_5715]) ).

cnf(c_0_5716_0,axiom,
    c_Divides_Oop_Advd(c_Suc(c_0),X1,tc_nat),
    inference(literals_permutation,[status(thm)],[c_0_5716]) ).

cnf(c_0_5717_0,axiom,
    c_less(c_0,c_Suc(c_0),tc_nat),
    inference(literals_permutation,[status(thm)],[c_0_5717]) ).

cnf(c_0_5718_0,axiom,
    c_append(X1,c_List_Olist_ONil,X2) = X1,
    inference(literals_permutation,[status(thm)],[c_0_5718]) ).

cnf(c_0_5719_0,axiom,
    c_append(c_List_Olist_ONil,X1,X2) = X1,
    inference(literals_permutation,[status(thm)],[c_0_5719]) ).

cnf(c_0_5720_0,axiom,
    c_append(X1,c_List_Olist_ONil,X2) = X1,
    inference(literals_permutation,[status(thm)],[c_0_5720]) ).

cnf(c_0_5721_0,axiom,
    c_append(c_List_Olist_ONil,X1,X2) = X1,
    inference(literals_permutation,[status(thm)],[c_0_5721]) ).

cnf(c_0_5726_0,axiom,
    c_in(X1,c_UNIV,X2),
    inference(literals_permutation,[status(thm)],[c_0_5726]) ).

cnf(c_0_5728_0,axiom,
    c_Equiv__Relations_Oquotient(c_emptyset,X1,X2) = c_emptyset,
    inference(literals_permutation,[status(thm)],[c_0_5728]) ).

cnf(c_0_5729_0,axiom,
    c_Equiv__Relations_Oquotient(c_emptyset,X1,X2) = c_emptyset,
    inference(literals_permutation,[status(thm)],[c_0_5729]) ).

cnf(c_0_5730_0,axiom,
    c_lessequals(c_0,X1,tc_nat),
    inference(literals_permutation,[status(thm)],[c_0_5730]) ).

cnf(c_0_5731_0,axiom,
    c_Divides_Oop_Advd(c_1,X1,tc_IntDef_Oint),
    inference(literals_permutation,[status(thm)],[c_0_5731]) ).

cnf(c_0_5732_0,axiom,
    c_Divides_Oop_Advd(X1,c_0,tc_IntDef_Oint),
    inference(literals_permutation,[status(thm)],[c_0_5732]) ).

cnf(c_0_5733_0,axiom,
    c_Divides_Oop_Advd(X1,c_0,tc_nat),
    inference(literals_permutation,[status(thm)],[c_0_5733]) ).

cnf(c_0_5734_0,axiom,
    c_union(c_emptyset,c_emptyset,X1) = c_emptyset,
    inference(literals_permutation,[status(thm)],[c_0_5734]) ).

cnf(c_0_5735_0,axiom,
    c_append(c_List_Olist_ONil,c_List_Olist_ONil,X1) = c_List_Olist_ONil,
    inference(literals_permutation,[status(thm)],[c_0_5735]) ).

cnf(c_0_5736_0,axiom,
    c_append(c_List_Olist_ONil,c_List_Olist_ONil,X1) = c_List_Olist_ONil,
    inference(literals_permutation,[status(thm)],[c_0_5736]) ).

cnf(c_0_5737_0,axiom,
    c_less(c_0,c_1,tc_nat),
    inference(literals_permutation,[status(thm)],[c_0_5737]) ).

cnf(c_0_5738_0,axiom,
    c_lessequals(c_0,c_0,tc_nat),
    inference(literals_permutation,[status(thm)],[c_0_5738]) ).

cnf(c_0_5739_0,axiom,
    c_plus(c_0,c_0,tc_nat) = c_0,
    inference(literals_permutation,[status(thm)],[c_0_5739]) ).

cnf(c_0_5740_0,axiom,
    c_Divides_Oop_Advd(c_0,c_0,tc_IntDef_Oint),
    inference(literals_permutation,[status(thm)],[c_0_5740]) ).

cnf(c_0_5741_0,axiom,
    c_Divides_Oop_Advd(c_0,c_0,tc_nat),
    inference(literals_permutation,[status(thm)],[c_0_5741]) ).

cnf(c_0_5751_0,axiom,
    c_List_Odistinct(c_List_Oremdups(X1,X2),X2),
    inference(literals_permutation,[status(thm)],[c_0_5751]) ).

cnf(c_0_5753_0,axiom,
    class_Nat_Opower(tc_fun(X1,X2)),
    inference(literals_permutation,[status(thm)],[c_0_5753]) ).

cnf(c_0_5760_0,axiom,
    c_Nat_Osize(c_List_Olist_ONil,tc_List_Olist(X1)) = c_0,
    inference(literals_permutation,[status(thm)],[c_0_5760]) ).

cnf(c_0_5765_0,axiom,
    c_Wellfounded__Recursion_Owf(c_emptyset,X1),
    inference(literals_permutation,[status(thm)],[c_0_5765]) ).

cnf(c_0_5766_0,axiom,
    c_List_Oset(c_List_Olist_ONil,X1) = c_emptyset,
    inference(literals_permutation,[status(thm)],[c_0_5766]) ).

cnf(c_0_5767_0,axiom,
    c_List_Oset(c_List_Olist_ONil,X1) = c_emptyset,
    inference(literals_permutation,[status(thm)],[c_0_5767]) ).

cnf(c_0_5768_0,axiom,
    c_List_Orev(c_List_Olist_ONil,X1) = c_List_Olist_ONil,
    inference(literals_permutation,[status(thm)],[c_0_5768]) ).

cnf(c_0_5769_0,axiom,
    c_List_Orev(c_List_Olist_ONil,X1) = c_List_Olist_ONil,
    inference(literals_permutation,[status(thm)],[c_0_5769]) ).

cnf(c_0_6677_0,axiom,
    c_Wellfounded__Recursion_Owf(c_Wellfounded__Relations_Oless__than,tc_nat),
    inference(literals_permutation,[status(thm)],[c_0_6677]) ).

cnf(c_0_6678_0,axiom,
    c_Relation_Otrans(c_Wellfounded__Relations_Oless__than,tc_nat),
    inference(literals_permutation,[status(thm)],[c_0_6678]) ).

cnf(c_0_6679_0,axiom,
    class_Nat_Opower(tc_set(X1)),
    inference(literals_permutation,[status(thm)],[c_0_6679]) ).

cnf(c_0_6680_0,axiom,
    class_Orderings_Oorder(tc_set(X1)),
    inference(literals_permutation,[status(thm)],[c_0_6680]) ).

cnf(c_0_6681_0,axiom,
    class_Orderings_Oord(tc_set(X1)),
    inference(literals_permutation,[status(thm)],[c_0_6681]) ).

cnf(c_0_6682_0,axiom,
    class_HOL_Ominus(tc_set(X1)),
    inference(literals_permutation,[status(thm)],[c_0_6682]) ).

cnf(c_0_6685_0,axiom,
    class_HOL_Ominus(tc_nat),
    inference(literals_permutation,[status(thm)],[c_0_6685]) ).

cnf(c_0_6686_0,axiom,
    class_Wellfounded__Recursion_Owellorder(tc_nat),
    inference(literals_permutation,[status(thm)],[c_0_6686]) ).

cnf(c_0_6687_0,axiom,
    class_Orderings_Olinorder(tc_nat),
    inference(literals_permutation,[status(thm)],[c_0_6687]) ).

cnf(c_0_6688_0,axiom,
    class_LOrder_Olorder(tc_nat),
    inference(literals_permutation,[status(thm)],[c_0_6688]) ).

cnf(c_0_6689_0,axiom,
    class_LOrder_Ojoin__semilorder(tc_nat),
    inference(literals_permutation,[status(thm)],[c_0_6689]) ).

cnf(c_0_6690_0,axiom,
    class_Parity_Oeven__odd(tc_nat),
    inference(literals_permutation,[status(thm)],[c_0_6690]) ).

cnf(c_0_6691_0,axiom,
    class_Numeral_Onumber(tc_nat),
    inference(literals_permutation,[status(thm)],[c_0_6691]) ).

cnf(c_0_6692_0,axiom,
    class_Power_Orecpower(tc_nat),
    inference(literals_permutation,[status(thm)],[c_0_6692]) ).

cnf(c_0_6693_0,axiom,
    class_Divides_Odiv(tc_nat),
    inference(literals_permutation,[status(thm)],[c_0_6693]) ).

cnf(c_0_6694_0,axiom,
    class_Ring__and__Field_Oordered__semidom(tc_nat),
    inference(literals_permutation,[status(thm)],[c_0_6694]) ).

cnf(c_0_6695_0,axiom,
    class_Ring__and__Field_Oordered__comm__semiring__strict(tc_nat),
    inference(literals_permutation,[status(thm)],[c_0_6695]) ).

cnf(c_0_6696_0,axiom,
    class_Ring__and__Field_Opordered__cancel__comm__semiring(tc_nat),
    inference(literals_permutation,[status(thm)],[c_0_6696]) ).

cnf(c_0_6697_0,axiom,
    class_Ring__and__Field_Opordered__comm__semiring(tc_nat),
    inference(literals_permutation,[status(thm)],[c_0_6697]) ).

cnf(c_0_6698_0,axiom,
    class_LOrder_Omeet__semilorder(tc_nat),
    inference(literals_permutation,[status(thm)],[c_0_6698]) ).

cnf(c_0_6699_0,axiom,
    class_Ring__and__Field_Oordered__semiring__strict(tc_nat),
    inference(literals_permutation,[status(thm)],[c_0_6699]) ).

cnf(c_0_6700_0,axiom,
    class_Ring__and__Field_Opordered__cancel__semiring(tc_nat),
    inference(literals_permutation,[status(thm)],[c_0_6700]) ).

cnf(c_0_6701_0,axiom,
    class_Ring__and__Field_Opordered__semiring(tc_nat),
    inference(literals_permutation,[status(thm)],[c_0_6701]) ).

cnf(c_0_6702_0,axiom,
    class_OrderedGroup_Oordered__cancel__ab__semigroup__add(tc_nat),
    inference(literals_permutation,[status(thm)],[c_0_6702]) ).

cnf(c_0_6703_0,axiom,
    class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat),
    inference(literals_permutation,[status(thm)],[c_0_6703]) ).

cnf(c_0_6704_0,axiom,
    class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat),
    inference(literals_permutation,[status(thm)],[c_0_6704]) ).

cnf(c_0_6705_0,axiom,
    class_OrderedGroup_Opordered__ab__semigroup__add(tc_nat),
    inference(literals_permutation,[status(thm)],[c_0_6705]) ).

cnf(c_0_6706_0,axiom,
    class_Ring__and__Field_Ocomm__semiring__1__cancel(tc_nat),
    inference(literals_permutation,[status(thm)],[c_0_6706]) ).

cnf(c_0_6707_0,axiom,
    class_Ring__and__Field_Ocomm__semiring__0__cancel(tc_nat),
    inference(literals_permutation,[status(thm)],[c_0_6707]) ).

cnf(c_0_6708_0,axiom,
    class_Ring__and__Field_Osemiring__1__cancel(tc_nat),
    inference(literals_permutation,[status(thm)],[c_0_6708]) ).

cnf(c_0_6709_0,axiom,
    class_Orderings_Oorder(tc_nat),
    inference(literals_permutation,[status(thm)],[c_0_6709]) ).

cnf(c_0_6710_0,axiom,
    class_Ring__and__Field_Osemiring__0__cancel(tc_nat),
    inference(literals_permutation,[status(thm)],[c_0_6710]) ).

cnf(c_0_6711_0,axiom,
    class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat),
    inference(literals_permutation,[status(thm)],[c_0_6711]) ).

cnf(c_0_6712_0,axiom,
    class_OrderedGroup_Ocancel__semigroup__add(tc_nat),
    inference(literals_permutation,[status(thm)],[c_0_6712]) ).

cnf(c_0_6713_0,axiom,
    class_Ring__and__Field_Ocomm__semiring__1(tc_nat),
    inference(literals_permutation,[status(thm)],[c_0_6713]) ).

cnf(c_0_6714_0,axiom,
    class_Ring__and__Field_Osemiring__1(tc_nat),
    inference(literals_permutation,[status(thm)],[c_0_6714]) ).

cnf(c_0_6715_0,axiom,
    class_OrderedGroup_Ocomm__monoid__mult(tc_nat),
    inference(literals_permutation,[status(thm)],[c_0_6715]) ).

cnf(c_0_6716_0,axiom,
    class_OrderedGroup_Omonoid__mult(tc_nat),
    inference(literals_permutation,[status(thm)],[c_0_6716]) ).

cnf(c_0_6717_0,axiom,
    class_Ring__and__Field_Ocomm__semiring__0(tc_nat),
    inference(literals_permutation,[status(thm)],[c_0_6717]) ).

cnf(c_0_6718_0,axiom,
    class_Ring__and__Field_Osemiring__0(tc_nat),
    inference(literals_permutation,[status(thm)],[c_0_6718]) ).

cnf(c_0_6719_0,axiom,
    class_OrderedGroup_Ocomm__monoid__add(tc_nat),
    inference(literals_permutation,[status(thm)],[c_0_6719]) ).

cnf(c_0_6720_0,axiom,
    class_Orderings_Oord(tc_nat),
    inference(literals_permutation,[status(thm)],[c_0_6720]) ).

cnf(c_0_6721_0,axiom,
    class_Ring__and__Field_Ocomm__semiring(tc_nat),
    inference(literals_permutation,[status(thm)],[c_0_6721]) ).

cnf(c_0_6722_0,axiom,
    class_Ring__and__Field_Osemiring(tc_nat),
    inference(literals_permutation,[status(thm)],[c_0_6722]) ).

cnf(c_0_6723_0,axiom,
    class_OrderedGroup_Oab__semigroup__mult(tc_nat),
    inference(literals_permutation,[status(thm)],[c_0_6723]) ).

cnf(c_0_6724_0,axiom,
    class_OrderedGroup_Osemigroup__mult(tc_nat),
    inference(literals_permutation,[status(thm)],[c_0_6724]) ).

cnf(c_0_6725_0,axiom,
    class_OrderedGroup_Oab__semigroup__add(tc_nat),
    inference(literals_permutation,[status(thm)],[c_0_6725]) ).

cnf(c_0_6726_0,axiom,
    class_OrderedGroup_Osemigroup__add(tc_nat),
    inference(literals_permutation,[status(thm)],[c_0_6726]) ).

cnf(c_0_6727_0,axiom,
    class_Ring__and__Field_Oaxclass__0__neq__1(tc_nat),
    inference(literals_permutation,[status(thm)],[c_0_6727]) ).

cnf(c_0_6728_0,axiom,
    class_Nat_Opower(tc_nat),
    inference(literals_permutation,[status(thm)],[c_0_6728]) ).

cnf(c_0_6729_0,axiom,
    class_HOL_Otimes(tc_nat),
    inference(literals_permutation,[status(thm)],[c_0_6729]) ).

cnf(c_0_6730_0,axiom,
    class_HOL_Oplus(tc_nat),
    inference(literals_permutation,[status(thm)],[c_0_6730]) ).

cnf(c_0_6731_0,axiom,
    class_HOL_Ozero(tc_nat),
    inference(literals_permutation,[status(thm)],[c_0_6731]) ).

cnf(c_0_6732_0,axiom,
    class_HOL_Oone(tc_nat),
    inference(literals_permutation,[status(thm)],[c_0_6732]) ).

cnf(c_0_6733_0,axiom,
    class_Finite__Set_Ofinite(tc_bool),
    inference(literals_permutation,[status(thm)],[c_0_6733]) ).

cnf(c_0_6734_0,axiom,
    class_Finite__Set_Ofinite(tc_Product__Type_Ounit),
    inference(literals_permutation,[status(thm)],[c_0_6734]) ).

cnf(c_0_6735_0,axiom,
    class_OrderedGroup_Oab__semigroup__mult(tc_IntDef_Oint),
    inference(literals_permutation,[status(thm)],[c_0_6735]) ).

cnf(c_0_6736_0,axiom,
    class_OrderedGroup_Osemigroup__mult(tc_IntDef_Oint),
    inference(literals_permutation,[status(thm)],[c_0_6736]) ).

cnf(c_0_6737_0,axiom,
    class_OrderedGroup_Oab__semigroup__add(tc_IntDef_Oint),
    inference(literals_permutation,[status(thm)],[c_0_6737]) ).

cnf(c_0_6738_0,axiom,
    class_Parity_Oeven__odd(tc_IntDef_Oint),
    inference(literals_permutation,[status(thm)],[c_0_6738]) ).

cnf(c_0_6739_0,axiom,
    class_Power_Orecpower(tc_IntDef_Oint),
    inference(literals_permutation,[status(thm)],[c_0_6739]) ).

cnf(c_0_6740_0,axiom,
    class_Nat_Opower(tc_IntDef_Oint),
    inference(literals_permutation,[status(thm)],[c_0_6740]) ).

cnf(c_0_6741_0,axiom,
    class_Divides_Odiv(tc_IntDef_Oint),
    inference(literals_permutation,[status(thm)],[c_0_6741]) ).

cnf(c_0_6742_0,axiom,
    class_Numeral_Onumber__ring(tc_IntDef_Oint),
    inference(literals_permutation,[status(thm)],[c_0_6742]) ).

cnf(c_0_6743_0,axiom,
    class_OrderedGroup_Osemigroup__add(tc_IntDef_Oint),
    inference(literals_permutation,[status(thm)],[c_0_6743]) ).

cnf(c_0_6744_0,axiom,
    class_Numeral_Onumber(tc_IntDef_Oint),
    inference(literals_permutation,[status(thm)],[c_0_6744]) ).

cnf(c_0_6745_0,axiom,
    class_Ring__and__Field_Oordered__idom(tc_IntDef_Oint),
    inference(literals_permutation,[status(thm)],[c_0_6745]) ).

cnf(c_0_6746_0,axiom,
    class_Ring__and__Field_Oidom(tc_IntDef_Oint),
    inference(literals_permutation,[status(thm)],[c_0_6746]) ).

cnf(c_0_6747_0,axiom,
    class_Ring__and__Field_Oordered__semidom(tc_IntDef_Oint),
    inference(literals_permutation,[status(thm)],[c_0_6747]) ).

cnf(c_0_6748_0,axiom,
    class_Ring__and__Field_Oordered__ring__strict(tc_IntDef_Oint),
    inference(literals_permutation,[status(thm)],[c_0_6748]) ).

cnf(c_0_6749_0,axiom,
    class_Ring__and__Field_Oaxclass__no__zero__divisors(tc_IntDef_Oint),
    inference(literals_permutation,[status(thm)],[c_0_6749]) ).

cnf(c_0_6750_0,axiom,
    class_Ring__and__Field_Olordered__ring(tc_IntDef_Oint),
    inference(literals_permutation,[status(thm)],[c_0_6750]) ).

cnf(c_0_6751_0,axiom,
    class_OrderedGroup_Olordered__ab__group__join(tc_IntDef_Oint),
    inference(literals_permutation,[status(thm)],[c_0_6751]) ).

cnf(c_0_6752_0,axiom,
    class_OrderedGroup_Olordered__ab__group__meet(tc_IntDef_Oint),
    inference(literals_permutation,[status(thm)],[c_0_6752]) ).

cnf(c_0_6753_0,axiom,
    class_OrderedGroup_Olordered__ab__group__abs(tc_IntDef_Oint),
    inference(literals_permutation,[status(thm)],[c_0_6753]) ).

cnf(c_0_6754_0,axiom,
    class_Orderings_Oord(tc_IntDef_Oint),
    inference(literals_permutation,[status(thm)],[c_0_6754]) ).

cnf(c_0_6755_0,axiom,
    class_Ring__and__Field_Opordered__ring(tc_IntDef_Oint),
    inference(literals_permutation,[status(thm)],[c_0_6755]) ).

cnf(c_0_6756_0,axiom,
    class_OrderedGroup_Olordered__ab__group(tc_IntDef_Oint),
    inference(literals_permutation,[status(thm)],[c_0_6756]) ).

cnf(c_0_6757_0,axiom,
    class_OrderedGroup_Opordered__ab__group__add(tc_IntDef_Oint),
    inference(literals_permutation,[status(thm)],[c_0_6757]) ).

cnf(c_0_6758_0,axiom,
    class_Ring__and__Field_Oaxclass__abs__if(tc_IntDef_Oint),
    inference(literals_permutation,[status(thm)],[c_0_6758]) ).

cnf(c_0_6759_0,axiom,
    class_Ring__and__Field_Oordered__comm__semiring__strict(tc_IntDef_Oint),
    inference(literals_permutation,[status(thm)],[c_0_6759]) ).

cnf(c_0_6760_0,axiom,
    class_Ring__and__Field_Opordered__cancel__comm__semiring(tc_IntDef_Oint),
    inference(literals_permutation,[status(thm)],[c_0_6760]) ).

cnf(c_0_6761_0,axiom,
    class_Ring__and__Field_Opordered__comm__semiring(tc_IntDef_Oint),
    inference(literals_permutation,[status(thm)],[c_0_6761]) ).

cnf(c_0_6762_0,axiom,
    class_Ring__and__Field_Oordered__semiring__strict(tc_IntDef_Oint),
    inference(literals_permutation,[status(thm)],[c_0_6762]) ).

cnf(c_0_6763_0,axiom,
    class_Ring__and__Field_Opordered__cancel__semiring(tc_IntDef_Oint),
    inference(literals_permutation,[status(thm)],[c_0_6763]) ).

cnf(c_0_6764_0,axiom,
    class_Ring__and__Field_Opordered__semiring(tc_IntDef_Oint),
    inference(literals_permutation,[status(thm)],[c_0_6764]) ).

cnf(c_0_6765_0,axiom,
    class_HOL_Ozero(tc_IntDef_Oint),
    inference(literals_permutation,[status(thm)],[c_0_6765]) ).

cnf(c_0_6766_0,axiom,
    class_OrderedGroup_Oordered__cancel__ab__semigroup__add(tc_IntDef_Oint),
    inference(literals_permutation,[status(thm)],[c_0_6766]) ).

cnf(c_0_6767_0,axiom,
    class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_IntDef_Oint),
    inference(literals_permutation,[status(thm)],[c_0_6767]) ).

cnf(c_0_6768_0,axiom,
    class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_IntDef_Oint),
    inference(literals_permutation,[status(thm)],[c_0_6768]) ).

cnf(c_0_6769_0,axiom,
    class_OrderedGroup_Opordered__ab__semigroup__add(tc_IntDef_Oint),
    inference(literals_permutation,[status(thm)],[c_0_6769]) ).

cnf(c_0_6770_0,axiom,
    class_Orderings_Olinorder(tc_IntDef_Oint),
    inference(literals_permutation,[status(thm)],[c_0_6770]) ).

cnf(c_0_6771_0,axiom,
    class_LOrder_Olorder(tc_IntDef_Oint),
    inference(literals_permutation,[status(thm)],[c_0_6771]) ).

cnf(c_0_6772_0,axiom,
    class_LOrder_Ojoin__semilorder(tc_IntDef_Oint),
    inference(literals_permutation,[status(thm)],[c_0_6772]) ).

cnf(c_0_6773_0,axiom,
    class_LOrder_Omeet__semilorder(tc_IntDef_Oint),
    inference(literals_permutation,[status(thm)],[c_0_6773]) ).

cnf(c_0_6774_0,axiom,
    class_Orderings_Oorder(tc_IntDef_Oint),
    inference(literals_permutation,[status(thm)],[c_0_6774]) ).

cnf(c_0_6775_0,axiom,
    class_Ring__and__Field_Ocomm__ring__1(tc_IntDef_Oint),
    inference(literals_permutation,[status(thm)],[c_0_6775]) ).

cnf(c_0_6776_0,axiom,
    class_HOL_Otimes(tc_IntDef_Oint),
    inference(literals_permutation,[status(thm)],[c_0_6776]) ).

cnf(c_0_6777_0,axiom,
    class_Ring__and__Field_Ocomm__semiring__1__cancel(tc_IntDef_Oint),
    inference(literals_permutation,[status(thm)],[c_0_6777]) ).

cnf(c_0_6778_0,axiom,
    class_Ring__and__Field_Oring__1(tc_IntDef_Oint),
    inference(literals_permutation,[status(thm)],[c_0_6778]) ).

cnf(c_0_6779_0,axiom,
    class_Ring__and__Field_Osemiring__1__cancel(tc_IntDef_Oint),
    inference(literals_permutation,[status(thm)],[c_0_6779]) ).

cnf(c_0_6780_0,axiom,
    class_Ring__and__Field_Ocomm__semiring__1(tc_IntDef_Oint),
    inference(literals_permutation,[status(thm)],[c_0_6780]) ).

cnf(c_0_6781_0,axiom,
    class_Ring__and__Field_Osemiring__1(tc_IntDef_Oint),
    inference(literals_permutation,[status(thm)],[c_0_6781]) ).

cnf(c_0_6782_0,axiom,
    class_OrderedGroup_Ocomm__monoid__mult(tc_IntDef_Oint),
    inference(literals_permutation,[status(thm)],[c_0_6782]) ).

cnf(c_0_6783_0,axiom,
    class_OrderedGroup_Omonoid__mult(tc_IntDef_Oint),
    inference(literals_permutation,[status(thm)],[c_0_6783]) ).

cnf(c_0_6784_0,axiom,
    class_Ring__and__Field_Oaxclass__0__neq__1(tc_IntDef_Oint),
    inference(literals_permutation,[status(thm)],[c_0_6784]) ).

cnf(c_0_6785_0,axiom,
    class_Ring__and__Field_Ocomm__ring(tc_IntDef_Oint),
    inference(literals_permutation,[status(thm)],[c_0_6785]) ).

cnf(c_0_6786_0,axiom,
    class_Ring__and__Field_Ocomm__semiring__0__cancel(tc_IntDef_Oint),
    inference(literals_permutation,[status(thm)],[c_0_6786]) ).

cnf(c_0_6787_0,axiom,
    class_HOL_Oplus(tc_IntDef_Oint),
    inference(literals_permutation,[status(thm)],[c_0_6787]) ).

cnf(c_0_6788_0,axiom,
    class_Ring__and__Field_Oring(tc_IntDef_Oint),
    inference(literals_permutation,[status(thm)],[c_0_6788]) ).

cnf(c_0_6789_0,axiom,
    class_Ring__and__Field_Osemiring__0__cancel(tc_IntDef_Oint),
    inference(literals_permutation,[status(thm)],[c_0_6789]) ).

cnf(c_0_6790_0,axiom,
    class_OrderedGroup_Oab__group__add(tc_IntDef_Oint),
    inference(literals_permutation,[status(thm)],[c_0_6790]) ).

cnf(c_0_6791_0,axiom,
    class_OrderedGroup_Ocancel__ab__semigroup__add(tc_IntDef_Oint),
    inference(literals_permutation,[status(thm)],[c_0_6791]) ).

cnf(c_0_6792_0,axiom,
    class_OrderedGroup_Ocancel__semigroup__add(tc_IntDef_Oint),
    inference(literals_permutation,[status(thm)],[c_0_6792]) ).

cnf(c_0_6793_0,axiom,
    class_Ring__and__Field_Ocomm__semiring__0(tc_IntDef_Oint),
    inference(literals_permutation,[status(thm)],[c_0_6793]) ).

cnf(c_0_6794_0,axiom,
    class_Ring__and__Field_Osemiring__0(tc_IntDef_Oint),
    inference(literals_permutation,[status(thm)],[c_0_6794]) ).

cnf(c_0_6795_0,axiom,
    class_OrderedGroup_Ocomm__monoid__add(tc_IntDef_Oint),
    inference(literals_permutation,[status(thm)],[c_0_6795]) ).

cnf(c_0_6796_0,axiom,
    class_Ring__and__Field_Ocomm__semiring(tc_IntDef_Oint),
    inference(literals_permutation,[status(thm)],[c_0_6796]) ).

cnf(c_0_6797_0,axiom,
    class_Ring__and__Field_Osemiring(tc_IntDef_Oint),
    inference(literals_permutation,[status(thm)],[c_0_6797]) ).

cnf(c_0_6798_0,axiom,
    class_HOL_Oone(tc_IntDef_Oint),
    inference(literals_permutation,[status(thm)],[c_0_6798]) ).

cnf(c_0_6799_0,axiom,
    class_HOL_Ominus(tc_IntDef_Oint),
    inference(literals_permutation,[status(thm)],[c_0_6799]) ).

% CNF of non-axioms
% Start CNF derivation
fof(c_0_0_001,negated_conjecture,
    ! [X1] :
      ( c_lessequals(c_Zorn_Osucc(v_S,X1,t_a),v_m,tc_set(tc_set(t_a)))
      | X1 = v_m
      | ~ c_lessequals(X1,v_m,tc_set(tc_set(t_a)))
      | ~ c_in(X1,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))) ),
    file('<stdin>',cls_conjecture_5) ).

fof(c_0_1_002,negated_conjecture,
    ! [X1] :
      ( c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),X1,tc_set(tc_set(t_a)))
      | c_lessequals(X1,v_m,tc_set(tc_set(t_a)))
      | ~ c_in(X1,v_Y,tc_set(tc_set(t_a))) ),
    file('<stdin>',cls_conjecture_4) ).

fof(c_0_2_003,negated_conjecture,
    ~ c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),c_Union(v_Y,tc_set(t_a)),tc_set(tc_set(t_a))),
    file('<stdin>',cls_conjecture_3) ).

fof(c_0_3_004,negated_conjecture,
    ~ c_lessequals(c_Union(v_Y,tc_set(t_a)),v_m,tc_set(tc_set(t_a))),
    file('<stdin>',cls_conjecture_2) ).

fof(c_0_4_005,negated_conjecture,
    c_lessequals(v_Y,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(tc_set(t_a)))),
    file('<stdin>',cls_conjecture_1) ).

fof(c_0_5_006,negated_conjecture,
    c_in(v_m,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))),
    file('<stdin>',cls_conjecture_0) ).

fof(c_0_6_007,negated_conjecture,
    ! [X1] :
      ( c_lessequals(c_Zorn_Osucc(v_S,X1,t_a),v_m,tc_set(tc_set(t_a)))
      | X1 = v_m
      | ~ c_lessequals(X1,v_m,tc_set(tc_set(t_a)))
      | ~ c_in(X1,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))) ),
    inference(fof_simplification,[status(thm)],[c_0_0]) ).

fof(c_0_7_008,negated_conjecture,
    ! [X1] :
      ( c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),X1,tc_set(tc_set(t_a)))
      | c_lessequals(X1,v_m,tc_set(tc_set(t_a)))
      | ~ c_in(X1,v_Y,tc_set(tc_set(t_a))) ),
    inference(fof_simplification,[status(thm)],[c_0_1]) ).

fof(c_0_8_009,negated_conjecture,
    ~ c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),c_Union(v_Y,tc_set(t_a)),tc_set(tc_set(t_a))),
    inference(fof_simplification,[status(thm)],[c_0_2]) ).

fof(c_0_9_010,negated_conjecture,
    ~ c_lessequals(c_Union(v_Y,tc_set(t_a)),v_m,tc_set(tc_set(t_a))),
    inference(fof_simplification,[status(thm)],[c_0_3]) ).

fof(c_0_10_011,negated_conjecture,
    c_lessequals(v_Y,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(tc_set(t_a)))),
    c_0_4 ).

fof(c_0_11_012,negated_conjecture,
    c_in(v_m,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))),
    c_0_5 ).

fof(c_0_12_013,negated_conjecture,
    ! [X2] :
      ( c_lessequals(c_Zorn_Osucc(v_S,X2,t_a),v_m,tc_set(tc_set(t_a)))
      | X2 = v_m
      | ~ c_lessequals(X2,v_m,tc_set(tc_set(t_a)))
      | ~ c_in(X2,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))) ),
    inference(variable_rename,[status(thm)],[c_0_6]) ).

fof(c_0_13_014,negated_conjecture,
    ! [X2] :
      ( c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),X2,tc_set(tc_set(t_a)))
      | c_lessequals(X2,v_m,tc_set(tc_set(t_a)))
      | ~ c_in(X2,v_Y,tc_set(tc_set(t_a))) ),
    inference(variable_rename,[status(thm)],[c_0_7]) ).

fof(c_0_14_015,negated_conjecture,
    ~ c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),c_Union(v_Y,tc_set(t_a)),tc_set(tc_set(t_a))),
    c_0_8 ).

fof(c_0_15_016,negated_conjecture,
    ~ c_lessequals(c_Union(v_Y,tc_set(t_a)),v_m,tc_set(tc_set(t_a))),
    c_0_9 ).

fof(c_0_16_017,negated_conjecture,
    c_lessequals(v_Y,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(tc_set(t_a)))),
    c_0_10 ).

fof(c_0_17_018,negated_conjecture,
    c_in(v_m,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))),
    c_0_11 ).

cnf(c_0_18_019,negated_conjecture,
    ( X1 = v_m
    | c_lessequals(c_Zorn_Osucc(v_S,X1,t_a),v_m,tc_set(tc_set(t_a)))
    | ~ c_in(X1,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
    | ~ c_lessequals(X1,v_m,tc_set(tc_set(t_a))) ),
    inference(split_conjunct,[status(thm)],[c_0_12]) ).

cnf(c_0_19_020,negated_conjecture,
    ( c_lessequals(X1,v_m,tc_set(tc_set(t_a)))
    | c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),X1,tc_set(tc_set(t_a)))
    | ~ c_in(X1,v_Y,tc_set(tc_set(t_a))) ),
    inference(split_conjunct,[status(thm)],[c_0_13]) ).

cnf(c_0_20_021,negated_conjecture,
    ~ c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),c_Union(v_Y,tc_set(t_a)),tc_set(tc_set(t_a))),
    inference(split_conjunct,[status(thm)],[c_0_14]) ).

cnf(c_0_21_022,negated_conjecture,
    ~ c_lessequals(c_Union(v_Y,tc_set(t_a)),v_m,tc_set(tc_set(t_a))),
    inference(split_conjunct,[status(thm)],[c_0_15]) ).

cnf(c_0_22_023,negated_conjecture,
    c_lessequals(v_Y,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(tc_set(t_a)))),
    inference(split_conjunct,[status(thm)],[c_0_16]) ).

cnf(c_0_23_024,negated_conjecture,
    c_in(v_m,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))),
    inference(split_conjunct,[status(thm)],[c_0_17]) ).

cnf(c_0_24_025,negated_conjecture,
    ( X1 = v_m
    | c_lessequals(c_Zorn_Osucc(v_S,X1,t_a),v_m,tc_set(tc_set(t_a)))
    | ~ c_in(X1,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
    | ~ c_lessequals(X1,v_m,tc_set(tc_set(t_a))) ),
    c_0_18,
    [final] ).

cnf(c_0_25_026,negated_conjecture,
    ( c_lessequals(X1,v_m,tc_set(tc_set(t_a)))
    | c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),X1,tc_set(tc_set(t_a)))
    | ~ c_in(X1,v_Y,tc_set(tc_set(t_a))) ),
    c_0_19,
    [final] ).

cnf(c_0_26_027,negated_conjecture,
    ~ c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),c_Union(v_Y,tc_set(t_a)),tc_set(tc_set(t_a))),
    c_0_20,
    [final] ).

cnf(c_0_27_028,negated_conjecture,
    ~ c_lessequals(c_Union(v_Y,tc_set(t_a)),v_m,tc_set(tc_set(t_a))),
    c_0_21,
    [final] ).

cnf(c_0_28_029,negated_conjecture,
    c_lessequals(v_Y,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(tc_set(t_a)))),
    c_0_22,
    [final] ).

cnf(c_0_29_030,negated_conjecture,
    c_in(v_m,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))),
    c_0_23,
    [final] ).

% End CNF derivation

%-------------------------------------------------------------
% Proof by iprover

cnf(c_2572,negated_conjecture,
    ( c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),X0,tc_set(tc_set(t_a)))
    | c_lessequals(X0,v_m,tc_set(tc_set(t_a)))
    | ~ c_in(X0,v_Y,tc_set(tc_set(t_a))) ),
    file('/export/starexec/sandbox/tmp/iprover_modulo_1b7079.p',c_0_25) ).

cnf(c_3772,negated_conjecture,
    ( c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),X0,tc_set(tc_set(t_a)))
    | c_lessequals(X0,v_m,tc_set(tc_set(t_a)))
    | ~ c_in(X0,v_Y,tc_set(tc_set(t_a))) ),
    inference(copy,[status(esa)],[c_2572]) ).

cnf(c_3795,negated_conjecture,
    ( c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),X0,tc_set(tc_set(t_a)))
    | c_lessequals(X0,v_m,tc_set(tc_set(t_a)))
    | ~ c_in(X0,v_Y,tc_set(tc_set(t_a))) ),
    inference(copy,[status(esa)],[c_3772]) ).

cnf(c_3804,negated_conjecture,
    ( c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),X0,tc_set(tc_set(t_a)))
    | c_lessequals(X0,v_m,tc_set(tc_set(t_a)))
    | ~ c_in(X0,v_Y,tc_set(tc_set(t_a))) ),
    inference(copy,[status(esa)],[c_3795]) ).

cnf(c_3807,negated_conjecture,
    ( c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),X0,tc_set(tc_set(t_a)))
    | c_lessequals(X0,v_m,tc_set(tc_set(t_a)))
    | ~ c_in(X0,v_Y,tc_set(tc_set(t_a))) ),
    inference(copy,[status(esa)],[c_3804]) ).

cnf(c_11517,plain,
    ( c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),X0,tc_set(tc_set(t_a)))
    | c_lessequals(X0,v_m,tc_set(tc_set(t_a)))
    | ~ c_in(X0,v_Y,tc_set(tc_set(t_a))) ),
    inference(copy,[status(esa)],[c_3807]) ).

cnf(c_2437,plain,
    ( c_lessequals(c_Union(X0,X1),X2,tc_set(X1))
    | c_lessequals(X3,c_Union(X0,X1),tc_set(X1))
    | ~ c_lessequals(X3,c_Zorn_OUnion__lemma0__1(X2,X3,X0,X1),tc_set(X1)) ),
    file('/export/starexec/sandbox/tmp/iprover_modulo_1b7079.p',c_0_5500_2) ).

cnf(c_11247,plain,
    ( c_lessequals(c_Union(X0,X1),X2,tc_set(X1))
    | c_lessequals(X3,c_Union(X0,X1),tc_set(X1))
    | ~ c_lessequals(X3,c_Zorn_OUnion__lemma0__1(X2,X3,X0,X1),tc_set(X1)) ),
    inference(copy,[status(esa)],[c_2437]) ).

cnf(c_11607,plain,
    ( c_lessequals(c_Union(X0,tc_set(t_a)),X1,tc_set(tc_set(t_a)))
    | c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),c_Union(X0,tc_set(t_a)),tc_set(tc_set(t_a)))
    | c_lessequals(c_Zorn_OUnion__lemma0__1(X1,c_Zorn_Osucc(v_S,v_m,t_a),X0,tc_set(t_a)),v_m,tc_set(tc_set(t_a)))
    | ~ c_in(c_Zorn_OUnion__lemma0__1(X1,c_Zorn_Osucc(v_S,v_m,t_a),X0,tc_set(t_a)),v_Y,tc_set(tc_set(t_a))) ),
    inference(resolution,[status(thm)],[c_11517,c_11247]) ).

cnf(c_11608,plain,
    ( c_lessequals(c_Union(X0,tc_set(t_a)),X1,tc_set(tc_set(t_a)))
    | c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),c_Union(X0,tc_set(t_a)),tc_set(tc_set(t_a)))
    | c_lessequals(c_Zorn_OUnion__lemma0__1(X1,c_Zorn_Osucc(v_S,v_m,t_a),X0,tc_set(t_a)),v_m,tc_set(tc_set(t_a)))
    | ~ c_in(c_Zorn_OUnion__lemma0__1(X1,c_Zorn_Osucc(v_S,v_m,t_a),X0,tc_set(t_a)),v_Y,tc_set(tc_set(t_a))) ),
    inference(rewriting,[status(thm)],[c_11607]) ).

cnf(c_2405,plain,
    ( c_lessequals(c_Union(X0,X1),X2,tc_set(X1))
    | c_lessequals(X3,c_Union(X0,X1),tc_set(X1))
    | c_in(c_Zorn_OUnion__lemma0__1(X2,X3,X0,X1),X0,tc_set(X1)) ),
    file('/export/starexec/sandbox/tmp/iprover_modulo_1b7079.p',c_0_5519_2) ).

cnf(c_11183,plain,
    ( c_lessequals(c_Union(X0,X1),X2,tc_set(X1))
    | c_lessequals(X3,c_Union(X0,X1),tc_set(X1))
    | c_in(c_Zorn_OUnion__lemma0__1(X2,X3,X0,X1),X0,tc_set(X1)) ),
    inference(copy,[status(esa)],[c_2405]) ).

cnf(c_12508,plain,
    ( c_lessequals(c_Union(v_Y,tc_set(t_a)),X0,tc_set(tc_set(t_a)))
    | c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),c_Union(v_Y,tc_set(t_a)),tc_set(tc_set(t_a)))
    | c_lessequals(c_Zorn_OUnion__lemma0__1(X0,c_Zorn_Osucc(v_S,v_m,t_a),v_Y,tc_set(t_a)),v_m,tc_set(tc_set(t_a))) ),
    inference(resolution,[status(thm)],[c_11608,c_11183]) ).

cnf(c_12509,plain,
    ( c_lessequals(c_Union(v_Y,tc_set(t_a)),X0,tc_set(tc_set(t_a)))
    | c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),c_Union(v_Y,tc_set(t_a)),tc_set(tc_set(t_a)))
    | c_lessequals(c_Zorn_OUnion__lemma0__1(X0,c_Zorn_Osucc(v_S,v_m,t_a),v_Y,tc_set(t_a)),v_m,tc_set(tc_set(t_a))) ),
    inference(rewriting,[status(thm)],[c_12508]) ).

cnf(c_2573,negated_conjecture,
    ~ c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),c_Union(v_Y,tc_set(t_a)),tc_set(tc_set(t_a))),
    file('/export/starexec/sandbox/tmp/iprover_modulo_1b7079.p',c_0_26) ).

cnf(c_3774,negated_conjecture,
    ~ c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),c_Union(v_Y,tc_set(t_a)),tc_set(tc_set(t_a))),
    inference(copy,[status(esa)],[c_2573]) ).

cnf(c_3796,negated_conjecture,
    ~ c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),c_Union(v_Y,tc_set(t_a)),tc_set(tc_set(t_a))),
    inference(copy,[status(esa)],[c_3774]) ).

cnf(c_3803,negated_conjecture,
    ~ c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),c_Union(v_Y,tc_set(t_a)),tc_set(tc_set(t_a))),
    inference(copy,[status(esa)],[c_3796]) ).

cnf(c_3808,negated_conjecture,
    ~ c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),c_Union(v_Y,tc_set(t_a)),tc_set(tc_set(t_a))),
    inference(copy,[status(esa)],[c_3803]) ).

cnf(c_11519,negated_conjecture,
    ~ c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),c_Union(v_Y,tc_set(t_a)),tc_set(tc_set(t_a))),
    inference(copy,[status(esa)],[c_3808]) ).

cnf(c_16717,plain,
    ( c_lessequals(c_Union(v_Y,tc_set(t_a)),X0,tc_set(tc_set(t_a)))
    | c_lessequals(c_Zorn_OUnion__lemma0__1(X0,c_Zorn_Osucc(v_S,v_m,t_a),v_Y,tc_set(t_a)),v_m,tc_set(tc_set(t_a))) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_12509,c_11519]) ).

cnf(c_16718,plain,
    ( c_lessequals(c_Union(v_Y,tc_set(t_a)),X0,tc_set(tc_set(t_a)))
    | c_lessequals(c_Zorn_OUnion__lemma0__1(X0,c_Zorn_Osucc(v_S,v_m,t_a),v_Y,tc_set(t_a)),v_m,tc_set(tc_set(t_a))) ),
    inference(rewriting,[status(thm)],[c_16717]) ).

cnf(c_2434,plain,
    ( c_lessequals(c_Union(X0,X1),X2,tc_set(X1))
    | c_lessequals(X3,c_Union(X0,X1),tc_set(X1))
    | ~ c_lessequals(c_Zorn_OUnion__lemma0__1(X2,X3,X0,X1),X2,tc_set(X1)) ),
    file('/export/starexec/sandbox/tmp/iprover_modulo_1b7079.p',c_0_5501_2) ).

cnf(c_11241,plain,
    ( c_lessequals(c_Union(X0,X1),X2,tc_set(X1))
    | c_lessequals(X3,c_Union(X0,X1),tc_set(X1))
    | ~ c_lessequals(c_Zorn_OUnion__lemma0__1(X2,X3,X0,X1),X2,tc_set(X1)) ),
    inference(copy,[status(esa)],[c_2434]) ).

cnf(c_11242,plain,
    ( c_lessequals(c_Union(X0,X1),X2,tc_set(X1))
    | ~ c_lessequals(c_Zorn_OUnion__lemma0__1(X2,X3,X0,X1),X2,tc_set(X1))
    | c_lessequals(X3,c_Union(X0,X1),tc_set(X1)) ),
    inference(rewriting,[status(thm)],[c_11241]) ).

cnf(c_16735,plain,
    ( c_lessequals(c_Union(v_Y,tc_set(t_a)),v_m,tc_set(tc_set(t_a)))
    | c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),c_Union(v_Y,tc_set(t_a)),tc_set(tc_set(t_a))) ),
    inference(resolution,[status(thm)],[c_16718,c_11242]) ).

cnf(c_16736,plain,
    ( c_lessequals(c_Union(v_Y,tc_set(t_a)),v_m,tc_set(tc_set(t_a)))
    | c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),c_Union(v_Y,tc_set(t_a)),tc_set(tc_set(t_a))) ),
    inference(rewriting,[status(thm)],[c_16735]) ).

cnf(c_2574,negated_conjecture,
    ~ c_lessequals(c_Union(v_Y,tc_set(t_a)),v_m,tc_set(tc_set(t_a))),
    file('/export/starexec/sandbox/tmp/iprover_modulo_1b7079.p',c_0_27) ).

cnf(c_3776,negated_conjecture,
    ~ c_lessequals(c_Union(v_Y,tc_set(t_a)),v_m,tc_set(tc_set(t_a))),
    inference(copy,[status(esa)],[c_2574]) ).

cnf(c_3797,negated_conjecture,
    ~ c_lessequals(c_Union(v_Y,tc_set(t_a)),v_m,tc_set(tc_set(t_a))),
    inference(copy,[status(esa)],[c_3776]) ).

cnf(c_3802,negated_conjecture,
    ~ c_lessequals(c_Union(v_Y,tc_set(t_a)),v_m,tc_set(tc_set(t_a))),
    inference(copy,[status(esa)],[c_3797]) ).

cnf(c_3809,negated_conjecture,
    ~ c_lessequals(c_Union(v_Y,tc_set(t_a)),v_m,tc_set(tc_set(t_a))),
    inference(copy,[status(esa)],[c_3802]) ).

cnf(c_11521,negated_conjecture,
    ~ c_lessequals(c_Union(v_Y,tc_set(t_a)),v_m,tc_set(tc_set(t_a))),
    inference(copy,[status(esa)],[c_3809]) ).

cnf(c_16739,plain,
    $false,
    inference(forward_subsumption_resolution,[status(thm)],[c_16736,c_11519,c_11521]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : SET852-1 : TPTP v8.1.0. Released v3.2.0.
% 0.13/0.13  % Command  : iprover_modulo %s %d
% 0.14/0.34  % Computer : n028.cluster.edu
% 0.14/0.34  % Model    : x86_64 x86_64
% 0.14/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34  % Memory   : 8042.1875MB
% 0.14/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34  % CPULimit : 300
% 0.14/0.34  % WCLimit  : 600
% 0.14/0.34  % DateTime : Mon Jul 11 03:29:13 EDT 2022
% 0.14/0.34  % CPUTime  : 
% 0.19/0.34  % Running in mono-core mode
% 0.19/0.54  % Orienting using strategy Equiv(ClausalAll)
% 0.19/0.54  % Orientation found
% 0.19/0.54  % Executing iprover_moduloopt --modulo true --schedule none --sub_typing false --res_to_prop_solver none --res_prop_simpl_given false --res_lit_sel kbo_max --large_theory_mode false --res_time_limit 1000 --res_orphan_elimination false --prep_sem_filter none --prep_unflatten false --comb_res_mult 1000 --comb_inst_mult 300 --clausifier .//eprover --clausifier_options "--tstp-format  " --proof_out_file /export/starexec/sandbox/tmp/iprover_proof_6d92b5.s --tptp_safe_out true --time_out_real 150 /export/starexec/sandbox/tmp/iprover_modulo_1b7079.p | tee /export/starexec/sandbox/tmp/iprover_modulo_out_6610b6 | grep -v "SZS"
% 0.38/0.56  
% 0.38/0.56  %---------------- iProver v2.5 (CASC-J8 2016) ----------------%
% 0.38/0.56  
% 0.38/0.56  % 
% 0.38/0.56  % ------  iProver source info 
% 0.38/0.56  
% 0.38/0.56  % git: sha1: 57accf6c58032223c7708532cf852a99fa48c1b3
% 0.38/0.56  % git: non_committed_changes: true
% 0.38/0.56  % git: last_make_outside_of_git: true
% 0.38/0.56  
% 0.38/0.56  % 
% 0.38/0.56  % ------ Input Options
% 0.38/0.56  
% 0.38/0.56  % --out_options                         all
% 0.38/0.56  % --tptp_safe_out                       true
% 0.38/0.56  % --problem_path                        ""
% 0.38/0.56  % --include_path                        ""
% 0.38/0.56  % --clausifier                          .//eprover
% 0.38/0.56  % --clausifier_options                  --tstp-format  
% 0.38/0.56  % --stdin                               false
% 0.38/0.56  % --dbg_backtrace                       false
% 0.38/0.56  % --dbg_dump_prop_clauses               false
% 0.38/0.56  % --dbg_dump_prop_clauses_file          -
% 0.38/0.56  % --dbg_out_stat                        false
% 0.38/0.56  
% 0.38/0.56  % ------ General Options
% 0.38/0.56  
% 0.38/0.56  % --fof                                 false
% 0.38/0.56  % --time_out_real                       150.
% 0.38/0.56  % --time_out_prep_mult                  0.2
% 0.38/0.56  % --time_out_virtual                    -1.
% 0.38/0.56  % --schedule                            none
% 0.38/0.56  % --ground_splitting                    input
% 0.38/0.56  % --splitting_nvd                       16
% 0.38/0.56  % --non_eq_to_eq                        false
% 0.38/0.56  % --prep_gs_sim                         true
% 0.38/0.56  % --prep_unflatten                      false
% 0.38/0.56  % --prep_res_sim                        true
% 0.38/0.56  % --prep_upred                          true
% 0.38/0.56  % --res_sim_input                       true
% 0.38/0.56  % --clause_weak_htbl                    true
% 0.38/0.56  % --gc_record_bc_elim                   false
% 0.38/0.56  % --symbol_type_check                   false
% 0.38/0.56  % --clausify_out                        false
% 0.38/0.56  % --large_theory_mode                   false
% 0.38/0.56  % --prep_sem_filter                     none
% 0.38/0.56  % --prep_sem_filter_out                 false
% 0.38/0.56  % --preprocessed_out                    false
% 0.38/0.56  % --sub_typing                          false
% 0.38/0.56  % --brand_transform                     false
% 0.38/0.56  % --pure_diseq_elim                     true
% 0.38/0.56  % --min_unsat_core                      false
% 0.38/0.56  % --pred_elim                           true
% 0.38/0.56  % --add_important_lit                   false
% 0.38/0.56  % --soft_assumptions                    false
% 0.38/0.56  % --reset_solvers                       false
% 0.38/0.56  % --bc_imp_inh                          []
% 0.38/0.56  % --conj_cone_tolerance                 1.5
% 0.38/0.56  % --prolific_symb_bound                 500
% 0.38/0.56  % --lt_threshold                        2000
% 0.38/0.56  
% 0.38/0.56  % ------ SAT Options
% 0.38/0.56  
% 0.38/0.56  % --sat_mode                            false
% 0.38/0.56  % --sat_fm_restart_options              ""
% 0.38/0.56  % --sat_gr_def                          false
% 0.38/0.56  % --sat_epr_types                       true
% 0.38/0.56  % --sat_non_cyclic_types                false
% 0.38/0.56  % --sat_finite_models                   false
% 0.38/0.56  % --sat_fm_lemmas                       false
% 0.38/0.56  % --sat_fm_prep                         false
% 0.38/0.56  % --sat_fm_uc_incr                      true
% 0.38/0.56  % --sat_out_model                       small
% 0.38/0.56  % --sat_out_clauses                     false
% 0.38/0.56  
% 0.38/0.56  % ------ QBF Options
% 0.38/0.56  
% 0.38/0.56  % --qbf_mode                            false
% 0.38/0.56  % --qbf_elim_univ                       true
% 0.38/0.56  % --qbf_sk_in                           true
% 0.38/0.56  % --qbf_pred_elim                       true
% 0.38/0.56  % --qbf_split                           32
% 0.38/0.56  
% 0.38/0.56  % ------ BMC1 Options
% 0.38/0.56  
% 0.38/0.56  % --bmc1_incremental                    false
% 0.38/0.56  % --bmc1_axioms                         reachable_all
% 0.38/0.56  % --bmc1_min_bound                      0
% 0.38/0.56  % --bmc1_max_bound                      -1
% 0.38/0.56  % --bmc1_max_bound_default              -1
% 0.38/0.56  % --bmc1_symbol_reachability            true
% 0.38/0.56  % --bmc1_property_lemmas                false
% 0.38/0.56  % --bmc1_k_induction                    false
% 0.38/0.56  % --bmc1_non_equiv_states               false
% 0.38/0.56  % --bmc1_deadlock                       false
% 0.38/0.56  % --bmc1_ucm                            false
% 0.38/0.56  % --bmc1_add_unsat_core                 none
% 0.38/0.56  % --bmc1_unsat_core_children            false
% 0.38/0.56  % --bmc1_unsat_core_extrapolate_axioms  false
% 0.38/0.56  % --bmc1_out_stat                       full
% 0.38/0.56  % --bmc1_ground_init                    false
% 0.38/0.56  % --bmc1_pre_inst_next_state            false
% 0.38/0.56  % --bmc1_pre_inst_state                 false
% 0.38/0.56  % --bmc1_pre_inst_reach_state           false
% 0.38/0.56  % --bmc1_out_unsat_core                 false
% 0.38/0.56  % --bmc1_aig_witness_out                false
% 0.38/0.56  % --bmc1_verbose                        false
% 0.38/0.56  % --bmc1_dump_clauses_tptp              false
% 1.01/1.34  % --bmc1_dump_unsat_core_tptp           false
% 1.01/1.34  % --bmc1_dump_file                      -
% 1.01/1.34  % --bmc1_ucm_expand_uc_limit            128
% 1.01/1.34  % --bmc1_ucm_n_expand_iterations        6
% 1.01/1.34  % --bmc1_ucm_extend_mode                1
% 1.01/1.34  % --bmc1_ucm_init_mode                  2
% 1.01/1.34  % --bmc1_ucm_cone_mode                  none
% 1.01/1.34  % --bmc1_ucm_reduced_relation_type      0
% 1.01/1.34  % --bmc1_ucm_relax_model                4
% 1.01/1.34  % --bmc1_ucm_full_tr_after_sat          true
% 1.01/1.34  % --bmc1_ucm_expand_neg_assumptions     false
% 1.01/1.34  % --bmc1_ucm_layered_model              none
% 1.01/1.34  % --bmc1_ucm_max_lemma_size             10
% 1.01/1.34  
% 1.01/1.34  % ------ AIG Options
% 1.01/1.34  
% 1.01/1.34  % --aig_mode                            false
% 1.01/1.34  
% 1.01/1.34  % ------ Instantiation Options
% 1.01/1.34  
% 1.01/1.34  % --instantiation_flag                  true
% 1.01/1.34  % --inst_lit_sel                        [+prop;+sign;+ground;-num_var;-num_symb]
% 1.01/1.34  % --inst_solver_per_active              750
% 1.01/1.34  % --inst_solver_calls_frac              0.5
% 1.01/1.34  % --inst_passive_queue_type             priority_queues
% 1.01/1.34  % --inst_passive_queues                 [[-conj_dist;+conj_symb;-num_var];[+age;-num_symb]]
% 1.01/1.34  % --inst_passive_queues_freq            [25;2]
% 1.01/1.34  % --inst_dismatching                    true
% 1.01/1.34  % --inst_eager_unprocessed_to_passive   true
% 1.01/1.34  % --inst_prop_sim_given                 true
% 1.01/1.34  % --inst_prop_sim_new                   false
% 1.01/1.34  % --inst_orphan_elimination             true
% 1.01/1.34  % --inst_learning_loop_flag             true
% 1.01/1.34  % --inst_learning_start                 3000
% 1.01/1.34  % --inst_learning_factor                2
% 1.01/1.34  % --inst_start_prop_sim_after_learn     3
% 1.01/1.34  % --inst_sel_renew                      solver
% 1.01/1.34  % --inst_lit_activity_flag              true
% 1.01/1.34  % --inst_out_proof                      true
% 1.01/1.34  
% 1.01/1.34  % ------ Resolution Options
% 1.01/1.34  
% 1.01/1.34  % --resolution_flag                     true
% 1.01/1.34  % --res_lit_sel                         kbo_max
% 1.01/1.34  % --res_to_prop_solver                  none
% 1.01/1.34  % --res_prop_simpl_new                  false
% 1.01/1.34  % --res_prop_simpl_given                false
% 1.01/1.34  % --res_passive_queue_type              priority_queues
% 1.01/1.34  % --res_passive_queues                  [[-conj_dist;+conj_symb;-num_symb];[+age;-num_symb]]
% 1.01/1.34  % --res_passive_queues_freq             [15;5]
% 1.01/1.34  % --res_forward_subs                    full
% 1.01/1.34  % --res_backward_subs                   full
% 1.01/1.34  % --res_forward_subs_resolution         true
% 1.01/1.34  % --res_backward_subs_resolution        true
% 1.01/1.34  % --res_orphan_elimination              false
% 1.01/1.34  % --res_time_limit                      1000.
% 1.01/1.34  % --res_out_proof                       true
% 1.01/1.34  % --proof_out_file                      /export/starexec/sandbox/tmp/iprover_proof_6d92b5.s
% 1.01/1.34  % --modulo                              true
% 1.01/1.34  
% 1.01/1.34  % ------ Combination Options
% 1.01/1.34  
% 1.01/1.34  % --comb_res_mult                       1000
% 1.01/1.34  % --comb_inst_mult                      300
% 1.01/1.34  % ------ 
% 1.01/1.34  
% 1.01/1.34  % ------ Parsing...% successful
% 1.01/1.34  
% 1.01/1.34  % ------ 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 % 
% 1.01/1.34  
% 1.01/1.34  % ------ Proving...
% 1.01/1.34  % ------ Problem Properties 
% 1.01/1.34  
% 1.01/1.34  % 
% 1.01/1.34  % EPR                                   false
% 1.01/1.34  % Horn                                  false
% 1.01/1.34  % Has equality                          true
% 1.01/1.34  
% 1.01/1.34  % % ------ Input Options Time Limit: Unbounded
% 1.01/1.34  
% 1.01/1.34  
% 1.01/1.34  Compiling...
% 1.01/1.34  Loading plugin: done.
% 1.01/1.34  Compiling...
% 1.01/1.34  Loading plugin: done.
% 1.01/1.34  Compiling...
% 1.01/1.34  Loading plugin: done.
% 1.01/1.34  Compiling...
% 1.01/1.34  Loading plugin: done.
% 1.01/1.34  Compiling...
% 1.01/1.34  Loading plugin: done.
% 1.01/1.34  Compiling...
% 1.01/1.34  Loading plugin: done.
% 1.01/1.34  % % ------ Current options:
% 1.01/1.34  
% 1.01/1.34  % ------ Input Options
% 1.01/1.34  
% 1.01/1.34  % --out_options                         all
% 1.01/1.34  % --tptp_safe_out                       true
% 1.01/1.34  % --problem_path                        ""
% 1.01/1.34  % --include_path                        ""
% 1.01/1.34  % --clausifier                          .//eprover
% 1.01/1.34  % --clausifier_options                  --tstp-format  
% 1.01/1.34  % --stdin                               false
% 1.01/1.34  % --dbg_backtrace                       false
% 1.01/1.34  % --dbg_dump_prop_clauses               false
% 1.01/1.34  % --dbg_dump_prop_clauses_file          -
% 1.01/1.34  % --dbg_out_stat                        false
% 1.01/1.34  
% 1.01/1.34  % ------ General Options
% 1.01/1.34  
% 1.01/1.34  % --fof                                 false
% 1.01/1.34  % --time_out_real                       150.
% 1.01/1.34  % --time_out_prep_mult                  0.2
% 1.01/1.34  % --time_out_virtual                    -1.
% 1.01/1.34  % --schedule                            none
% 1.01/1.34  % --ground_splitting                    input
% 1.01/1.34  % --splitting_nvd                       16
% 1.01/1.34  % --non_eq_to_eq                        false
% 1.01/1.34  % --prep_gs_sim                         true
% 1.01/1.34  % --prep_unflatten                      false
% 1.01/1.34  % --prep_res_sim                        true
% 1.01/1.34  % --prep_upred                          true
% 1.01/1.34  % --res_sim_input                       true
% 1.01/1.34  % --clause_weak_htbl                    true
% 1.01/1.34  % --gc_record_bc_elim                   false
% 1.01/1.34  % --symbol_type_check                   false
% 1.01/1.34  % --clausify_out                        false
% 1.01/1.34  % --large_theory_mode                   false
% 1.01/1.34  % --prep_sem_filter                     none
% 1.01/1.34  % --prep_sem_filter_out                 false
% 1.01/1.34  % --preprocessed_out                    false
% 1.01/1.34  % --sub_typing                          false
% 1.01/1.34  % --brand_transform                     false
% 1.01/1.34  % --pure_diseq_elim                     true
% 1.01/1.34  % --min_unsat_core                      false
% 1.01/1.34  % --pred_elim                           true
% 1.01/1.34  % --add_important_lit                   false
% 1.01/1.34  % --soft_assumptions                    false
% 1.01/1.34  % --reset_solvers                       false
% 1.01/1.34  % --bc_imp_inh                          []
% 1.01/1.34  % --conj_cone_tolerance                 1.5
% 1.01/1.34  % --prolific_symb_bound                 500
% 1.01/1.34  % --lt_threshold                        2000
% 1.01/1.34  
% 1.01/1.34  % ------ SAT Options
% 1.01/1.34  
% 1.01/1.34  % --sat_mode                            false
% 1.01/1.34  % --sat_fm_restart_options              ""
% 1.01/1.34  % --sat_gr_def                          false
% 1.01/1.34  % --sat_epr_types                       true
% 1.01/1.34  % --sat_non_cyclic_types                false
% 1.01/1.34  % --sat_finite_models                   false
% 1.01/1.34  % --sat_fm_lemmas                       false
% 1.01/1.34  % --sat_fm_prep                         false
% 1.01/1.34  % --sat_fm_uc_incr                      true
% 1.01/1.34  % --sat_out_model                       small
% 1.01/1.34  % --sat_out_clauses                     false
% 1.01/1.34  
% 1.01/1.34  % ------ QBF Options
% 1.01/1.34  
% 1.01/1.34  % --qbf_mode                            false
% 1.01/1.34  % --qbf_elim_univ                       true
% 1.01/1.34  % --qbf_sk_in                           true
% 1.01/1.34  % --qbf_pred_elim                       true
% 1.01/1.34  % --qbf_split                           32
% 1.01/1.34  
% 1.01/1.34  % ------ BMC1 Options
% 1.01/1.34  
% 1.01/1.34  % --bmc1_incremental                    false
% 1.01/1.34  % --bmc1_axioms                         reachable_all
% 1.01/1.34  % --bmc1_min_bound                      0
% 1.01/1.34  % --bmc1_max_bound                      -1
% 1.01/1.34  % --bmc1_max_bound_default              -1
% 1.01/1.34  % --bmc1_symbol_reachability            true
% 1.01/1.34  % --bmc1_property_lemmas                false
% 1.01/1.34  % --bmc1_k_induction                    false
% 1.01/1.34  % --bmc1_non_equiv_states               false
% 1.01/1.34  % --bmc1_deadlock                       false
% 1.01/1.34  % --bmc1_ucm                            false
% 1.01/1.34  % --bmc1_add_unsat_core                 none
% 1.01/1.34  % --bmc1_unsat_core_children            false
% 1.01/1.34  % --bmc1_unsat_core_extrapolate_axioms  false
% 1.01/1.34  % --bmc1_out_stat                       full
% 1.01/1.34  % --bmc1_ground_init                    false
% 1.01/1.34  % --bmc1_pre_inst_next_state            false
% 1.01/1.34  % --bmc1_pre_inst_state                 false
% 1.01/1.34  % --bmc1_pre_inst_reach_state           false
% 1.01/1.34  % --bmc1_out_unsat_core                 false
% 1.01/1.34  % --bmc1_aig_witness_out                false
% 1.01/1.34  % --bmc1_verbose                        false
% 1.01/1.34  % --bmc1_dump_clauses_tptp              false
% 1.01/1.34  % --bmc1_dump_unsat_core_tptp           false
% 1.01/1.34  % --bmc1_dump_file                      -
% 1.01/1.34  % --bmc1_ucm_expand_uc_limit            128
% 1.01/1.34  % --bmc1_ucm_n_expand_iterations        6
% 1.01/1.34  % --bmc1_ucm_extend_mode                1
% 1.01/1.34  % --bmc1_ucm_init_mode                  2
% 1.01/1.34  % --bmc1_ucm_cone_mode                  none
% 1.01/1.34  % --bmc1_ucm_reduced_relation_type      0
% 1.01/1.34  % --bmc1_ucm_relax_model                4
% 1.01/1.34  % --bmc1_ucm_full_tr_after_sat          true
% 1.01/1.34  % --bmc1_ucm_expand_neg_assumptions     false
% 1.01/1.34  % --bmc1_ucm_layered_model              none
% 1.01/1.34  % --bmc1_ucm_max_lemma_size             10
% 1.01/1.34  
% 1.01/1.34  % ------ AIG Options
% 1.01/1.34  
% 1.01/1.34  % --aig_mode                            false
% 1.01/1.34  
% 1.01/1.34  % ------ Instantiation Options
% 1.01/1.34  
% 1.01/1.34  % --instantiation_flag                  true
% 1.01/1.34  % --inst_lit_sel                        [+prop;+sign;+ground;-num_var;-num_symb]
% 1.01/1.34  % --inst_solver_per_active              750
% 1.01/1.34  % --inst_solver_calls_frac              0.5
% 1.01/1.34  % --inst_passive_queue_type             priority_queues
% 1.01/1.34  % --inst_passive_queues                 [[-conj_dist;+conj_symb;-num_var];[+age;-num_symb]]
% 150.28/150.56  % --inst_passive_queues_freq            [25;2]
% 150.28/150.56  % --inst_dismatching                    true
% 150.28/150.56  % --inst_eager_unprocessed_to_passive   true
% 150.28/150.56  % --inst_prop_sim_given                 true
% 150.28/150.56  % --inst_prop_sim_new                   false
% 150.28/150.56  % --inst_orphan_elimination             true
% 150.28/150.56  % --inst_learning_loop_flag             true
% 150.28/150.56  % --inst_learning_start                 3000
% 150.28/150.56  % --inst_learning_factor                2
% 150.28/150.56  % --inst_start_prop_sim_after_learn     3
% 150.28/150.56  % --inst_sel_renew                      solver
% 150.28/150.56  % --inst_lit_activity_flag              true
% 150.28/150.56  % --inst_out_proof                      true
% 150.28/150.56  
% 150.28/150.56  % ------ Resolution Options
% 150.28/150.56  
% 150.28/150.56  % --resolution_flag                     true
% 150.28/150.56  % --res_lit_sel                         kbo_max
% 150.28/150.56  % --res_to_prop_solver                  none
% 150.28/150.56  % --res_prop_simpl_new                  false
% 150.28/150.56  % --res_prop_simpl_given                false
% 150.28/150.56  % --res_passive_queue_type              priority_queues
% 150.28/150.56  % --res_passive_queues                  [[-conj_dist;+conj_symb;-num_symb];[+age;-num_symb]]
% 150.28/150.56  % --res_passive_queues_freq             [15;5]
% 150.28/150.56  % --res_forward_subs                    full
% 150.28/150.56  % --res_backward_subs                   full
% 150.28/150.56  % --res_forward_subs_resolution         true
% 150.28/150.56  % --res_backward_subs_resolution        true
% 150.28/150.56  % --res_orphan_elimination              false
% 150.28/150.56  % --res_time_limit                      1000.
% 150.28/150.56  % --res_out_proof                       true
% 150.28/150.56  % --proof_out_file                      /export/starexec/sandbox/tmp/iprover_proof_6d92b5.s
% 150.28/150.56  % --modulo                              true
% 150.28/150.56  
% 150.28/150.56  % ------ Combination Options
% 150.28/150.56  
% 150.28/150.56  % --comb_res_mult                       1000
% 150.28/150.56  % --comb_inst_mult                      300
% 150.28/150.56  % ------ 
% 150.28/150.56  
% 150.28/150.56  
% 150.28/150.56  
% 150.28/150.56  % ------ Proving...
% 150.28/150.56  % 
% 150.28/150.56  
% 150.28/150.56  
% 150.28/150.56  % Time Out Real
% 150.28/150.56  
% 150.28/150.56  % ------                             Statistics
% 150.28/150.56  
% 150.28/150.56  % ------ General
% 150.28/150.56  
% 150.28/150.56  % num_of_input_clauses:                 2577
% 150.28/150.56  % num_of_input_neg_conjectures:         6
% 150.28/150.56  % num_of_splits:                        0
% 150.28/150.56  % num_of_split_atoms:                   0
% 150.28/150.56  % num_of_sem_filtered_clauses:          0
% 150.28/150.56  % num_of_subtypes:                      0
% 150.28/150.56  % monotx_restored_types:                0
% 150.28/150.56  % sat_num_of_epr_types:                 0
% 150.28/150.56  % sat_num_of_non_cyclic_types:          0
% 150.28/150.56  % sat_guarded_non_collapsed_types:      0
% 150.28/150.56  % is_epr:                               0
% 150.28/150.56  % is_horn:                              0
% 150.28/150.56  % has_eq:                               1
% 150.28/150.56  % num_pure_diseq_elim:                  0
% 150.28/150.56  % simp_replaced_by:                     0
% 150.28/150.56  % res_preprocessed:                     12
% 150.28/150.56  % prep_upred:                           0
% 150.28/150.56  % prep_unflattend:                      0
% 150.28/150.56  % pred_elim_cands:                      0
% 150.28/150.56  % pred_elim:                            0
% 150.28/150.56  % pred_elim_cl:                         0
% 150.28/150.56  % pred_elim_cycles:                     0
% 150.28/150.56  % forced_gc_time:                       0
% 150.28/150.56  % gc_basic_clause_elim:                 0
% 150.28/150.56  % parsing_time:                         0.069
% 150.28/150.56  % sem_filter_time:                      0.
% 150.28/150.56  % pred_elim_time:                       0.
% 150.28/150.56  % out_proof_time:                       0.
% 150.28/150.56  % monotx_time:                          0.
% 150.28/150.56  % subtype_inf_time:                     0.
% 150.28/150.56  % unif_index_cands_time:                0.487
% 150.28/150.56  % unif_index_add_time:                  0.103
% 150.28/150.56  % total_time:                           150.018
% 150.28/150.56  % num_of_symbols:                       233
% 150.28/150.56  % num_of_terms:                         636145
% 150.28/150.56  
% 150.28/150.56  % ------ Propositional Solver
% 150.28/150.56  
% 150.28/150.56  % prop_solver_calls:                    19
% 150.28/150.56  % prop_fast_solver_calls:               33
% 150.28/150.56  % prop_num_of_clauses:                  85774
% 150.28/150.56  % prop_preprocess_simplified:           128607
% 150.28/150.56  % prop_fo_subsumed:                     0
% 150.28/150.56  % prop_solver_time:                     0.025
% 150.28/150.56  % prop_fast_solver_time:                0.
% 150.28/150.56  % prop_unsat_core_time:                 0.
% 150.28/150.56  
% 150.28/150.56  % ------ QBF 
% 150.28/150.56  
% 150.28/150.56  % qbf_q_res:                            0
% 150.28/150.56  % qbf_num_tautologies:                  0
% 150.28/150.56  % qbf_prep_cycles:                      0
% 150.28/150.56  
% 150.28/150.56  % ------ BMC1
% 150.28/150.56  
% 150.28/150.56  % bmc1_current_bound:                   -1
% 150.28/150.56  % bmc1_last_solved_bound:               -1
% 150.28/150.56  % bmc1_unsat_core_size:                 -1
% 150.28/150.56  % bmc1_unsat_core_parents_size:         -1
% 150.28/150.56  % bmc1_merge_next_fun:                  0
% 150.28/150.56  % bmc1_unsat_core_clauses_time:         0.
% 150.28/150.56  
% 150.28/150.56  % ------ Instantiation
% 150.36/150.57  
% 150.36/150.57  % inst_num_of_clauses:                  13176
% 150.36/150.57  % inst_num_in_passive:                  11860
% 150.36/150.57  % inst_num_in_active:                   1169
% 150.36/150.57  % inst_num_in_unprocessed:              145
% 150.36/150.57  % inst_num_of_loops:                    1199
% 150.36/150.57  % inst_num_of_learning_restarts:        1
% 150.36/150.57  % inst_num_moves_active_passive:        27
% 150.36/150.57  % inst_lit_activity:                    7481
% 150.36/150.57  % inst_lit_activity_moves:              0
% 150.36/150.57  % inst_num_tautologies:                 2
% 150.36/150.57  % inst_num_prop_implied:                0
% 150.36/150.57  % inst_num_existing_simplified:         0
% 150.36/150.57  % inst_num_eq_res_simplified:           0
% 150.36/150.57  % inst_num_child_elim:                  0
% 150.36/150.57  % inst_num_of_dismatching_blockings:    1395
% 150.36/150.57  % inst_num_of_non_proper_insts:         5642
% 150.36/150.57  % inst_num_of_duplicates:               13083
% 150.36/150.57  % inst_inst_num_from_inst_to_res:       0
% 150.36/150.57  % inst_dismatching_checking_time:       3.364
% 150.36/150.57  
% 150.36/150.57  % ------ Resolution
% 150.36/150.57  
% 150.36/150.57  % res_num_of_clauses:                   579442
% 150.36/150.57  % res_num_in_passive:                   567329
% 150.36/150.57  % res_num_in_active:                    12137
% 150.36/150.57  % res_num_of_loops:                     14856
% 150.36/150.57  % res_forward_subset_subsumed:          43696
% 150.36/150.57  % res_backward_subset_subsumed:         1315
% 150.36/150.57  % res_forward_subsumed:                 3965
% 150.36/150.57  % res_backward_subsumed:                57
% 150.36/150.57  % res_forward_subsumption_resolution:   506
% 150.36/150.57  % res_backward_subsumption_resolution:  0
% 150.36/150.57  % res_clause_to_clause_subsumption:     2946416
% 150.36/150.57  % res_orphan_elimination:               0
% 150.36/150.57  % res_tautology_del:                    3250
% 150.36/150.57  % res_num_eq_res_simplified:            0
% 150.36/150.57  % res_num_sel_changes:                  0
% 150.36/150.57  % res_moves_from_active_to_pass:        0
% 150.36/150.57  
% 150.36/150.57  % 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/sandbox/tmp/iprover_proof_6d92b5.s --tptp_safe_out true --time_out_real 150 /export/starexec/sandbox/tmp/iprover_modulo_1b7079.p | tee /export/starexec/sandbox/tmp/iprover_modulo_out_ef2636 | grep -v "SZS"
% 150.54/150.73  
% 150.54/150.73  %---------------- iProver v2.5 (CASC-J8 2016) ----------------%
% 150.54/150.73  
% 150.54/150.73  % 
% 150.54/150.73  % ------  iProver source info 
% 150.54/150.73  
% 150.54/150.73  % git: sha1: 57accf6c58032223c7708532cf852a99fa48c1b3
% 150.54/150.73  % git: non_committed_changes: true
% 150.54/150.73  % git: last_make_outside_of_git: true
% 150.54/150.73  
% 150.54/150.73  % 
% 150.54/150.73  % ------ Input Options
% 150.54/150.73  
% 150.54/150.73  % --out_options                         all
% 150.54/150.73  % --tptp_safe_out                       true
% 150.54/150.73  % --problem_path                        ""
% 150.54/150.73  % --include_path                        ""
% 150.54/150.73  % --clausifier                          .//eprover
% 150.54/150.73  % --clausifier_options                  --tstp-format  
% 150.54/150.73  % --stdin                               false
% 150.54/150.73  % --dbg_backtrace                       false
% 150.54/150.73  % --dbg_dump_prop_clauses               false
% 150.54/150.73  % --dbg_dump_prop_clauses_file          -
% 150.54/150.73  % --dbg_out_stat                        false
% 150.54/150.73  
% 150.54/150.73  % ------ General Options
% 150.54/150.73  
% 150.54/150.73  % --fof                                 false
% 150.54/150.73  % --time_out_real                       150.
% 150.54/150.73  % --time_out_prep_mult                  0.2
% 150.54/150.73  % --time_out_virtual                    -1.
% 150.54/150.73  % --schedule                            none
% 150.54/150.73  % --ground_splitting                    input
% 150.54/150.73  % --splitting_nvd                       16
% 150.54/150.73  % --non_eq_to_eq                        false
% 150.54/150.73  % --prep_gs_sim                         true
% 150.54/150.73  % --prep_unflatten                      false
% 150.54/150.73  % --prep_res_sim                        true
% 150.54/150.73  % --prep_upred                          true
% 150.54/150.73  % --res_sim_input                       true
% 150.54/150.73  % --clause_weak_htbl                    true
% 150.54/150.73  % --gc_record_bc_elim                   false
% 150.54/150.73  % --symbol_type_check                   false
% 150.54/150.73  % --clausify_out                        false
% 150.54/150.73  % --large_theory_mode                   false
% 150.54/150.73  % --prep_sem_filter                     none
% 150.54/150.73  % --prep_sem_filter_out                 false
% 150.54/150.73  % --preprocessed_out                    false
% 150.54/150.73  % --sub_typing                          false
% 150.54/150.73  % --brand_transform                     false
% 150.54/150.73  % --pure_diseq_elim                     true
% 150.54/150.73  % --min_unsat_core                      false
% 150.54/150.73  % --pred_elim                           true
% 150.54/150.73  % --add_important_lit                   false
% 150.54/150.73  % --soft_assumptions                    false
% 150.54/150.73  % --reset_solvers                       false
% 150.54/150.73  % --bc_imp_inh                          []
% 150.54/150.73  % --conj_cone_tolerance                 1.5
% 150.54/150.73  % --prolific_symb_bound                 500
% 150.54/150.73  % --lt_threshold                        2000
% 150.54/150.73  
% 150.54/150.73  % ------ SAT Options
% 150.54/150.73  
% 150.54/150.73  % --sat_mode                            false
% 150.54/150.73  % --sat_fm_restart_options              ""
% 150.54/150.73  % --sat_gr_def                          false
% 150.54/150.73  % --sat_epr_types                       true
% 150.54/150.73  % --sat_non_cyclic_types                false
% 150.54/150.73  % --sat_finite_models                   false
% 150.54/150.73  % --sat_fm_lemmas                       false
% 150.54/150.73  % --sat_fm_prep                         false
% 150.54/150.73  % --sat_fm_uc_incr                      true
% 150.54/150.73  % --sat_out_model                       small
% 150.54/150.73  % --sat_out_clauses                     false
% 150.54/150.73  
% 150.54/150.73  % ------ QBF Options
% 150.54/150.73  
% 150.54/150.73  % --qbf_mode                            false
% 150.54/150.73  % --qbf_elim_univ                       true
% 150.54/150.73  % --qbf_sk_in                           true
% 150.54/150.73  % --qbf_pred_elim                       true
% 150.54/150.73  % --qbf_split                           32
% 150.54/150.73  
% 150.54/150.73  % ------ BMC1 Options
% 150.54/150.73  
% 150.54/150.73  % --bmc1_incremental                    false
% 150.54/150.73  % --bmc1_axioms                         reachable_all
% 150.54/150.73  % --bmc1_min_bound                      0
% 150.54/150.73  % --bmc1_max_bound                      -1
% 150.54/150.73  % --bmc1_max_bound_default              -1
% 150.54/150.73  % --bmc1_symbol_reachability            true
% 150.54/150.73  % --bmc1_property_lemmas                false
% 150.54/150.73  % --bmc1_k_induction                    false
% 150.54/150.73  % --bmc1_non_equiv_states               false
% 150.54/150.73  % --bmc1_deadlock                       false
% 150.54/150.73  % --bmc1_ucm                            false
% 150.54/150.73  % --bmc1_add_unsat_core                 none
% 150.54/150.73  % --bmc1_unsat_core_children            false
% 150.54/150.73  % --bmc1_unsat_core_extrapolate_axioms  false
% 150.54/150.73  % --bmc1_out_stat                       full
% 150.54/150.73  % --bmc1_ground_init                    false
% 150.54/150.73  % --bmc1_pre_inst_next_state            false
% 150.54/150.73  % --bmc1_pre_inst_state                 false
% 150.54/150.73  % --bmc1_pre_inst_reach_state           false
% 150.54/150.73  % --bmc1_out_unsat_core                 false
% 150.54/150.73  % --bmc1_aig_witness_out                false
% 150.54/150.73  % --bmc1_verbose                        false
% 150.54/150.73  % --bmc1_dump_clauses_tptp              false
% 151.40/151.61  % --bmc1_dump_unsat_core_tptp           false
% 151.40/151.61  % --bmc1_dump_file                      -
% 151.40/151.61  % --bmc1_ucm_expand_uc_limit            128
% 151.40/151.61  % --bmc1_ucm_n_expand_iterations        6
% 151.40/151.61  % --bmc1_ucm_extend_mode                1
% 151.40/151.61  % --bmc1_ucm_init_mode                  2
% 151.40/151.61  % --bmc1_ucm_cone_mode                  none
% 151.40/151.61  % --bmc1_ucm_reduced_relation_type      0
% 151.40/151.61  % --bmc1_ucm_relax_model                4
% 151.40/151.61  % --bmc1_ucm_full_tr_after_sat          true
% 151.40/151.61  % --bmc1_ucm_expand_neg_assumptions     false
% 151.40/151.61  % --bmc1_ucm_layered_model              none
% 151.40/151.61  % --bmc1_ucm_max_lemma_size             10
% 151.40/151.61  
% 151.40/151.61  % ------ AIG Options
% 151.40/151.61  
% 151.40/151.61  % --aig_mode                            false
% 151.40/151.61  
% 151.40/151.61  % ------ Instantiation Options
% 151.40/151.61  
% 151.40/151.61  % --instantiation_flag                  true
% 151.40/151.61  % --inst_lit_sel                        [+prop;+sign;+ground;-num_var;-num_symb]
% 151.40/151.61  % --inst_solver_per_active              750
% 151.40/151.61  % --inst_solver_calls_frac              0.5
% 151.40/151.61  % --inst_passive_queue_type             priority_queues
% 151.40/151.61  % --inst_passive_queues                 [[-conj_dist;+conj_symb;-num_var];[+age;-num_symb]]
% 151.40/151.61  % --inst_passive_queues_freq            [25;2]
% 151.40/151.61  % --inst_dismatching                    true
% 151.40/151.61  % --inst_eager_unprocessed_to_passive   true
% 151.40/151.61  % --inst_prop_sim_given                 true
% 151.40/151.61  % --inst_prop_sim_new                   false
% 151.40/151.61  % --inst_orphan_elimination             true
% 151.40/151.61  % --inst_learning_loop_flag             true
% 151.40/151.61  % --inst_learning_start                 3000
% 151.40/151.61  % --inst_learning_factor                2
% 151.40/151.61  % --inst_start_prop_sim_after_learn     3
% 151.40/151.61  % --inst_sel_renew                      solver
% 151.40/151.61  % --inst_lit_activity_flag              true
% 151.40/151.61  % --inst_out_proof                      true
% 151.40/151.61  
% 151.40/151.61  % ------ Resolution Options
% 151.40/151.61  
% 151.40/151.61  % --resolution_flag                     true
% 151.40/151.61  % --res_lit_sel                         kbo_max
% 151.40/151.61  % --res_to_prop_solver                  none
% 151.40/151.61  % --res_prop_simpl_new                  false
% 151.40/151.61  % --res_prop_simpl_given                false
% 151.40/151.61  % --res_passive_queue_type              priority_queues
% 151.40/151.61  % --res_passive_queues                  [[-conj_dist;+conj_symb;-num_symb];[+age;-num_symb]]
% 151.40/151.61  % --res_passive_queues_freq             [15;5]
% 151.40/151.61  % --res_forward_subs                    full
% 151.40/151.61  % --res_backward_subs                   full
% 151.40/151.61  % --res_forward_subs_resolution         true
% 151.40/151.61  % --res_backward_subs_resolution        true
% 151.40/151.61  % --res_orphan_elimination              false
% 151.40/151.61  % --res_time_limit                      1000.
% 151.40/151.61  % --res_out_proof                       true
% 151.40/151.61  % --proof_out_file                      /export/starexec/sandbox/tmp/iprover_proof_6d92b5.s
% 151.40/151.61  % --modulo                              true
% 151.40/151.61  
% 151.40/151.61  % ------ Combination Options
% 151.40/151.61  
% 151.40/151.61  % --comb_res_mult                       1000
% 151.40/151.61  % --comb_inst_mult                      300
% 151.40/151.61  % ------ 
% 151.40/151.61  
% 151.40/151.61  % ------ Parsing...% successful
% 151.40/151.61  
% 151.40/151.61  % ------ 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 % 
% 151.40/151.61  
% 151.40/151.61  % ------ Proving...
% 151.40/151.61  % ------ Problem Properties 
% 151.40/151.61  
% 151.40/151.61  % 
% 151.40/151.61  % EPR                                   false
% 151.40/151.61  % Horn                                  false
% 151.40/151.61  % Has equality                          true
% 151.40/151.61  
% 151.40/151.61  % % ------ Input Options Time Limit: Unbounded
% 151.40/151.61  
% 151.40/151.61  
% 151.40/151.61  Compiling...
% 151.40/151.61  Loading plugin: done.
% 151.40/151.61  Compiling...
% 151.40/151.61  Loading plugin: done.
% 151.40/151.61  Compiling...
% 151.40/151.61  Loading plugin: done.
% 151.40/151.61  Compiling...
% 151.40/151.61  Loading plugin: done.
% 151.40/151.61  Compiling...
% 151.40/151.61  Loading plugin: done.
% 151.40/151.61  Compiling...
% 151.40/151.61  Loading plugin: done.
% 151.40/151.61  Compiling...
% 151.40/151.61  Loading plugin: done.
% 151.40/151.61  % % ------ Current options:
% 151.40/151.61  
% 151.40/151.61  % ------ Input Options
% 151.40/151.61  
% 151.40/151.61  % --out_options                         all
% 151.40/151.61  % --tptp_safe_out                       true
% 151.40/151.61  % --problem_path                        ""
% 151.40/151.61  % --include_path                        ""
% 151.40/151.61  % --clausifier                          .//eprover
% 151.40/151.61  % --clausifier_options                  --tstp-format  
% 151.40/151.61  % --stdin                               false
% 151.40/151.61  % --dbg_backtrace                       false
% 151.40/151.61  % --dbg_dump_prop_clauses               false
% 151.40/151.61  % --dbg_dump_prop_clauses_file          -
% 151.40/151.61  % --dbg_out_stat                        false
% 151.40/151.61  
% 151.40/151.61  % ------ General Options
% 151.40/151.61  
% 151.40/151.61  % --fof                                 false
% 151.40/151.61  % --time_out_real                       150.
% 151.40/151.61  % --time_out_prep_mult                  0.2
% 151.40/151.61  % --time_out_virtual                    -1.
% 151.40/151.61  % --schedule                            none
% 151.40/151.61  % --ground_splitting                    input
% 151.40/151.61  % --splitting_nvd                       16
% 151.40/151.61  % --non_eq_to_eq                        false
% 151.40/151.61  % --prep_gs_sim                         true
% 151.40/151.61  % --prep_unflatten                      false
% 151.40/151.61  % --prep_res_sim                        true
% 151.40/151.61  % --prep_upred                          true
% 151.40/151.61  % --res_sim_input                       true
% 151.40/151.61  % --clause_weak_htbl                    true
% 151.40/151.61  % --gc_record_bc_elim                   false
% 151.40/151.61  % --symbol_type_check                   false
% 151.40/151.61  % --clausify_out                        false
% 151.40/151.61  % --large_theory_mode                   false
% 151.40/151.61  % --prep_sem_filter                     none
% 151.40/151.61  % --prep_sem_filter_out                 false
% 151.40/151.61  % --preprocessed_out                    false
% 151.40/151.61  % --sub_typing                          false
% 151.40/151.61  % --brand_transform                     false
% 151.40/151.61  % --pure_diseq_elim                     true
% 151.40/151.61  % --min_unsat_core                      false
% 151.40/151.61  % --pred_elim                           true
% 151.40/151.61  % --add_important_lit                   false
% 151.40/151.61  % --soft_assumptions                    false
% 151.40/151.61  % --reset_solvers                       false
% 151.40/151.61  % --bc_imp_inh                          []
% 151.40/151.61  % --conj_cone_tolerance                 1.5
% 151.40/151.61  % --prolific_symb_bound                 500
% 151.40/151.61  % --lt_threshold                        2000
% 151.40/151.61  
% 151.40/151.61  % ------ SAT Options
% 151.40/151.61  
% 151.40/151.61  % --sat_mode                            false
% 151.40/151.61  % --sat_fm_restart_options              ""
% 151.40/151.61  % --sat_gr_def                          false
% 151.40/151.61  % --sat_epr_types                       true
% 151.40/151.61  % --sat_non_cyclic_types                false
% 151.40/151.61  % --sat_finite_models                   false
% 151.40/151.61  % --sat_fm_lemmas                       false
% 151.40/151.61  % --sat_fm_prep                         false
% 151.40/151.61  % --sat_fm_uc_incr                      true
% 151.40/151.61  % --sat_out_model                       small
% 151.40/151.61  % --sat_out_clauses                     false
% 151.40/151.61  
% 151.40/151.61  % ------ QBF Options
% 151.40/151.61  
% 151.40/151.61  % --qbf_mode                            false
% 151.40/151.61  % --qbf_elim_univ                       true
% 151.40/151.61  % --qbf_sk_in                           true
% 151.40/151.61  % --qbf_pred_elim                       true
% 151.40/151.61  % --qbf_split                           32
% 151.40/151.61  
% 151.40/151.61  % ------ BMC1 Options
% 151.40/151.61  
% 151.40/151.61  % --bmc1_incremental                    false
% 151.40/151.61  % --bmc1_axioms                         reachable_all
% 151.40/151.61  % --bmc1_min_bound                      0
% 151.40/151.61  % --bmc1_max_bound                      -1
% 151.40/151.61  % --bmc1_max_bound_default              -1
% 151.40/151.61  % --bmc1_symbol_reachability            true
% 151.40/151.61  % --bmc1_property_lemmas                false
% 151.40/151.61  % --bmc1_k_induction                    false
% 151.40/151.61  % --bmc1_non_equiv_states               false
% 151.40/151.61  % --bmc1_deadlock                       false
% 151.40/151.61  % --bmc1_ucm                            false
% 151.40/151.61  % --bmc1_add_unsat_core                 none
% 151.40/151.61  % --bmc1_unsat_core_children            false
% 151.40/151.61  % --bmc1_unsat_core_extrapolate_axioms  false
% 151.40/151.61  % --bmc1_out_stat                       full
% 151.40/151.61  % --bmc1_ground_init                    false
% 151.40/151.61  % --bmc1_pre_inst_next_state            false
% 151.40/151.61  % --bmc1_pre_inst_state                 false
% 151.40/151.61  % --bmc1_pre_inst_reach_state           false
% 151.40/151.61  % --bmc1_out_unsat_core                 false
% 151.40/151.61  % --bmc1_aig_witness_out                false
% 151.40/151.61  % --bmc1_verbose                        false
% 151.40/151.61  % --bmc1_dump_clauses_tptp              false
% 151.40/151.61  % --bmc1_dump_unsat_core_tptp           false
% 151.40/151.61  % --bmc1_dump_file                      -
% 151.40/151.61  % --bmc1_ucm_expand_uc_limit            128
% 151.40/151.61  % --bmc1_ucm_n_expand_iterations        6
% 151.40/151.61  % --bmc1_ucm_extend_mode                1
% 151.40/151.61  % --bmc1_ucm_init_mode                  2
% 151.40/151.61  % --bmc1_ucm_cone_mode                  none
% 151.40/151.61  % --bmc1_ucm_reduced_relation_type      0
% 151.40/151.61  % --bmc1_ucm_relax_model                4
% 151.40/151.61  % --bmc1_ucm_full_tr_after_sat          true
% 151.40/151.61  % --bmc1_ucm_expand_neg_assumptions     false
% 151.40/151.61  % --bmc1_ucm_layered_model              none
% 151.40/151.61  % --bmc1_ucm_max_lemma_size             10
% 151.40/151.61  
% 151.40/151.61  % ------ AIG Options
% 151.40/151.61  
% 151.40/151.61  % --aig_mode                            false
% 151.40/151.61  
% 151.40/151.61  % ------ Instantiation Options
% 151.40/151.61  
% 151.40/151.61  % --instantiation_flag                  true
% 151.40/151.61  % --inst_lit_sel                        [+prop;+sign;+ground;-num_var;-num_symb]
% 151.40/151.61  % --inst_solver_per_active              750
% 151.40/151.61  % --inst_solver_calls_frac              0.5
% 151.40/151.61  % --inst_passive_queue_type             priority_queues
% 151.40/151.61  % --inst_passive_queues                 [[-conj_dist;+conj_symb;-num_var];[+age;-num_symb]]
% 151.65/151.87  % --inst_passive_queues_freq            [25;2]
% 151.65/151.87  % --inst_dismatching                    true
% 151.65/151.87  % --inst_eager_unprocessed_to_passive   true
% 151.65/151.87  % --inst_prop_sim_given                 true
% 151.65/151.87  % --inst_prop_sim_new                   false
% 151.65/151.87  % --inst_orphan_elimination             true
% 151.65/151.87  % --inst_learning_loop_flag             true
% 151.65/151.87  % --inst_learning_start                 3000
% 151.65/151.87  % --inst_learning_factor                2
% 151.65/151.87  % --inst_start_prop_sim_after_learn     3
% 151.65/151.87  % --inst_sel_renew                      solver
% 151.65/151.87  % --inst_lit_activity_flag              true
% 151.65/151.87  % --inst_out_proof                      true
% 151.65/151.87  
% 151.65/151.87  % ------ Resolution Options
% 151.65/151.87  
% 151.65/151.87  % --resolution_flag                     true
% 151.65/151.87  % --res_lit_sel                         kbo_max
% 151.65/151.87  % --res_to_prop_solver                  none
% 151.65/151.87  % --res_prop_simpl_new                  false
% 151.65/151.87  % --res_prop_simpl_given                false
% 151.65/151.87  % --res_passive_queue_type              priority_queues
% 151.65/151.87  % --res_passive_queues                  [[-conj_dist;+conj_symb;-num_symb];[+age;-num_symb]]
% 151.65/151.87  % --res_passive_queues_freq             [15;5]
% 151.65/151.87  % --res_forward_subs                    full
% 151.65/151.87  % --res_backward_subs                   full
% 151.65/151.87  % --res_forward_subs_resolution         true
% 151.65/151.87  % --res_backward_subs_resolution        true
% 151.65/151.87  % --res_orphan_elimination              false
% 151.65/151.87  % --res_time_limit                      1000.
% 151.65/151.87  % --res_out_proof                       true
% 151.65/151.87  % --proof_out_file                      /export/starexec/sandbox/tmp/iprover_proof_6d92b5.s
% 151.65/151.87  % --modulo                              true
% 151.65/151.87  
% 151.65/151.87  % ------ Combination Options
% 151.65/151.87  
% 151.65/151.87  % --comb_res_mult                       1000
% 151.65/151.87  % --comb_inst_mult                      300
% 151.65/151.87  % ------ 
% 151.65/151.87  
% 151.65/151.87  
% 151.65/151.87  
% 151.65/151.87  % ------ Proving...
% 151.65/151.87  % 
% 151.65/151.87  
% 151.65/151.87  
% 151.65/151.87  %  Resolution empty clause
% 151.65/151.87  
% 151.65/151.87  % ------                             Statistics
% 151.65/151.87  
% 151.65/151.87  % ------ General
% 151.65/151.87  
% 151.65/151.87  % num_of_input_clauses:                 2577
% 151.65/151.87  % num_of_input_neg_conjectures:         6
% 151.65/151.87  % num_of_splits:                        0
% 151.65/151.87  % num_of_split_atoms:                   0
% 151.65/151.87  % num_of_sem_filtered_clauses:          0
% 151.65/151.87  % num_of_subtypes:                      0
% 151.65/151.87  % monotx_restored_types:                0
% 151.65/151.87  % sat_num_of_epr_types:                 0
% 151.65/151.87  % sat_num_of_non_cyclic_types:          0
% 151.65/151.87  % sat_guarded_non_collapsed_types:      0
% 151.65/151.87  % is_epr:                               0
% 151.65/151.87  % is_horn:                              0
% 151.65/151.87  % has_eq:                               1
% 151.65/151.87  % num_pure_diseq_elim:                  0
% 151.65/151.87  % simp_replaced_by:                     0
% 151.65/151.87  % res_preprocessed:                     12
% 151.65/151.87  % prep_upred:                           0
% 151.65/151.87  % prep_unflattend:                      0
% 151.65/151.87  % pred_elim_cands:                      0
% 151.65/151.87  % pred_elim:                            0
% 151.65/151.87  % pred_elim_cl:                         0
% 151.65/151.87  % pred_elim_cycles:                     0
% 151.65/151.87  % forced_gc_time:                       0
% 151.65/151.87  % gc_basic_clause_elim:                 0
% 151.65/151.87  % parsing_time:                         0.092
% 151.65/151.87  % sem_filter_time:                      0.
% 151.65/151.87  % pred_elim_time:                       0.
% 151.65/151.87  % out_proof_time:                       0.001
% 151.65/151.87  % monotx_time:                          0.
% 151.65/151.87  % subtype_inf_time:                     0.
% 151.65/151.87  % unif_index_cands_time:                0.
% 151.65/151.87  % unif_index_add_time:                  0.01
% 151.65/151.87  % total_time:                           1.163
% 151.65/151.87  % num_of_symbols:                       233
% 151.65/151.87  % num_of_terms:                         9991
% 151.65/151.87  
% 151.65/151.87  % ------ Propositional Solver
% 151.65/151.87  
% 151.65/151.87  % prop_solver_calls:                    1
% 151.65/151.87  % prop_fast_solver_calls:               33
% 151.65/151.87  % prop_num_of_clauses:                  2713
% 151.65/151.87  % prop_preprocess_simplified:           7391
% 151.65/151.87  % prop_fo_subsumed:                     0
% 151.65/151.87  % prop_solver_time:                     0.
% 151.65/151.87  % prop_fast_solver_time:                0.
% 151.65/151.87  % prop_unsat_core_time:                 0.
% 151.65/151.87  
% 151.65/151.87  % ------ QBF 
% 151.65/151.87  
% 151.65/151.87  % qbf_q_res:                            0
% 151.65/151.87  % qbf_num_tautologies:                  0
% 151.65/151.87  % qbf_prep_cycles:                      0
% 151.65/151.87  
% 151.65/151.87  % ------ BMC1
% 151.65/151.87  
% 151.65/151.87  % bmc1_current_bound:                   -1
% 151.65/151.87  % bmc1_last_solved_bound:               -1
% 151.65/151.87  % bmc1_unsat_core_size:                 -1
% 151.65/151.87  % bmc1_unsat_core_parents_size:         -1
% 151.65/151.87  % bmc1_merge_next_fun:                  0
% 151.65/151.87  % bmc1_unsat_core_clauses_time:         0.
% 151.65/151.87  
% 151.65/151.87  % ------ Instantiation
% 151.65/151.87  
% 151.65/151.87  % inst_num_of_clauses:                  2552
% 151.65/151.87  % inst_num_in_passive:                  0
% 151.65/151.87  % inst_num_in_active:                   0
% 151.65/151.87  % inst_num_in_unprocessed:              2577
% 151.65/151.87  % inst_num_of_loops:                    0
% 151.65/151.87  % inst_num_of_learning_restarts:        0
% 151.65/151.87  % inst_num_moves_active_passive:        0
% 151.65/151.87  % inst_lit_activity:                    0
% 151.65/151.87  % inst_lit_activity_moves:              0
% 151.65/151.87  % inst_num_tautologies:                 0
% 151.65/151.87  % inst_num_prop_implied:                0
% 151.65/151.87  % inst_num_existing_simplified:         0
% 151.65/151.87  % inst_num_eq_res_simplified:           0
% 151.65/151.87  % inst_num_child_elim:                  0
% 151.65/151.87  % inst_num_of_dismatching_blockings:    0
% 151.65/151.87  % inst_num_of_non_proper_insts:         0
% 151.65/151.87  % inst_num_of_duplicates:               0
% 151.65/151.87  % inst_inst_num_from_inst_to_res:       0
% 151.65/151.87  % inst_dismatching_checking_time:       0.
% 151.65/151.87  
% 151.65/151.87  % ------ Resolution
% 151.65/151.87  
% 151.65/151.87  % res_num_of_clauses:                   4724
% 151.65/151.87  % res_num_in_passive:                   1972
% 151.65/151.87  % res_num_in_active:                    1524
% 151.65/151.87  % res_num_of_loops:                     197
% 151.65/151.87  % res_forward_subset_subsumed:          1307
% 151.65/151.87  % res_backward_subset_subsumed:         0
% 151.65/151.87  % res_forward_subsumed:                 23
% 151.65/151.87  % res_backward_subsumed:                0
% 151.65/151.87  % res_forward_subsumption_resolution:   4
% 151.65/151.87  % res_backward_subsumption_resolution:  0
% 151.65/151.87  % res_clause_to_clause_subsumption:     573
% 151.65/151.87  % res_orphan_elimination:               0
% 151.65/151.87  % res_tautology_del:                    1
% 151.65/151.87  % res_num_eq_res_simplified:            0
% 151.65/151.87  % res_num_sel_changes:                  0
% 151.65/151.87  % res_moves_from_active_to_pass:        0
% 151.65/151.87  
% 151.65/151.87  % Status Unsatisfiable
% 151.65/151.87  % SZS status Unsatisfiable
% 151.65/151.87  % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------